All-optical regenerator of multi-channel signals.

PubMed

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

2017-10-12

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

Focusing of Shear Shock Waves

NASA Astrophysics Data System (ADS)

Giammarinaro, Bruno; Espíndola, David; Coulouvrat, François; Pinton, Gianmarco

2018-01-01

Focusing is a ubiquitous way to transform waves. Recently, a new type of shock wave has been observed experimentally with high-frame-rate ultrasound: shear shock waves in soft solids. These strongly nonlinear waves are characterized by a high Mach number, because the shear wave velocity is much slower, by 3 orders of magnitude, than the longitudinal wave velocity. Furthermore, these waves have a unique cubic nonlinearity which generates only odd harmonics. Unlike longitudinal waves for which only compressional shocks are possible, shear waves exhibit cubic nonlinearities which can generate positive and negative shocks. Here we present the experimental observation of shear shock wave focusing, generated by the vertical motion of a solid cylinder section embedded in a soft gelatin-graphite phantom to induce linearly vertically polarized motion. Raw ultrasound data from high-frame-rate (7692 images per second) acquisitions in combination with algorithms that are tuned to detect small displacements (approximately 1 μ m ) are used to generate quantitative movies of gel motion. The features of shear shock wave focusing are analyzed by comparing experimental observations with numerical simulations of a retarded-time elastodynamic equation with cubic nonlinearities and empirical attenuation laws for soft solids.

Intermittency and emergence of coherent structures in wave turbulence of a vibrating plate.

PubMed

Mordant, Nicolas; Miquel, Benjamin

2017-10-01

We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long-time numerical simulations makes this system extremely valuable for wave turbulence studies. The purely 2D character of dynamics of the elastic plate makes it much simpler to handle compared to much more complex 3D physical systems that are typical of geo- and astrophysical issues (ocean surface or internal waves, magnetized plasmas or strongly rotating and/or stratified flows). When the forcing is small the observed wave turbulence is consistent with the predictions of the weak turbulent theory. Here we focus on the case of stronger forcing for which coherent structures can be observed. These structures look similar to the folds and D-cones that are commonly observed for strongly deformed static thin elastic sheets (crumpled paper) except that they evolve dynamically in our forced system. We describe their evolution and show that their emergence is associated with statistical intermittency (lack of self similarity) of strongly nonlinear wave turbulence. This behavior is reminiscent of intermittency in Navier-Stokes turbulence. Experimental data show hints of the weak to strong turbulence transition. However, due to technical limitations and dissipation, the strong nonlinear regime remains out of reach of experiments and therefore has been explored numerically.

Intermittency and emergence of coherent structures in wave turbulence of a vibrating plate

NASA Astrophysics Data System (ADS)

Mordant, Nicolas; Miquel, Benjamin

2017-10-01

We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long-time numerical simulations makes this system extremely valuable for wave turbulence studies. The purely 2D character of dynamics of the elastic plate makes it much simpler to handle compared to much more complex 3D physical systems that are typical of geo- and astrophysical issues (ocean surface or internal waves, magnetized plasmas or strongly rotating and/or stratified flows). When the forcing is small the observed wave turbulence is consistent with the predictions of the weak turbulent theory. Here we focus on the case of stronger forcing for which coherent structures can be observed. These structures look similar to the folds and D-cones that are commonly observed for strongly deformed static thin elastic sheets (crumpled paper) except that they evolve dynamically in our forced system. We describe their evolution and show that their emergence is associated with statistical intermittency (lack of self similarity) of strongly nonlinear wave turbulence. This behavior is reminiscent of intermittency in Navier-Stokes turbulence. Experimental data show hints of the weak to strong turbulence transition. However, due to technical limitations and dissipation, the strong nonlinear regime remains out of reach of experiments and therefore has been explored numerically.

Extremely frequency-widened terahertz wave generation using Cherenkov-type radiation.

PubMed

Suizu, Koji; Koketsu, Kaoru; Shibuya, Takayuki; Tsutsui, Toshihiro; Akiba, Takuya; Kawase, Kodo

2009-04-13

Terahertz (THz) wave generation based on nonlinear frequency conversion is promising way for realizing a tunable monochromatic bright THz-wave source. Such a development of efficient and wide tunable THz-wave source depends on discovery of novel brilliant nonlinear crystal. Important factors of a nonlinear crystal for THz-wave generation are, 1. High nonlinearity and 2. Good transparency at THz frequency region. Unfortunately, many nonlinear crystals have strong absorption at THz frequency region. The fact limits efficient and wide tunable THz-wave generation. Here, we show that Cherenkov radiation with waveguide structure is an effective strategy for achieving efficient and extremely wide tunable THz-wave source. We fabricated MgO-doped lithium niobate slab waveguide with 3.8 microm of thickness and demonstrated difference frequency generation of THz-wave generation with Cherenkov phase matching. Extremely frequency-widened THz-wave generation, from 0.1 to 7.2 THz, without no structural dips successfully obtained. The tuning frequency range of waveguided Cherenkov radiation source was extremely widened compare to that of injection seeded-Terahertz Parametric Generator. The tuning range obtained in this work for THz-wave generation using lithium niobate crystal was the widest value in our knowledge. The highest THz-wave energy obtained was about 3.2 pJ, and the energy conversion efficiency was about 10(-5) %. The method can be easily applied for many conventional nonlinear crystals, results in realizing simple, reasonable, compact, high efficient and ultra broad band THz-wave sources.

Strong terahertz emission by optical rectification of shaped laser pulse in transversely magnetized plasma

NASA Astrophysics Data System (ADS)

Singh, Ram Kishor; Singh, Monika; Rajouria, Satish Kumar; Sharma, R. P.

2017-07-01

This communication presents a theoretical model for efficient terahertz (THz) radiation generation by the optical rectification of shaped laser pulse in transversely magnetised ripple density plasma. The laser beam imparts a nonlinear ponderomotive force to the electron and this force exerts a nonlinear velocity component in both transverse and axial directions which have spectral components in the THz range. These velocity components couple with the pre-existing density ripple and give rise to a strong nonlinear current density which drives the THz wave in the plasma. The THz yield increases with the increasing strength of the background magnetic field and the sensitivity depends on the ripple wave number. The emitted power is directly proportional to the square of the amplitude of the density ripple. For exact phase matching condition, the normalised power of the generated THz wave can be achieved of the order of 10-4.

Nonlinear electric field structures in the inner magnetosphere

DOE PAGES

Malaspina, D. M.; Andersson, L.; Ergun, R. E.; ...

2014-08-28

Recent observations by the Van Allen Probes spacecraft have demonstrated that a variety of electric field structures and nonlinear waves frequently occur in the inner terrestrial magnetosphere, including phase space holes, kinetic field-line resonances, nonlinear whistler-mode waves, and several types of double layer. However, it is nuclear whether such structures and waves have a significant impact on the dynamics of the inner magnetosphere, including the radiation belts and ring current. To make progress toward quantifying their importance, this study statistically evaluates the correlation of such structures and waves with plasma boundaries. A strong correlation is found. These statistical results, combinedmore » with observations of electric field activity at propagating plasma boundaries, are consistent with the identification of these boundaries as the source of free energy responsible for generating the electric field structures and nonlinear waves of interest. Therefore, the ability of these structures and waves to influence plasma in the inner magnetosphere is governed by the spatial extent and dynamics of macroscopic plasma boundaries in that region.« less

Single-cycle high-intensity electromagnetic pulse generation in the interaction of a plasma wakefield with regular nonlinear structures.

PubMed

Bulanov, S S; Esirkepov, T Zh; Kamenets, F F; Pegoraro, F

2006-03-01

The interaction of regular nonlinear structures (such as subcycle solitons, electron vortices, and wake Langmuir waves) with a strong wake wave in a collisionless plasma can be exploited in order to produce ultrashort electromagnetic pulses. The electromagnetic field of the nonlinear structure is partially reflected by the electron density modulations of the incident wake wave and a single-cycle high-intensity electromagnetic pulse is formed. Due to the Doppler effect the length of this pulse is much shorter than that of the nonlinear structure. This process is illustrated with two-dimensional particle-in-cell simulations. The considered laser-plasma interaction regimes can be achieved in present day experiments and can be used for plasma diagnostics.

Spherical nonlinear ion-acoustic solitary waves in Titan's atmosphere

NASA Astrophysics Data System (ADS)

Selim, M. M.

2016-03-01

Propagation of spherical nonlinear ion-acoustic solitary waves in positive and negative ion plasmas with superthermal electrons is investigated. The effects of perturbations of the azimuthal and zenith-angle as well as the radial coordinate on the solitary wave profile are reported. The existence domains and the characteristics of the spherical solitary pulses are examined. The solitary excitations are found to be strongly dependent on the plasma parameters; the mass ratio of the positive-to-negative ions, electrons superthermality, and the spherical geometry. The role of superthermal electrons in formation of the spherical nonlinear ion-acoustic solitary excitations for two ion mass groups in Titan's upper atmosphere is investigated.

Nonlinear dispersive waves in repulsive lattices

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Evaluating the role of higher order nonlinearity in water of finite and shallow depth with a direct numerical simulation method of Euler equations

NASA Astrophysics Data System (ADS)

Fernandez, L.; Toffoli, A.; Monbaliu, J.

2012-04-01

In deep water, the dynamics of surface gravity waves is dominated by the instability of wave packets to side band perturbations. This mechanism, which is a nonlinear third order in wave steepness effect, can lead to a particularly strong focusing of wave energy, which in turn results in the formation of waves of very large amplitude also known as freak or rogue waves [1]. In finite water depth, however, the interaction between waves and the ocean floor induces a mean current. This subtracts energy from wave instability and causes it to cease for relative water depth , where k is the wavenumber and h the water depth [2]. Yet, this contradicts field observations of extreme waves such as the infamous 26-m "New Year" wave that have mainly been recorded in regions of relatively shallow water . In this respect, recent studies [3] seem to suggest that higher order nonlinearity in water of finite depth may sustain instability. In order to assess the role of higher order nonlinearity in water of finite and shallow depth, here we use a Higher Order Spectral Method [4] to simulate the evolution of surface gravity waves according to the Euler equations of motion. This method is based on an expansion of the vertical velocity about the surface elevation under the assumption of weak nonlinearity and has a great advantage of allowing the activation or deactivation of different orders of nonlinearity. The model is constructed to deal with an arbitrary order of nonlinearity and water depths so that finite and shallow water regimes can be analyzed. Several wave configurations are considered with oblique and collinear with the primary waves disturbances and different water depths. The analysis confirms that nonlinearity higher than third order play a substantial role in the destabilization of a primary wave train and subsequent growth of side band perturbations.

Rayleigh wave nonlinear inversion based on the Firefly algorithm

NASA Astrophysics Data System (ADS)

Zhou, Teng-Fei; Peng, Geng-Xin; Hu, Tian-Yue; Duan, Wen-Sheng; Yao, Feng-Chang; Liu, Yi-Mou

2014-06-01

Rayleigh waves have high amplitude, low frequency, and low velocity, which are treated as strong noise to be attenuated in reflected seismic surveys. This study addresses how to identify useful shear wave velocity profile and stratigraphic information from Rayleigh waves. We choose the Firefly algorithm for inversion of surface waves. The Firefly algorithm, a new type of particle swarm optimization, has the advantages of being robust, highly effective, and allows global searching. This algorithm is feasible and has advantages for use in Rayleigh wave inversion with both synthetic models and field data. The results show that the Firefly algorithm, which is a robust and practical method, can achieve nonlinear inversion of surface waves with high resolution.

X-Ray generation in strongly nonlinear plasma waves.

NASA Astrophysics Data System (ADS)

Kiselev, Sergey; Pukhov, Alexander; Kostyukov, Igor

2004-11-01

Using three-dimensional particle-in-cell simulations we show that a strongly nonlinear plasma wave excited by an ultrahigh intensity laser pulse works as a compact high-brightness source of Xray radiation. It has been recently suggested by A. Pukhov and J. Meyer-ter-Vehn, Appl. Phys. B 74, 355 (2002), that in a strongly nonlinear regime the plasma wave transforms to a ``bubble'', which is almost free from background electrons. Inside the bubble, a dense bunch of relativistic electrons is produced. These accelerated electrons make betatron oscillations in the transverse fields of the bubble and emit a bright broadband X-ray radiation with a maximum about 50 keV. The emission is confined to a small angle of about 0.1 rad. In addition, we make simulations of X-ray generation by an external 28.5-GeV electron bunch injected into the bubble. Gamma-quanta with up to GeV energies are observed in the simulation in a good agreement with analytical results. The energy conversion is efficient, leading to a significant stopping of the electron bunch over 5 mm interaction distance.

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

NASA Astrophysics Data System (ADS)

Nadkarni, Neel; Daraio, Chiara; Kochmann, Dennis M.

2014-08-01

We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.

Four wave mixing as a probe of the vacuum

NASA Astrophysics Data System (ADS)

Tennant, Daniel M.

2016-06-01

Much attention has been paid to the quantum structure of the vacuum. Higher order processes in quantum electrodynamics are strongly believed to cause polarization and even breakdown of the vacuum in the presence of strong fields soon to be accessible in high intensity laser experiments. Less explored consequences of strong field electrodynamics include effects from Born-Infeld type of electromagnetic theories, a nonlinear electrodynamics that follows from classical considerations as opposed to coupling to virtual fluctuations. In this article, I will demonstrate how vacuum four wave mixing has the possibility to differentiate between these two types of vacuum responses: quantum effects on one hand and nonlinear classical extensions on the other.

Spectral element modelling of seismic wave propagation in visco-elastoplastic media including excess-pore pressure development

NASA Astrophysics Data System (ADS)

Oral, Elif; Gélis, Céline; Bonilla, Luis Fabián; Delavaud, Elise

2017-12-01

Numerical modelling of seismic wave propagation, considering soil nonlinearity, has become a major topic in seismic hazard studies when strong shaking is involved under particular soil conditions. Indeed, when strong ground motion propagates in saturated soils, pore pressure is another important parameter to take into account when successive phases of contractive and dilatant soil behaviour are expected. Here, we model 1-D seismic wave propagation in linear and nonlinear media using the spectral element numerical method. The study uses a three-component (3C) nonlinear rheology and includes pore-pressure excess. The 1-D-3C model is used to study the 1987 Superstition Hills earthquake (ML 6.6), which was recorded at the Wildlife Refuge Liquefaction Array, USA. The data of this event present strong soil nonlinearity involving pore-pressure effects. The ground motion is numerically modelled for different assumptions on soil rheology and input motion (1C versus 3C), using the recorded borehole signals as input motion. The computed acceleration-time histories show low-frequency amplification and strong high-frequency damping due to the development of pore pressure in one of the soil layers. Furthermore, the soil is found to be more nonlinear and more dilatant under triaxial loading compared to the classical 1C analysis, and significant differences in surface displacements are observed between the 1C and 3C approaches. This study contributes to identify and understand the dominant phenomena occurring in superficial layers, depending on local soil properties and input motions, conditions relevant for site-specific studies.

Wave kinetics of random fibre lasers

PubMed Central

Churkin, D V.; Kolokolov, I V.; Podivilov, E V.; Vatnik, I D.; Nikulin, M A.; Vergeles, S S.; Terekhov, I S.; Lebedev, V V.; Falkovich, G.; Babin, S A.; Turitsyn, S K.

2015-01-01

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. PMID:25645177

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

NASA Astrophysics Data System (ADS)

Sleep, N. H.

2017-12-01

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

Nonlinear response and bistability of driven ion acoustic waves

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-08-01

The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.

Experimental study of the third-order nonlinearity of atomic and molecular gases using 10-μm laser pulses

NASA Astrophysics Data System (ADS)

Pigeon, J. J.; Tochitsky, S. Ya.; Welch, E. C.; Joshi, C.

2018-04-01

We present measurements of the third-order optical nonlinearity of Kr, Xe, N2, O2, and air at a wavelength near 10 µm by using four-wave mixing of ˜15 -GW /c m2 , 200-ps (full width at half maximum) C O2 laser pulses. Measurements in molecular gases resulted in an asymmetric four-wave mixing spectrum indicating that the nonlinear response is strongly affected by the delayed, rotational contribution to the effective nonlinear refractive index. Within the uncertainty of our measurements, we have found that the long-wavelength nonlinear refractive indices of these gases are consistent with measurements performed in the near IR.

Saturation amplitude of the f-mode instability

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

Kastaun, Wolfgang; Willburger, Beatrix; Kokkotas, Kostas D.

2010-11-15

We investigate strong nonlinear damping effects which occur during high amplitude oscillations of neutron stars, and the gravitational waves they produce. For this, we use a general relativistic nonlinear hydrodynamics code in conjunction with a fixed spacetime (Cowling approximation) and a polytropic equation of state (EOS). Gravitational waves are estimated using the quadrupole formula. Our main interest are l=m=2 f modes subject to the CFS (Chandrasekhar, Friedman, Schutz) instability, but we also investigate axisymmetric and quasiradial modes. We study various models to determine the influence of rotation rate and EOS. We find that axisymmetric oscillations at high amplitudes are predominantlymore » damped by shock formation, while the nonaxisymmetric f modes are mainly damped by wave breaking and, for rapidly rotating models, coupling to nonaxisymmetric inertial modes. From the observed nonlinear damping, we derive upper limits for the saturation amplitude of CFS-unstable f modes. Finally, we estimate that the corresponding gravitational waves for an oscillation amplitude at the upper limit should be detectable with the advanced LIGO (Laser Interferometer Gravitational Wave Observatory) and VIRGO interferometers at distances above 10 Mpc. This strongly depends on the stellar model, in particular, on the mode frequency.« less

Wave propagation in strongly dispersive superthermal dusty plasma

NASA Astrophysics Data System (ADS)

El-Labany, S. K.; El-Shewy, E. K.; Abd El-Razek, H. N.; El-Rahman, A. A.

2017-04-01

The attributes of acoustic envelope waves in a collisionless dust ion unmagnetized plasmas model composed of cold ions, superthermal electrons and positive-negative dust grains have been studied. Using the derivative expansion technique in a strong dispersive medium, the system model is reduced to a nonlinearly form of Schrodinger equation (NLSE). Rational solution of NLSE in unstable region is responsible for the creation of large shape waves; namely rogue waves. The subjection of instability regions upon electron superthermality (via κ), carrier wave number and dusty grains charge is discussed.

Effects of group velocity and multiplasmon resonances on the modulation of Langmuir waves in a degenerate plasma

NASA Astrophysics Data System (ADS)

Misra, Amar P.; Chatterjee, Debjani; Brodin, Gert

2017-11-01

We study the nonlinear wave modulation of Langmuir waves (LWs) in a fully degenerate plasma. Using the Wigner-Moyal equation coupled to the Poisson equation and the multiple scale expansion technique, a modified nonlocal nonlinear Schrödinger (NLS) equation is derived which governs the evolution of LW envelopes in degenerate plasmas. The nonlocal nonlinearity in the NLS equation appears due to the group velocity and multiplasmon resonances, i.e., resonances induced by the simultaneous particle absorption of multiple wave quanta. We focus on the regime where the resonant velocity of electrons is larger than the Fermi velocity and thereby the linear Landau damping is forbidden. As a result, the nonlinear wave-particle resonances due to the group velocity and multiplasmon processes are the dominant mechanisms for wave-particle interaction. It is found that in contrast to classical or semiclassical plasmas, the group velocity resonance does not necessarily give rise the wave damping in the strong quantum regime where ℏ k ˜m vF with ℏ denoting the reduced Planck's constant, m the electron mass, and vF the Fermi velocity; however, the three-plasmon process plays a dominant role in the nonlinear Landau damping of wave envelopes. In this regime, the decay rate of the wave amplitude is also found to be higher compared to that in the modest quantum regime where the multiplasmon effects are forbidden.

Rotation-induced nonlinear wavepackets in internal waves

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

Whitfield, A. J., E-mail: ashley.whitfield.12@ucl.ac.uk; Johnson, E. R., E-mail: e.johnson@ucl.ac.uk

2014-05-15

The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets.more » It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.« less

Numerical Simulation of Focused Shock Shear Waves in Soft Solids and a Two-Dimensional Nonlinear Homogeneous Model of the Brain

PubMed Central

Giammarinaro, B.; Coulouvrat, F.; Pinton, G.

2016-01-01

Shear waves that propagate in soft solids, such as the brain, are strongly nonlinear and can develop into shock waves in less than one wavelength. We hypothesize that these shear shock waves could be responsible for certain types of traumatic brain injuries (TBI) and that the spherical geometry of the skull bone could focus shear waves deep in the brain, generating diffuse axonal injuries. Theoretical models and numerical methods that describe nonlinear polarized shear waves in soft solids such as the brain are presented. They include the cubic nonlinearities that are characteristic of soft solids and the specific types of nonclassical attenuation and dispersion observed in soft tissues and the brain. The numerical methods are validated with analytical solutions, where possible, and with self-similar scaling laws where no known solutions exist. Initial conditions based on a human head X-ray microtomography (CT) were used to simulate focused shear shock waves in the brain. Three regimes are investigated with shock wave formation distances of 2.54 m, 0.018 m, and 0.0064 m. We demonstrate that under realistic loading scenarios, with nonlinear properties consistent with measurements in the brain, and when the shock wave propagation distance and focal distance coincide, nonlinear propagation can easily overcome attenuation to generate shear shocks deep inside the brain. Due to these effects, the accelerations in the focal are larger by a factor of 15 compared to acceleration at the skull surface. These results suggest that shock wave focusing could be responsible for diffuse axonal injuries. PMID:26833489

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

NASA Technical Reports Server (NTRS)

Bennett, J.; Hall, P.; Smith, F. T.

1988-01-01

Viscous fluid flows with curved streamlines can support both centrifugal and viscous traveling wave instabilities. Here the interaction of these instabilities in the context of the fully developed flow in a curved channel is discussed. The viscous (Tollmein-Schlichting) instability is described asymptotically at high Reynolds numbers and it is found that it can induce a Taylor-Goertler flow even at extremely small amplitudes. In this interaction, the Tollmein-Schlichting wave can drive a vortex state with wavelength either comparable with the channel width or the wavelength of lower branch viscous modes. The nonlinear equations which describe these interactions are solved for nonlinear equilibrium states.

Study of diffusion of wave packets in a square lattice under external fields along the discrete nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

de Brito, P. E.; Nazareno, H. N.

2012-09-01

The object of the present work is to analyze the effect of nonlinearity on wave packet propagation in a square lattice subject to a magnetic and an electric field in the Hall configuration, by using the Discrete Nonlinear Schrödinger Equation (DNLSE). In previous works we have shown that without the nonlinear term, the presence of the magnetic field induces the formation of vortices that remain stationary, while a wave packet is introduced in the system. As for the effect of an applied electric field, it was shown that the vortices propagate in a direction perpendicular to the electric field, similar behavior as presented in the classical treatment, we provide a quantum mechanics explanation for that. We have performed the calculations considering first the action of the magnetic field as well as the nonlinearity. The results indicate that for low values of the nonlinear parameter U the vortices remain stationary while preserving the form. For greater values of the parameter the picture gets distorted, the more so, the greater the nonlinearity. As for the inclusion of the electric field, we note that for small U, the wave packet propagates perpendicular to the applied field, until for greater values of U the wave gets partially localized in a definite region of the lattice. That is, for strong nonlinearity the wave packet gets partially trapped, while the tail of it can propagate through the lattice. Note that this tail propagation is responsible for the over-diffusion for long times of the wave packet under the action of an electric field. We have produced short films that show clearly the time evolution of the wave packet, which can add to the understanding of the dynamics.

Harmonic generation and parametric decay in the ion cyclotron frequency range

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

Skiff, F.N.; Wong, K.L.; Ono, M.

1984-06-01

Harmonic generation and parametric decay are examined in a toroidal ACT-I plasma using electrostatic plate antennas. The harmonic generation, which is consistent with sheath rectification, is sufficiently strong that the nonlinearly generated harmonic modes themselves decay parametrically. Resonant and nonresonant parametric decay of the second harmonic are observed and compared with uniform pump theory. Resonant decay of lower hybrid waves into lower hybrid waves and slow ion cyclotron waves is seen for the first time. Surprisingly, the decay processes are nonlinearly saturated, indicating absolute instability.

Self-reflection of extremely short light pulses in nonlinear optical waveguides

NASA Astrophysics Data System (ADS)

Kurasov, Alexander E.; Kozlov, Sergei A.

2004-07-01

An equation describing the generation of reflected radiation during the propagation of high-intensity extremely short pulses in a nonlinear optical waveguide is derived. The phenomena taking place during the strong self-inducted changes of the temporal structure of the forward wave are studied. It is shown that the duration of the backward pulse is much greater than the duration of the forward pulse and that the main part of the energy of the backward wave is carried by lower frequencies than the central frequency of the forward wave.

Spiral density waves and vertical circulation in protoplanetary discs

NASA Astrophysics Data System (ADS)

Riols, A.; Latter, H.

2018-06-01

Spiral density waves dominate several facets of accretion disc dynamics - planet-disc interactions and gravitational instability (GI) most prominently. Though they have been examined thoroughly in two-dimensional simulations, their vertical structures in the non-linear regime are somewhat unexplored. This neglect is unwarranted given that any strong vertical motions associated with these waves could profoundly impact dust dynamics, dust sedimentation, planet formation, and the emissivity of the disc surface. In this paper, we combine linear calculations and shearing box simulations in order to investigate the vertical structure of spiral waves for various polytropic stratifications and wave amplitudes. For sub-adiabatic profiles, we find that spiral waves develop a pair of counter-rotating poloidal rolls. Particularly strong in the non-linear regime, these vortical structures issue from the baroclinicity supported by the background vertical entropy gradient. They are also intimately connected to the disc's g modes which appear to interact non-linearly with the density waves. Furthermore, we demonstrate that the poloidal rolls are ubiquitous in gravitoturbulence, emerging in the vicinity of GI spiral wakes, and potentially transporting grains off the disc mid-plane. Other than hindering sedimentation and planet formation, this phenomena may bear on observations of the disc's scattered infrared luminosity. The vortical features could also impact on the turbulent dynamo operating in young protoplanetary discs subject to GI, or possibly even galactic discs.

Nonlinear Gyro-Landau-Fluid Equations

NASA Astrophysics Data System (ADS)

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

1996-11-01

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

Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses.

PubMed

Kim, Kihong; Phung, D K; Rotermund, F; Lim, H

2008-01-21

We develop a generalized version of the invariant imbedding method, which allows us to solve the electromagnetic wave equations in arbitrarily inhomogeneous stratified media where both the dielectric permittivity and magnetic permeability depend on the strengths of the electric and magnetic fields, in a numerically accurate and efficient manner. We apply our method to a uniform nonlinear slab and find that in the presence of strong external radiation, an initially uniform medium of positive refractive index can spontaneously change into a highly inhomogeneous medium where regions of positive or negative refractive index as well as metallic regions appear. We also study the wave transmission properties of periodic nonlinear media and the influence of nonlinearity on the mode conversion phenomena in inhomogeneous plasmas. We argue that our theory is very useful in the study of the optical properties of a variety of nonlinear media including nonlinear negative index media fabricated using wires and split-ring resonators.

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.

Computation of nonlinear ultrasound fields using a linearized contrast source method.

PubMed

Verweij, Martin D; Demi, Libertario; van Dongen, Koen W A

2013-08-01

Nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts. Second harmonic imaging is currently standard, and higher harmonic imaging is under investigation. The efficient development of novel imaging modalities and equipment requires accurate simulations of nonlinear wave fields in large volumes of realistic (lossy, inhomogeneous) media. The Iterative Nonlinear Contrast Source (INCS) method has been developed to deal with spatiotemporal domains measuring hundreds of wavelengths and periods. This full wave method considers the nonlinear term of the Westervelt equation as a nonlinear contrast source, and solves the equivalent integral equation via the Neumann iterative solution. Recently, the method has been extended with a contrast source that accounts for spatially varying attenuation. The current paper addresses the problem that the Neumann iterative solution converges badly for strong contrast sources. The remedy is linearization of the nonlinear contrast source, combined with application of more advanced methods for solving the resulting integral equation. Numerical results show that linearization in combination with a Bi-Conjugate Gradient Stabilized method allows the INCS method to deal with fairly strong, inhomogeneous attenuation, while the error due to the linearization can be eliminated by restarting the iterative scheme.

Interharmonic modulation products as a means to quantify nonlinear D-region interactions

NASA Astrophysics Data System (ADS)

Moore, Robert

Experimental observations performed during dual beam ionospheric HF heating experiments at the High frequency Active Auroral Research Program (HAARP) HF transmitter in Gakona, Alaska are used to quantify the relative importance of specific nonlinear interactions that occur within the D region ionosphere. During these experiments, HAARP broadcast two amplitude modulated HF beams whose center frequencies were separated by less than 20 kHz. One beam was sinusoidally modulated at 500 Hz while the second beam was sinusoidally modulated using a 1-7 kHz linear frequency-time chirp. ELF/VLF observations performed at two different locations (3 and 98 km from HAARP) provide clear evidence of strong interactions between all field components of the two HF beams in the form of low and high order interharmonic modulation products. From a theoretical standpoint, the observed interharmonic modulation products could be produced by several different nonlinearities. The two primary nonlinearities take the form of wave-medium interactions (i.e., cross modulation), wherein the ionospheric conductivity modulation produced by one signal crosses onto the other signal via collision frequency modification, and wave-wave interactions, wherein the conduction current associated with one wave mixes with the electric field of the other wave to produce electron temperature oscillations. We are able to separate and quantify these two different nonlinearities, and we conclude that the wave-wave interactions dominate the wave-medium interactions by a factor of two. These results are of great importance for the modeling of transioinospheric radio wave propagation, in that both the wave-wave and the wave-medium interactions could be responsible for a significant amount of anomalous absorption.

Mathematical nonlinear optics

NASA Astrophysics Data System (ADS)

McLaughlin, David W.

1995-08-01

The principal investigator, together with a post-doctoral fellows Tetsuji Ueda and Xiao Wang, several graduate students, and colleagues, has applied the modern mathematical theory of nonlinear waves to problems in nonlinear optics and to equations directly relevant to nonlinear optics. Projects included the interaction of laser light with nematic liquid crystals and chaotic, homoclinic, small dispersive, and random behavior of solutions of the nonlinear Schroedinger equation. In project 1, the extremely strong nonlinear response of a continuous wave laser beam in a nematic liquid crystal medium has produced striking undulation and filamentation of the laser beam which has been observed experimentally and explained theoretically. In project 2, qualitative properties of the nonlinear Schroedinger equation (which is the fundamental equation for nonlinear optics) have been identified and studied. These properties include optical shocking behavior in the limit of very small dispersion, chaotic and homoclinic behavior in discretizations of the partial differential equation, and random behavior.

Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1988-01-01

The nonlinear reaction between two oblique 3-D Tollmein-Schlichting (TS) waves and their induced streamwise-vortex flow is considered theoretically for an imcompressible boundary layer. The same theory applies to the destabilization of an incident vortex motion by subharmonic TS waves, followed by interaction. The scales and flow structure involved are addressed for high Reynolds numbers. The nonlionear interaction is powerful, starting at quite low amplitudes with a triple-deck structure for the TS waves but a large-scale structure for the induced vortex, after which strong nonlinear amplification occurs. This includes nonparallel-flow effects. The nonlinear interaction is governed by a partial differential system for the vortex flow coupled with an ordinary-differential one for the TS pressure. The solution properties found sometimes produce a breakup within a finite distance and sometimes further downstream, depending on the input amplitudes upstream and on the wave angles, and that then leads to the second stages of interaction associated with higher amplitudes, the main second stages giving either long-scale phenomena significantly affected by nonparallelism or shorter quasi-parallel ones governed by the full nonlinear triple-deck response.

Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate

NASA Astrophysics Data System (ADS)

Issokolo, Remi J. Noumana; Dikandé, Alain M.

2018-05-01

A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e., rivulet structures) to modulated nonlinear wavetrain structures. Some of these structures have been observed experimentally; however, conditions under which they form are still not well understood. In this work, we examine profiles of nonlinear wave patterns formed by a thin liquid film falling on a uniformly heated horizontal plate. For this purpose, the Benney model is considered assuming a uniform temperature distribution along the film propagation on the horizontal surface. It is shown that for strong surface tension but a relatively small Biot number, spatially localized periodic-wave structures can be analytically obtained by solving the governing equation under appropriate conditions. In the regime of weak nonlinearity, a multiple-scale expansion combined with the reductive perturbation method leads to a complex Ginzburg-Landau equation: the solutions of which are modulated periodic pulse trains which amplitude and width and period are expressed in terms of characteristic parameters of the model.

Modulational instability in a PT-symmetric vector nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Optical Random Riemann Waves in Integrable Turbulence

NASA Astrophysics Data System (ADS)

Randoux, Stéphane; Gustave, François; Suret, Pierre; El, Gennady

2017-06-01

We examine integrable turbulence (IT) in the framework of the defocusing cubic one-dimensional nonlinear Schrödinger equation. This is done theoretically and experimentally, by realizing an optical fiber experiment in which the defocusing Kerr nonlinearity strongly dominates linear dispersive effects. Using a dispersive-hydrodynamic approach, we show that the development of IT can be divided into two distinct stages, the initial, prebreaking stage being described by a system of interacting random Riemann waves. We explain the low-tailed statistics of the wave intensity in IT and show that the Riemann invariants of the asymptotic nonlinear geometric optics system represent the observable quantities that provide new insight into statistical features of the initial stage of the IT development by exhibiting stationary probability density functions.

Relativistically strong electromagnetic radiation in a plasma

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

Bulanov, S. V., E-mail: svbulanov@gmail.com, E-mail: bulanov.sergei@jaea.go.jp; Esirkepov, T. Zh.; Kando, M.

Physical processes in a plasma under the action of relativistically strong electromagnetic waves generated by high-power lasers have been briefly reviewed. These processes are of interest in view of the development of new methods for acceleration of charged particles, creation of sources of bright hard electromagnetic radiation, and investigation of macroscopic quantum-electrodynamical processes. Attention is focused on nonlinear waves in a laser plasma for the creation of compact electron accelerators. The acceleration of plasma bunches by the radiation pressure of light is the most efficient regime of ion acceleration. Coherent hard electromagnetic radiation in the relativistic plasma is generated inmore » the form of higher harmonics and/or electromagnetic pulses, which are compressed and intensified after reflection from relativistic mirrors created by nonlinear waves. In the limit of extremely strong electromagnetic waves, radiation friction, which accompanies the conversion of radiation from the optical range to the gamma range, fundamentally changes the behavior of the plasma. This process is accompanied by the production of electron–positron pairs, which is described within quantum electrodynamics theory.« less

Nonlinear lower hybrid structures in auroral plasmas: comparison of theory with observations

NASA Astrophysics Data System (ADS)

Robinson, P. A.

1999-01-01

Intense, localized lower hybrid wave structures are widely observed in auroral plasmas, often associated with density depletions. Commonly it is concluded without further analysis that these structures are solitons, collapsing wave packets, or other nonlinear entities. Such conclusions are often not justified on theoretical grounds. This review outlines theoretical constraints on field intensity, wave-packet scale length, timescales, and levels of density perturbations that must be met before nonlinear phenomena such as wave collapse and strong turbulence can occur. These criteria are determined within the framework of the modern nucleation scenario for the maintenance of strong turbulence, which involves collapse and dissipation (burnout) of each wave packet, followed by relaxation of its associated density perturbation, then renucleation of further energy into fields trapped in this relaxing perturbation, often leading to further collapse. The criteria are illustrated by applying them to a range of in situ auroral data that have been commonly interpreted in terms of lower hybrid solitons. It will be shown that the data are consistent with some of these criteria, but violate others if packets are all assumed to be observed in the collapse phase. However, theory and observations are consistent within the full nucleation scenario in which packets spend most of their time in the relaxation and renucleation phases, rather than undergoing collapse or burnout.

Ultrasound wave propagation in tissue and scattering from microbubbles for echo particle image velocimetry technique.

PubMed

Mukdadi, Osama; Shandas, Robin

2004-01-01

Nonlinear wave propagation in tissue can be employed for tissue harmonic imaging, ultrasound surgery, and more effective tissue ablation for high intensity focused ultrasound (HIFU). Wave propagation in soft tissue and scattering from microbubbles (ultrasound contrast agents) are modeled to improve detectability, signal-to-noise ratio, and contrast harmonic imaging used for echo particle image velocimetry (Echo-PIV) technique. The wave motion in nonlinear material (tissue) is studied using KZK-type parabolic evolution equation. This model considers ultrasound beam diffraction, attenuation, and tissue nonlinearity. Time-domain numerical model is based on that originally developed by Lee and Hamilton [J. Acoust. Soc. Am 97:906-917 (1995)] for axi-symmetric acoustic field. The initial acoustic waveform emitted from the transducer is assumed to be a broadband wave modulated by Gaussian envelope. Scattering from microbubbles seeded in the blood stream is characterized. Hence, we compute the pressure field impinges the wall of a coated microbubble; the dynamics of oscillating microbubble can be modeled using Rayleigh-Plesset-type equation. Here, the continuity and the radial-momentum equation of encapsulated microbubbles are used to account for the lipid layer surrounding the microbubble. Numerical results show the effects of tissue and microbubble nonlinearities on the propagating pressure wave field. These nonlinearities have a strong influence on the waveform distortion and harmonic generation of the propagating and scattering waves. Results also show that microbubbles have stronger nonlinearity than tissue, and thus improves S/N ratio. These theoretical predictions of wave phenomena provide further understanding of biomedical imaging technique and provide better system design.

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

PubMed

Kim, Sangbum; Kim, Kihong

2017-12-11

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

Shock wave structure in a strongly nonlinear lattice with viscous dissipation.

PubMed

Herbold, E B; Nesterenko, V F

2007-02-01

The shock wave structure in a one-dimensional lattice (e.g., granular chain of elastic particles) with a power law dependence of force on displacement between particles (F proportional to delta(n)) with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included to investigate its influence on the shape of a steady shock. The critical viscosity coefficient p(c), defining the transition from an oscillatory to a monotonic shock profile in strongly nonlinear systems, is obtained from the long-wave approximation for arbitrary values of the exponent n. The expression for the critical viscosity is comparable to the value obtained in the numerical analysis of a discrete system with a Hertzian contact interaction (n=3/2) . The expression for p(c) in the weakly nonlinear case converges to the known equation for the critical viscosity. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.

Modulation of a compressional electromagnetic wave in a magnetized electron-positron quantum plasma.

PubMed

Amin, M R

2015-09-01

Amplitude modulation of a compressional electromagnetic wave in a strongly magnetized electron-positron pair plasma is considered in the quantum magnetohydrodynamic regime. The important ingredients of this study are the inclusion of the external strong magnetic field, Fermi quantum degeneracy pressure, particle exchange potential, quantum diffraction effects via the Bohm potential, and dissipative effect due to collision of the charged carriers. A modified-nonlinear Schödinger equation is developed for the compressional magnetic field of the electromagnetic wave by employing the standard reductive perturbation technique. The linear and nonlinear dispersions of the electromagnetic wave are discussed in detail. For some parameter ranges, relevant to dense astrophysical objects such as the outer layers of white dwarfs, neutron stars, and magnetars, etc., it is found that the compressional electromagnetic wave is modulationally unstable and propagates as a dissipated electromagnetic wave. It is also found that the quantum effects due to the particle exchange potential and the Bohm potential are negligibly small in comparison to the effects of the Fermi quantum degeneracy pressure. The numerical results on the growth rate of the modulation instability is also presented.

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.

Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion

NASA Astrophysics Data System (ADS)

Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin

2014-09-01

We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.

Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion.

PubMed

Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin

2014-09-01

We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.

Numerical modeling of nonlinear modulation of coda wave interferometry in a multiple scattering medium with the presence of a localized micro-cracked zone

NASA Astrophysics Data System (ADS)

Chen, Guangzhi; Pageot, Damien; Legland, Jean-Baptiste; Abraham, Odile; Chekroun, Mathieu; Tournat, Vincent

2018-04-01

The spectral element method is used to perform a parametric sensitivity study of the nonlinear coda wave interferometry (NCWI) method in a homogeneous sample with localized damage [1]. The influence of a strong pump wave on a localized nonlinear damage zone is modeled as modifications to the elastic properties of an effective damage zone (EDZ), depending on the pump wave amplitude. The local change of the elastic modulus and the attenuation coefficient have been shown to vary linearly with respect to the excitation amplitude of the pump wave as in previous experimental studies of Zhang et al. [2]. In this study, the boundary conditions of the cracks, i.e. clapping effects is taken into account in the modeling of the damaged zone. The EDZ is then modeled with random cracks of random orientations, new parametric studies are established to model the pump wave influence with two new parameters: the change of the crack length and the crack density. The numerical results reported constitute another step towards quantification and forecasting of the nonlinear acoustic response of a cracked material, which proves to be necessary for quantitative non-destructive evaluation.

Nonlinear mechanism for the generation of electromagnetic fields in a magnetized plasma by the beatings of waves

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

Aburjania, G. D.; Machabeli, G. Z.; Kharshiladze, O. A.

2006-07-15

The modulational instability in a plasma in a strong constant external magnetic field is considered. The plasmon condensate is modulated not by conventional low-frequency ion sound but by the beatings of two high-frequency transverse electromagnetic waves propagating along the magnetic field. The instability reduces the spatial scales of Langmuir turbulence along the external magnetic field and generates electromagnetic fields. It is shown that, for a pump wave with a sufficiently large amplitude, the effect described in the present paper can be a dominant nonlinear process.

Frequency chirpings in Alfven continuum

NASA Astrophysics Data System (ADS)

Wang, Ge; Berk, Herb; Breizman, Boris; Zheng, Linjin

2017-10-01

We have used a self-consistent mapping technique to describe both the nonlinear wave-energetic particle resonant interaction and its spatial mode structure that depends upon the resonant energetic particle pressure. At the threshold for the onset of the energetic particle mode (EPM), strong chirping emerges in the lower continuum close to the TAE gap and then, driven by strong continuum damping, chirps rapidly to lower frequencies in the Alfven continuum. An adiabatic theory was developed that accurately replicated the results from the simulation where the nonlinearity was only due to the EPM resonant particles. The results show that the EPM-trapped particles have their action conserved during the time of rapid chirping. This adiabaticity enabled wave trapped particles to be confined within their separatrix, and produce even larger resonant structures, that can produce a large amplitude mode far from linearly predicted frequencies. In the present work we describe the effect of additional MHD nonlinearity to this calculation. We studied how the zonal flow component and its nonlinear feedback to the fundamental frequency and found that the MHD nonlinearity doesn't significantly alter the frequency chirping response that is predicted by the calculation that neglects the MHD nonlinearity.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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.

Wave Tank Studies of Strong Modulation of Wind Ripples Due To Long Waves

NASA Astrophysics Data System (ADS)

Ermakov, S.; Sergievskaya, I.; Shchegolkov, Yu.

Modulation of wind capillary-gravity ripples due to long waves has been studied in wave tank experiment at low wind speeds using Ka-band radar. The experiments were carried out both for clean water and the water surface covered with surfactant films. It is obtained that the modulation of radar signals is quite strong and can increase with surfactant concentration and fetch. It is shown that the hydrodynamic Modulation Transfer Function (MTF) calculated for free wind ripples and taking into account the kinematic (straining) effect, variations of the wind stress and variations of surfactant concentration strongly underestimates experimental MTF-values. The effect of strong modulation is assumed to be connected with nonlinear harmonics of longer dm-cm- scale waves - bound waves ("parasitic ripples"). The intensity of bound waves depends strongly on the amplitude of decimetre-scale waves, therefore even weak modulation of the dm-scale waves due to long waves results to strong ("cascade") modulation of bound waves. Modulation of the system of "free/bound waves" is estimated using results of wave tank studies of bound waves generation and is shown to be in quali- tative agreement with experiment. This work was supported by MOD, UK via DERA Winfrith (Project ISTC 1774P) and by RFBR (Project 02-05-65102).

New nonlinear optical effect: self-reflection phenomenon due to exciton-biexciton-light interaction in semiconductors

NASA Astrophysics Data System (ADS)

Khadzhi, P. I.; Lyakhomskaya, K. D.; Nadkin, L. Y.; Markov, D. A.

2002-05-01

The characteristic peculiarities of the self-reflection of a strong electromagnetic wave in a system of coherent excitons and biexcitons due to the exciton-photon interaction and optical exciton-biexciton conversion in semiconductors were investigated as one of the manifestations of nonlinear optical Stark-effect. It was found that a monotonously decreasing standing wave with an exponential decreasing spatial tail is formed in the semiconductor. Under the action of the field of a strong pulse, an optically homogeneous medium is converted, into the medium with distributed feedback. The appearance of the spatially separated narrow pears of the reflective index, extinction and reflection coefficients is predicted.

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.

Strong Langmuir Turbulence and Four-Wave Mixing

NASA Astrophysics Data System (ADS)

Glanz, James

1991-02-01

The staircase expansion is a new mathematical technique for deriving reduced, nonlinear-PDE descriptions from the plasma-moment equations. Such descriptions incorporate only the most significant linear and nonlinear terms of more complex systems. The technique is used to derive a set of Dawson-Zakharov or "master" equations, which unify and generalize previous work and show the limitations of models commonly used to describe nonlinear plasma waves. Fundamentally new wave-evolution equations are derived that admit of exact nonlinear solutions (solitary waves). Analytic calculations illustrate the competition between well-known effects of self-focusing, which require coupling to ion motion, and pure-electron nonlinearities, which are shown to be especially important in curved geometries. Also presented is an N -moment hydrodynamic model derived from the Vlasov equation. In this connection, the staircase expansion is shown to remain useful for all values of N >= 3. The relevance of the present work to nonlocally truncated hierarchies, which more accurately model dissipation, is briefly discussed. Finally, the general formalism is applied to the problem of electromagnetic emission from counterpropagating Langmuir pumps. It is found that previous treatments have neglected order-unity effects that increase the emission significantly. Detailed numerical results are presented to support these conclusions. The staircase expansion--so called because of its appearance when written out--should be effective whenever the largest contribution to the nonlinear wave remains "close" to some given frequency. Thus the technique should have application to studies of wake-field acceleration schemes and anomalous damping of plasma waves.

Modelling of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

Lehmann, M.; Schmidt, J.; Salo, H.

2014-04-01

Density wave theory, originally proposed to explain the spiral structure of galactic disks, has been applied to explain parts of the complex sub-structure in Saturn's rings, such as the wavetrains excited at the inner Lindblad resonances (ILR) of various satellites. The linear theory for the excitation and damping of density waves in Saturn's rings is fairly well developed (e.g. Goldreich & Tremaine [1979]; Shu [1984]). However, it fails to describe certain aspects of the observed waves. The non-applicability of the linear theory is already indicated by the "cusplike" shape of many of the observed wave profiles. This is a typical nonlinear feature which is also present in overstability wavetrains (Schmidt & Salo [2003]; Latter & Ogilvie [2010]). In particular, it turns out that the detailed damping mechanism, as well as the role of different nonlinear effects on the propagation of density waves remain intransparent. First attemps are being made to investigate the excitation and propagation of nonlinear density waves within a hydrodynamical formalism, which is also the natural formalism for describing linear density waves. A simple weakly nonlinear model, derived from a multiple-scale expansion of the hydrodynamic equations, is presented. This model describes the damping of "free" spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients, where the effects of the hydrodynamic nonlinearities are included. The model predicts that density waves are linearly unstable in a ring region where the conditions for viscous overstability are met, which translates to a steep dependence of the shear viscosity with respect to the disk's surface density. The possibility that this dependence could lead to a growth of density waves with increasing distance from the resonance, was already mentioned in Goldreich & Tremaine [1978]. Sufficiently far away from the ILR, the surface density perturbation caused by the wave, is predicted to saturate to a constant value due to the effects of nonlinear viscous damping. A qualitatively similar behaviour has also been predicted for the damping of nonlinear density waves, as described within a streamline formalism (Borderies, Goldreich & Tremaine [1985]). The damping lengths which follow from the weakly nonlinear model depend more or less strongly on a set of different input parameters, such as the viscosity and the surface density of the unperturbed ring state. Further, they depend on the wave's amplitude at resonance. For a real wave, which has been excited by an external satellite, this amplitude can be deduced from the magnitude of the satellite's forcing potential. Appart from that, hydrodynamical simulations are being developed to study the nonlinear damping of resonantly forced density waves.

Optical rogue waves generation in a nonlinear metamaterial

NASA Astrophysics Data System (ADS)

Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin

2014-11-01

We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.

Efficient non-linear two-photon effects from the Cesium 6D manifold

NASA Astrophysics Data System (ADS)

Haluska, Nathan D.; Perram, Glen P.; Rice, Christopher A.

2018-02-01

We report several non-linear process that occur when two-photon pumping the cesium 6D states. Cesium vapor possess some of the largest two-photon pump cross sections in nature. Pumping these cross sections leads to strong amplified spontaneous emission that we observe on over 17 lasing lines. These new fields are strong enough to couple with the pump to create additional tunable lines. We use a heat pipe with cesium densities of 1014 to 1016 cm-3 and 0 to 5 Torr of helium buffer gas. The cesium 6D States are interrogated by both high energy pulses and low power CW sources. We observe four-wave mixing, six-wave mixing, potential two-photon lasing, other unknown nonlinear processes, and the persistence of some processes at low thresholds. This system is also uniquely qualified to support two-photon lasing under the proper conditions.

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

Benisti, Didier; Morice, Olivier; Gremillet, Laurent

The propagation of an electrostatic wave packet inside a collisionless and initially Maxwellian plasma is always dissipative because of the irreversible acceleration of the electrons by the wave. Then, in the linear regime, the wave packet is Landau damped, so that in the reference frame moving at the group velocity, the wave amplitude decays exponentially with time. In the nonlinear regime, once phase mixing has occurred and when the electron motion is nearly adiabatic, the damping rate is strongly reduced compared to the Landau one, so that the wave amplitude remains nearly constant along the characteristics. Yet, we show heremore » that the electrons are still globally accelerated by the wave packet, and in one dimension, this leads to a non local amplitude dependence of the group velocity. As a result, a freely propagating wave packet would shrink, and therefore, so would its total energy. In more than one dimension, not only does the magnitude of the group velocity nonlinearly vary, but also its direction. In the weakly nonlinear regime, when the collisionless damping rate is still significant compared to its linear value, the group velocity is directed towards the outside of the wave packet and tends to increase its transverse extent, while the opposite is true once the wave is essentially undamped. The impact of the nonlinear variation of the group velocity on the transverse size of the wave packet is quantified, and compared to that induced by the self-focussing due to wave front bowing.« less

Nonlinear optical magnetometry with accessible in situ optical squeezing

DOE PAGES

Otterstrom, N.; Pooser, R. C.; Lawrie, B. J.

2014-11-14

In this paper, we demonstrate compact and accessible squeezed-light magnetometry using four-wave mixing in a single hot rubidium vapor cell. The strong intrinsic coherence of the four-wave mixing process results in nonlinear magneto-optical rotation (NMOR) on each mode of a two-mode relative-intensity squeezed state. Finally, this framework enables 4.7 dB of quantum noise reduction while the opposing polarization rotation signals of the probe and conjugate fields add to increase the total signal to noise ratio.

Higgs Mode in the d -Wave Superconductor Bi 2 Sr 2 CaCu 2 O 8 + x Driven by an Intense Terahertz Pulse

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

Katsumi, Kota; Tsuji, Naoto; Hamada, Yuki I.

We investigated the terahertz (THz)-pulse driven nonlinear response in the d-wave cuprate superconductor Bi 2Sr 2CaCu 2O 8+x (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We have observed an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is strongly enhanced below Tc. The corresponding third-order nonlinear effect exhibits both A 1g and B 1g symmetry components, which are decomposed from polarization-resolved measurements. Comparison with a BCS calculation of the nonlinear susceptibility indicates that the A 1g component is associated with the Higgs mode of the d-wave order parameter.

Higgs Mode in the d -Wave Superconductor Bi 2 Sr 2 CaCu 2 O 8 + x Driven by an Intense Terahertz Pulse

DOE PAGES

Katsumi, Kota; Tsuji, Naoto; Hamada, Yuki I.; ...

2018-03-14

We investigated the terahertz (THz)-pulse driven nonlinear response in the d-wave cuprate superconductor Bi 2Sr 2CaCu 2O 8+x (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We have observed an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is strongly enhanced below Tc. The corresponding third-order nonlinear effect exhibits both A 1g and B 1g symmetry components, which are decomposed from polarization-resolved measurements. Comparison with a BCS calculation of the nonlinear susceptibility indicates that the A 1g component is associated with the Higgs mode of the d-wave order parameter.

Continuous-wave supercontinuum laser based on an erbium-doped fiber ring cavity incorporating a highly nonlinear optical fiber.

PubMed

Lee, Ju Han; Takushima, Yuichi; Kikuchi, Kazuro

2005-10-01

We experimentally demonstrate a novel erbium-doped fiber based continuous-wave (cw) supercontinuum laser. The laser has a simple ring-cavity structure incorporating an erbium-doped fiber and a highly nonlinear dispersion-shifted fiber (HNL-DSF). Differently from previously demonstrated cw supercontinuum sources based on single propagation of a strong Raman pump laser beam through a highly nonlinear fiber, erbium gain inside the cavity generates a seed light oscillation, and the oscillated light subsequently evolves into a supercontinuum by nonlinear effects such as modulation instability and stimulated Raman scattering in the HNL-DSF. High quality of the depolarized supercontinuum laser output with a spectral bandwidth larger than 250 nm is readily achieved.

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 mixing of electromagnetic waves in plasmas.

PubMed

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

1989-01-27

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

Peculiarities of evolutions of elastic-plastic shock compression waves in different materials

NASA Astrophysics Data System (ADS)

Kanel, G. I.; Savinykh, A. S.; Garkushin, G. V.; Razorenov, S. V.; Ashitkov, S. I.; Zaretsky, E. B.

2016-11-01

In the paper, we discuss such unexpected features in the wave evolution in solids as strongly nonlinear uniaxial elastic compression in a picosecond time range, a departure from self-similar development of the wave process which is accompanied with apparent sub-sonic wave propagation, changes of shape of elastic precursor wave as a result of variations in the material structure and the temperature, unexpected peculiarities of reflection of elastic-plastic waves from free surface.

Long-range parametric amplification of THz wave with absorption loss exceeding parametric gain.

PubMed

Wang, Tsong-Dong; Huang, Yen-Chieh; Chuang, Ming-Yun; Lin, Yen-Hou; Lee, Ching-Han; Lin, Yen-Yin; Lin, Fan-Yi; Kitaeva, Galiya Kh

2013-01-28

Optical parametric mixing is a popular scheme to generate an idler wave at THz frequencies, although the THz wave is often absorbing in the nonlinear optical material. It is widely suggested that the useful material length for co-directional parametric mixing with strong THz-wave absorption is comparable to the THz-wave absorption length in the material. Here we show that, even in the limit of the absorption loss exceeding parametric gain, the THz idler wave can grows monotonically from optical parametric amplification over a much longer distance in a nonlinear optical material until pump depletion. The coherent production of the non-absorbing signal wave can assist the growth of the highly absorbing idler wave. We also show that, for the case of an equal input pump and signal in difference frequency generation, the quick saturation of the THz idler wave predicted from a much simplified and yet popular plane-wave model fails when fast diffraction of the THz wave from the co-propagating optical mixing waves is considered.

Energy transport in weakly nonlinear wave systems with narrow frequency band excitation.

PubMed

Kartashova, Elena

2012-10-01

A novel discrete model (D model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of energy transport between modes, namely, intermittency and energy cascade, and gives the conditions under which each regime will take place. Conditions for the formation of a cascade, cascade direction, conditions for cascade termination, etc., are given and depend strongly on the choice of excitation parameters. The energy spectra of a cascade may be computed, yielding discrete and continuous energy spectra. The model does not require statistical assumptions, as all effects are derived from the interaction of distinct modes. In the example given-surface water waves with dispersion function ω(2)=gk and small nonlinearity-the D model predicts asymmetrical growth of side-bands for Benjamin-Feir instability, while the transition from discrete to continuous energy spectrum, excitation parameters properly chosen, yields the saturated Phillips' power spectrum ~g(2)ω(-5). The D model can be applied to the experimental and theoretical study of numerous wave systems appearing in hydrodynamics, nonlinear optics, electrodynamics, plasma, convection theory, etc.

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.

Nonlinear coseismic infrasound waves in the upper atmosphere and ionosphere

NASA Astrophysics Data System (ADS)

Chum, J.; Liu, J. Y.; Cabrera, M. A.

2017-12-01

Vertical motion of the ground surface caused by seismic waves generates acoustic waves that propagate nearly vertically upward because of supersonic speed of seismic waves. As the air density decreases with height, the amplitude of acoustic waves increases to conserve the energy flux. If the initial perturbation is large enough (larger than 10 mm/s) and the period of waves is long (>10 s), then the amplitude reaches significant values in the upper atmosphere (e.g. oscillation velocities of the air particles become comparable with sound speed) and the nonlinear phenomena start to play an important role before the wave is dissipated. The nonlinear phenomena lead to changes of spectral content of the wave packet. The energy is transferred to lower frequencies, which can cause the formation of roughly bipolar N-shaped pulse in the vicinity of the epicenters (up to distance about 1000-1500 km) of strong, M>7, earthquakes. The nonlinear propagation is studied on the basis of numerical solution of continuity, momentum and heat equations in 1D (along vertical axis) for viscous compressible atmosphere. Boundary conditions on the ground are determined by real measurements of the vertical motion of the ground surface. The results of numerical simulations are in a good agreement with atmospheric fluctuations observed by continuous Doppler sounding at heights of about 200 km and epicenter distance around 800 km. In addition, the expected fluctuations of GSP-TEC are calculated.

Burnett-Cattaneo continuum theory for shock waves.

PubMed

Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon

2011-02-01

We model strong shock-wave propagation, both in the ideal gas and in the dense Lennard-Jones fluid, using a refinement of earlier work, which accounts for the cold compression in the early stages of the shock rise by a nonlinear, Burnett-like, strain-rate dependence of the thermal conductivity, and relaxation of kinetic-temperature components on the hot, compressed side of the shock front. The relaxation of the disequilibrium among the three components of the kinetic temperature, namely, the difference between the component in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, is accomplished at a much more quantitative level by a rigorous application of the Cattaneo-Maxwell relaxation equation to a reference solution, namely, the steady shock-wave solution of linear Navier-Stokes-Fourier theory, along with the nonlinear Burnett heat-flux term. Our new continuum theory is in nearly quantitative agreement with nonequilibrium molecular-dynamics simulations under strong shock-wave conditions, using relaxation parameters obtained from the reference solution. ©2011 American Physical Society

Intermittency in generalized NLS equation with focusing six-wave interactions

NASA Astrophysics Data System (ADS)

Agafontsev, D. S.; Zakharov, V. E.

2015-10-01

We study numerically the statistics of waves for generalized one-dimensional Nonlinear Schrödinger (NLS) equation that takes into account focusing six-wave interactions, dumping and pumping terms. We demonstrate the universal behavior of this system for the region of parameters when six-wave interactions term affects significantly only the largest waves. In particular, in the statistically steady state of this system the probability density function (PDF) of wave amplitudes turns out to be strongly non-Rayleigh one for large waves, with characteristic "fat tail" decaying with amplitude | Ψ | close to ∝ exp ⁡ (- γ | Ψ |), where γ > 0 is constant. The corresponding non-Rayleigh addition to the PDF indicates strong intermittency, vanishes in the absence of six-wave interactions, and increases with six-wave coupling coefficient.

Effect of temperature degeneracy and Landau quantization on drift solitary waves and double layers

NASA Astrophysics Data System (ADS)

Shan, Shaukat Ali; Haque, Q.

2018-01-01

The linear and nonlinear drift ion acoustic waves have been investigated in an inhomogeneous, magnetized, dense degenerate, and quantized magnetic field plasma. The linear drift ion acoustic wave propagation along with the nonlinear structures like double layers and solitary waves has been found to be strongly dependent on the drift speed, magnetic field quantization parameter β, and the temperature degeneracy. The graphical illustrations show that the frequency of linear waves and the amplitude of the solitary waves increase with the increase in temperature degeneracy and Landau quantization effect, while the amplitude of the double layers decreases with the increase in η and T. The relevance of the present study is pointed out in the plasma environment of fast ignition inertial confinement fusion, the white dwarf stars, and short pulsed petawatt laser technology.

Multidimensional nonlinear ion-acoustic waves in a plasma in view of relativistic effects

NASA Astrophysics Data System (ADS)

Belashov, V. Yu.

2017-05-01

The structure and dynamics of ion-acoustic waves in an unmagnetized plasma, including the case of weakly relativistic collisional plasma (when it is necessary to take into account the high energy particle flows which are observed in the magnetospheric plasma), are studied analytically and numerically on the basis of a model of the Kadomtsev-Petviashvili (KP) equation. It is shown that, if the velocity of plasma particles approaches the speed of light, the relativistic effects start to strongly influence on the wave characteristics, such as its phase velocity, amplitude, and characteristic wavelength, with the propagation of the twodimensional solitary ion-acoustic wave. The results can be used in the study of nonlinear wave processes in the magnetosphere and in laser and astrophysical plasma.

Turbulence and wave particle interactions in solar-terrestrial plasmas

NASA Technical Reports Server (NTRS)

Dulk, G. A.; Goldman, M. V.; Toomre, J.

1985-01-01

Activities in the following study areas are reported: (1) particle and wave processes in solar flares; (2) solar convection zone turbulence; and (3) solar radiation emission. To investigate the amplification of cyclotron maser radiation in solar flares, a radio frequency. (RF) heating model was developed for the corona surrounding the energy release site. Then nonlinear simulations of compressible convection display prominent penetration by plumes into regions of stable stratification at the base of the solar convection zone, leading to the excitation of internal gravity waves there. Lastly, linear saturation of electron-beam-driven Langmuir waves by ambient density fluctuations, nonlinear saturation by strong turbulence processes, and radiation emission mechanisms are examined. An additional section discusses solar magnetic fields and hydromagnetic waves in inhomogeneous media, and the effect of magnetic fields on stellar oscillation.

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

Falling films on flexible inclines

NASA Astrophysics Data System (ADS)

Matar, O. K.; Craster, R. V.; Kumar, S.

2007-11-01

The nonlinear stability and dynamic behavior of falling fluid films is studied for flow over a flexible substrate. We use asymptotic methods to deduce governing equations valid in various limits. Long-wave theory is used to derive Benney-like coupled equations for the film thickness and substrate deflection. Weakly nonlinear equations are then derived from these equations that, in the limit of large wall damping and/or large wall tension, reduce to the Kuramoto-Sivashinsky equation. These models break down when inertia becomes more significant, so we also use a long-wave approximation in conjunction with integral theory to derive three strongly coupled nonlinear evolution equations for the film thickness, substrate deflection, and film volumetric flow rate valid at higher Reynolds numbers. These equations, accounting for inertia, capillary, viscous, wall tension, and damping effects, are solved over a wide range of parameters. Our results suggest that decreasing wall damping and/or wall tension can promote the development of chaos in the weakly nonlinear regime and lead to severe substrate deformations in the strongly nonlinear regime; these can give rise to situations in which the free surface and underlying substrate come into contact in finite time.

Ultrafast Terahertz Nonlinear Optics of Landau Level Transitions in a Monolayer Graphene

NASA Astrophysics Data System (ADS)

Yumoto, Go; Matsunaga, Ryusuke; Hibino, Hiroki; Shimano, Ryo

2018-03-01

We investigated the ultrafast terahertz (THz) nonlinearity in a monolayer graphene under the strong magnetic field using THz pump-THz probe spectroscopy. An ultrafast suppression of the Faraday rotation associated with inter-Landau level (LL) transitions is observed, reflecting the Dirac electron character of nonequidistant LLs with large transition dipole moments. A drastic modulation of electron distribution in LLs is induced by far off-resonant THz pulse excitation in the transparent region. Numerical simulation based on the density matrix formalism without rotating-wave approximation reproduces the experimental results. Our results indicate that the strong light-matter coupling regime is realized in graphene, with the Rabi frequency exceeding the carrier wave frequency and even the relevant energy scale of the inter-LL transition.

Toward a System-Based Approach to Electromagnetic Ion Cyclotron Waves in Earth's Magnetosphere

NASA Astrophysics Data System (ADS)

Gamayunov, K. V.; Engebretson, M. J.; Rassoul, H.

2015-12-01

We consider a nonlinear wave energy cascade from the low frequency range into the higher frequency domain of electromagnetic ion cyclotron (EMIC) wave generation as a possible source of seed fluctuations for EMIC wave growth due to the ion cyclotron instability in Earth's magnetosphere. The theoretical analysis shows that energy cascade from the Pc 4-5 frequency range (2-22 mHz) into the range of Pc 1-2 pulsations (0.1-5 Hz) is able to supply the level of seed fluctuations that guarantees growth of EMIC waves up to an observable level during one pass through the near equatorial region where the ion cyclotron instability takes place. We also analyze magnetic field data from the Polar and Van Allen Probes spacecraft to test this nonlinear mechanism. We restrict our analysis to magnetic spectra only. We do not analyze the third-order moment for total energy of the magnetic and velocity fluctuations, but judge whether a nonlinear energy cascade is present or whether it is not by only analyzing the appearance of power-law distributions in the low frequency part of the magnetic field spectra. While the power-law spectrum alone does not guarantee that a nonlinear cascade is present, the power-law distribution is a strong indication of the possible development of a nonlinear cascade. Our data analysis shows that a nonlinear energy cascade is indeed observed in both the outer and inner magnetosphere, and EMIC waves are growing from this nonthermal background. All the analyzed data are in good agreement with the theoretical model presented in this study. Overall, the results of this study support a nonlinear energy cascade in Earth's magnetosphere as a mechanism which is responsible for supplying seed fluctuating energy in the higher frequency domain where EMIC waves grow due to the ion cyclotron instability. Keywords: nonlinear energy cascade, ultra low frequency waves, electromagnetic ion cyclotron waves, seed fluctuationsAcknowledgments: This paper is based upon work supported by the National Science Foundation under Grant Number AGS-1203516.

Source of seed fluctuations for electromagnetic ion cyclotron waves in Earth's magnetosphere

NASA Astrophysics Data System (ADS)

Gamayunov, K. V.; Engebretson, M. J.; Zhang, M.; Rassoul, H. K.

2015-06-01

We consider a nonlinear wave energy cascade from the low frequency range into the higher frequency domain of electromagnetic ion cyclotron (EMIC) wave generation as a possible source of seed fluctuations for EMIC wave growth due to the ion cyclotron instability in Earth's magnetosphere. The presented theoretical analysis shows that energy cascade from the Pc 4-5 frequency range (2-22 mHz) into the range of Pc 1-2 pulsations (0.1-5 Hz), i.e. into the frequency range of EMIC waves, is able to supply the needed level of seed fluctuations that guarantees growth of EMIC waves up to the observable level during one pass through the near equatorial region where the ion cyclotron instability takes place. We also analyze the magnetic field data from the Polar and Van Allen Probes spacecraft to test the suggested nonlinear mechanism. In this initial study we restrict our analysis to magnetic fluctuation spectra only. We do not analyze the third-order structure function, but judge whether a nonlinear energy cascade is present or whether it is not by only analyzing the appearance of power-law distributions in the low-frequency part of the magnetic field spectra. While the power-law spectrum alone does not guarantee that a nonlinear cascade is present, the power-law distribution is a strong indication of the possible development of a nonlinear cascade. Our analysis shows that a nonlinear energy cascade is indeed observed in both the outer and inner magnetosphere data, and EMIC waves are growing from this nonthermal background. All the analyzed data are in good agreement with the theoretical model presented in this study. Overall, the results of this study support a nonlinear energy cascade in Earth's magnetosphere as a mechanism which is responsible for supplying seed fluctuating energy in the higher frequency domain where EMIC waves grow due to the ion cyclotron instability.

Modelling strong seismic ground motion: three-dimensional loading path versus wavefield polarization

NASA Astrophysics Data System (ADS)

Santisi d'Avila, Maria Paola; Lenti, Luca; Semblat, Jean-François

2012-09-01

Seismic waves due to strong earthquakes propagating in surficial soil layers may both reduce soil stiffness and increase the energy dissipation into the soil. To investigate seismic wave amplification in such cases, past studies have been devoted to one-directional shear wave propagation in a soil column (1D-propagation) considering one motion component only (1C-polarization). Three independent purely 1C computations may be performed ('1D-1C' approach) and directly superimposed in the case of weak motions (linear behaviour). This research aims at studying local site effects by considering seismic wave propagation in a 1-D soil profile accounting for the influence of the 3-D loading path and non-linear hysteretic behaviour of the soil. In the proposed '1D-3C' approach, the three components (3C-polarization) of the incident wave are simultaneously propagated into a horizontal multilayered soil. A 3-D non-linear constitutive relation for the soil is implemented in the framework of the Finite Element Method in the time domain. The complex rheology of soils is modelled by mean of a multisurface cyclic plasticity model of the Masing-Prandtl-Ishlinskii-Iwan type. The great advantage of this choice is that the only data needed to describe the model is the modulus reduction curve. A parametric study is carried out to characterize the changes in the seismic motion of the surficial layers due to both incident wavefield properties and soil non-linearities. The numerical simulations show a seismic response depending on several parameters such as polarization of seismic waves, material elastic and dynamic properties, as well as on the impedance contrast between layers and frequency content and oscillatory character of the input motion. The 3-D loading path due to the 3C-polarization leads to multi-axial stress interaction that reduces soil strength and increases non-linear effects. The non-linear behaviour of the soil may have beneficial or detrimental effects on the seismic response at the free surface, depending on the energy dissipation rate. Free surface time histories, stress-strain hysteresis loops and in-depth profiles of octahedral stress and strain are estimated for each soil column. The combination of three separate 1D-1C non-linear analyses is compared to the proposed 1D-3C approach, evidencing the influence of the 3C-polarization and the 3-D loading path on strong seismic motions.

Prism-coupled Cherenkov phase-matched terahertz wave generation using a DAST crystal.

PubMed

Suizu, Koji; Shibuya, Takayuki; Uchida, Hirohisa; Kawase, Kodo

2010-02-15

Terahertz (THz) wave generation based on nonlinear frequency conversion is a promising method for realizing a tunable monochromatic high-power THz-wave source. Unfortunately, many nonlinear crystals have strong absorption in the THz frequency region. This limits efficient and widely tunable THz-wave generation. The Cherenkov phase-matching method is one of the most promising techniques for overcoming these problems. Here, we propose a prism-coupled Cherenkov phase-matching (PCC-PM) method, in which a prism with a suitable refractive index at THz frequencies is coupled to a nonlinear crystal. This has the following advantages. Many crystals can be used as THz-wave emitters; the phase-matching condition inside the crystal does not have to be observed; the absorption of the crystal does not prevent efficient generation of radiation; and pump sources with arbitrary wavelengths can be employed. Here we demonstrate PCC-PM THz-wave generation using the organic crystal 4-dimethylamino-N-metyl-4-stilbazolium tosylate (DAST) and a Si prism coupler. We obtain THz-wave radiation with tunability of approximately 0.1 to 10 THz and with no deep absorption features resulting from the absorption spectrum of the crystal. The obtained spectra did not depend on the pump wavelength in the range 1300 to 1450 nm. This simple technique shows promise for generating THz radiation using a wide variety of nonlinear crystals.

Synchronism of nonlinear internal waves in a three-layer fluid

NASA Astrophysics Data System (ADS)

Talipova, Tatiana; Kurkina, Oxana; Terletska, Katerina; Rouvinskaya, Ekaterina

2017-04-01

In a three layer fluid with arbitrary layer widths and densities the existence of long internal solitons and breathers is proven theoretically and numerically, see for example (Pelinovsky et al., 2007; Lamb et al., 2007). The existence of breather-like waves of the intermediate length is also shown in numerical simulations (Terletska et al., 2016). For such waves conditions of synchronism are valid when a breather of the first mode and a soliton of the second mode move together with the same speed and form an asymmetric solitary wave of the second mode. The process of strong interaction of long nonlinear internal waves in the framework of three-layer Camassa-Choi model demonstrates the same effect (Jo&Choi, 2014; Barros, 2016). We analyze possible synchronism conditions for steady-state internal waves in a three-layer fluid analytically the framework of the Gardner equation, which is valid for long weakly nonlinear internal waves. The equations for synchronism conditions are derived and considered in terms of wave amplitudes, layer widths and density jumps. The configurations of three-layer fluid are found for which such a synchronism is possible. References: Barros R. Large amplitude internal waves in three-layer flows. The forth international conference "Nonlinear Waves - Theory and Applications", MS7, Beijing, China, June 25 - 28, 2016 Pelinovsky E., Polukhina O., Slunyaev A., Talipova T. Internal solitary waves // Chapter 4 in the book "Solitary Waves in Fluids". WIT Press. Southampton, Boston. 2007. P. 85 - 110. K. Terletska., K. T. Jung, T. Talipova, V. Maderich, I. Brovchenko and R. Grimshaw Internal breather-like wave generation by the second mode solitary wave interaction with a step// Physics of Fluids, 2016, accepted

Damping of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki

2016-10-01

We address the stability of resonantly forced density waves in dense planetary rings.Already by Goldreich and Tremaine (1978) it has been argued that density waves might be unstable, depending on the relationship between the ring's viscosity and the surface mass density. In the recent paper (Schmidt et al. 2016) we have pointed out that when - within a fluid description of the ring dynamics - the criterion for viscous overstability is satisfied, forced spiral density waves become unstable as well. In this case, linear theory fails to describe the damping.We apply the multiple scale formalism to derive a weakly nonlinear damping relation from a hydrodynamical model.This relation describes the resonant excitation and nonlinear viscous damping of spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients. The model consistently predicts linear instability of density waves in a ring region where the conditions for viscous overstability are met. In this case, sufficiently far away from the Lindblad resonance, the surface mass density perturbation is predicted to saturate to a constant value due to nonlinear viscous damping. In general the model wave damping lengths depend on a set of input parameters, such as the distance to the threshold for viscous overstability and the ground state surface mass density.Our new model compares reasonably well with the streamline model for nonlinear density waves of Borderies et al. 1986.Deviations become substantial in the highly nonlinear regime, corresponding to strong satellite forcing.Nevertheless, we generally observe good or at least qualitative agreement between the wave amplitude profiles of both models. The streamline approach is superior at matching the total wave profile of waves observed in Saturn's rings, while our new damping relation is a comparably handy tool to gain insight in the evolution of the wave amplitude with distance from resonance, and the different regimes of wave formation and the dependence on the parameters of the model.

Acoustics of One-Dimensional Homogeneous Granular Chains

NASA Astrophysics Data System (ADS)

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

The Chapter 1 provided a brief glimpse of the general ordered granular chain/lattices, their subtle features and the intricacies associated with their analysis. By now it should be clear that this class of highly-inhomogeneous and discontinuous systems poses new challenges in the form of strongly nonlinear behavior, bead separations, and twice (at most) differentiable interaction potential. It follows that the traditional analytical methodologies may need to be modified to effectively address these challenges. To begin with, we consider the simplest case of the homogeneous granular chains, wherein, the particles are identical and are perfectly in contact (no gaps) initially. We consider the case of both the uncompressed (strongly nonlinear) and the pre-compressed (weakly nonlinear) chains and elucidate the striking differences between their dynamical behaviors. In the latter case, the long wave/continuum approximation is invoked in this analysis thus precluding any bead separations. A landmark discovery in this class of systems is the realization of the solitary wave propagation [1-3]. These waves are highly localized spatially symmetric disturbances which propagate in the nonlinear medium. In general, it is well known that the linear nondispersive waves have a characteristic wave speed (property of the medium), and a disturbance of any amplitude or waveform propagates at the same speed undistorted. In contrast, the propagation velocity of the solitary waves in a nonlinear medium is a function of the wave amplitude (a general nonlinear behavior) and the physical properties of the medium. It is worth noting that any arbitrary disturbance set in motion in a homogeneous granular chain eventually disintegrates into a train of the solitary waves of varying amplitudes propagating at the proportional velocities (higher the amplitude, higher the propagation velocity). Although these waves are called solitary waves, they do not necessarily conform to the definition [4] provided in the previous chapter. In fact such a definition is applicable when the medium is a continuum and does not consist of a discrete set of particles. Thus such localized waves are alternatively given the name compactons as they span a limited spatial domain of about 6-7 beads or in other words they only require compact support in the media where they propagate (although the characterization as solitary wave is also common in the research community). We briefly dwell on the concept of the compactons [5] and the decaying characteristic [6] of these waves. An aspect that has interested many researchers is the interaction of these solitary waves with the mass defects/intruders (disparity in masses). Such defects, e.g., in the form of a large mass disparity, can lead to the discrete breathers that transiently entrap the energy in space. In the final part of this chapter we consider the effects of the periodic intruders on the wave propagation and the shock mitigation of pulse propagating in the granular chains.

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

NASA Astrophysics Data System (ADS)

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

2014-09-01

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

Underwater acoustic wave generation by filamentation of terawatt ultrashort laser pulses.

PubMed

Jukna, Vytautas; Jarnac, Amélie; Milián, Carles; Brelet, Yohann; Carbonnel, Jérôme; André, Yves-Bernard; Guillermin, Régine; Sessarego, Jean-Pierre; Fattaccioli, Dominique; Mysyrowicz, André; Couairon, Arnaud; Houard, Aurélien

2016-06-01

Acoustic signals generated by filamentation of ultrashort terawatt laser pulses in water are characterized experimentally. Measurements reveal a strong influence of input pulse duration on the shape and intensity of the acoustic wave. Numerical simulations of the laser pulse nonlinear propagation and the subsequent water hydrodynamics and acoustic wave generation show that the strong acoustic emission is related to the mechanism of superfilamention in water. The elongated shape of the plasma volume where energy is deposited drives the far-field profile of the acoustic signal, which takes the form of a radially directed pressure wave with a single oscillation and a very broad spectrum.

Integrated analysis of energy transfers in elastic-wave turbulence.

PubMed

Yokoyama, Naoto; Takaoka, Masanori

2017-08-01

In elastic-wave turbulence, strong turbulence appears in small wave numbers while weak turbulence does in large wave numbers. Energy transfers in the coexistence of these turbulent states are numerically investigated in both the Fourier space and the real space. An analytical expression of a detailed energy balance reveals from which mode to which mode energy is transferred in the triad interaction. Stretching energy excited by external force is transferred nonlocally and intermittently to large wave numbers as the kinetic energy in the strong turbulence. In the weak turbulence, the resonant interactions according to the weak turbulence theory produce cascading net energy transfer to large wave numbers. Because the system's nonlinearity shows strong temporal intermittency, the energy transfers are investigated at active and moderate phases separately. The nonlocal interactions in the Fourier space are characterized by the intermittent bundles of fibrous structures in the real space.

Frequency sweep rates of rising tone electromagnetic ion cyclotron waves: Comparison between nonlinear theory and Cluster observation

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

He, Zhaoguo; University of Chinese Academy of Sciences, Beijing 100049; Zong, Qiugang, E-mail: qgzong@gmail.com

2014-12-15

Resonant pitch angle scattering by electromagnetic ion cyclotron (EMIC) waves has been suggested to account for the rapid loss of ring current ions and radiation belt electrons. For the rising tone EMIC wave (classified as triggered EMIC emission), its frequency sweep rate strongly affects the efficiency of pitch-angle scattering. Based on the Cluster observations, we analyze three typical cases of rising tone EMIC waves. Two cases locate at the nightside (22.3 and 22.6 magnetic local time (MLT)) equatorial region and one case locates at the duskside (18MLT) higher magnetic latitude (λ = –9.3°) region. For the three cases, the time-dependent wave amplitude,more » cold electron density, and cold ion density ratio are derived from satellite data; while the ambient magnetic field, thermal proton perpendicular temperature, and the wave spectral can be directly provided by observation. These parameters are input into the nonlinear wave growth model to simulate the time-frequency evolutions of the rising tones. The simulated results show good agreements with the observations of the rising tones, providing further support for the previous finding that the rising tone EMIC wave is excited through the nonlinear wave growth process.« less

Self-action of Bessel wave packets in a system of coupled light guides and formation of light bullets

NASA Astrophysics Data System (ADS)

Balakin, A. A.; Mironov, V. A.; Skobelev, S. A.

2017-01-01

The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the "kaleidoscopic" picture of a wave packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.

Two-dimensional dissipative rogue waves due to time-delayed feedback in cavity nonlinear optics.

PubMed

Tlidi, Mustapha; Panajotov, Krassimir

2017-01-01

We demonstrate a way to generate two-dimensional rogue waves in two types of broad area nonlinear optical systems subject to time-delayed feedback: in the generic Lugiato-Lefever model and in the model of a broad-area surface-emitting laser with saturable absorber. The delayed feedback is found to induce a spontaneous formation of rogue waves. In the absence of delayed feedback, spatial pulses are stationary. The rogue waves are exited and controlled by the delay feedback. We characterize their formation by computing the probability distribution of the pulse height. The long-tailed statistical contribution, which is often considered as a signature of the presence of rogue waves, appears for sufficiently strong feedback. The generality of our analysis suggests that the feedback induced instability leading to the spontaneous formation of two-dimensional rogue waves is a universal phenomenon.

Magnetospheric Multiscale observations of large-amplitude, parallel, electrostatic waves associated with magnetic reconnection at the magnetopause

NASA Astrophysics Data System (ADS)

Ergun, R. E.; Holmes, J. C.; Goodrich, K. A.; Wilder, F. D.; Stawarz, J. E.; Eriksson, S.; Newman, D. L.; Schwartz, S. J.; Goldman, M. V.; Sturner, A. P.; Malaspina, D. M.; Usanova, M. E.; Torbert, R. B.; Argall, M.; Lindqvist, P.-A.; Khotyaintsev, Y.; Burch, J. L.; Strangeway, R. J.; Russell, C. T.; Pollock, C. J.; Giles, B. L.; Dorelli, J. J. C.; Avanov, L.; Hesse, M.; Chen, L. J.; Lavraud, B.; Le Contel, O.; Retino, A.; Phan, T. D.; Eastwood, J. P.; Oieroset, M.; Drake, J.; Shay, M. A.; Cassak, P. A.; Nakamura, R.; Zhou, M.; Ashour-Abdalla, M.; André, M.

2016-06-01

We report observations from the Magnetospheric Multiscale satellites of large-amplitude, parallel, electrostatic waves associated with magnetic reconnection at the Earth's magnetopause. The observed waves have parallel electric fields (E||) with amplitudes on the order of 100 mV/m and display nonlinear characteristics that suggest a possible net E||. These waves are observed within the ion diffusion region and adjacent to (within several electron skin depths) the electron diffusion region. They are in or near the magnetosphere side current layer. Simulation results support that the strong electrostatic linear and nonlinear wave activities appear to be driven by a two stream instability, which is a consequence of mixing cold (<10 eV) plasma in the magnetosphere with warm (~100 eV) plasma from the magnetosheath on a freshly reconnected magnetic field line. The frequent observation of these waves suggests that cold plasma is often present near the magnetopause.

Numerical Simulations of Laminar Air-Water Flow of a Non-linear Progressive Wave at Low Wind Speed

NASA Astrophysics Data System (ADS)

Wen, X.; Mobbs, S.

2014-03-01

A numerical simulation for two-dimensional laminar air-water flow of a non-linear progressive water wave with large steepness is performed when the background wind speed varies from zero to the wave phase speed. It is revealed that in the water the difference between the analytical solution of potential flow and numerical solution of viscous flow is very small, indicating that both solutions of the potential flow and viscous flow describe the water wave very accurately. In the air the solutions of potential and viscous flows are very different due to the effects of viscosity. The velocity distribution in the airflow is strongly influenced by the background wind speed and it is found that three wind speeds, , (the maximum orbital velocity of a water wave), and (the wave phase speed), are important in distinguishing different features of the flow patterns.

Unidirectional Transition Waves in Bistable Lattices

NASA Astrophysics Data System (ADS)

Nadkarni, Neel; Arrieta, Andres F.; Chong, Christopher; Kochmann, Dennis M.; Daraio, Chiara

2016-06-01

We present a model system for strongly nonlinear transition waves generated in a periodic lattice of bistable members connected by magnetic links. The asymmetry of the on-site energy wells created by the bistable members produces a mechanical diode that supports only unidirectional transition wave propagation with constant wave velocity. We theoretically justify the cause of the unidirectionality of the transition wave and confirm these predictions by experiments and simulations. We further identify how the wave velocity and profile are uniquely linked to the double-well energy landscape, which serves as a blueprint for transition wave control.

Strong plasma turbulence in the earth's electron foreshock

NASA Technical Reports Server (NTRS)

Robinson, P. A.; Newman, D. L.

1991-01-01

A quantitative model is developed to account for the distribution in magnitude and location of the intense plasma waves observed in the earth's electron foreshock given the observed rms levels of waves. In this model, nonlinear strong-turbulence effects cause solitonlike coherent wave packets to form and decouple from incoherent background beam-excited weak turbulence, after which they convect downstream with the solar wind while collapsing to scales as short as 100 m and fields as high as 2 V/m. The existence of waves with energy densities above the strong-turbulence wave-collapse threshold is inferred from observations from IMP 6 and ISEE 1 and quantitative agreement is found between the predicted distribution of fields in an ensemble of such wave packets and the actual field distribution observed in situ by IMP 6. Predictions for the polarization of plasma waves and the bandwidth of ion-sound waves are also consistent with the observations. It is shown that strong-turbulence effects must be incorporated in any comprehensive theory of the propagation and evolution of electron beams in the foreshock. Previous arguments against the existence of strong turbulence in the foreshock are refuted.

Seismically damaged regolith as self-organized fragile geological feature

NASA Astrophysics Data System (ADS)

Sleep, Norman H.

2011-12-01

The S-wave velocity in the shallow subsurface within seismically active regions self-organizes so that typical strong dynamic shear stresses marginally exceed the Coulomb elastic limit. The dynamic velocity from major strike-slip faults yields simple dimensional relations. The near-field velocity pulse is essentially a Love wave. The dynamic shear strain is the ratio of the measured particle velocity over the deep S-wave velocity. The shallow dynamic shear stress is this quantity times the local shear modulus. The dynamic shear traction on fault parallel vertical planes is finite at the free surface. Coulomb failure occurs on favorably oriented fractures and internally in intact rock. I obtain the equilibrium shear modulus by starting a sequence of earthquakes with intact stiff rock extending all the way to the surface. The imposed dynamic shear strain in stiff rock causes Coulomb failure at shallow depths and leaves cracks in it wake. Cracked rock is more compliant than the original intact rock. Cracked rock is also weaker in friction, but shear modulus changes have a larger effect. Each subsequent event causes additional shallow cracking until the rock becomes compliant enough that it just reaches Coulomb failure over a shallow depth range of tens to hundreds of meters. Further events maintain the material at the shear modulus as a function where it just fails. The formalism provided in the paper yields reasonable representation of the S-wave velocity in exhumed sediments near Cajon Pass and the San Fernando Valley of California. A general conclusion is that shallow rocks in seismically active areas just become nonlinear during typical shaking. This process causes transient changes in S-wave velocity, but not strong nonlinear attenuation of seismic waves. Wave amplitudes significantly larger than typical ones would strongly attenuate and strongly damage the rock.

O Wave Interactions: Explosive Resonant Triads and Critical Layers.

NASA Astrophysics Data System (ADS)

Mahoney, Daniel J.

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

Linear and nonlinear Biot waves in a noncohesive granular medium slab: transfer function, self-action, second harmonic generation.

PubMed

Legland, J-B; Tournat, V; Dazel, O; Novak, A; Gusev, V

2012-06-01

Experimental results are reported on second harmonic generation and self-action in a noncohesive granular medium supporting wave energy propagation both in the solid frame and in the saturating fluid. The acoustic transfer function of the probed granular slab can be separated into two main frequency regions: a low frequency region where the wave propagation is controlled by the solid skeleton elastic properties, and a higher frequency region where the behavior is dominantly due to the air saturating the beads. Experimental results agree well with a recently developed nonlinear Biot wave model applied to granular media. The linear transfer function, second harmonic generation, and self-action effect are studied as a function of bead diameter, compaction step, excitation amplitude, and frequency. This parametric study allows one to isolate different propagation regimes involving a range of described and interpreted linear and nonlinear processes that are encountered in granular media experiments. In particular, a theoretical interpretation is proposed for the observed strong self-action effect.

Slow light enhanced optical nonlinearity in a silicon photonic crystal coupled-resonator optical waveguide.

PubMed

Matsuda, Nobuyuki; Kato, Takumi; Harada, Ken-Ichi; Takesue, Hiroki; Kuramochi, Eiichi; Taniyama, Hideaki; Notomi, Masaya

2011-10-10

We demonstrate highly enhanced optical nonlinearity in a coupled-resonator optical waveguide (CROW) in a four-wave mixing experiment. Using a CROW consisting of 200 coupled resonators based on width-modulated photonic crystal nanocavities in a line defect, we obtained an effective nonlinear constant exceeding 10,000 /W/m, thanks to slow light propagation combined with a strong spatial confinement of light achieved by the wavelength-sized cavities.

Jet crackle: skewness transport budget and a mechanistic source model

NASA Astrophysics Data System (ADS)

Buchta, David; Freund, Jonathan

2016-11-01

The sound from high-speed (supersonic) jets, such as on military aircraft, is distinctly different than that from lower-speed jets, such as on commercial airliners. Atop the already loud noise, a higher speed adds an intense, fricative, and intermittent character. The observed pressure wave patterns have strong peaks which are followed by relatively long shallows; notably, their pressure skewness is Sk >= 0 . 4 . Direct numerical simulation of free-shear-flow turbulence show that these skewed pressure waves occur immediately adjacent to the turbulence source for M >= 2 . 5 . Additionally, the near-field waves are seen to intersect and nonlinearly merge with other waves. Statistical analysis of terms in a pressure skewness transport equation show that starting just beyond δ99 the nonlinear wave mechanics that add to Sk are balanced by damping molecular effects, consistent with this aspect of the sound arising in the source region. A gas dynamics description is developed that neglects rotational turbulence dynamics and yet reproduces the key crackle features. At its core, this mechanism shows simply that nonlinear compressive effects lead directly to stronger compressions than expansions and thus Sk > 0 .

Observation of soliton compression in silicon photonic crystals

PubMed Central

Blanco-Redondo, A.; Husko, C.; Eades, D.; Zhang, Y.; Li, J.; Krauss, T.F.; Eggleton, B.J.

2014-01-01

Solitons are nonlinear waves present in diverse physical systems including plasmas, water surfaces and optics. In silicon, the presence of two photon absorption and accompanying free carriers strongly perturb the canonical dynamics of optical solitons. Here we report the first experimental demonstration of soliton-effect pulse compression of picosecond pulses in silicon, despite two photon absorption and free carriers. Here we achieve compression of 3.7 ps pulses to 1.6 ps with <10 pJ energy. We demonstrate a ~1-ps free-carrier-induced pulse acceleration and show that picosecond input pulses are critical to these observations. These experiments are enabled by a dispersion-engineered slow-light photonic crystal waveguide and an ultra-sensitive frequency-resolved electrical gating technique to detect the ultralow energies in the nanostructured device. Strong agreement with a nonlinear Schrödinger model confirms the measurements. These results further our understanding of nonlinear waves in silicon and open the way to soliton-based functionalities in complementary metal-oxide-semiconductor-compatible platforms. PMID:24423977

Generation and Propagation of Nonlinear Internal Waves in Sheared Currents Over the Washington Continental Shelf

NASA Astrophysics Data System (ADS)

Hamann, Madeleine M.; Alford, Matthew H.; Mickett, John B.

2018-04-01

The generation, propagation, and dissipation of nonlinear internal waves (NLIW) in sheared background currents is examined using 7 days of shipboard microstructure surveys and two moorings on the continental shelf offshore of Washington state. Surveys near the hypothesized generation region show semi-diurnal (D2) energy flux is onshore and that the ratio of energy flux to group speed times energy (F/cgE) increases sharply at the shelf break, suggesting that the incident D2 internal tide is partially reflected and partially transmitted. NLIW appear at an inshore mooring at the leading edge of the onshore phase of the baroclinic tide, consistent with nonlinear transformation of the shoaling internal tide as their generation mechanism. Of the D2 energy flux observed at the eastern extent of the generation region (133 ± 18 Wm-1), approximately 30% goes into the NLIW observed inshore (36 ± 11 Wm-1). Inshore of the moorings, 7 waves are tracked into shallow (30-40 m) water, where a vertically sheared, southward current becomes strong. As train-like waves propagate onshore, wave amplitudes of 25-30 m and energies of 5 MJ decrease to 12 m and 10 kJ, respectively. The observed direction of propagation rotates from 30° N of E to ˜30° S of E in the strongly sheared region. Linear ray tracing using the Taylor-Goldstein equation to incorporate parallel shear effects accounts for only a small portion of the observed rotation, suggesting that three-dimensionality of the wave crests and the background currents is important here.

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.

Self-consistent theory for the linear and nonlinear propagation of a sinusoidal electron plasma wave. Application to stimulated Raman scattering in a non-uniform and non-stationary plasma

NASA Astrophysics Data System (ADS)

Bénisti, Didier

2018-01-01

In this paper, we address the theoretical resolution of the Vlasov-Gauss system from the linear regime to the strongly nonlinear one, when significant trapping has occurred. The electric field is that of a sinusoidal electron plasma wave (EPW) which is assumed to grow from the noise level, and to keep growing at least up to the amplitude when linear theory in no longer valid (while the wave evolution in the nonlinear regime may be arbitrary). The ions are considered as a neutralizing fluid, while the electron response to the wave is derived by matching two different techniques. We make use of a perturbation analysis similar to that introduced to prove the Kolmogorov-Arnold-Moser theorem, up to amplitudes large enough for neo-adiabatic results to be valid. Our theory is applied to the growth and saturation of the beam-plasma instability, and to the three-dimensional propagation of a driven EPW in a non-uniform and non-stationary plasma. For the latter example, we lay a special emphasis on nonlinear collisionless dissipation. We provide an explicit theoretical expression for the nonlinear Landau-like damping rate which, in some instances, is amenable to a simple analytic formula. We also insist on the irreversible evolution of the electron distribution function, which is nonlocal in the wave amplitude and phase velocity. This makes trapping an effective means of dissipation for the electrostatic energy, and also makes the wave dispersion relation nonlocal. Our theory is generalized to allow for stimulated Raman scattering, which we address up to saturation by accounting for plasma inhomogeneity and non-stationarity, nonlinear kinetic effects, and interspeckle coupling.

Nonlinear MHD Waves in a Prominence Foot

NASA Astrophysics Data System (ADS)

Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.

2015-11-01

We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ˜ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5-11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5-14 G. For the typical prominence density the corresponding fast magnetosonic speed is ˜20 km s-1, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.

AKNS eigenvalue spectrum for densely spaced envelope solitary waves

NASA Astrophysics Data System (ADS)

Slunyaev, Alexey; Starobor, Alexey

2010-05-01

The problem of the influence of one envelope soliton to the discrete eigenvalues of the associated scattering problem for the other envelope soliton, which is situated close to the first one, is discussed. Envelope solitons are exact solutions of the integrable nonlinear Schrödinger equation (NLS). Their generalizations (taking into account the background nonlinear waves [1-4] or strongly nonlinear effects [5, 6]) are possible candidates to rogue waves in the ocean. The envelope solitary waves could be in principle detected in the stochastic wave field by approaches based on the Inverse Scattering Technique in terms of ‘unstable modes' (see [1-3]), or envelope solitons [7-8]. However, densely spaced intense groups influence the spectrum of the associated scattering problem, so that the solitary trains cannot be considered alone. Here we solve the initial-value problem exactly for some simplified configurations of the wave field, representing two closely placed intense wave groups, within the frameworks of the NLS equation by virtue of the solution of the AKNS system [9]. We show that the analogues of the level splitting and the tunneling effects, known in quantum physics, exist in the context of the NLS equation, and thus may be observed in application to sea waves [10]. These effects make the detecting of single solitary wave groups surrounded by other nonlinear wave groups difficult. [1]. A.L. Islas, C.M. Schober (2005) Predicting rogue waves in random oceanic sea states. Phys. Fluids 17, 031701-1-4. [2]. A.R. Osborne, M. Onorato, M. Serio (2005) Nonlinear Fourier analysis of deep-water random surface waves: Theoretical formulation and and experimental observations of rogue waves. 14th Aha Huliko's Winter Workshop, Honolulu, Hawaii. [3]. C.M. Schober, A. Calini (2008) Rogue waves in higher order nonlinear Schrödinger models. In: Extreme Waves (Eds.: E. Pelinovsky & C. Kharif), Springer. [4]. N. Akhmediev, A. Ankiewicz, M. Taki (2009) Waves that appear from nowhere and disappear without a trace. Phys. Lett. A 373, 675-678. [5]. A.I. Dyachenko, V.E. Zakharov (2008) On the formation of freak waves on the surface of deep water. JETP Lett. 88 (5), 307-311. [6]. A.V. Slunyaev (2009) Numerical simulation of "limiting" envelope solitons of gravity waves on deep water. JETP 109, 676-686. [7]. A. Slunyaev, E. Pelinovsky, and C. Guedes Soares (2005) Modeling freak waves from the North Sea. Appl. Ocean Res. 27, 12-22. [8]. A. Slunyaev (2006) Nonlinear analysis and simulations of measured freak wave time series. Eur. J. Mech. B / Fluids 25, 621-635. [9]. M.J. Ablowitz, D.J. Kaup, A.C. Newell, H. Segur (1974) The inverse scattering transform - Fourier analysis for nonlinear problems. Stud. Appl. Math. 53, 249-315. [10]. A.V. Starobor (2009) Interpretation of the inverse scattering data for the analysis of wave groups on water surface. Bachelor degree thesis. N. Novgorod State University, in Russian.

Nonlinear acoustics in biomedical ultrasound

NASA Astrophysics Data System (ADS)

Cleveland, Robin O.

2015-10-01

Ultrasound is widely used to image inside the body; it is also used therapeutically to treat certain medical conditions. In both imaging and therapy applications the amplitudes employed in biomedical ultrasound are often high enough that nonlinear acoustic effects are present in the propagation: the effects have the potential to be advantageous in some scenarios but a hindrance in others. In the case of ultrasound imaging the nonlinearity produces higher harmonics that result in images of greater quality. However, nonlinear effects interfere with the imaging of ultrasound contrast agents (typically micron sized bubbles with a strong nonlinear response of their own) and nonlinear effects also result in complications when derating of pressure measurements in water to in situ values in tissue. High intensity focused ultrasound (HIFU) is emerging as a non-invasive therapeutic modality which can result in thermal ablation of tissue. For thermal ablation, the extra effective attenuation resulting from nonlinear effects can result in enhanced heating of tissue if shock formation occurs in the target region for ablation - a highly desirable effect. However, if nonlinearity is too strong it can also result in undesired near-field heating and reduced ablation in the target region. The disruption of tissue (histotripsy) and fragmentation of kidney stones (lithotripsy) exploits shock waves to produce mechanically based effects, with minimal heating present. In these scenarios it is necessary for the waves to be of sufficient amplitude that a shock exists when the waveform reaches the target region. This talk will discuss how underlying nonlinear phenomenon act in all the diagnostic and therapeutic applications described above.

Induced dynamic nonlinear ground response at Gamer Valley, California

USGS Publications Warehouse

Lawrence, Z.; Bodin, P.; Langston, C.A.; Pearce, F.; Gomberg, J.; Johnson, P.A.; Menq, F.-Y.; Brackman, T.

2008-01-01

We present results from a prototype experiment in which we actively induce, observe, and quantify in situ nonlinear sediment response in the near surface. This experiment was part of a suite of experiments conducted during August 2004 in Garner Valley, California, using a large mobile shaker truck from the Network for Earthquake Engineering Simulation (NEES) facility. We deployed a dense accelerometer array within meters of the mobile shaker truck to replicate a controlled, laboratory-style soil dynamics experiment in order to observe wave-amplitude-dependent sediment properties. Ground motion exceeding 1g acceleration was produced near the shaker truck. The wave field was dominated by Rayleigh surface waves and ground motions were strong enough to produce observable nonlinear changes in wave velocity. We found that as the force load of the shaker increased, the Rayleigh-wave phase velocity decreased by as much as ???30% at the highest frequencies used (up to 30 Hz). Phase velocity dispersion curves were inverted for S-wave velocity as a function of depth using a simple isotropic elastic model to estimate the depth dependence of changes to the velocity structure. The greatest change in velocity occurred nearest the surface, within the upper 4 m. These estimated S-wave velocity values were used with estimates of surface strain to compare with laboratory-based shear modulus reduction measurements from the same site. Our results suggest that it may be possible to characterize nonlinear soil properties in situ using a noninvasive field technique.

Self-action of Bessel wave packets in a system of coupled light guides and formation of light bullets

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

Balakin, A. A., E-mail: balakin.alexey@yandex.ru; Mironov, V. A.; Skobelev, S. A., E-mail: sk.sa1981@gmail.com

The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the “kaleidoscopic” picture of a wavemore » packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.« less

Approximate non-linear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-03-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-waves scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform (GRT). After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic non-linear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P-wave and S-wave information.

Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

DOE PAGES

Chong, C.; Kevrekidis, P. G.; Ablowitz, M. J.; ...

2016-01-25

We explore linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. Formore » weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. Lastly, the transition between these two types of propagation is explored.« less

Nonlinear generation of kinetic-scale waves by magnetohydrodynamic Alfvén waves and nonlocal spectral transport in the solar wind

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

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

We study the nonlocal nonlinear coupling and generation of kinetic Alfvén waves (KAWs) and kinetic slow waves (KSWs) by magnetohydrodynamic Alfvén waves (MHD AWs) in conditions typical for the solar wind in the inner heliosphere. This cross-scale process provides an alternative to the turbulent energy cascade passing through many intermediate scales. The nonlinearities we study are proportional to the scalar products of wave vectors and hence are called 'scalar' ones. Despite the strong Landau damping of kinetic waves, we found fast growing KAWs and KSWs at perpendicular wavelengths close to the ion gyroradius. Using the parametric decay formalism, we investigatemore » two independent decay channels for the pump AW: forward decay (involving co-propagating product waves) and backward decay (involving counter-propagating product waves). The growth rate of the forward decay is typically 0.05 but can exceed 0.1 of the pump wave frequency. The resulting spectral transport is nonlocal and anisotropic, sharply increasing perpendicular wavenumbers but not parallel ones. AWs and KAWs propagating against the pump AW grow with about the same rate and contribute to the sunward wave flux in the solar wind. Our results suggest that the nonlocal decay of MHD AWs into KAWs and KSWs is a robust mechanism for the cross-scale spectral transport of the wave energy from MHD to dissipative kinetic scales in the solar wind and similar media.« less

Generation of Squeezed Light Using Photorefractive Degenerate Two-Wave Mixing

NASA Technical Reports Server (NTRS)

Lu, Yajun; Wu, Meijuan; Wu, Ling-An; Tang, Zheng; Li, Shiqun

1996-01-01

We present a quantum nonlinear model of two-wave mixing in a lossless photorefractive medium. A set of equations describing the quantum nonlinear coupling for the field operators is obtained. It is found that, to the second power term, the commutation relationship is maintained. The expectation values for the photon number concur with those of the classical electromagnetic theory when the initial intensities of the two beams are strong. We also calculate the quantum fluctuations of the two beams initially in the coherent state. With an appropriate choice of phase, quadrature squeezing or number state squeezing can be produced.

Nonlinear Wave Chaos and the Random Coupling Model

NASA Astrophysics Data System (ADS)

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

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

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

NASA Technical Reports Server (NTRS)

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

2000-01-01

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

The dynamics of magnetic Rossby waves in spherical dynamo simulations: A signature of strong-field dynamos?

NASA Astrophysics Data System (ADS)

Hori, K.; Teed, R. J.; Jones, C. A.

2018-03-01

We investigate slow magnetic Rossby waves in convection-driven dynamos in rotating spherical shells. Quasi-geostrophic waves riding on a mean zonal flow may account for some of the geomagnetic westward drifts and have the potential to allow the toroidal field strength within the planetary fluid core to be estimated. We extend the work of Hori et al. (2015) to include a wider range of models, and perform a detailed analysis of the results. We find that a predicted dispersion relation matches well with the longitudinal drifts observed in our strong-field dynamos. We discuss the validity of our linear theory, since we also find that the nonlinear Lorentz terms influence the observed waveforms. These wave motions are excited by convective instability, which determines the preferred azimuthal wavenumbers. Studies of linear rotating magnetoconvection have suggested that slow magnetic Rossby modes emerge in the magnetostrophic regime, in which the Lorentz and Coriolis forces are in balance in the vorticity equation. We confirm this to be predominant balance for the slow waves we have detected in nonlinear dynamo systems. We also show that a completely different wave regime emerges if the magnetic field is not present. Finally we report the corresponding radial magnetic field variations observed at the surface of the shell in our simulations and discuss the detectability of these waves in the geomagnetic secular variation.

Nonlinear Bloch waves in metallic photonic band-gap filaments

NASA Astrophysics Data System (ADS)

Kaso, Artan; John, Sajeev

2007-11-01

We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10 50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell’s equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament.

Approximate nonlinear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-07-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-wave scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform. After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic nonlinear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P- and S-wave information.

Nonlinear Propagation of Planet-Generated Tidal Waves

NASA Technical Reports Server (NTRS)

Rafikov, R. R.

2002-01-01

The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to shock formation and wake dissipation, is followed in the weakly nonlinear regime. The 2001 local approach of Goodman and Rafikov is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process spanning a significant fraction of the disk. Torques induced by the planet could be significant drivers of disk evolution on timescales of approx. 10(exp 6)-10(exp 7) yr, even in the absence of strong background viscosity. A global prescription for angular momentum deposition is developed that could be incorporated into the study of gap formation in a gaseous disk around the planet.

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.

Kinetic treatment of nonlinear magnetized plasma motions - General geometry and parallel waves

NASA Technical Reports Server (NTRS)

Khabibrakhmanov, I. KH.; Galinskii, V. L.; Verheest, F.

1992-01-01

The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is 3D, this very general result is used only to focus on the parallel propagation of nonlinear Alfven waves. The derivative nonlinear Schroedinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfven speed, and that parallel heat fluxes cannot be neglected, not even in the case of low parallel plasma beta. A truly stationary soliton solution is derived.

Nonlinear Wave Process Hierarchies and the Cyclic Development of Quasi-Ordered Structures in Turbulent Shear Flows.

DTIC Science & Technology

1979-11-01

can be evaluated semi- analitically in both the strongly nonlinear inner (critical layer) region and the weakly nonlinear outer region, reproduce the...experimental evidence of Ref. 8 (Figure 3, stage 3). Whereas the exact s~lutions of the Schridinger equation (Ref. 13) predict that an arbitrary smooth...peaks and valleys, different from the comon rate predicted by linear theory) arise suddenly and at surpris- ingly low disturbance levels [(u’/U 10-2] as

Bistability in mushroom-type metamaterials

NASA Astrophysics Data System (ADS)

Fernandes, David E.; Silveirinha, Mário G.

2017-07-01

Here, we study the electromagnetic response of asymmetric mushroom-type metamaterials loaded with nonlinear elements. It is shown that near a Fano resonance, these structures may have a strong tunable, bistable, and switchable response and enable giant nonlinear effects. By using an effective medium theory and full wave simulations, it is proven that the nonlinear elements may allow the reflection and transmission coefficients to follow hysteresis loops, and to switch the metamaterial between "go" and "no-go" states similar to an ideal electromagnetic switch.

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.

Rogue waves for a system of coupled derivative nonlinear Schrödinger equations.

PubMed

Chan, H N; Malomed, B A; Chow, K W; Ding, E

2016-01-01

Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schrödinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics, plasmas, etc., exhibits RWs only in the regime of modulation instability (MI) of the background. For a system of multiple waveguides, the governing coupled NLSEs can produce regimes of MI and RWs, even if each component has dispersion and cubic nonlinearity of opposite signs. A similar effect is demonstrated here for a system of coupled derivative NLSEs (DNLSEs) where the special feature is the nonlinear self-steepening of narrow pulses. More precisely, these additional regimes of MI and RWs for coupled DNLSEs depend on the mismatch in group velocities between the components, and the parameters for cubic nonlinearity and self-steepening. RWs considered in this paper differ from those of the NLSEs in terms of the amplification ratio and criteria of existence. Applications to optics and plasma physics are discussed.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Filamentation of plasma in the auroral region by an ion-ion instability: A process for the formation of bidimensional potential structures

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

Mottez, F.; Chanteur, G.; Roux, A.

1992-07-01

A two-dimensional, explicit, electrostatic particle code is used to investigate the nonlinear behavior of electrostatic ion waves generated by an ion beam flowing through a thermal ion and electron background in a strongly magnetized plasma ({omega}{sub ce} {much gt} {omega}{sub pe} where {omega}{sub ce} and {omega}{sub pe} are the electron gyrofrequency and the plasma frequency). To follow the nonlinear evolution of these ions waves, a long-lasting simulation is run with a large simulation grid: 128 {times} 512{lambda}{sub d}. Beam ions are shown to generate oblique waves. The nonlinear beatings between these oblique waves produce purely transverse waves, which leads tomore » a strong modulation of the density and of the electric potential in a direction transverse to the magnetic field. The transverse scale of these essentially field-aligned filaments is L{sub {perpendicular}} = 10 {rho}{sub i} where {rho}{sub i} is the ion Larmor radius of beam ions. Within these filaments, relatively stable field-aligned density and potential structures develop. The typical size, along the magnetic field, of these structures is L{sub {parallel}} = 10 {lambda}{sub d}, the density is modulated by 30%, and the electric potential is as large as T{sub e} within these structures. Unlike the potential structures that develop in a two-component plasma with downgoing electrons, these structures move upward. These characteristics are in good agreement with the weak double layers recently detected by Viking.« less

Magnetospheric Multiscale Observations of Large-Amplitude Parallel, Electrostatic Waves Associated with Magnetic Reconnection at the Magnetopause

NASA Technical Reports Server (NTRS)

Ergun, R. E.; Holmes, J. C.; Goodrich, K. A.; Wilder, F. D.; Stawarz, J. E.; Eriksson, S.; Newman, D. L.; Schwartz, S. J.; Goldman, M. V.; Sturner, A. P.;

Data dependence for the amplitude equation of surface waves

NASA Astrophysics Data System (ADS)

Secchi, Paolo

2016-04-01

We consider the amplitude equation for nonlinear surface wave solutions of hyperbolic conservation laws. This is an asymptotic nonlocal, Hamiltonian evolution equation with quadratic nonlinearity. For example, this equation describes the propagation of nonlinear Rayleigh waves (Hamilton et al. in J Acoust Soc Am 97:891-897, 1995), surface waves on current-vortex sheets in incompressible MHD (Alì and Hunter in Q Appl Math 61(3):451-474, 2003; Alì et al. in Stud Appl Math 108(3):305-321, 2002) and on the incompressible plasma-vacuum interface (Secchi in Q Appl Math 73(4):711-737, 2015). The local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables was shown in Hunter (J Hyperbolic Differ Equ 3(2):247-267, 2006), Secchi (Q Appl Math 73(4):711-737, 2015). In the present paper we prove the continuous dependence in strong norm of solutions on the initial data. This completes the proof of the well-posedness of the problem in the classical sense of Hadamard.

Existence and numerical simulation of periodic traveling wave solutions to the Casimir equation for the Ito system

NASA Astrophysics Data System (ADS)

Abbasbandy, S.; Van Gorder, R. A.; Hajiketabi, M.; Mesrizadeh, M.

2015-10-01

We consider traveling wave solutions to the Casimir equation for the Ito system (a two-field extension of the KdV equation). These traveling waves are governed by a nonlinear initial value problem with an interesting nonlinearity (which actually amplifies in magnitude as the size of the solution becomes small). The nonlinear problem is parameterized by two initial constant values, and we demonstrate that the existence of solutions is strongly tied to these parameter values. For our interests, we are concerned with positive, bounded, periodic wave solutions. We are able to classify parameter regimes which admit such solutions in full generality, thereby obtaining a nice existence result. Using the existence result, we are then able to numerically simulate the positive, bounded, periodic solutions. We elect to employ a group preserving scheme in order to numerically study these solutions, and an outline of this approach is provided. The numerical simulations serve to illustrate the properties of these solutions predicted analytically through the existence result. Physically, these results demonstrate the existence of a type of space-periodic structure in the Casimir equation for the Ito model, which propagates as a traveling wave.

Transverse effects in nonlinear optics: Toward the photon superfluid

NASA Astrophysics Data System (ADS)

McCormick, Colin Fraser

Nonlinear optics displays a wealth of transverse effects. These effects are particularly rich in the presence of an optical cavity. Many considerations suggest that in a Kerr nonlinear cavity a new state of light known as a "photon superfluid" can form, with strong analogies to atomic superfluids. The conditions for the formation of the photon superfluid include requirements on the cavity, input light fields and the nonlinear medium as well as various timescales. The most favorable candidate nonlinear medium for observing the photon super-fluid is an atomic vapor. With a strong and fast Kerr effect, atomic vapors also have the advantage of a Kerr coefficient that is tunable in both magnitude and sign. A series of z-scan experiments in far-detuned atomic rubidium vapor is reported, measuring the Kerr coefficient and determining its functional dependence on detuning to be that of a Doppler-broadened two-level model with adiabatic following of the electric field by the atom pseudomoment. Saturation effects are found to be important. Z-scan measurements for detunings within the Doppler profile are shown to agree well with numerical simulations based on the Doppler-broadened model. Agreement between absorptive and refractive non-linear coefficients is evidence of the Kramers-Kronig relations at work, even in this nonlinear system. The formation of the photon superfluid is discussed and the calculation of a new process, nearly collinear four-wave mixing, is presented. This process is essentially an inverse beam filamentation that is likely to be the underlying physical mechanism for transverse cooling and condensation of photons in a nonlinear optical cavity. Nearly collinear four-wave mixing may also be related to phenomena in general nonlinear physics, including modulation instability and Fermi-Pasta-Ulam recurrence.

Nonlinear stability of Halley comethosheath with transverse plasma motion

NASA Technical Reports Server (NTRS)

Srivastava, Krishna M.; Tsurutani, Bruce T.

1994-01-01

Weakly nonlinear Magneto Hydrodynamic (MHD) stability of the Halley cometosheath determined by the balance between the outward ion-neutral drag force and the inward Lorentz force is investigated including the transverse plasma motion as observed in the flanks with the help of the method of multiple scales. The eigenvalues and the eigenfunctions are obtained for the linear problem and the time evolution of the amplitude is obtained using the solvability condition for the solution of the second order problem. The diamagnetic cavity boundary and the adjacent layer of about 100 km thickness is found unstable for the travelling waves of certain wave numbers. Halley ionopause has been observed to have strong ripples with a wavelength of several hundred kilometers. It is found that nonlinear effects have stabilizing effect.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Nonlinear ionospheric responses to large-amplitude infrasonic-acoustic waves generated by undersea earthquakes

NASA Astrophysics Data System (ADS)

Zettergren, M. D.; Snively, J. B.; Komjathy, A.; Verkhoglyadova, O. P.

2017-02-01

Numerical models of ionospheric coupling with the neutral atmosphere are used to investigate perturbations of plasma density, vertically integrated total electron content (TEC), neutral velocity, and neutral temperature associated with large-amplitude acoustic waves generated by the initial ocean surface displacements from strong undersea earthquakes. A simplified source model for the 2011 Tohoku earthquake is constructed from estimates of initial ocean surface responses to approximate the vertical motions over realistic spatial and temporal scales. Resulting TEC perturbations from modeling case studies appear consistent with observational data, reproducing pronounced TEC depletions which are shown to be a consequence of the impacts of nonlinear, dissipating acoustic waves. Thermospheric acoustic compressional velocities are ˜±250-300 m/s, superposed with downward flows of similar amplitudes, and temperature perturbations are ˜300 K, while the dominant wave periodicity in the thermosphere is ˜3-4 min. Results capture acoustic wave processes including reflection, onset of resonance, and nonlinear steepening and dissipation—ultimately leading to the formation of ionospheric TEC depletions "holes"—that are consistent with reported observations. Three additional simulations illustrate the dependence of atmospheric acoustic wave and subsequent ionospheric responses on the surface displacement amplitude, which is varied from the Tohoku case study by factors of 1/100, 1/10, and 2. Collectively, results suggest that TEC depletions may only accompany very-large amplitude thermospheric acoustic waves necessary to induce a nonlinear response, here with saturated compressional velocities ˜200-250 m/s generated by sea surface displacements exceeding ˜1 m occurring over a 3 min time period.

Emergent rogue wave structures and statistics in spontaneous modulation instability.

PubMed

Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M

2015-05-20

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude "rogue waves" emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised "breather" or "soliton on finite background (SFB)" structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions.

Propagation of large-amplitude waves on dielectric liquid sheets in a tangential electric field: exact solutions in three-dimensional geometry.

PubMed

Zubarev, Nikolay M; Zubareva, Olga V

2010-10-01

Nonlinear waves on sheets of dielectric liquid in the presence of an external tangential electric field are studied theoretically. It is shown that waves of arbitrary shape in three-dimensional geometry can propagate along (or against) the electric field direction without distortion, i.e., the equations of motion admit a wide class of exact traveling wave solutions. This unusual situation occurs for nonconducting ideal liquids with high dielectric constants in the case of a sufficiently strong field strength. Governing equations for evolution of plane symmetric waves on fluid sheets are derived using conformal variables. A dispersion relation for the evolution of small perturbations of the traveling wave solutions is obtained. It follows from this relation that, regardless of the wave shape, the amplitudes of small-scale perturbations do not increase with time and, hence, the traveling waves are stable. We also study the interaction of counterpropagating symmetric waves with small but finite amplitudes. The corresponding solution of the equations of motion describes the nonlinear superposition of the oppositely directed waves. The results obtained are applicable for the description of long waves on fluid sheets in a horizontal magnetic field.

Thermally stimulated nonlinear refraction in gelatin stabilized Cu-PVP nanocomposite thin films

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

Tamgadge, Y. S., E-mail: ystamgadge@gmail.com; Atkare, D. V.; Pahurkar, V. G.

2016-05-06

This article illustrates investigations on thermally stimulated third order nonlinear refraction of Cu-PVP nanocomposite thin films. Cu nanoparticles have been synthesized using chemical reduction method and thin films in PVP matrix have been obtained using spin coating technique. Thin films have been characterized by X-ray diffraction (XRD) and Ultraviolet-visible (UV-vis) spectroscopyfor structural and linear optical studies. Third order nonlinear refraction studies have been performed using closed aperture z-scan technique under continuous wave (CW) He-Ne laser. Cu-PVP nanocomposites are found to exhibit strong nonlinear refractive index stimulated by thermal lensing effect.

Spontaneous generation and reversals of mean flows in a convectively-generated internal gravity wave field

NASA Astrophysics Data System (ADS)

Couston, Louis-Alexandre; Lecoanet, Daniel; Favier, Benjamin; Le Bars, Michael

2017-11-01

We investigate via direct numerical simulations the spontaneous generation and reversals of mean zonal flows in a stably-stratified fluid layer lying above a turbulent convective fluid. Contrary to the leading idealized theories of mean flow generation by self-interacting internal waves, the emergence of a mean flow in a convectively-generated internal gravity wave field is not always possible because nonlinear interactions of waves of different frequencies can disrupt the mean flow generation mechanism. Strong mean flows thus emerge when the divergence of the Reynolds stress resulting from the nonlinear interactions of internal waves produces a strong enough anti-diffusive acceleration for the mean flow, which, as we will demonstrate, is the case when the Prandtl number is sufficiently low, or when the energy input into the internal wavefield by the convection and density stratification are sufficiently large. Implications for mean zonal flow production as observed in the equatorial stratospheres of the Earth, Saturn and Jupiter, and possibly occurring in other geophysical systems such as planetary and stellar interiors will be briefly discussed. Funding provided by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program through Grant Agreement No. 681835-FLUDYCO-ERC-2015-CoG.

Long-range intercellular Ca2+ wave patterns

NASA Astrophysics Data System (ADS)

Tabi, C. B.; Maïna, I.; Mohamadou, A.; Ekobena, H. P. F.; Kofané, T. C.

2015-10-01

Modulational instability is utilized to investigate intercellular Ca2+ wave propagation in an array of diffusively coupled cells. Cells are supposed to be connected via paracrine signaling, where long-range effects, due to the presence of extracellular messengers, are included. The multiple-scale expansion is used to show that the whole dynamics of Ca2+ waves, from the endoplasmic reticulum to the cytosol, can be reduced to a single differential-difference nonlinear equation whose solutions are assumed to be plane waves. Their linear stability analysis is studied, with emphasis on the impact of long-range coupling, via the range parameter s. It is shown that s, as well as the number of interacting cells, importantly modifies the features of modulational instability, as small values of s imply a strong coupling, and increasing its value rather reduces the problem to a first-neighbor one. Our theoretical findings are numerically tested, as the generic equations are fully integrated, leading to the emergence of nonlinear patterns of Ca2+ waves. Strong long-range coupling is pictured by extended trains of breather-like structures whose frequency decreases with increasing s. We also show numerically that the number of interacting cells plays on the spatio-temporal formation of Ca2+ patterns, whilst the quasi-perfect intercellular communication depends on the paracrine coupling parameter.

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.).

Second harmonic generation of q-Gaussian laser beam in preformed collisional plasma channel with nonlinear absorption

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

Gupta, Naveen, E-mail: naveens222@rediffmail.com; Singh, Arvinder, E-mail: arvinder6@lycos.com; Singh, Navpreet, E-mail: navpreet.nit@gmail.com

2015-11-15

This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on amore » numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.« less

Nonlinear optical conductivity and subharmonic instabilities of graphene in a strong electromagnetic field

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Basov, Dimitri; Fogler, Michael

We study theoretically the second-order nonlinear optical conductivity σ (2) of graphene as a function of frequency and momentum. We distinguish two regimes. At frequencies ω higher than the temperature-dependent electron-electron collision rate γee- 1 , the conductivity σ (2) can be derived from the semiclassical kinetic equation. The calculation requires taking into account the photon drag (Lorentz force) due to the ac magnetic field. In the low-frequency hydrodynamic regime ω <<γee- 1 , the nonlinear conductivity has a different form and the photon drag effect is suppressed. As a consequence of the nonlinearity, a strong enough photoexcitation can cause spontaneous generation of collective modes in a graphene strip: plasmons in the high-frequency regime and energy waves (demons) in the hydrodynamic one. The dominant instability occurs at frequency ω / 2 .

Nonlinear water waves: introduction and overview

NASA Astrophysics Data System (ADS)

Constantin, A.

2017-12-01

For more than two centuries progress in the study of water waves proved to be interdependent with innovative and deep developments in theoretical and experimental directions of investigation. In recent years, considerable progress has been achieved towards the understanding of waves of large amplitude. Within this setting one cannot rely on linear theory as nonlinearity becomes an essential feature. Various analytic methods have been developed and adapted to come to terms with the challenges encountered in settings where approximations (such as those provided by linear or weakly nonlinear theory) are ineffective. Without relying on simpler models, progress becomes contingent upon the discovery of structural properties, the exploitation of which requires a combination of creative ideas and state-of-the-art technical tools. The successful quest for structure often reveals unexpected patterns and confers aesthetic value on some of these studies. The topics covered in this issue are both multi-disciplinary and interdisciplinary: there is a strong interplay between mathematical analysis, numerical computation and experimental/field data, interacting with each other via mutual stimulation and feedback. This theme issue reflects some of the new important developments that were discussed during the programme `Nonlinear water waves' that took place at the Isaac Newton Institute for Mathematical Sciences (Cambridge, UK) from 31st July to 25th August 2017. A cross-section of the experts in the study of water waves who participated in the programme authored the collected papers. These papers illustrate the diversity, intensity and interconnectivity of the current research activity in this area. They offer new insight, present emerging theoretical methodologies and computational approaches, and describe sophisticated experimental results. This article is part of the theme issue 'Nonlinear water waves'.

Nonlinear water waves: introduction and overview.

PubMed

Constantin, A

2018-01-28

For more than two centuries progress in the study of water waves proved to be interdependent with innovative and deep developments in theoretical and experimental directions of investigation. In recent years, considerable progress has been achieved towards the understanding of waves of large amplitude. Within this setting one cannot rely on linear theory as nonlinearity becomes an essential feature. Various analytic methods have been developed and adapted to come to terms with the challenges encountered in settings where approximations (such as those provided by linear or weakly nonlinear theory) are ineffective. Without relying on simpler models, progress becomes contingent upon the discovery of structural properties, the exploitation of which requires a combination of creative ideas and state-of-the-art technical tools. The successful quest for structure often reveals unexpected patterns and confers aesthetic value on some of these studies. The topics covered in this issue are both multi-disciplinary and interdisciplinary: there is a strong interplay between mathematical analysis, numerical computation and experimental/field data, interacting with each other via mutual stimulation and feedback. This theme issue reflects some of the new important developments that were discussed during the programme 'Nonlinear water waves' that took place at the Isaac Newton Institute for Mathematical Sciences (Cambridge, UK) from 31st July to 25th August 2017. A cross-section of the experts in the study of water waves who participated in the programme authored the collected papers. These papers illustrate the diversity, intensity and interconnectivity of the current research activity in this area. They offer new insight, present emerging theoretical methodologies and computational approaches, and describe sophisticated experimental results.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).

Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime

NASA Astrophysics Data System (ADS)

Lehmann, G.; Spatschek, K. H.

2013-07-01

Parametric plasma processes received renewed interest in the context of generating ultra-intense and ultra-short laser pulses up to the exawatt-zetawatt regime. Both Raman as well as Brillouin amplifications of seed pulses were proposed. Here, we investigate Brillouin processes in the one-dimensional (1D) backscattering geometry with the help of numerical simulations. For optimal seed amplification, Brillouin scattering is considered in the so called strong coupling (sc) regime. Special emphasis lies on the dependence of the amplification process on the finite duration of the initial seed pulses. First, the standard plane-wave instability predictions are generalized to pulse models, and the changes of initial seed pulse forms due to parametric instabilities are investigated. Three-wave-interaction results are compared to predictions by a new (kinetic) Vlasov code. The calculations are then extended to the nonlinear region with pump depletion. Generation of different seed layers is interpreted by self-similar solutions of the three-wave interaction model. Similar to Raman amplification, shadowing of the rear layers by the leading layers of the seed occurs. The shadowing is more pronounced for initially broad seed pulses. The effect is quantified for Brillouin amplification. Kinetic Vlasov simulations agree with the three-wave interaction predictions and thereby affirm the universal validity of self-similar layer formation during Brillouin seed amplification in the strong coupling regime.

Acoustic instability driven by cosmic-ray streaming

NASA Technical Reports Server (NTRS)

Begelman, Mitchell C.; Zweibel, Ellen G.

1994-01-01

We study the linear stability of compressional waves in a medium through which cosmic rays stream at the Alfven speed due to strong coupling with Alfven waves. Acoustic waves can be driven unstable by the cosmic-ray drift, provided that the streaming speed is sufficiently large compared to the thermal sound speed. Two effects can cause instability: (1) the heating of the thermal gas due to the damping of Alfven waves driven unstable by cosmic-ray streaming; and (2) phase shifts in the cosmic-ray pressure perturbation caused by the combination of cosmic-ray streaming and diffusion. The instability does not depend on the magnitude of the background cosmic-ray pressure gradient, and occurs whether or not cosmic-ray diffusion is important relative to streaming. When the cosmic-ray pressure is small compared to the gas pressure, or cosmic-ray diffusion is strong, the instability manifests itself as a weak overstability of slow magnetosonic waves. Larger cosmic-ray pressure gives rise to new hybrid modes, which can be strongly unstable in the limits of both weak and strong cosmic-ray diffusion and in the presence of thermal conduction. Parts of our analysis parallel earlier work by McKenzie & Webb (which were brought to our attention after this paper was accepted for publication), but our treatment of diffusive effects, thermal conduction, and nonlinearities represent significant extensions. Although the linear growth rate of instability is independent of the background cosmic-ray pressure gradient, the onset of nonlinear eff ects does depend on absolute value of DEL (vector differential operator) P(sub c). At the onset of nonlinearity the fractional amplitude of cosmic-ray pressure perturbations is delta P(sub C)/P(sub C) approximately (kL) (exp -1) much less than 1, where k is the wavenumber and L is the pressure scale height of the unperturbed cosmic rays. We speculate that the instability may lead to a mode of cosmic-ray transport in which plateaus of uniform cosmic-ray pressure are separated by either laminar or turbulent jumps in which the thermal gas is subject to intense heating.

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.)

The simulation of electromagnetically driven strong Langmuir turbulence effect on the backscatter radiation from ionosphere

NASA Astrophysics Data System (ADS)

Kochetov, Andrey

2016-07-01

Numerical simulations of the dynamics of electromagnetic fields in a smoothly inhomogeneous nonlinear plasma layer in frameworks of the nonlinear Schrödinger equation with boundary conditions responsible for the pumping of the field in the layer by an incident wave and the inverse radiation losses supplemented the volume field dissipation due to the electromagnetic excitation of Langmuir turbulence are carried out. The effects of the threshold of non-linearity and it's evolution, of the threshold and saturation levels of dissipation in the vicinity of the wave reflection point on the features of the dynamics of reflection and absorption indexes are investigated. We consider the hard drive damping depending on the local field amplitude and hysteresis losses with different in several times "on" and "off" absorption thresholds as well. The dependence of the thresholds of the steady-state, periodic and chaotic regimes of plasma-wave interaction on the scenario of turbulence evolution is demonstrated. The results are compared with the experimental observations of Langmuir stage ionospheric modification.

Josephson Metamaterial with a Widely Tunable Positive or Negative Kerr Constant

NASA Astrophysics Data System (ADS)

Zhang, Wenyuan; Huang, W.; Gershenson, M. E.; Bell, M. T.

2017-11-01

We report on the microwave characterization of a novel one-dimensional Josephson metamaterial composed of a chain of asymmetric superconducting quantum interference devices with nearest-neighbor coupling through common Josephson junctions. This metamaterial demonstrates a strong Kerr nonlinearity, with a Kerr constant tunable over a wide range, from positive to negative values, by a magnetic flux threading the superconducting quantum interference devices. The experimental results are in good agreement with the theory of nonlinear effects in Josephson chains. The metamaterial is very promising as an active medium for Josephson traveling-wave parametric amplifiers; its use facilitates phase matching in a four-wave-mixing process for efficient parametric gain.

Numerical Simulations of Multidimensional Flows in Presence of either Strong Shocks or Strong Gravitational Fields

NASA Astrophysics Data System (ADS)

Font, J. A.; Ibanez, J. M.; Marti, J. M.

1993-04-01

Some numerical solutions via local characteristic approach have been obtained describing multidimensional flows. These solutions have been used as tests of a two- dimensional code which extends some high-resolution shock-captunng methods, designed recently to solve nonlinear hyperbolic systems of conservation laws. K words: HYDRODYNAMICS - BLACK HOLE - RELATIVITY - SHOCK WAVES

Superdiffusive transport and energy localization in disordered granular crystals

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

Martinez, Alejandro J.; Kevrekidis, Panagiotis G.; Porter, Mason A.

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition.more » Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m ~2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder.« less

Superdiffusive transport and energy localization in disordered granular crystals

DOE PAGES

Martinez, Alejandro J.; Kevrekidis, Panagiotis G.; Porter, Mason A.

2016-02-12

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition.more » Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m ~2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder.« less

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

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

Experimental investigation of linear and nonlinear wave systems: A quantum chaos approach

NASA Astrophysics Data System (ADS)

Neicu, Toni

2002-09-01

An experimental and numerical study of linear and nonlinear wave systems using methods and ideas developed from quantum chaos is presented. We exploit the analogy of the wave equation for the flexural modes of a thin clover-shaped acoustic plate to the stationary solutions of the Schrodinger wave equation for a quantum clover-shaped billiard, a generic system that has regular and chaotic regions in its phase space. We observed periodic orbits in the spectral properties of the acoustic plate, the first such definitive acoustic experiment. We also solved numerically the linear wave equation of the acoustic plate for the first few hundred eigenmodes. The Fourier transform of the eigenvalues show peaks corresponding to the principal periodic orbits of the classical billiard. The signatures of the periodic orbits in the spectra were unambiguously verified by deforming one edge of the plate and observing that only the peaks corresponding to the orbits that hit this edge changed. The statistical measures of the eigenvalues are intermediate between universal forms for completely integrable and chaotic systems. The density distribution of the eigenfunctions agrees with the Porter-Thomas formula of chaotic systems. The viscosity dependence and effects of nonlinearity on the Faraday surface wave patterns in a stadium geometry were also investigated. The ray dynamics inside the stadium, a paradigm of quantum chaos, is completely chaotic. The majority of the observed patterns of the orbits resemble three eigenstates of the stadium: the bouncing ball, longitudinal, and bowtie patterns. We observed many disordered patterns that increase with the viscosity. The experimental results were analyzed using recent theoretical work that explains the suppression of certain modes. The theory also predicts that the perimeter dissipation is too strong for whispering gallery modes, which contradicts our observations of these modes for a fluid with low viscosity. Novel vortex patterns were observed in a strongly nonlinear, dissipative granular system of vertically vibrated rods. Above a critical packing fraction, moving domains of nearly vertical rods were seen to coexist with horizontal rods. The vertical domains coarsen to form several large vortices, which were driven by the anisotropy and inclination of the rods.

Development of a satellite SAR image spectra and altimeter wave height data assimilation system for ERS-1

NASA Technical Reports Server (NTRS)

Hasselmann, Klaus; Hasselmann, Susanne; Bauer, Eva; Bruening, Claus; Lehner, Susanne; Graber, Hans; Lionello, Piero

1988-01-01

The applicability of ERS-1 wind and wave data for wave models was studied using the WAM third generation wave model and SEASAT altimeter, scatterometer and SAR data. A series of global wave hindcasts is made for the surface stress and surface wind fields by assimilation of scatterometer data for the full 96-day SEASAT and also for two wind field analyses for shorter periods by assimilation with the higher resolution ECMWF T63 model and by subjective analysis methods. It is found that wave models respond very sensitively to inconsistencies in wind field analyses and therefore provide a valuable data validation tool. Comparisons between SEASAT SAR image spectra and theoretical SAR spectra derived from the hindcast wave spectra by Monte Carlo simulations yield good overall agreement for 32 cases representing a wide variety of wave conditions. It is concluded that SAR wave imaging is sufficiently well understood to apply SAR image spectra with confidence for wave studies if supported by realistic wave models and theoretical computations of the strongly nonlinear mapping of the wave spectrum into the SAR image spectrum. A closed nonlinear integral expression for this spectral mapping relation is derived which avoids the inherent statistical errors of Monte Carlo computations and may prove to be more efficient numerically.

Consequences of the Ion Cyclotron Instability in the Inner Magnetospheric Plasma

NASA Technical Reports Server (NTRS)

Khazanov, George V.

2011-01-01

The inner magnetospheric plasma is a very unique composition of different plasma particles and waves. Among these plasma particles and waves are Ring Current (RC) particles and Electromagnetic Ion Cyclotron (EMIC) waves. The RC is the source of free energy for the EMIC wave excitation provided by a temperature anisotropy of RC ions, which develops naturally during inward E x B convection from the plasma sheet. The cold plasmasphere, which is under the strong influence of the magnetospheric electric field, strongly mediates the RC-EMIC waves-coupling process, and ultimately becomes part of the particle and energy interplay, generated by the ion cyclotron instability of the inner magnetosphere. On the other hand, there is a strong influence of the RC on the inner magnetospheric electric and magnetic field configurations and these configurations, in turn, are important to RC dynamics. Therefore, one of the biggest needs for inner magnetospheric plasma physics research is the continued progression toward a coupled, interconnected system, with the inclusion of nonlinear feedback mechanisms between the plasma populations, the electric and magnetic fields, and plasma waves.

Non-linear solitary sound waves in lipid membranes and their possible role in biological signaling

NASA Astrophysics Data System (ADS)

Shrivastava, Shamit

Biological macromolecules self-assemble under entropic forces to form a dynamic 2D interfacial medium where the elastic properties arise from the curvature of the entropic potential of the interface. Elastic interfaces should be capable of propagating localized perturbations analogous to sound waves. However, (1) the existence and (2) the possible role of such waves in affecting biological functions remain unexplored. Both these aspects of "sound" as a signaling mechanism in biology are explored experimentally on mixed monolayers of lipids-fluorophores-proteins at the air/water interface as a model biological interface. This study shows - for the first time - that the nonlinear susceptibility near a thermodynamic transition in a lipid monolayer results in nonlinear solitary sound waves that are of 'all or none' nature. The state dependence of the nonlinear propagation is characterized by studying the velocity-amplitude relationship and results on distance dependence, effect of geometry and collision of solitary waves are presented. Given that the lipid bilayers and real biological membranes have such nonlinearities in their susceptibility diagrams, similar solitary phenomenon should be expected in biological membranes. In fact the observed characteristics of solitary sound waves such as, their all or none nature, a biphasic pulse shape with a long tail and optp-mechano-electro-thermal coupling etc. are strikingly similar to the phenomenon of nerve pulse propagation as observed in single nerve fibers. Finally given the strong correlation between the activity of membrane bound enzymes and the susceptibility and the fact that the later varies within a single solitary pulse, a new thermodynamic basis for biological signaling is proposed. The state of the interface controls both the nature of sound propagation and its impact on incorporated enzymes and proteins. The proof of concept is demonstrated for acetylcholine esterase embedded in a lipid monolayer, where the enzyme is spatiotemporally "knocked out" by a propagating sound wave.

A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation.

PubMed

Louisnard, O

2012-01-01

The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of each bubble, by thermal diffusion in the gas and viscous friction in the liquid. Both quantities and calculated numerically for a single inertial bubble driven at 20 kHz, and are found to be several orders of magnitude larger than the linear prediction. Viscous dissipation is found to be the predominant cause of energy loss for bubbles small enough. Then, the classical nonlinear Caflish equations describing the propagation of acoustic waves in a bubbly liquid are recast and simplified conveniently. The main harmonic part of the sound field is found to fulfill a nonlinear Helmholtz equation, where the imaginary part of the squared wave number is directly correlated with the energy lost by a single bubble. For low acoustic driving, linear theory is recovered, but for larger drivings, namely above the Blake threshold, the attenuation coefficient is found to be more than 3 orders of magnitude larger then the linear prediction. A huge attenuation of the wave is thus expected in regions where inertial bubbles are present, which is confirmed by numerical simulations of the nonlinear Helmholtz equation in a 1D standing wave configuration. The expected strong attenuation is not only observed but furthermore, the examination of the phase between the pressure field and its gradient clearly demonstrates that a traveling wave appears in the medium. Copyright © 2011 Elsevier B.V. All rights reserved.

Emergent rogue wave structures and statistics in spontaneous modulation instability

PubMed Central

Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M.

2015-01-01

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude “rogue waves” emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised “breather” or “soliton on finite background (SFB)” structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions. PMID:25993126

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.

SHEAR-DRIVEN DYNAMO WAVES IN THE FULLY NONLINEAR REGIME

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

Pongkitiwanichakul, P.; Nigro, G.; Cattaneo, F.

2016-07-01

Large-scale dynamo action is well understood when the magnetic Reynolds number ( Rm ) is small, but becomes problematic in the astrophysically relevant large Rm limit since the fluctuations may control the operation of the dynamo, obscuring the large-scale behavior. Recent works by Tobias and Cattaneo demonstrated numerically the existence of large-scale dynamo action in the form of dynamo waves driven by strongly helical turbulence and shear. Their calculations were carried out in the kinematic regime in which the back-reaction of the Lorentz force on the flow is neglected. Here, we have undertaken a systematic extension of their work tomore » the fully nonlinear regime. Helical turbulence and large-scale shear are produced self-consistently by prescribing body forces that, in the kinematic regime, drive flows that resemble the original velocity used by Tobias and Cattaneo. We have found four different solution types in the nonlinear regime for various ratios of the fluctuating velocity to the shear and Reynolds numbers. Some of the solutions are in the form of propagating waves. Some solutions show large-scale helical magnetic structure. Both waves and structures are permanent only when the kinetic helicity is non-zero on average.« less

Long-wave model for strongly anisotropic growth of a crystal step.

PubMed

Khenner, Mikhail

2013-08-01

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the "one-sided" model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed the nonlinear dynamics. Linear stability depends on whether the stiffness is minimum or maximum in the direction of the step growth. It also depends nontrivially on the combination of the anisotropy strength parameter and the atomic flux from the terrace to the step. Computations show formation and coarsening of a hill-and-valley structure superimposed onto a long-wavelength profile, which independently coarsens. Coarsening laws for the hill-and-valley structure are computed for two principal orientations of a maximum step stiffness, the increasing anisotropy strength, and the varying atomic flux.

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.

Optimization of the dynamic behavior of strongly nonlinear heterogeneous materials

NASA Astrophysics Data System (ADS)

Herbold, Eric B.

New aspects of strongly nonlinear wave and structural phenomena in granular media are developed numerically, theoretically and experimentally. One-dimensional chains of particles and compressed powder composites are the two main types of materials considered here. Typical granular assemblies consist of linearly elastic spheres or layers of masses and effective nonlinear springs in one-dimensional columns for dynamic testing. These materials are highly sensitive to initial and boundary conditions, making them useful for acoustic and shock-mitigating applications. One-dimensional assemblies of spherical particles are examples of strongly nonlinear systems with unique properties. For example, if initially uncompressed, these materials have a sound speed equal to zero (sonic vacuum), supporting strongly nonlinear compression solitary waves with a finite width. Different types of assembled metamaterials will be presented with a discussion of the material's response to static compression. The acoustic diode effect will be presented, which may be useful in shock mitigation applications. Systems with controlled dissipation will also be discussed from an experimental and theoretical standpoint emphasizing the critical viscosity that defines the transition from an oscillatory to monotonous shock profile. The dynamic compression of compressed powder composites may lead to self-organizing mesoscale structures in two and three dimensions. A reactive granular material composed of a compressed mixture of polytetrafluoroethylene (PTFE), tungsten (W) and aluminum (Al) fine-grain powders exhibit this behavior. Quasistatic, Hopkinson bar, and drop-weight experiments show that composite materials with a high porosity and fine metallic particles exhibit a higher strength than less porous mixtures with larger particles, given the same mass fraction of constituents. A two-dimensional Eulerian hydrocode is implemented to investigate the mechanical deformation and failure of the compressed powder samples in simulated drop-weight tests. The calculations indicate that the dynamic formation of mesoscale force chains increase the strength of the sample. This is also apparent in three-dimensional finite element calculations of drop-weight test simulations using LS-Dyna despite a higher granular bulk coordination number, and an increased mobility of individual grains.

Nonlinear processes generated by supercritical tidal flow in shallow straits

NASA Astrophysics Data System (ADS)

Bordois, Lucie; Auclair, Francis; Paci, Alexandre; Dossmann, Yvan; Nguyen, Cyril

2017-06-01

Numerical experiments have been carried out using a nonhydrostatic and non-Boussinesq regional oceanic circulation model to investigate the nonlinear processes generated by supercritical tidal flow in shallow straits. Our approach relies on idealized direct numerical simulations inspired by oceanic observations. By analyzing a large set of simulations, a regime diagram is proposed for the nonlinear processes generated in the lee of these straits. The results show that the topography shape of the strait plays a crucial role in the formation of internal solitary waves (ISWs) and in the occurrence of local breaking events. Both of these nonlinear processes are important turbulence producing phenomena. The topographic control, observed in mode 1 ISW formation in previous studies [Y. Dossmann, F. Auclair, and A. Paci, "Topographically induced internal solitary waves in a pycnocline: Primary generation and topographic control," Phys. Fluids 25, 066601 (2013) and Y. Dossmann et al., "Topographically induced internal solitary waves in a pycnocline: Ultrasonic probes and stereo-correlation measurements," Phys. Fluids 26, 056601 (2014)], is clearly reproducible for mode-2 ISW above shallow straits. Strong plunging breaking events are observed above "narrow" straits (straits with a width less than mode 1 wavelength) when the fluid velocity exceeds the local mode 1 wave speed. These results are a step towards future works on vertical mixing quantification and localization around complex strait areas.

Nonlinear standing wave excitation by series resonance-enhanced harmonics in low pressure capacitive discharges

NASA Astrophysics Data System (ADS)

Lieberman, M. A.; Lichtenberg, A. J.; Kawamura, Emi; Marakhtanov, A. M.

2015-09-01

It is well known that standing waves having radially center-high rf voltage profiles exist in high frequency capacitive discharges. It is also known that in radially uniform discharges, the capacitive sheath nonlinearities excite strong nonlinear series resonance harmonics that enhance the electron power deposition. In this work, we consider the coupling of the series resonance-enhanced harmonics to the standing waves. A one-dimensional, asymmetric radial transmission line model is developed incorporating the wave and nonlinear sheath physics and a self-consistent dc potential. The resulting coupled pde equation set is solved numerically to determine the discharge voltages and currents. A 10 mT argon base case is chosen with plasma density 2 ×1016 m-3, gap width 2 cm and conducting electrode radius 15 cm, driven by a high frequency 500 V source with source resistance 0.5 ohms. We find that nearby resonances lead to an enhanced ratio of 4.5 of the electron power per unit area on axis, compared to the average. The radial dependence of electron power with frequency shows significant variations, with the central enhancement and sharpness of the spatial resonances depending in a complicated way on the harmonic structure. Work supported by DOE Fusion Energy Science Contract DE-SC000193 and by a gift from the Lam Research Corporation.

3D DNS and LES of Breaking Inertia-Gravity Waves

NASA Astrophysics Data System (ADS)

Remmler, S.; Fruman, M. D.; Hickel, S.; Achatz, U.

2012-04-01

As inertia-gravity waves we refer to gravity waves that have a sufficiently low frequency and correspondingly large horizontal wavelength to be strongly influenced by the Coriolis force. Inertia-gravity waves are very active in the middle atmosphere and their breaking is potentially an important influence on the circulation in this region. The parametrization of this process requires a good theoretical understanding, which we want to enhance with the present study. Primary linear instabilities of an inertia-gravity wave and "2.5-dimensional" nonlinear simulations (where the spatial dependence is two dimensional but the velocity and vorticity fields are three-dimensional) with the wave perturbed by its leading primary instabilities by Achatz [1] have shown that the breaking differs significantly from that of high-frequency gravity waves due to the strongly sheared component of velocity perpendicular to the plane of wave-propagation. Fruman & Achatz [2] investigated the three-dimensionalization of the breaking by computing the secondary linear instabilities of the same waves using singular vector analysis. These secondary instabilities are variations perpendicular to the direction of the primary perturbation and the wave itself, and their wavelengths are an order of magnitude shorter than both. In continuation of this work, we carried out fully three-dimensional nonlinear simulations of inertia-gravity waves perturbed by their leading primary and secondary instabilities. The direct numerical simulation (DNS) was made tractable by restricting the domain size to the dominant scales selected by the linear analyses. The study includes both convectively stable and unstable waves. To the best of our knowledge, this is the first fully three-dimensional nonlinear direct numerical simulation of inertia-gravity waves at realistic Reynolds numbers with complete resolution of the smallest turbulence scales. Previous simulations either were restricted to high frequency gravity waves (e. g. Fritts et al. [3]), or the ratio N/f was artificially reduced (e. g. Lelong & Dunkerton [4]). The present simulations give us insight into the three-dimensional breaking process as well as the emerging turbulence. We assess the possibility of reducing the computational costs of three-dimensional simulations by using an implicit turbulence subgrid-scale parametrization based on the Adaptive Local Deconvolution Method (ALDM) for stratified turbulence [5]. In addition, we have performed ensembles of nonlinear 2.5-dimensional DNS, like those in Achatz [1] but with a small amount of noise superposed to the initial state, and compared the results with coarse-resolution simulations using either ALDM as well as with standard LES schemes. We found that the results of the models with parametrized turbulence, which are orders of magnitude more computationally economical than the DNS, compare favorably with the DNS in terms of the decay of the wave amplitude with time (the quantity most important for application to gravity-wave drag parametrization) suggesting that they may be trusted in future simulations of gravity wave breaking.

Analytical investigations of seismic responses for reinforced concrete bridge columns subjected to strong near-fault ground motion

NASA Astrophysics Data System (ADS)

Su, Chin-Kuo; Sung, Yu-Chi; Chang, Shuenn-Yih; Huang, Chao-Hsun

2007-09-01

Strong near-fault ground motion, usually caused by the fault-rupture and characterized by a pulse-like velocity-wave form, often causes dramatic instantaneous seismic energy (Jadhav and Jangid 2006). Some reinforced concrete (RC) bridge columns, even those built according to ductile design principles, were damaged in the 1999 Chi-Chi earthquake. Thus, it is very important to evaluate the seismic response of a RC bridge column to improve its seismic design and prevent future damage. Nonlinear time history analysis using step-by-step integration is capable of tracing the dynamic response of a structure during the entire vibration period and is able to accommodate the pulsing wave form. However, the accuracy of the numerical results is very sensitive to the modeling of the nonlinear load-deformation relationship of the structural member. FEMA 273 and ATC-40 provide the modeling parameters for structural nonlinear analyses of RC beams and RC columns. They use three parameters to define the plastic rotation angles and a residual strength ratio to describe the nonlinear load-deformation relationship of an RC member. Structural nonlinear analyses are performed based on these parameters. This method provides a convenient way to obtain the nonlinear seismic responses of RC structures. However, the accuracy of the numerical solutions might be further improved. For this purpose, results from a previous study on modeling of the static pushover analyses for RC bridge columns (Sung et al. 2005) is adopted for the nonlinear time history analysis presented herein to evaluate the structural responses excited by a near-fault ground motion. To ensure the reliability of this approach, the numerical results were compared to experimental results. The results confirm that the proposed approach is valid.

Analytic and computational modelling of super-radiant pulse compression in plasma and comparisons with experiment

NASA Astrophysics Data System (ADS)

Shvets, Gennady; Kalmykov, Serguei; Dreher, Matthias; Meyer-Ter-Vehn, Juergen

2003-10-01

The strongly non-linear regime of Raman backscattering [1,2] holds the promise of compressing long low-intensity laser beams into ultra-short high intensity pulses. As the short pulse is amplified by the long counter-propagating pump via backscattering the pump off the nonlinear plasma wave, its duration shrinks and intensity grows. The increase of the bandwidth of the amplified pulse only occurs in the nonlinear amplification regime, and is its most telling signature. Recent experiments at MPQ carried out in the strongly nonlinear regime reveal two previously unobserved features: (i) bandwidth expansion, and (ii) breakdown of the initially smooth amplified pulse into several spikes. Using semi-analytic model and particle-in-cell simulations, we explain the multiple pulse formation by the synchrotron motion of plasma electrons in the ponderomotive potential. Self-similar solutions consisting of multiple spikes are derived, and their nonlinear frequency shifts evaluated. The nonlinear focusing of the pulse by the pump is predicted and compared with experimental observations. [1] G. Shvets et. al., Phys. Rev. Lett. 81, 4879 (1998). [2] A. Pukhov, Rep. Progr. Phys. 66, 47 (1998).

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

NASA Astrophysics Data System (ADS)

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

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

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

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

Adcock, T. A. A.; Taylor, P. H.

2016-01-15

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest whichmore » leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.« less

Wave Amplitude Dependent Engineering Model of Propellant Slosh in Spherical Tanks

NASA Technical Reports Server (NTRS)

Brodnick, Jacob; Westra, Douglas G.; Eberhart, Chad J.; Yang, Hong Q.; West, Jeffrey S.

2016-01-01

Liquid propellant slosh is often a concern for the controllability of flight vehicles. Anti-slosh devices are traditionally included in propellant tank designs to limit the amount of sloshing allowed during flight. These devices and any necessary supports can be quite heavy to meet various structural requirements. Some of the burden on anti-slosh devices can be relieved by exploiting the nonlinear behavior of slosh waves in bare smooth wall tanks. A nonlinear regime slosh model for bare spherical tanks was developed through a joint analytical and experimental effort by NASA/MSFC. The developed slosh model accounts for the large damping inherent in nonlinear slosh waves which is more accurate and drives conservatism from vehicle stability analyses that use traditional bare tank slosh models. A more accurate slosh model will result in more realistic predicted slosh forces during flight reducing or removing the need for active controls during a maneuver or baffles in the tank design. Lower control gains and smaller or fewer tank baffles can reduce cost and system complexity while increasing vehicle performance. Both Computational Fluid Dynamics (CFD) simulation and slosh testing of three different spherical tank geometries were performed to develop the proposed slosh model. Several important findings were made during this effort in addition to determining the parameters to the nonlinear regime slosh model. The linear regime slosh damping trend for spherical tanks reported in NASA SP-106 was shown to be inaccurate for certain regions of a tank. Additionally, transition to the nonlinear regime for spherical tanks was only found to occur at very large wave amplitudes in the lower hemisphere and was a strong function of the propellant fill level in the upper hemisphere. The nonlinear regime damping trend was also found to be a function of the propellant fill level.

Using the HHT to Search for Gravitational Waves

NASA Technical Reports Server (NTRS)

Camp, Jordan

2008-01-01

Gravitational waves are a consequence of Einstein's theory of general relativity applied to the motion of very dense and massive objects such as black holes and neutron stars. Their detection will reveal a wealth of information about these mysterious objects that cannot be obtained with electromagnetic probes. Two projects are underway to attempt the detection of gravitational waves: NASA's Laser Interferometer Space Antenna (LISA), a space based mission being designed to search for waves from supermassive black holes at the centers of galaxies, and the NSF's Laser Interferometer Gravitational Wave Observatory (LIGO), a ground based facility that is now searching for waves from supernovae. pulsars, and the coalescence of black hole and neutron star systems. Because general relativity is an inherently non-linear theory, many of the predicted source waveforms show strong frequency modulation. In addition, the LIGO and LISA detectors are highly sensitive devices that produce a variety of non-linear transient noise features. Thus the unique capabilities of the HHT. the extraction of intrawave modulation and the characterization of non-linear and non-stationary signals, have a natural application to both signal detection and experimental characterization of the detectors. In this talk I will give an overview of the status of the field. including some of the expected sources of gravitational waves, and I will also describe the LISA and LIGO detectors. Then I will describe some applications of the HHT to waveform detection and detector noise characterization.

Sensitivity of a Wave Structure to Initial Conditions

NASA Technical Reports Server (NTRS)

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

2000-01-01

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

Analysis and gyrokinetic simulation of MHD Alfven wave interactions

NASA Astrophysics Data System (ADS)

Nielson, Kevin Derek

The study of low-frequency turbulence in magnetized plasmas is a difficult problem due to both the enormous range of scales involved and the variety of physics encompassed over this range. Much of the progress that has been made in turbulence theory is based upon a result from incompressible magnetohydrodynamics (MHD), in which energy is only transferred from large scales to small via the collision of Alfven waves propagating oppositely along the mean magnetic field. Improvements in laboratory devices and satellite measurements have demonstrated that, while theories based on this premise are useful over inertial ranges, describing turbulence at scales that approach particle gyroscales requires new theory. In this thesis, we examine the limits of incompressible MHD theory in describing collisions between pairs of Alfven waves. This interaction represents the fundamental unit of plasma turbulence. To study this interaction, we develop an analytic theory describing the nonlinear evolution of interacting Alfven waves and compare this theory to simulations performed using the gyrokinetic code AstroGK. Gyrokinetics captures a much richer set of physics than that described by incompressible MHD, and is well-suited to describing Alfvenic turbulence around the ion gyroscale. We demonstrate that AstroGK is well suited to the study of physical Alfven waves by reproducing laboratory Alfven dispersion data collected using the LAPD. Additionally, we have developed an initialization alogrithm for use with AstroGK that allows exact Alfven eigenmodes to be initialized with user specified amplitudes and phases. We demonstrate that our analytic theory based upon incompressible MHD gives excellent agreement with gyrokinetic simulations for weakly turbulent collisions in the limit that k⊥rho i << 1. In this limit, agreement is observed in the time evolution of nonlinear products, and in the strength of nonlinear interaction with respect to polarization and scale. We also examine the effect of wave amplitude upon the validity of our analytic solution, exploring the nature of strong turbulence. In the kinetic limit where k⊥ rhoi ≳ 1 where incompressible MHD is no longer a valid description, we illustrate how the nonlinear evolution departs from our analytic expression. The analytic theory we develop provides a framework from which more sophisticated of weak and strong inertial-range turbulence theories may be developed. Characterization of the limits of this theory may provide guidance in the development of kinetic Alfven wave turbulence.

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.

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

Johnson, Paul A.

Nonlinear dynamics induced by seismic sources and seismic waves are common in Earth. Observations range from seismic strong ground motion (the most damaging aspect of earthquakes), intense near-source effects, and distant nonlinear effects from the source that have important consequences. The distant effects include dynamic earthquake triggering-one of the most fascinating topics in seismology today-which may be elastically nonlinearly driven. Dynamic earthquake triggering is the phenomenon whereby seismic waves generated from one earthquake trigger slip events on a nearby or distant fault. Dynamic triggering may take place at distances thousands of kilometers from the triggering earthquake, and includes triggering ofmore » the entire spectrum of slip behaviors currently identified. These include triggered earthquakes and triggered slow, silent-slip during which little seismic energy is radiated. It appears that the elasticity of the fault gouge-the granular material located between the fault blocks-is key to the triggering phenomenon.« less

Observation of Tropical Cyclone-Induced Shallow Water Currents in Taiwan Strait

NASA Astrophysics Data System (ADS)

Shen, Junqiang; Qiu, Yun; Zhang, Shanwu; Kuang, Fangfang

2017-06-01

The data from three stations equipped with Acoustic Doppler Current Profilers (ADCPs) deployed in the shallow water of the Taiwan Strait (TWS) were used to study the shallow coastal ocean response to five quasi-continuous tropical cyclone (TC) events in the late summer 2006. We revealed that, in the forced stage, when the large and strong TC (Bilis) transited, the geostrophic currents were formed which dominated the whole event, while the strong but relatively small one (Saomai) or the weak one (Bopha) primarily leaded to the generation of Ekman currents. In the relaxation stage, the barotropic subinertial waves and/or the baroclinic near-inertial oscillations (NIOs) were triggered. Typically, during the transit of the Saomai, subinertial waves were induced which demonstrated a period of 2.8-4.1 days and a mean alongshore phase velocity of 14.9 ± 3.2 m/s in the form of free-barotropic continental shelf waves. However, the NIOs are only notable in the area in which the water column is stably stratified and also where the wind stress is dominated by the clockwise component and accompanied by high-frequency (near-inertial) variations. We also demonstrated that, due to the damping effects, the nonlinear wave-wave interaction (e.g., between NIO and semidiurnal tide in our case), together with the well-known bottom friction, led to the rapid decay of the observed TC-induced near-inertial currents, giving a typical e-folding time scale of 1-3 inertial periods. Moreover, such nonlinear wave-wave interaction was even found to play a major role during the spring tide in TWS.

Infrasound in the ionosphere from earthquakes and typhoons

NASA Astrophysics Data System (ADS)

Chum, J.; Liu, J.-Y.; Podolská, K.; Šindelářová, T.

2018-06-01

Infrasound waves are observed in the ionosphere relatively rarely, in contrast to atmospheric gravity waves. Infrasound waves excited by two distinguished sources as seismic waves from strong earthquakes (M > 7) and severe tropospheric weather systems (typhoons) are discussed and analyzed. Examples of observation by an international network of continuous Doppler sounders are presented. It is documented that the co-seismic infrasound is generated by vertical movement of the ground surface caused by seismic waves propagating at supersonic speeds. The coseismic infrasound propagates nearly vertically and has usually periods of several tens of seconds far away from the epicenter. However, in the vicinity of the epicenter (up to distance about 1000-1500 km), the large amplitudes might lead to nonlinear formation of N-shaped pulse in the upper atmosphere with much longer dominant period, e.g. around 2 min. The experimental observation is in good agreement with numerical modeling. The spectral content can also be nonlinearly changed at intermediate distances (around 3000-4000 km), though the N-shaped pulse is not obvious. Infrasound waves associated with seven typhoons that passed over Taiwan in 2014-2016 were investigated. The infrasound waves were observed at heights approximately from 200 to 300 km. Their spectra differed during the individual events and event from event and covered roughly the spectral range 3.5-20 mHz. The peak of spectral density was usually around 5 mHz. The observed spectra exhibited fine structures that likely resulted from modal resonances. The infrasound was recorded during several hours for strong events, especially for two typhoons in September 2016.

Wave propagation in a strongly nonlinear locally resonant granular crystal

NASA Astrophysics Data System (ADS)

Vorotnikov, K.; Starosvetsky, Y.; Theocharis, G.; Kevrekidis, P. G.

2018-02-01

In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degradation of the well-known traveling pulse of the standard Hertzian chain of elastic beads. Nevertheless, the present system is richer, in that as the primary pulse decays, secondary ones emerge and eventually interfere with it creating modulated wavetrains. Remarkably, upon suitable choices of parameters, this interference "distills" a weakly nonlocal solitary wave (a "nanopteron"). This motivates the consideration of such nonlinear structures through a separate Fourier space technique, whose results suggest the existence of such entities not only with a single-side tail, but also with periodic tails on both ends. These tails are found to oscillate with the intrinsic oscillation frequency of the out-of-phase motion between the outer hollow bead and its internal linear attachment.

Four-wave mixing in an asymmetric double quantum dot molecule

NASA Astrophysics Data System (ADS)

Kosionis, Spyridon G.

2018-06-01

The four-wave mixing (FWM) effect of a weak probe field, in an asymmetric semiconductor double quantum dot (QD) structure driven by a strong pump field is theoretically studied. Similarly to the case of examining several other nonlinear optical processes, the nonlinear differential equations of the density matrix elements are used, under the rotating wave approximation. By suitably tuning the intensity and the frequency of the pump field as well as by changing the value of the applied bias voltage, a procedure used to properly adjust the electron tunneling coupling, we control the FWM in the same way as several other nonlinear optical processes of the system. While in the weak electron tunneling regime, the impact of the pump field intensity on the FWM is proven to be of crucial importance, for even higher rates of the electron tunneling it is evident that the intensity of the pump field has only a slight impact on the form of the FWM spectrum. The number of the spectral peaks, depends on the relation between specific parameters of the system.

Stimulated scattering of electromagnetic waves carrying orbital angular momentum in quantum plasmas.

PubMed

Shukla, P K; Eliasson, B; Stenflo, L

2012-07-01

We investigate stimulated scattering instabilities of coherent circularly polarized electromagnetic (CPEM) waves carrying orbital angular momentum (OAM) in dense quantum plasmas with degenerate electrons and nondegenerate ions. For this purpose, we employ the coupled equations for the CPEM wave vector potential and the driven (by the ponderomotive force of the CPEM waves) equations for the electron and ion plasma oscillations. The electrons are significantly affected by the quantum forces (viz., the quantum statistical pressure, the quantum Bohm potential, as well as the electron exchange and electron correlations due to electron spin), which are included in the framework of the quantum hydrodynamical description of the electrons. Furthermore, our investigation of the stimulated Brillouin instability of coherent CPEM waves uses the generalized ion momentum equation that includes strong ion coupling effects. The nonlinear equations for the coupled CPEM and quantum plasma waves are then analyzed to obtain nonlinear dispersion relations which exhibit stimulated Raman, stimulated Brillouin, and modulational instabilities of CPEM waves carrying OAM. The present results are useful for understanding the origin of scattered light off low-frequency density fluctuations in high-energy density plasmas where quantum effects are eminent.

Controlled experiments in cosmological gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.; Shandarin, Sergei F.

1993-01-01

A systematic study is conducted of gravitational instability in 3D on the basis of power-law initial spectra with and without spectral cutoff, emphasizing nonlinear effects and measures of nonlinearity; effects due to short and long waves in the initial conditions are separated. The existence of second-general pancakes is confirmed, and it is noted that while these are inhomogeneous, they generate a visually strong signal of filamentarity. An explicit comparison of smoothed initial conditions with smoothed envelope models also reconfirms the need to smooth over a scale larger than any nonlinearity, in order to extrapolate directly by linear theory from Gaussian initial conditions.

Investigation on Nonlinear-Optical Properties of Palm Oil/Silver Nanoparticles

NASA Astrophysics Data System (ADS)

Zamiri, R.; Parvizi, R.; Zakaria, A.; Sadrolhosseini, A. R.; Zamiri, G.; Darroudi, M.; Husin, M. S.

2012-06-01

We have investigated the spatial self phase modulation of palm oil containing silver nanoparticles (palm oil/Ag-NPs). The study carried out using continuous wave diode pumped solid state laser with wavelength of 405 nm and power of 50 mW. The strong spatial self phase modulation patterns were observed that suggest the palm oil/Ag-NPs have a relatively large nonlinear refractive index. The obtained values of nonlinear refractive index were increased with the increment in the volume fractions. The observed experimental patterns were also theoretically modeled which are in good agreement with experimental results.

Nonlinear surge motions of a ship in bi-chromatic following waves

NASA Astrophysics Data System (ADS)

Spyrou, Kostas J.; Themelis, Nikos; Kontolefas, Ioannis

2018-03-01

Unintended motions of a ship operating in steep and long following waves are investigated. A well-known such case is ;surf-riding; where a ship is carried forward by a single wave, an event invoking sometimes lateral instability and even capsize. The dynamics underlying this behavior has been clarified earlier for monochromatic waves. However, the unsteadiness of the phase space associated with ship behavior in a multichromatic sea, combined with the intrinsically strong system nonlinearity, pose new challenges. Here, current theory is extended to cover surging and surf-riding behavior in unidirectional bi-chromatic waves encountering a ship from the stern. Excitation is provided by two unidirectional harmonic wave components having their lengths comparable to the ship length and their frequencies in rational ratio. The techniques applied include (a) continuation analysis; (b) tracking of Lagrangian coherent structures in phase space, approximated through a finite-time Lyapunov exponents' calculation; and (c) large scale simulation. A profound feature of surf-riding in bi-chromatic waves is that it is turned oscillatory. Initially it appears as a frequency-locked motion, ruled by the harmonic wave component dominating the excitation. Transformations of oscillatory surf-riding are realized as the waves become steeper. In particular, heteroclinic tanglings are identified, governing abrupt transitions between qualitatively different motions. Chaotic transients, as well as long-term chaotic motions, exist near to these events. Some extraordinary patterns of ship motion are discovered. These include a counterintuitive low speed motion at very high wave excitation level; and a hybrid motion characterized by a wildly fluctuating velocity. Due to the quite generic nature of the core mathematical model of our investigation, the current results are believed to offer clues about the behavior of a class of nonlinear dynamical systems having in their modeling some analogy with a perturbed pendulum with bias.

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

NASA Astrophysics Data System (ADS)

Cannon, Patrick; Honary, Farideh; Borisov, Nikolay

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

Nonlinear bounce resonances between magnetosonic waves and equatorially mirroring electrons

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

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

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

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

2016-07-15

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

Global Simulation of Electromagnetic Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov, George V.; Gallagher, D. L.; Kozyra, J. U.

2007-01-01

It is very well known that the effects of electromagnetic ion cyclotron (EMIC) waves on ring current (RC) ion and radiation belt (RB) electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. The consequence is that accurate modeling of EMIC waves and RC particles requires robust inclusion of the interdependent dynamics of wave growth/damping, wave propagation, and particles. Such a self-consistent model is being progressively developed by Khazanov et al. This model is based on a system of coupled kinetic equations for the RC and EMIC wave power spectral density along with the ray tracing equations. We will discuss the recent progress in understanding EMIC waves formation mechanisms in the inner magnetosphere. This problem remains unsettled in spite of many years of experimental and theoretical studies. Modern satellite observations by CRRES, Polar and Cluster still do not reveal the whole picture experimentally since they do not stay long enough in the generation region to give a full account of all the spatio-temporal structure of EMIC waves. The complete self-consistent theory taking into account all factors significant for EMIC waves generation remains to be developed. Several mechanisms are discussed with respect to formation of EMIC waves, among them are nonlinear modification of the ionospheric reflection by precipitating energetic protons, modulation of ion-cyclotron instability by long-period (Pc3/4) pulsations, reflection of waves from layers of heavy-ion gyroresonances, and nonlinearities of wave generation process. We show that each of these mechanisms have their attractive features and explains certain part experimental data but any of them, if taken alone, meets some difficulties when compared to observations. We conclude that development of a refined nonlinear theory and further correlated analysis of modern satellite and ground-based data is needed to solve this very intriguing problem.

Global Simulation of Electromagnetic Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gamayunov, K.; Gallagher, D. L.; Kozyra, J. U.

2007-01-01

It is well known that the effects of electromagnetic ion cyclotron (EMIC) waves on ring current (RC) ion and radiation belt (RB) electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. The consequence is that accurate modeling of EMIC waves and RC particles requires robust inclusion of the interdependent dynamics of wave growth/damping, wave propagation, and particles. Such a self-consistent model is being progressively developed by Khazanov et al. [2002 - 2007]. This model is based on a system of coupled kinetic equations for the RC and EMIC wave power spectral density along with the ray tracing equations. We will discuss the recent progress in understanding EMIC waves formation mechanisms in the inner magnetosphere. This problem remains unsettled in spite of many years of experimental and theoretical studies. Modern satellite observations by CRRES, Polar and Cluster still do not reveal the whole picture experimentally since they do not stay long enough in the generation region to give a full account of all the spatio-temporal structure of EMIC waves. The complete self-consistent theory taking into account all factors significant for EMIC waves generation remains to be developed. Several mechanisms are discussed with respect to formation of EMIC waves, among them are nonlinear modification of the ionospheric reflection by precipitating energetic protons, modulation of ion-cyclotron instability by long-period (Pc3/4) pulsations, reflection of waves from layers of heavy-ion gyroresonances, and nonlinearities of wave generation process. We show that each of these mechanisms have their attractive features and explains certain part experimental data but any of them, if taken alone, meets some difficulties when compared to observations. We conclude that development of a refined nonlinear theory and further correlated analysis of modern satellite and ground-based data is needed to solve this very intriguing problem.

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

Ofman, L.; Knizhnik, K.; Kucera, T.

We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ∼ δn/n). The waves are evidentmore » as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5–11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5–14 G. For the typical prominence density the corresponding fast magnetosonic speed is ∼20 km s{sup −1}, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.« less

Time-resolved nonlinear optics in strongly correlated insulators

NASA Astrophysics Data System (ADS)

Dodge, J. Steven

2000-03-01

Transition metal oxides form the basis for much of our understanding of Mott insulators, and have enjoyed a renaissance of interest since the discovery of high temperature superconductivity in the cuprates. They are characterized by complex interactions among spin, lattice, orbital and charge degrees of freedom, which lead to dynamical behavior on time scales ranging from femtoseconds to microseconds. We have applied time resolved nonlinear optical spectroscopy to probe these dynamics. In one well-studied antiferromagnetic insulator, Cr_2O_3, we observed spin-wave dynamics on a picosecond time scale by performing pump-probe spectroscopy of the exciton-magnon transition(J. S. Dodge, et al.), Phys. Rev. Lett. 83, 4650 (1999).. At excitation densities ~ 10-3/Cr, a lineshape associated with the exciton-magnon absorption appears in the pump-probe spectrum. We assign this nonlinearity to a time-dependent renormalization of the magnon band structure, which in turn modifies the lineshape of the exciton-magnon transition. At long time delays, this assignment agrees semiquantitatively with calculations based on spin-wave theory. However, the initial population at the zone-boundary induces surprisingly little renormalization effect, indicating that spin-wave theory is insufficient to describe our observations in this regime. The renormalization lineshape grows on a time scale of ~ 50 ps, which we associate with the decay of the photoexcited, nonequilibrium population of zone-boundary spin-waves into a thermalized population of zone-center spin-waves. We have also performed a study of the linear and nonlinear optical properties of Sr_2CuO_2Cl_2, an insulating, two-dimensional cuprate. In the nonlinear optical experiments, we have performed pump-probe spectroscopy over a 1 eV spectral range, varying both the pump and the probe energy. We observe a pump-probe lineshape which varies considerably as a function of pump energy and temperature, and which differs sharply from those typically observed in band insulators. At low-temperatures, in particular, we observe an overall increase of spectral weight in our probe range, indicating that states are shifting over an energy scale larger than 1 eV. We attribute this behavior to the strongly correlated nature of the electronic structure in this material. Studies of the elementary excitations in other magnetic oxides, currently in progress, will be discussed.

Toward nonlinear magnonics: Intensity-dependent spin-wave switching in insulating side-coupled magnetic stripes

NASA Astrophysics Data System (ADS)

Sadovnikov, A. V.; Odintsov, S. A.; Beginin, E. N.; Sheshukova, S. E.; Sharaevskii, Yu. P.; Nikitov, S. A.

2017-10-01

We demonstrate that the nonlinear spin-wave transport in two laterally parallel magnetic stripes exhibit the intensity-dependent power exchange between the adjacent spin-wave channels. By the means of Brillouin light scattering technique, we investigate collective nonlinear spin-wave dynamics in the presence of magnetodipolar coupling. The nonlinear intensity-dependent effect reveals itself in the spin-wave mode transformation and differential nonlinear spin-wave phase shift in each adjacent magnetic stripe. The proposed analytical theory, based on the coupled Ginzburg-Landau equations, predicts the geometry design involving the reduction of power requirement to the all-magnonic switching. A very good agreement between calculation and experiment was found. In addition, a micromagnetic and finite-element approach has been independently used to study the nonlinear behavior of spin waves in adjacent stripes and the nonlinear transformation of spatial profiles of spin-wave modes. Our results show that the proposed spin-wave coupling mechanism provides the basis for nonlinear magnonic circuits and opens the perspectives for all-magnonic computing architecture.

Microphysics of Waves and Instabilities in the Solar Wind and their Macro Manifestations in the Corona and Interplanetary Space

NASA Technical Reports Server (NTRS)

Habbal, Shadia R.; Gurman, Joseph (Technical Monitor)

2003-01-01

Investigations of the physical processes responsible for the acceleration of the solar wind were pursued with the development of two new solar wind codes: a hybrid code and a 2-D MHD code. Hybrid simulations were performed to investigate the interaction between ions and parallel propagating low frequency ion cyclotron waves in a homogeneous plasma. In a low-beta plasma such as the solar wind plasma in the inner corona, the proton thermal speed is much smaller than the Alfven speed. Vlasov linear theory predicts that protons are not in resonance with low frequency ion cyclotron waves. However, non-linear effect makes it possible that these waves can strongly heat and accelerate protons. This study has important implications for study of the corona and the solar wind. Low frequency ion cyclotron waves or Alfven waves are commonly observed in the solar wind. Until now, it is believed that these waves are not able to heat the solar wind plasma unless some cascading processes transfer the energy of these waves to high frequency part. However, this study shows that these waves may directly heat and accelerate protons non-linearly. This process may play an important role in the coronal heating and the solar wind acceleration, at least in some parameter space.

Simulations of neutral wind shear effect on the equatorial ionosphere irregularities

NASA Astrophysics Data System (ADS)

Kim, J.; Chagelishvili, G.; Horton, W.

2005-12-01

We present numerical calculations of the large-scale electron density driven by the gradient drift instability in the daytime equatorial electrojet. Under two-fluid theory the linear analysis for kilometer scale waves lead to the result that all the perturbations are transformed to small scales through linear convection by shear and then damped by diffusion. The inclusion of the nonlinearity enables inverse energy cascade to provide energy to long scale. The feedback between velocity shear and nonlinearity keeps waves growing and leads to the turbulence. In strongly turbulent regime, the nonlinear states are saturated [1]. Since the convective nonlinearities are isotropic while the interactions of velocity shear with waves are anisotropic, the feedback do not necessarily enable waves to grow. The growth of waves are highly variable on k-space configuration [2]. Our simulations show that the directional relationship between vorticity of irregularities and shear are one of key factors. Thus during the transient period, the irregularities show the anisotropy of the vorticity power spectrum. We report the evolution of the power spectrum of the vorticity and density of irregularties and its anistropic nature as observed. The work was supported in part by the Department of NSF Grant ATM-0229863 and ISTC Grant G-553. C. Ronchi, R.N. Sudan, and D.T. Farley. Numerical simulations of large-scale plasma turbulece in teh day time equatorial electrojet. J. Geophys. Res., 96:21263--21279, 1991. G.D. Chagelishvili, R.G. Chanishvili, T.S. Hristov, and J.G. Lominadze. A turbulence model in unbounded smooth shear flows : The weak turbulence approach. JETP, 94(2):434--445, 2002.

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.

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.

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

PubMed

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

2016-08-08

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

Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

PubMed

Ecke, Robert E

2015-09-01

The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

Colossal terahertz nonlinearity of tunneling van der Waals gap (Conference Presentation)

NASA Astrophysics Data System (ADS)

Bahk, Young-Mi; Kang, Bong Joo; Kim, Yong Seung; Kim, Joon-Yeon; Kim, Won Tae; Kim, Tae Yun; Kang, Taehee; Rhie, Ji Yeah; Han, Sanghoon; Park, Cheol-Hwan; Rotermund, Fabian; Kim, Dai-Sik

2016-09-01

We manufactured an array of three angstrom-wide, five millimeter-long van der Waals gaps of copper-graphene-copper composite, in which unprecedented nonlinearity was observed. To probe and manipulate van der Waals gaps with long wavelength electromagnetic waves such as terahertz waves, one is required to fabricate vertically oriented van der Waals gaps sandwiched between two metal planes with an infinite length in the sense of being much larger than any of the wavelengths used. By comparison with the simple vertical stacking of metal-graphene-metal structure, in our structure, background signals are completely blocked enabling all the light to squeeze through the gap without any strays. When the angstrom-sized van der Waals gaps are irradiated with intense terahertz pulses, the transient voltage across the gap reaches up to 5 V with saturation, sufficiently strong to deform the quantum barrier of angstrom gaps. The large transient potential difference across the gap facilitates electron tunneling through the quantum barrier, blocking terahertz waves completely. This negative feedback of electron tunneling leads to colossal nonlinear optical response, a 97% decrease in the normalized transmittance. Our technology for infinitely long van der Waals gaps can be utilized for other atomically thin materials than single layer graphene, enabling linear and nonlinear angstrom optics in a broad spectral range.

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

NASA Astrophysics Data System (ADS)

Zonca, Fulvio; Chen, Liu

2007-11-01

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

Microwave phase conjugation using artificial nonlinear microwave surfaces

NASA Astrophysics Data System (ADS)

Chang, Yian

1997-09-01

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

Stix Award: The ponderomotive effect beyond the ponderomotive force

NASA Astrophysics Data System (ADS)

Dodin, I. Y.

2014-10-01

The classical ponderomotive effect (PE) is typically understood as the nonlinear time-average force produced by a rapidly oscillating electromagnetic field on a nonresonant particle. It is instructive to contrast this understanding with the common quantum interpretation of the PE as the ac Stark shift, i.e., phase modulation, or a Kerr effect experienced by the wave function. Then the PE is naturally extended from particles to waves and can be calculated efficiently in general settings, including for strongly nonlinear interactions and resonant dynamics. In particular, photons (plasmons, etc.) are hence seen to have polarizability and contribute to the linear dielectric tensor exactly like ``true'' particles such as electrons and ions. The talk will briefly review the underlying variational theory and some nonintuitive PE-based techniques of wave and particle manipulation that the theory predicts. It will also be shown that the PE can be understood as the cause for the basic properties of both linear and nonlinear waves in plasma, including their dispersion, energy-momentum transport, and various modulational instabilities. Linear collisionless dissipation (both on particles and classical waves, treated on the same footing) also appears merely as a special case of the modulational dynamics. The work was supported by NNSA grant DE274-FG52-08NA28553, DOE contract DE-AC02-09CH11466, and DTRA grant HDTRA1-11-1-0037.

Hydrodynamic modeling of tsunamis from the Currituck landslide

USGS Publications Warehouse

Geist, E.L.; Lynett, P.J.; Chaytor, J.D.

2009-01-01

Tsunami generation from the Currituck landslide offshore North Carolina and propagation of waves toward the U.S. coastline are modeled based on recent geotechnical analysis of slide movement. A long and intermediate wave modeling package (COULWAVE) based on the non-linear Boussinesq equations are used to simulate the tsunami. This model includes procedures to incorporate bottom friction, wave breaking, and overland flow during runup. Potential tsunamis generated from the Currituck landslide are analyzed using four approaches: (1) tsunami wave history is calculated from several different scenarios indicated by geotechnical stability and mobility analyses; (2) a sensitivity analysis is conducted to determine the effects of both landslide failure duration during generation and bottom friction along the continental shelf during propagation; (3) wave history is calculated over a regional area to determine the propagation of energy oblique to the slide axis; and (4) a high-resolution 1D model is developed to accurately model wave breaking and the combined influence of nonlinearity and dispersion during nearshore propagation and runup. The primary source parameter that affects tsunami severity for this case study is landslide volume, with failure duration having a secondary influence. Bottom friction during propagation across the continental shelf has a strong influence on the attenuation of the tsunami during propagation. The high-resolution 1D model also indicates that the tsunami undergoes nonlinear fission prior to wave breaking, generating independent, short-period waves. Wave breaking occurs approximately 40-50??km offshore where a tsunami bore is formed that persists during runup. These analyses illustrate the complex nature of landslide tsunamis, necessitating the use of detailed landslide stability/mobility models and higher-order hydrodynamic models to determine their hazard.

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

PubMed

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

2018-06-01

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

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Nonlinear damping based semi-active building isolation system

NASA Astrophysics Data System (ADS)

Ho, Carmen; Zhu, Yunpeng; Lang, Zi-Qiang; Billings, Stephen A.; Kohiyama, Masayuki; Wakayama, Shizuka

2018-06-01

Many buildings in Japan currently have a base-isolation system with a low stiffness that is designed to shift the natural frequency of the building below the frequencies of the ground motion due to earthquakes. However, the ground motion observed during the 2011 Tohoku earthquake contained strong long-period waves that lasted for a record length of 3 min. To provide a novel and better solution against the long-period waves while maintaining the performance of the standard isolation range, the exploitation of the characteristics of nonlinear damping is proposed in this paper. This is motivated by previous studies of the authors, which have demonstrated that nonlinear damping can achieve desired performance over both low and high frequency regions and the optimal nonlinear damping force can be realized by closed loop controlled semi-active dampers. Simulation results have shown strong vibration isolation performance on a building model with identified parameters and have indicated that nonlinear damping can achieve low acceleration transmissibilities round the structural natural frequency as well as the higher ground motion frequencies that have been frequently observed during most earthquakes in Japan. In addition, physical building model based laboratory experiments are also conducted, The results demonstrate the advantages of the proposed nonlinear damping technologies over both traditional linear damping and more advanced Linear-Quadratic Gaussian (LQG) feedback control which have been used in practice to address building isolation system design and implementation problems. In comparison with the tuned-mass damper and other active control methods, the proposed solution offers a more pragmatic, low-cost, robust and effective alternative that can be readily installed into the base-isolation system of most buildings.

Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma.

PubMed

El-Shamy, E F

2015-03-01

The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

The Strong Effects Of On-Axis Focal Shift And Its Nonlinear Variation In Ultrasound Beams Radiated By Low Fresnel Number Transducers

NASA Astrophysics Data System (ADS)

Makov, Y. N.; Espinosa, V.; Sánchez-Morcillo, V. J.; Ramis, J.; Cruañes, J.; Camarena, F.

2006-05-01

On the basis of theoretical concepts, an accurate and complete experimental and numerical examination of the on-axis distribution and the corresponding temporal profiles for low-Fresnel-number focused ultrasound beams under increasing transducer input voltage has been performed. For a real focusing transducer with sufficiently small Fresnel number, a strong initial (linear) shift of the main on-axis pressure maximum from geometrical focal point towards the transducer, and its following displacement towards the focal point and backward motion as the driving transducer voltage increase until highly nonlinear regimes were fixed. The simultaneous monitoring of the temporal waveform modifications determines the real roles and interplay between different nonlinear effects (refraction and attenuation) in the observed dynamics of on-axis pressure maximum. The experimental results are in good agreement with numerical solutions of KZK equation, confirming that the observed dynamic shift of the maximum pressure point is related only to the interplay between diffraction, dissipation and nonlinearity of the acoustic wave.

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.

Deterministic quantum nonlinear optics with single atoms and virtual photons

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Relativistic Tennis with Photons: Frequency Up-Shifting, Light Intensification and Ion Acceleration with Flying Mirrors

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

Bulanov, S. V.; Esirkepov, T. Zh.; Kando, M.

2011-01-04

We formulate the Flying Mirror Concept for relativistic interaction of ultra-intense electromagnetic waves with plasmas, present its theoretical description and the results of computer simulations and laboratory experiments. In collisionless plasmas, the relativistic flying mirrors are thin and dense electron or electron-ion layers accelerated by the high intensity electromagnetic waves up to velocity close to the speed of light in vacuum; in nonlinear-media and in nonlinear vacuum they are the ionization fronts and the refraction index modulations induced by a strong electromagnetic wave. The reflection of the electromagnetic wave at the relativistic mirror results in its energy and frequency changemore » due to the double Doppler effect. In the co-propagating configuration, in the radiation pressure dominant regime, the energy of the electromagnetic wave is transferred to the ion energy providing a highly efficient acceleration mechanism. In the counter-propagation configuration the frequency of the reflected wave is multiplied by the factor proportional to the gamma-factor squared. If the relativistic mirror performs an oscillatory motion as in the case of the electron motion at the plasma-vacuum interface, the reflected light spectrum is enriched with high order harmonics.« less

Nonlinear Right-Hand Polarized Wave in Plasma in the Electron Cyclotron Resonance Region

NASA Astrophysics Data System (ADS)

Krasovitskiy, V. B.; Turikov, V. A.

2018-05-01

The propagation of a nonlinear right-hand polarized wave along an external magnetic field in subcritical plasma in the electron cyclotron resonance region is studied using numerical simulations. It is shown that a small-amplitude plasma wave excited in low-density plasma is unstable against modulation instability with a modulation period equal to the wavelength of the excited wave. The modulation amplitude in this case increases with decreasing detuning from the resonance frequency. The simulations have shown that, for large-amplitude waves of the laser frequency range propagating in plasma in a superstrong magnetic field, the maximum amplitude of the excited longitudinal electric field increases with the increasing external magnetic field and can reach 30% of the initial amplitude of the electric field in the laser wave. In this case, the energy of plasma electrons begins to substantially increase already at magnetic fields significantly lower than the resonance value. The laser energy transferred to plasma electrons in a strong external magnetic field is found to increase severalfold compared to that in isotropic plasma. It is shown that this mechanism of laser radiation absorption depends only slightly on the electron temperature.

Modeling of Inner Magnetosphere Coupling Processes

NASA Technical Reports Server (NTRS)

Khazanov, George V.

2011-01-01

The Ring Current (RC) is the biggest energy player in the inner magnetosphere. It is the source of free energy for Electromagnetic Ion Cyclotron (EMIC) wave excitation provided by a temperature anisotropy of RC ions, which develops naturally during inward E B convection from the plasmasheet. The cold plasmasphere, which is under the strong influence of the magnetospheric electric field, strongly mediates the RC-EMIC wave-particle-coupling process and ultimately becomes part of the particle and energy interplay. On the other hand, there is a strong influence of the RC on the inner magnetospheric electric and magnetic field configurations and these configurations, in turn, are important to RC dynamics. Therefore, one of the biggest needs for inner magnetospheric research is the continued progression toward a coupled, interconnected system with the inclusion of nonlinear feedback mechanisms between the plasma populations, the electric and magnetic fields, and plasma waves. As we clearly demonstrated in our studies, EMIC waves strongly interact with electrons and ions of energies ranging from approx.1 eV to approx.10 MeV, and that these waves strongly affect the dynamics of resonant RC ions, thermal electrons and ions, and the outer RB relativistic electrons. As we found, the rate of ion and electron scattering/heating in the Earth's magnetosphere is not only controlled by the wave intensity-spatial-temporal distribution but also strongly depends on the spectral distribution of the wave power. The latter is also a function of the plasmaspheric heavy ion content, and the plasma density and temperature distributions along the magnetic field lines. The above discussion places RC-EMIC wave coupling dynamics in context with inner magnetospheric coupling processes and, ultimately, relates RC studies with plasmaspheric and Superthermal Electrons formation processes as well as with outer RB physics.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Three-wave and four-wave interactions in gravity wave turbulence

NASA Astrophysics Data System (ADS)

Aubourg, Quentin; Campagne, Antoine; Peureux, Charles; Ardhuin, Fabrice; Sommeria, Joel; Viboud, Samuel; Mordant, Nicolas

2017-11-01

Weak-turbulence theory is a statistical framework to describe a large ensemble of nonlinearly interacting waves. The archetypal example of such system is the ocean surface that is made of interacting surface gravity waves. Here we describe a laboratory experiment dedicated to probe the statistical properties of turbulent gravity waves. We set up an isotropic state of interacting gravity waves in the Coriolis facility (13-m-diam circular wave tank) by exciting waves at 1 Hz by wedge wave makers. We implement a stereoscopic technique to obtain a measurement of the surface elevation that is resolved in both space and time. Fourier analysis shows that the laboratory spectra are systematically steeper than the theoretical predictions and the field observations in the Black Sea by Leckler et al. [F. Leckler et al., J. Phys. Oceanogr. 45, 2484 (2015), 10.1175/JPO-D-14-0237.1]. We identify a strong impact of surface dissipation on the scaling of the Fourier spectrum at the scales that are accessible in the experiments. We use bicoherence and tricoherence statistical tools in frequency and/or wave-vector space to identify the active nonlinear coupling. These analyses are also performed on the field data by Leckler et al. for comparison with the laboratory data. Three-wave coupling is characterized by and shown to involve mostly quasiresonances of waves with second- or higher-order harmonics. Four-wave coupling is not observed in the laboratory but is evidenced in the field data. We discuss temporal scale separation to explain our observations.

Nonlinear Waves, Instabilities and Singularities in Plasma and Hydrodynamics

NASA Astrophysics Data System (ADS)

Silantyev, Denis Albertovich

Nonlinear effects are present in almost every area of science as soon as one tries to go beyond the first order approximation. In particular, nonlinear waves emerge in such areas as hydrodynamics, nonlinear optics, plasma physics, quantum physics, etc. The results of this work are related to nonlinear waves in two areas, plasma physics and hydrodynamics, united by concepts of instability, singularity and advanced numerical methods used for their investigation. The first part of this work concentrates on Langmuir wave filamentation instability in the kinetic regime of plasma. In Internal Confinement Fusion Experiments (ICF) at National Ignition Facility (NIF), where attempts are made to achieve fusion by compressing a small target by many powerful lasers to extremely high temperatures and pressures, plasma is created in the first moments of the laser reaching the target and undergoes complicated dynamics. Some of the most challenging difficulties arise from various plasma instabilities that occur due to interaction of the laser beam and a plasma surrounding the target. In this work we consider one of such instabilities that describes a decay of nonlinear plasma wave, initially excited due to interaction of the laser beam with the plasma, into many filaments in direction perpendicular to the laser beam, therefore named Langmuir filamentation instability. This instability occurs in the kinetic regime of plasma, klambda D > 0.2, where k is the wavenumber and lambda D is the Debye length. The filamentation of Langmuir waves in turn leads to the saturation of the stimulated Raman scattering (SRS) in laser-plasma interaction experiments which plays an essential role in ICF experiments. The challenging part of this work was that unlike in hydrodynamics we needed to use fully kinetic description of plasma to capture the physics in question properly, meaning that we needed to consider the distribution function of charged particles and its evolution in time not only with respect to spatial coordinates but with respect to velocities as well. To study Langmuir filamentation instability in its simplest form we performed 2D+2V numerical simulations. Taking into account that the distribution function in question was 4-dimensional function, making these simulation quite challenging, we developed an efficient numerical method making these simulations possible on modern desktop computers. Using the developed numerical method we studied how Langmuir wave filamentation instability depends on the parameters of the Langmuir wave such as wave length and amplitude that are relevant to ICF experiments. We considered several types of Langmuir waves, including nonlinear Langmuir waves exited by external electric field as well as an idealized approximation of such Langmuir waves by a particular family of Bernstein-Greene-Kruskal (BGK) modes that bifurcates from the linear Langmuir wave. The results of these simulations were compared to the theoretical predictions in our recent papers. An alternative approach to overcome computational difficulty of this problem was considered by our research group in Ref. It involves reducing the number of transverse direction in the model therefore lowering computational difficulty at a cost of lesser accuracy of the model. The second part of this work concentrates on 2D free surface hydrodynamics and in particular on computing Stokes waves with high-precision using conformal maps and spectral methods. Stokes waves are fully nonlinear periodic gravity waves propagating with the constant velocity on a free surface of two-dimensional potential flow of the ideal incompressible fluid of infinite depth. The increase of the scaled wave height H/lambda, where H is the wave height and lambda is the wavelength, from H/lambda = 0 to the critical value Hmax/lambda marks the transition from almost linear wave to a strongly nonlinear limiting Stokes wave. The Stokes wave of the greatest height H = Hmax has an angle of 120° at the crest. To obtain Stokes wave fully nonlinear Euler equations describing the flow can be reformulated in terms of conformal map of the fluid domain into the complex lower half-plane, with fluid free surface mapped into the real line. This description is convenient for analysis and numerical simulations since the whole problem is then reduced to a single nonlinear equation on the real line. Having computed solutions on the real line we extend them to the rest of the complex plane to analyze the singularities above real line. The distance vc from the closest singularity in the upper half-plane to the real line goes to zero as we approach the limiting Stokes wave with maximum hight Hmax/lambda, which is the reason for the widening of the solution's Fourier spectrum. (Abstract shortened by ProQuest.).

Current structure of strongly nonlinear interfacial solitary waves

NASA Astrophysics Data System (ADS)

Semin, Sergey; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim; Churaev, Egor

2015-04-01

The characteristics of highly nonlinear solitary internal waves (solitons) in two-layer flow are computed within the fully nonlinear Navier-Stokes equations with use of numerical model of the Massachusetts Institute of Technology (MITgcm). The verification and adaptation of the model is based on the data from laboratory experiments [Carr & Davies, 2006]. The present paper also compares the results of our calculations with the computations performed in the framework of the fully nonlinear Bergen Ocean Model [Thiem et al, 2011]. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the interface and near the bottom are computed. The results demonstrated completely different trajectories at different depths of the model area. Thus, in the surface layer is observed the largest displacement of Lagrangian particles, which can be more than two and a half times larger than the characteristic width of the soliton. Located at the initial moment along the middle pycnocline fluid particles move along the elongated vertical loop at a distance of not more than one third of the width of the solitary wave. In the bottom layer of the fluid moves in the opposite direction of propagation of the internal wave, but under the influence of the reverse flow, when the bulk of the velocity field of the soliton ceases to influence the trajectory, it moves in the opposite direction. The magnitude of displacement of fluid particles in the bottom layer is not more than the half-width of the solitary wave. 1. Carr, M., and Davies, P.A. The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Phys. Fluids, 2006, vol. 18, No. 1, 1 - 10. 2. Thiem, O., Carr, M., Berntsen, J., and Davies, P.A. Numerical simulation of internal solitary wave-induced reverse flow and associated vortices in a shallow, two-layer fluid benthic boundary layer. Ocean Dynamics, 2011, vol. 61, No. 6, 857 - 872.

Experimental study of strong nonlinear-optics effects in liquid crystals

NASA Astrophysics Data System (ADS)

Darbin, S. D.; Arakelyan, S. M.; Cheung, M. M.; Shen, Y. R.

1984-07-01

Nonlinear optical effects that arise in nematic liquid crystals as a result of a change in the index of refraction induced by a laser field are considered. Since the resultant nonlinearity is extremely high, the approximation of perturbation theory cannot be used in calculations. However, the change in refractive index results mainly in phase advance as waves propagate through a thin film of liquid crystal, while the change of intensity is significant. Moreover, if there is no change in polarization of the pumping field, calculations are relatively simple. An investigation is made of the propagation of a cross sectionally bounded laser beam through a homeotropically oriented liquid crystal, giving rise to spatial phase modulation of emission. When the intensity of the laser beam exceeds a certain value, a system of aberation rings is observed in the output radiation. Effects of dynamic self-diffraction accompanying degenerate four-wave mixing when a change in refractive index is induced in a homeotropic liquid crystal film, and optical bistability in a nonlinear Fabry-Perot optical cavity, as well as generation of a self-oscillatory state in such a resonator are discussed.

Current induced multi-mode propagating spin waves in a spin transfer torque nano-contact with strong perpendicular magnetic anisotropy

NASA Astrophysics Data System (ADS)

Mohseni, S. Morteza; Yazdi, H. F.; Hamdi, M.; Brächer, T.; Mohseni, S. Majid

2018-03-01

Current induced spin wave excitations in spin transfer torque nano-contacts are known as a promising way to generate exchange-dominated spin waves at the nano-scale. It has been shown that when these systems are magnetized in the film plane, broken spatial symmetry of the field around the nano-contact induced by the Oersted field opens the possibility for spin wave mode co-existence including a non-linear self-localized spin-wave bullet and a propagating mode. By means of micromagnetic simulations, here we show that in systems with strong perpendicular magnetic anisotropy (PMA) in the free layer, two propagating spin wave modes with different frequency and spatial distribution can be excited simultaneously. Our results indicate that in-plane magnetized spin transfer nano-contacts in PMA materials do not host a solitonic self-localized spin-wave bullet, which is different from previous studies for systems with in plane magnetic anisotropy. This feature renders them interesting for nano-scale magnonic waveguides and crystals since magnon transport can be configured by tuning the applied current.

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.

Study of dispersive and nonlinear effects of coastal wave dynamics with a fully nonlinear potential flow model

NASA Astrophysics Data System (ADS)

Benoit, Michel; Yates, Marissa L.; Raoult, Cécile

2017-04-01

Efficient and accurate numerical models simulating wave propagation are required for a variety of engineering projects including the evaluation of coastal risks, the design of protective coastal structures, and the estimation of the potential for marine renewable energy devices. Nonlinear and dispersive effects are particularly significant in the coastal zone where waves interact with the bottom, the shoreline, and coastal structures. The main challenge in developing a numerical models is finding a compromise between computational efficiency and the required accuracy of the simulated wave field. Here, a potential approach is selected and the (fully nonlinear) water wave problem is formulated using the Euler-Zakharov equations (Zakharov, 1968) describing the temporal evolution of the free surface elevation and velocity potential. The proposed model (Yates and Benoit, 2015) uses a spectral approach in the vertical (i.e. the vertical variation of the potential is approximated by a linear combination of the first NT+1 Chebyshev polynomials, following the work of Tian and Sato (2008)). The Zakharov equations are integrated in time using a fourth-order Runge-Kutta scheme with a constant time step. At each sub-timestep, the Laplace Boundary Value Problem (BVP) is solved to estimate the free surface vertical velocity using the spectral approach, with typical values of NT between 5 to 8 for practical applications. The 1DH version of the code is validated with comparisons to the experimental data set of Becq-Girard et al. (1999), which studied the propagation of irregular waves over a beach profile with a submerged bar. The nonlinear and dispersive capacities of the model are verified with the correct representation of wave-wave interactions, in particular the transfer of energy between different harmonic components during wave propagation (analysis of the transformation of the variance spectrum along the channel). Evolution of wave skewness, asymmetry and kurtosis along the bathymetric profile also compare well with the measured values. The statistical distributions of the free surface elevation and wave height, calculated from the simulated time series, are compared to those of the measurements, with particular attention paid to the extreme waves. To use this model for realistic cases with complex bathymetric variations and multidirectional wave fields, the model has been extended to two horizontal dimensions (2DH). The spectral approach in the vertical dimension is retained, while the horizontal plane is discretized with scattered nodes to maintain the model's flexibility. The horizontal derivatives are estimated with finite-difference type formulas using Radial Basis Functions (Wright and Fornberg, 2006). The 2DH version of the code is applied to simulate the propagation of regular waves over a semi-circular step, which acts as a focusing lens. The simulation results are compared to the experimental data set of Whalin (1971). The evolution of the higher harmonic amplitudes in the shallow-water zone demonstrates the ability of the model to simulate wave propagation over complex 2DH coastal bathymetries. References: Becq-Girard F., Forget P., Benoit M. (1999) Non-linear propagation of unidirectional wave fields over varying topography. Coastal Eng., 38, 91-113. Tian Y., Sato S. (2008) A numerical model on the interaction between nearshore nonlinear waves and strong currents. Coast. Eng. Journal, 50(4), 369-395. Whalin R.W. (1971) The limit of applicability of linear wave refraction theory in a convergence zone. Technical report, DTIC Documents. Wright G.B., Fornberg B. (2006) Scattered node compact finite difference-type formulas generated from radial basis functions. J. Comp. Phys., 212, 99-123. Yates M.L., Benoit M. (2015) Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves. Int. J. Numer. Meth. Fluids, 77, 616-640. Zakharov V.E. (1968) Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys., 9(2), 190-194.

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.

Spiral waves in driven dusty plasma medium: Generalized hydrodynamic fluid description

NASA Astrophysics Data System (ADS)

Kumar, Sandeep; Patel, Bhavesh; Das, Amita

2018-04-01

Spiral waves are observed in many natural phenomena. They have been extensively represented by the mathematical FitzHugh-Nagumo model [Barkley et al., Phys. Rev. A 42, 2489 (1990)] of excitable media. Also, in incompressible fluid simulations, the excitation of thermal spiral waves has been reported by Li et al. [Phys. of Fluids 22, 011701 (2010)]. In the present paper, the spatiotemporal development of spiral waves in the context of weak and strong coupling limits has been shown. While the weakly coupled medium has been represented by a simple fluid description, for strong coupling, a generalized visco-elastic fluid description has been employed. The medium has been driven by an external force in the form of a rotating electric field. It is shown that when the amplitude of force is small, the density perturbations in the medium are also small. In this case, the excitations do not develop as a spiral wave. Only when the amplitude of force is high so as to drive the density perturbations to nonlinear amplitudes does the spiral density wave formation occurs. The role of the forcing frequency and the effect of strong coupling and the sound velocity of medium in the formation and evolution of spiral waves have been investigated in detail.

Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light

NASA Astrophysics Data System (ADS)

Turnbull, M. T.; Petrov, P. G.; Embrey, C. S.; Marino, A. M.; Boyer, V.

2013-09-01

Nondegenerate forward four-wave mixing in hot atomic vapors has been shown to produce strong quantum correlations between twin beams of light [McCormick , Opt. Lett.OPLEDP0146-959210.1364/OL.32.000178 32, 178 (2007)], in a configuration which minimizes losses by absorption. In this paper, we look at the role of the phase-matching condition in the trade-off that occurs between the efficiency of the nonlinear process and the absorption of the twin beams. To this effect, we develop a semiclassical model by deriving the atomic susceptibilities in the relevant double-Λ configuration and by solving the classical propagation of the twin-beam fields for parameters close to those found in typical experiments. These theoretical results are confirmed by a simple experimental study of the nonlinear gain experienced by the twin beams as a function of the phase mismatch. The model shows that the amount of phase mismatch is key to the realization of the physical conditions in which the absorption of the twin beams is minimized while the cross coupling between the twin beams is maintained at the level required for the generation of strong quantum correlations. The optimum is reached when the four-wave mixing process is not phase matched for fully resonant four-wave mixing.

Dust acoustic solitary and shock excitations in a Thomas-Fermi magnetoplasma

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

Rahim, Z.; Qamar, A.; National Center for Physics

The linear and nonlinear properties of dust-acoustic waves are investigated in a collisionless Thomas-Fermi magnetoplasma, whose constituents are electrons, ions, and negatively charged dust particles. At dust time scale, the electron and ion number densities follow the Thomas-Fermi distribution, whereas the dust component is described by the classical fluid equations. A linear dispersion relation is analyzed to show that the wave frequencies associated with the upper and lower modes are enhanced with the variation of dust concentration. The effect of the latter is seen more strongly on the upper mode as compared to the lower mode. For nonlinear analysis, wemore » obtain magnetized Korteweg-de Vries (KdV) and Zakharov-Kuznetsov (ZK) equations involving the dust-acoustic solitary waves in the framework of reductive perturbation technique. Furthermore, the shock wave excitations are also studied by allowing dissipation effects in the model, leading to the Korteweg-de Vries-Burgers (KdVB) and ZKB equations. The analysis reveals that the dust-acoustic solitary and shock excitations in a Thomas-Fermi plasma are strongly influenced by the plasma parameters, e.g., dust concentration, dust temperature, obliqueness, magnetic field strength, and dust fluid viscosity. The present results should be important for understanding the solitary and shock excitations in the environments of white dwarfs or supernova, where dust particles can exist.« less

Book review: Modern Plasma Physics, Vol. I: Physical Kinetics of Turbulent Plasmas, by Patrick H. Diamond, Sanae-I. Itoh and Kimitaka Itoh, Cambridge University Press, Cambridge (UK), 2010, IX, 417 p., ISBN 978-0-521-86920-1 (Hardback)

NASA Astrophysics Data System (ADS)

Somov, B. V.

If you want to learn not only the most fundamental things about the physics of turbulent plasmas but also the current state of the problem including the most recent results in theoretical and experimental investigations - and certainly many physicists and astrophysicists do - this series of three excellent monographs is just for you. The first volume "Physical Kinetics of Turbulent Plasmas" develops the kinetic theory of turbulence through a focus on quasi-particle models and dynamics. It discusses the concepts and theoretical methods for describing weak and strong fluid and phase space turbulence in plasma systems far from equilibrium. The core material includes fluctuation theory, self-similar cascades and transport, mean field theory, resonance broadening and nonlinear wave-particle interaction, wave-wave interaction and wave turbulence, strong turbulence theory and renormalization. The book gives readers a deep understanding of the fields under consideration and builds a foundation for future applications to multi-scale processes of self-organization in tokamaks and other confined plasmas. In spite of a short pedagogical introduction, the book is addressed mainly to well prepared readers with a serious background in plasma physics, to researchers and advanced graduate students in nonlinear plasma physics, controlled fusions and related fields such as cosmic plasma physics

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.

Kinetic effects on Alfven wave nonlinearity. II - The modified nonlinear wave equation

NASA Technical Reports Server (NTRS)

Spangler, Steven R.

1990-01-01

A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.

Generation of intermittent gravitocapillary waves via parametric forcing

NASA Astrophysics Data System (ADS)

Castillo, Gustavo; Falcón, Claudio

2018-04-01

We report on the generation of an intermittent wave field driven by a horizontally moving wave maker interacting with Faraday waves. The spectrum of the local gravitocapillary surface wave fluctuations displays a power law in frequency for a wide range of forcing parameters. We compute the probability density function of the local surface height increments, which show that they change strongly across time scales. The structure functions of these increments are shown to display power laws as a function of the time lag, with exponents that are nonlinear functions of the order of the structure function. We argue that the origin of this scale-invariant intermittent spectrum is the Faraday wave pattern breakup due to its advection by the propagating gravity waves. Finally, some interpretations are proposed to explain the appearance of this intermittent spectrum.

Pondermotive versus mirror force in creation of the filamentary cavities in auroral plasma

NASA Technical Reports Server (NTRS)

Singh, Nagendra

1994-01-01

Recently rocket observations on spikelets of lower-hybrid waves along with strong density cavities and transversely heated ions were reported. The observed thin filamentary cavities oriented along the magnetic field in the auroral plasma have density depletions up to several tens of percent. These observations have been interpreted in terms of a theory for lower-hybrid wave condensation and collapse. The modulational instability leading to the wave consensation of the lower-hybrid waves yields only weak density perturbations, which cannot explain the above strong density depletions. The wave collapse theory is based on the nonlinear pondermotive force in a homogeneous ambient plasma and the density depletion is determined by the balance between the wave pressure (pondermotive force) and the plasma pressure. In the auroral plasma, the balance is achieved in a time tau(sub wc) equal to or less than 1 ms. It is shown here that the mirror force, acting on the transversely heated ions at a relatively long time scale, is an effective mechanism for creating the strong plasma cavities. We suggest that the process of wave condensation, through the pondermotive force causing generation of short wavelength waves from relatively long wavelength waves, is a dominant process until the former waves evolve and become effective in the transverse heating of ions. As soon as this happens, mirror force on ions becomes an important factor in the creation of the density cavities, which may further trap and enhance the waves. Results from a model of cavity formation by transverse ion heating show that the observed depletions in the density cavities can be produced by the heating rates determined by the observed wave amplitudes near the lower-hybrid frequency. It is found that the creation of a strong density cavity takes a few minutes.

Controllable optical rogue waves via nonlinearity management.

PubMed

Yang, Zhengping; Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi

2018-03-19

Using a similarity transformation, we obtain analytical solutions to a class of nonlinear Schrödinger (NLS) equations with variable coefficients in inhomogeneous Kerr media, which are related to the optical rogue waves of the standard NLS equation. We discuss the dynamics of such optical rogue waves via nonlinearity management, i.e., by selecting the appropriate nonlinearity coefficients and integration constants, and presenting the solutions. In addition, we investigate higher-order rogue waves by suitably adjusting the nonlinearity coefficient and the rogue wave parameters, which could help in realizing complex but controllable optical rogue waves in properly engineered fibers and other photonic materials.

Theory of multinonlinear media and its application to the soliton processes in ferrite–ferroelectric structures

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

Cherkasskii, M. A., E-mail: macherkasskii@hotmail.com; Nikitin, A. A.; Kalinikos, B. A.

A theory is developed to describe the wave processes that occur in waveguide media having several types of nonlinearity, specifically, multinonlinear media. It is shown that the nonlinear Schrödinger equation can be used to describe the general wave process that occurs in such media. The competition between the electric wave nonlinearity and the magnetic wave nonlinearity in a layered multinonlinear ferrite–ferroelectric structure is found to change a total repulsive nonlinearity into a total attractive nonlinearity.

Study of nonlinear electron-acoustic solitary and shock waves in a dissipative, nonplanar space plasma with superthermal hot electrons

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

Han, Jiu-Ning, E-mail: hanjiuning@126.com; He, Yong-Lin; Luo, Jun-Hua

2014-01-15

With the consideration of the superthermal electron distribution, we present a theoretical investigation about the nonlinear propagation of electron-acoustic solitary and shock waves in a dissipative, nonplanar non-Maxwellian plasma comprised of cold electrons, superthermal hot electrons, and stationary ions. The reductive perturbation technique is used to obtain a modified Korteweg-de Vries Burgers equation for nonlinear waves in this plasma. We discuss the effects of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision between planar solitary waves. It is found that these parameters have significantmore » effects on the properties of nonlinear waves and collision-induced nonlinear structure.« less

Toward Active Control of Noise from Hot Supersonic Jets

DTIC Science & Technology

2012-02-15

bears little relevance to practical systems of engineering interest. However, the high Mach number does ensure the formation of strong Mach waves which...waveforms of the experiment and the linear and nonlinear numerical predictions. 5Tam, C. K. W., Viswanathan, K., Ahuja, K. K., and Panda , J., "The

Kolakoski sequence as an element to radiate giant forward and backward second harmonic signals

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

Parvini, T. S.; Tehranchi, M. M., E-mail: m-hamidi@sbu.ac.ir, E-mail: teranchi@sbu.ac.ir; Laser and Plasma Research Institute, Shahid Beheshti University, Tehran

2015-11-14

We propose a novel type of aperiodic one-dimensional photonic crystal structures which can be used for generating giant forward and backward second harmonic signals. The studied structure is formed by stacking together the air and nonlinear layers according to the Kolakoski self-generation scheme in which each nonlinear layer contains a pair of antiparallel 180° poled LiNbO{sub 3} crystal layers. For different generation stages of the structure, conversion efficiencies of forward and backward second harmonic waves have been calculated by nonlinear transfer matrix method. Numerical simulations show that conversion efficiencies in the Kolakoski-based multilayer are larger than the perfect ones formore » at least one order of magnitude. Especially for 33rd and 39th generation stages, forward second harmonic wave are 42 and 19 times larger, respectively. In this paper, we validate the strong fundamental field enhancement and localization within Kolakoski-based multilayer due to periodicity breaking which consequently leads to very strong radiation of backward and forward second harmonic signals. Following the applications of analogous aperiodic structures, we expect that Kolakosi-based multilayer can play a role in optical parametric devices such as multicolor second harmonic generators with high efficiency.« less

Efficient nonlinear metasurface based on nonplanar plasmonic nanocavities

DOE PAGES

Wang, Feng; Martinson, Alex B. F.; Harutyunyan, Hayk

2017-04-03

Since their discovery in the 1960s, nonlinear optical effects have revolutionized optical technologies and laser industry. Development of efficient nanoscale nonlinear sources will pave the way for new applications in photonic circuitry, quantum optics and biosensing. However, nonlinear signal generation at dimensions smaller than the wavelength of light brings new challenges. The fundamental difficulty of designing an efficient nonlinear source is that some of the contributing factors involved in nonlinear wave-mixing at the nanoscale are often hard to satisfy simultaneously. Here, we overcome these limitations by developing a new type of nonplanar plasmonic metasurfaces, which can greatly enhance the secondmore » harmonic generation (SHG) at visible frequencies and achieve conversion efficiency of ~6 × 10 -5 at a peak pump intensity of ~0.5 GW/cm 2. This is 4-5 orders of magnitude larger than the efficiencies observed for nonlinear thin films and doubly resonant plasmonic antennas. The proposed metasurface consists of an array of metal-dielectric-metal (MDM) nanocavities formed by conformally cross-linked nanowires separated by an ultrathin nonlinear material layer. The nonplanar MDM geometry minimizes the destructive interference of nonlinear emission into the far-field, provides strongly enhanced independently tunable resonances both for fundamental and harmonic frequencies, a good mutual overlap of the modes and a strong interaction with the nonlinear spacer. Lastly, our findings enable the development of efficient nanoscale single photon sources, integrated frequency converters, and other nonlinear devices.« less

Rossby and drift wave turbulence and zonal flows: The Charney-Hasegawa-Mima model and its extensions

NASA Astrophysics Data System (ADS)

Connaughton, Colm; Nazarenko, Sergey; Quinn, Brenda

2015-12-01

A detailed study of the Charney-Hasegawa-Mima model and its extensions is presented. These simple nonlinear partial differential equations suggested for both Rossby waves in the atmosphere and drift waves in a magnetically-confined plasma, exhibit some remarkable and nontrivial properties, which in their qualitative form, survive in more realistic and complicated models. As such, they form a conceptual basis for understanding the turbulence and zonal flow dynamics in real plasma and geophysical systems. Two idealised scenarios of generation of zonal flows by small-scale turbulence are explored: a modulational instability and turbulent cascades. A detailed study of the generation of zonal flows by the modulational instability reveals that the dynamics of this zonal flow generation mechanism differ widely depending on the initial degree of nonlinearity. The jets in the strongly nonlinear case further roll up into vortex streets and saturate, while for the weaker nonlinearities, the growth of the unstable mode reverses and the system oscillates between a dominant jet, which is slightly inclined to the zonal direction, and a dominant primary wave. A numerical proof is provided for the extra invariant in Rossby and drift wave turbulence-zonostrophy. While the theoretical derivations of this invariant stem from the wave kinetic equation which assumes weak wave amplitudes, it is shown to be relatively well-conserved for higher nonlinearities also. Together with the energy and enstrophy, these three invariants cascade into anisotropic sectors in the k-space as predicted by the Fjørtoft argument. The cascades are characterised by the zonostrophy pushing the energy to the zonal scales. A small scale instability forcing applied to the model has demonstrated the well-known drift wave-zonal flow feedback loop. The drift wave turbulence is generated from this primary instability. The zonal flows are then excited by either one of the generation mechanisms, extracting energy from the drift waves as they grow. Eventually the turbulence is completely suppressed and the zonal flows saturate. The turbulence spectrum is shown to diffuse in a manner which has been mathematically predicted. The insights gained from this simple model could provide a basis for equivalent studies in more sophisticated plasma and geophysical fluid dynamics models in an effort to fully understand the zonal flow generation, the turbulent transport suppression and the zonal flow saturation processes in both the plasma and geophysical contexts as well as other wave and turbulence systems where order evolves from chaos.

Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: Exact solutions and stability.

PubMed

Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A

2016-12-01

An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.

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.

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.

A novel method for predicting the power outputs of wave energy converters

NASA Astrophysics Data System (ADS)

Wang, Yingguang

2018-03-01

This paper focuses on realistically predicting the power outputs of wave energy converters operating in shallow water nonlinear waves. A heaving two-body point absorber is utilized as a specific calculation example, and the generated power of the point absorber has been predicted by using a novel method (a nonlinear simulation method) that incorporates a second order random wave model into a nonlinear dynamic filter. It is demonstrated that the second order random wave model in this article can be utilized to generate irregular waves with realistic crest-trough asymmetries, and consequently, more accurate generated power can be predicted by subsequently solving the nonlinear dynamic filter equation with the nonlinearly simulated second order waves as inputs. The research findings demonstrate that the novel nonlinear simulation method in this article can be utilized as a robust tool for ocean engineers in their design, analysis and optimization of wave energy converters.

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.

Nonlinear terahertz devices utilizing semiconducting plasmonic metamaterials

DOE PAGES

Seren, Huseyin R.; Zhang, Jingdi; Keiser, George R.; ...

2016-01-26

The development of responsive metamaterials has enabled the realization of compact tunable photonic devices capable of manipulating the amplitude, polarization, wave vector and frequency of light. Integration of semiconductors into the active regions of metallic resonators is a proven approach for creating nonlinear metamaterials through optoelectronic control of the semiconductor carrier density. Metal-free subwavelength resonant semiconductor structures offer an alternative approach to create dynamic metamaterials. We present InAs plasmonic disk arrays as a viable resonant metamaterial at terahertz frequencies. Importantly, InAs plasmonic disks exhibit a strong nonlinear response arising from electric field-induced intervalley scattering, resulting in a reduced carrier mobilitymore » thereby damping the plasmonic response. here, we demonstrate nonlinear perfect absorbers configured as either optical limiters or saturable absorbers, including flexible nonlinear absorbers achieved by transferring the disks to polyimide films. Nonlinear plasmonic metamaterials show potential for use in ultrafast terahertz (THz) optics and for passive protection of sensitive electromagnetic devices.« less

Nonlinear terahertz devices utilizing semiconducting plasmonic metamaterials

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

Seren, Huseyin R.; Zhang, Jingdi; Keiser, George R.

The development of responsive metamaterials has enabled the realization of compact tunable photonic devices capable of manipulating the amplitude, polarization, wave vector and frequency of light. Integration of semiconductors into the active regions of metallic resonators is a proven approach for creating nonlinear metamaterials through optoelectronic control of the semiconductor carrier density. Metal-free subwavelength resonant semiconductor structures offer an alternative approach to create dynamic metamaterials. We present InAs plasmonic disk arrays as a viable resonant metamaterial at terahertz frequencies. Importantly, InAs plasmonic disks exhibit a strong nonlinear response arising from electric field-induced intervalley scattering, resulting in a reduced carrier mobilitymore » thereby damping the plasmonic response. here, we demonstrate nonlinear perfect absorbers configured as either optical limiters or saturable absorbers, including flexible nonlinear absorbers achieved by transferring the disks to polyimide films. Nonlinear plasmonic metamaterials show potential for use in ultrafast terahertz (THz) optics and for passive protection of sensitive electromagnetic devices.« less

Newtonian self-gravitation in the neutral meson system

NASA Astrophysics Data System (ADS)

Großardt, André; Hiesmayr, Beatrix C.

2015-03-01

We derive the effect of the Schrödinger-Newton equation, which can be considered as a nonrelativistic limit of classical gravity, for a composite quantum system in the regime of high energies. Such meson-antimeson systems exhibit very unique properties, e.g., distinct masses due to strong and electroweak interactions. This raises an immediate question: what does one mean by mass in gravity for a state that is a superposition of mass eigenstates due to strong and electroweak interactions? We find conceptually different physical scenarios due to lacking of a clear physical guiding principle to explain which mass is the relevant one and due to the fact that it is not clear how the flavor wave function relates to the spatial wave function. There seems to be no principal contradiction. However, a nonlinear extension of the Schrödinger equation in this manner strongly depends on the relation between the flavor wave function and spatial wave function and its particular shape. In opposition to the continuous spontaneous localization collapse models we find a change in the oscillating behavior and not in the damping of the flavor oscillation.

Theoretical analysis of rotating two phase detonation in a rocket motor

NASA Technical Reports Server (NTRS)

Shen, I.; Adamson, T. C., Jr.

1973-01-01

Tangential mode, non-linear wave motion in a liquid propellant rocket engine is studied, using a two phase detonation wave as the reaction model. Because the detonation wave is followed immediately by expansion waves, due to the side relief in the axial direction, it is a Chapman-Jouguet wave. The strength of this wave, which may be characterized by the pressure ratio across the wave, as well as the wave speed and the local wave Mach number, are related to design parameters such as the contraction ratio, chamber speed of sound, chamber diameter, propellant injection density and velocity, and the specific heat ratio of the burned gases. In addition, the distribution of flow properties along the injector face can be computed. Numerical calculations show favorable comparison with experimental findings. Finally, the effects of drop size are discussed and a simple criterion is found to set the lower limit of validity of this strong wave analysis.

Helicon mode formation and radio frequency power deposition in a helicon-produced plasma

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

Niemi, K.; Kraemer, M.

2008-07-15

Time- and space-resolved magnetic (B-dot) probe measurements in combination with measurements of the plasma parameters were carried out to investigate the relationship between the formation and propagation of helicon modes and the radio frequency (rf) power deposition in the core of a helicon plasma. The Poynting flux and the absorbed power density are deduced from the measured rf magnetic field distribution in amplitude and phase. Special attention is devoted to the helicon absorption under linear and nonlinear conditions. The present investigations are attached to recent observations in which the nonlinear nature of the helicon wave absorption has been demonstrated bymore » showing that the strong absorption of helicon waves is correlated with parametric excitation of electrostatic fluctuations.« less

Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium

PubMed Central

Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying

2015-01-01

A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066

From Discrete Breathers to Many Body Localization and Flatbands

NASA Astrophysics Data System (ADS)

Flach, Sergej

Discrete breathers (DB) and intrinsic localized modes (ILM) are synonymic dynamical states on nonlinear lattices - periodic in time and localized in space, and widely observed in many applications. I will discuss the connections between DBs and many-body localization (MBL) and the properties of DBs on flatband networks. A dense quantized gas of strongly excited DBs can lead to a MBL phase in a variety of different lattice models. Its classical counterpart corresponds to a 'nonergodic metal' in the MBL language, or to a nonGibbsean selftrapped state in the language of nonlinear dynamics. Flatband networks are lattices with small amplitude waves exhibiting macroscopic degeneracy in their band structure due to local symmetries, destructive interference, compact localized eigenstates and horizontal flat bands. DBs can preserve the compactness of localization in the presence of nonlinearity with properly tuned internal phase relationships, making them promising tools for control of the phase coherence of waves. Also at New Zealand Institute of Advanced Study, Massey University, Auckland, New Zealand.

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.

Simulating energy cascade of shock wave formation process in a resonator by gas kinetic scheme

NASA Astrophysics Data System (ADS)

Qu, Chengwu; Zhang, Xiaoqing; Feng, Heying

2017-12-01

The temporal-spatial evolution of gas oscillation was simulated by gas kinetic scheme (GKS) in a cylindrical resonator, driven by a piston at one end and rigidly closed at the other end. Periodic shock waves propagating back and forth were observed in the resonator under finite amplitude of gas oscillation. The studied results demonstrated that the acoustic pressure is a saw-tooth waveform and the oscillatory velocity is a square waveform at the central position of the resonant tube. Moreover, it was found by harmonic analysis that there was no presence of obvious feature for pressure node in such a typical standing wave resonator, and the distribution of acoustic fields displayed a one-dimensional feature for the acoustic pressure while a quasi-one-dimensional form for oscillatory velocity, which demonstrated the nonlinear effects. The simulation results for axial distribution of acoustic intensity showed a good consistency with the published experimental data in the open literature domain, which provides a verification for the effectiveness of the GKS model proposed. The influence of displacement amplitude of the driving piston on the formation of shock wave was numerically investigated, and the simulated results revealed the cascade process of harmonic wave energy from the fundamental wave to higher harmonics. In addition, this study found that the acoustic intensity at the driving end of the resonant tube would increase linearly with the displacement amplitude of the piston due to nonlinear effects, rather than the exponential variation by linear theory. This research demonstrates that the GKS model is strongly capable of simulating nonlinear acoustic problems.

An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

NASA Astrophysics Data System (ADS)

Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei

2016-07-01

Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

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.

Experimental investigation of material nonlinearity using the Rayleigh surface waves excited and detected by angle beam wedge transducers.

PubMed

Zhang, Shuzeng; Li, Xiongbing; Jeong, Hyunjo; Hu, Hongwei

2018-05-12

Angle beam wedge transducers are widely used in nonlinear Rayleigh wave experiments as they can generate Rayleigh wave easily and produce high intensity nonlinear waves for detection. When such a transducer is used, the spurious harmonics (source nonlinearity) and wave diffraction may occur and will affect the measurement results, so it is essential to fully understand its acoustic nature. This paper experimentally investigates the nonlinear Rayleigh wave beam fields generated and received by angle beam wedge transducers, in which the theoretical predictions are based on the acoustic model developed previously for angle beam wedge transducers [S. Zhang, et al., Wave Motion, 67, 141-159, (2016)]. The source of the spurious harmonics is fully characterized by scrutinizing the nonlinear Rayleigh wave behavior in various materials with different driving voltages. Furthermore, it is shown that the attenuation coefficients for both fundamental and second harmonic Rayleigh waves can be extracted by comparing the measurements with the predictions when the experiments are conducted at many locations along the propagation path. A technique is developed to evaluate the material nonlinearity by making appropriate corrections for source nonlinearity, diffraction and attenuation. The nonlinear parameters of three aluminum alloy specimens - Al 2024, Al 6061 and Al 7075 - are measured, and the results indicate that the measurement results can be significantly improved using the proposed method. Copyright © 2018. Published by Elsevier B.V.

Cubic nonlinearity in shear wave beams with different polarizations

PubMed Central

Wochner, Mark S.; Hamilton, Mark F.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.

2008-01-01

A coupled pair of nonlinear parabolic equations is derived for the two components of the particle motion perpendicular to the axis of a shear wave beam in an isotropic elastic medium. The equations account for both quadratic and cubic nonlinearity. The present paper investigates, analytically and numerically, effects of cubic nonlinearity in shear wave beams for several polarizations: linear, elliptical, circular, and azimuthal. Comparisons are made with effects of quadratic nonlinearity in compressional wave beams. PMID:18529167

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

NASA Astrophysics Data System (ADS)

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

2008-05-01

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

Multifluid Theory of Solitons

NASA Astrophysics Data System (ADS)

Verheest, Frank

2008-03-01

After introducing the basic multifluid model equations, this review discusses three different methods to describe nonlinear plasma waves, by giving a rather general overview of the relevant methodology, followed by a specific and recent application. First, reductive perturbation analysis is applicable to waves that are not too strongly nonlinear, if their linear counterparts have an acoustic-like dispersion at low frequencies. It is discussed for electrostatic modes, with a brief application to dusty plasma waves. The typical paradigm for such problems is the well known KdV equation and its siblings. Stationary waves with larger amplitudes can be treated, i.a., via the fluid-dynamic approach pioneered by McKenzie, which focuses on essential insights into the limitations that restrict the range of available solitary electrostatic solutions. As an illustration, novel electrostatic solutions have been found in plasmas with two-temperature electron species that are relevant in understanding certain magnetospheric plasma observations. The older cousin of the large-amplitude technique is the Sagdeev pseudopotential description, to which the newer fluid-dynamic approach is essentially equivalent. Because the Sagdeev analysis has mostly been applied to electrostatic waves, some recent results are given for electromagnetic modes in pair plasmas, to show its versatility.

Nonlinear dead water resistance at subcritical speed

NASA Astrophysics Data System (ADS)

Grue, John

2015-08-01

The dead water resistance F 1 = /1 2 C d w ρ S U 2 (ρ fluid density, U ship speed, S wetted body surface, Cdw resistance coefficient) on a ship moving at subcritical speed along the upper layer of a two-layer fluid is calculated by a strongly nonlinear method assuming potential flow in each layer. The ship dimensions correspond to those of the Polar ship Fram. The ship draught, b0, is varied in the range 0.25h0-0.9h0 (h0 the upper layer depth). The calculations show that Cdw/(b0/h0)2 depends on the Froude number only, in the range close to critical speed, Fr = U/c0 ˜ 0.875-1.125 (c0 the linear internal long wave speed), irrespective of the ship draught. The function Cdw/(b0/h0)2 attains a maximum at subcritical Froude number depending on the draught. Maximum Cdw/(b0/h0)2 becomes 0.15 for Fr = 0.76, b0/h0 = 0.9, and 0.16 for Fr = 0.74, b0/h0 = 1, where the latter extrapolated value of the dead water resistance coefficient is about 60 times higher than the frictional drag coefficient and relevant for the historical dead water observations. The nonlinear Cdw significantly exceeds linear theory (Fr < 0.85). The ship generated waves have a wave height comparable to the upper layer depth. Calculations of three-dimensional wave patterns at critical speed compare well to available laboratory experiments. Upstream solitary waves are generated in a wave tank of finite width, when the layer depths differ, causing an oscillation of the force. In a wide ocean, a very wide wave system develops at critical speed. The force approaches a constant value for increasing time.

Radiative corrections to the Coulomb law and model of dense quantum plasmas: Dispersion of longitudinal waves in magnetized quantum plasmas

NASA Astrophysics Data System (ADS)

Andreev, Pavel A.

2018-04-01

Two kinds of quantum electrodynamic radiative corrections to electromagnetic interactions and their influence on the properties of highly dense quantum plasmas are considered. Linear radiative correction to the Coulomb interaction is considered. Its contribution in the spectrum of the Langmuir waves is presented. The second kind of radiative corrections are related to the nonlinearity of the Maxwell equations for the strong electromagnetic field. Their contribution in the spectrum of transverse waves of magnetized plasmas is briefly discussed. At the consideration of the Langmuir wave spectrum, we included the effect of different distributions of the spin-up and spin-down electrons revealing in the Fermi pressure shift.

Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves

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

Shestov, S. V.; Nakariakov, V. M.; Ulyanov, A. S.

2017-05-10

We analyze nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low- β plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform a numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, which constitutes a bulk plasma motion along the magnetic field, the tube wave, andmore » also transverse flows in the radial direction, associated with sausage fast magnetoacoustic modes. In addition, the nonlinear torsional wave steepens and its propagation speed increases. The latter effect leads to the progressive distortion of the torsional wave front, i.e., nonlinear phase mixing. Because of the intrinsic non-uniformity of the torsional wave amplitude across the tube radius, the nonlinear effects are more pronounced in regions with higher wave amplitudes. They are always absent at the axes of the flux tube. In the case of a linear radial profile of the wave amplitude, the nonlinear effects are localized in an annulus region near the tube boundary. Thus, the parallel compressive flows driven by torsional Alfvén waves in the solar and stellar coronae, are essentially non-uniform in the perpendicular direction. The presence of additional sinks for the wave energy reduces the efficiency of the nonlinear parallel cascade in torsional Alfvén waves.« less

Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves

NASA Astrophysics Data System (ADS)

Shestov, S. V.; Nakariakov, V. M.; Ulyanov, A. S.; Reva, A. A.; Kuzin, S. V.

2017-05-01

We analyze nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low-β plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform a numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, which constitutes a bulk plasma motion along the magnetic field, the tube wave, and also transverse flows in the radial direction, associated with sausage fast magnetoacoustic modes. In addition, the nonlinear torsional wave steepens and its propagation speed increases. The latter effect leads to the progressive distortion of the torsional wave front, I.e., nonlinear phase mixing. Because of the intrinsic non-uniformity of the torsional wave amplitude across the tube radius, the nonlinear effects are more pronounced in regions with higher wave amplitudes. They are always absent at the axes of the flux tube. In the case of a linear radial profile of the wave amplitude, the nonlinear effects are localized in an annulus region near the tube boundary. Thus, the parallel compressive flows driven by torsional Alfvén waves in the solar and stellar coronae, are essentially non-uniform in the perpendicular direction. The presence of additional sinks for the wave energy reduces the efficiency of the nonlinear parallel cascade in torsional Alfvén waves.

Asymmetric nonlinear system is not sufficient for a nonreciprocal wave diode

NASA Astrophysics Data System (ADS)

Wu, Gaomin; Long, Yang; Ren, Jie

2018-05-01

We demonstrate symmetric wave propagations in asymmetric nonlinear systems. By solving the nonlinear Schördinger equation, we first analytically prove the existence of symmetric transmission in asymmetric systems with a single nonlinear delta-function interface. We then point out that a finite width of the nonlinear interface region is necessary to produce nonreciprocity in asymmetric systems. However, a geometrical resonant condition for breaking nonreciprocal propagation is then identified theoretically and verified numerically. With such a resonant condition, the nonlinear interface region of finite width behaves like a single nonlinear delta-barrier so that wave propagations in the forward and backward directions are identical under arbitrary incident wave intensity. As such, reciprocity reemerges periodically in the asymmetric nonlinear system when changing the width of interface region. Finally, similar resonant conditions of discrete nonlinear Schördinger equation are discussed. Therefore, we have identified instances of reciprocity that breaking spatial symmetry in nonlinear interface systems is not sufficient to produce nonreciprocal wave propagation.

Book review: Nonlinear ocean waves and the inverse scattering transform

USGS Publications Warehouse

Geist, Eric L.

2011-01-01

Nonlinear Ocean Waves and the Inverse Scattering Transform is a comprehensive examination of ocean waves built upon the theory of nonlinear Fourier analysis. The renowned author, Alfred R. Osborne, is perhaps best known for the discovery of internal solitons in the Andaman Sea during the 1970s. In this book, he provides an extensive treatment of nonlinear water waves based on a nonlinear spectral theory known as the inverse scattering transform. The writing is exceptional throughout the book, which is particularly useful in explaining some of the more difficult mathematical concepts.  Review info: Nonlinear Ocean Waves and the Inverse Scattering Transform. By Alfred R. Osborne, 2010. ISBN: 978-125286299, 917 pp.

Observationally constrained modeling of sound in curved ocean internal waves: examination of deep ducting and surface ducting at short range.

PubMed

Duda, Timothy F; Lin, Ying-Tsong; Reeder, D Benjamin

2011-09-01

A study of 400 Hz sound focusing and ducting effects in a packet of curved nonlinear internal waves in shallow water is presented. Sound propagation roughly along the crests of the waves is simulated with a three-dimensional parabolic equation computational code, and the results are compared to measured propagation along fixed 3 and 6 km source/receiver paths. The measurements were made on the shelf of the South China Sea northeast of Tung-Sha Island. Construction of the time-varying three-dimensional sound-speed fields used in the modeling simulations was guided by environmental data collected concurrently with the acoustic data. Computed three-dimensional propagation results compare well with field observations. The simulations allow identification of time-dependent sound forward scattering and ducting processes within the curved internal gravity waves. Strong acoustic intensity enhancement was observed during passage of high-amplitude nonlinear waves over the source/receiver paths, and is replicated in the model. The waves were typical of the region (35 m vertical displacement). Two types of ducting are found in the model, which occur asynchronously. One type is three-dimensional modal trapping in deep ducts within the wave crests (shallow thermocline zones). The second type is surface ducting within the wave troughs (deep thermocline zones). © 2011 Acoustical Society of America

On the generation of internal wave modes by surface waves

NASA Astrophysics Data System (ADS)

Harlander, Uwe; Kirschner, Ian; Maas, Christian; Zaussinger, Florian

2016-04-01

Internal gravity waves play an important role in the ocean since they transport energy and momentum and the can lead to mixing when they break. Surface waves and internal gravity waves can interact. On the one hand, long internal waves imply a slow varying shear current that modifies the propagation of surface waves. Surface waves generated by the atmosphere can, on the other hand, excite internal waves by nonlinear interaction. Thereby a surface wave packet consisting of two close frequencies can resonate with a low frequency internal wave (Phillips, 1966). From a theoretical point of view, the latter has been studied intensively by using a 2-layer model, i.e. a surface layer with a strong density contrast and an internal layer with a comparable weak density contrast (Ball, 1964; Craig et al., 2010). In the present work we analyse the wave coupling for a continuously stratified fluid using a fully non-linear 2D numerical model (OpenFoam) and compare this with laboratory experiments (see Lewis et al. 1974). Surface wave modes are used as initial condition and the time development of the dominant surface and internal waves are studied by spectral and harmonic analysis. For the simple geometry of a box, the results are compared with analytical spectra of surface and gravity waves. Ball, F.K. 1964: Energy transfer between external and internal gravity waves. J. Fluid Mech. 19, 465. Craig, W., Guyenne, P., Sulem, C. 2010: Coupling between internal and surface waves. Natural Hazards 57, 617-642. Lewis, J.E., Lake, B.M., Ko, D.R.S 1974: On the interaction of internal waves and surfacr gravity waves, J. Fluid Mech. 63, 773-800. Phillips, O.M. 1966: The dynamics of the upper ocean, Cambridge University Press, 336pp.

Experimental Study of the Effect of the Initial Spectrum Width on the Statistics of Random Wave Groups

NASA Astrophysics Data System (ADS)

Shemer, L.; Sergeeva, A.

2009-12-01

The statistics of random water wave field determines the probability of appearance of extremely high (freak) waves. This probability is strongly related to the spectral wave field characteristics. Laboratory investigation of the spatial variation of the random wave-field statistics for various initial conditions is thus of substantial practical importance. Unidirectional nonlinear random wave groups are investigated experimentally in the 300 m long Large Wave Channel (GWK) in Hannover, Germany, which is the biggest facility of its kind in Europe. Numerous realizations of a wave field with the prescribed frequency power spectrum, yet randomly-distributed initial phases of each harmonic, were generated by a computer-controlled piston-type wavemaker. Several initial spectral shapes with identical dominant wave length but different width were considered. For each spectral shape, the total duration of sampling in all realizations was long enough to yield sufficient sample size for reliable statistics. Through all experiments, an effort had been made to retain the characteristic wave height value and thus the degree of nonlinearity of the wave field. Spatial evolution of numerous statistical wave field parameters (skewness, kurtosis and probability distributions) is studied using about 25 wave gauges distributed along the tank. It is found that, depending on the initial spectral shape, the frequency spectrum of the wave field may undergo significant modification in the course of its evolution along the tank; the values of all statistical wave parameters are strongly related to the local spectral width. A sample of the measured wave height probability functions (scaled by the variance of surface elevation) is plotted in Fig. 1 for the initially narrow rectangular spectrum. The results in Fig. 1 resemble findings obtained in [1] for the initial Gaussian spectral shape. The probability of large waves notably surpasses that predicted by the Rayleigh distribution and is the highest at the distance of about 100 m. Acknowledgement This study is carried out in the framework of the EC supported project "Transnational access to large-scale tests in the Large Wave Channel (GWK) of Forschungszentrum Küste (Contract HYDRALAB III - No. 022441). [1] L. Shemer and A. Sergeeva, J. Geophys. Res. Oceans 114, C01015 (2009). Figure 1. Variation along the tank of the measured wave height distribution for rectangular initial spectral shape, the carrier wave period T0=1.5 s.

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.

Numerical investigation of freak waves

NASA Astrophysics Data System (ADS)

Chalikov, D.

2009-04-01

Paper describes the results of more than 4,000 long-term (up to thousands of peak-wave periods) numerical simulations of nonlinear gravity surface waves performed for investigation of properties and estimation of statistics of extreme (‘freak') waves. The method of solution of 2-D potential wave's equations based on conformal mapping is applied to the simulation of wave behavior assigned by different initial conditions, defined by JONSWAP and Pierson-Moskowitz spectra. It is shown that nonlinear wave evolution sometimes results in appearance of very big waves. The shape of freak waves varies within a wide range: some of them are sharp-crested, others are asymmetric, with a strong forward inclination. Some of them can be very big, but not steep enough to create dangerous conditions for vessels (but not for fixed objects). Initial generation of extreme waves can occur merely as a result of group effects, but in some cases the largest wave suddenly starts to grow. The growth is followed sometimes by strong concentration of wave energy around a peak vertical. It is taking place in the course of a few peak wave periods. The process starts with an individual wave in a physical space without significant exchange of energy with surrounding waves. Sometimes, a crest-to-trough wave height can be as large as nearly three significant wave heights. On the average, only one third of all freak waves come to breaking, creating extreme conditions, however, if a wave height approaches the value of three significant wave heights, all of the freak waves break. The most surprising result was discovery that probability of non-dimensional freak waves (normalized by significant wave height) is actually independent of density of wave energy. It does not mean that statistics of extreme waves does not depend on wave energy. It just proves that normalization of wave heights by significant wave height is so effective, that statistics of non-dimensional extreme waves tends to be independent of wave energy. It is naive to expect that high order moments such as skewness and kurtosis can serve as predictors or even indicators of freak waves. Firstly, the above characteristics cannot be calculated with the use of spectrum usually determined with low accuracy. Such calculations are definitely unstable to a slight perturbation of spectrum. Secondly, even if spectrum is determined with high accuracy (for example calculated with the use of exact model), the high order moments cannot serve as the predictors, since they change synchronically with variations of extreme wave heights. Appearance of freak waves occurs simultaneously with increase of the local kurtosis, hence, kurtosis is simply a passive indicator of the same local geometrical properties of a wave field. This effect disappears completely, if spectrum is calculated over a very wide ensemble of waves. In this case existence of a freak wave is just disguised by other, non freak waves. Thirdly, all high order moments are dependant of spectral presentation - they increase with increasing of spectral resolution and cut-frequency. Statistics of non-dimensional waves as well as emergence of extreme waves is the innate property of a nonlinear wave field. Probability function for steep waves has been constructed. Such type function can be used for development of operational forecast of freak waves based on a standard forecast provided by the 3-d generation wave prediction model (WAVEWATCH or WAM).

Measurement of the Acoustic Nonlinearity Parameter for Biological Media.

NASA Astrophysics Data System (ADS)

Cobb, Wesley Nelson

In vitro measurements of the acoustic nonlinearity parameter are presented for several biological media. With these measurements it is possible to predict the distortion of a finite amplitude wave in biological tissues of current diagnostic and research interest. The measurement method is based on the finite amplitude distortion of a sine wave that is emmitted by a piston source. The growth of the second harmonic component of this wave is measured by a piston receiver which is coaxial with and has the same size as the source. The experimental measurements and theory are compared in order to determine the nonlinearity parameter. The density, sound speed, and attenuation for the medium are determined in order to make this comparison. The theory developed for this study accounts for the influence of both diffraction and attenuation on the experimental measurements. The effects of dispersion, tissue inhomogeneity and gas bubbles within the excised tissues are studied. To test the measurement method, experimental results are compared with established values for the nonlinearity parameter of distilled water, ethylene glycol and glycerol. The agreement between these values suggests that the measurement uncertainty is (+OR-) 5% for liquids and (+OR-) 10% for solid tissues. Measurements are presented for dog blood and bovine serum albumen as a function of concentration. The nonlinearity parameters for liver, kidney and spleen are reported for both human and canine tissues. The values for the fresh tissues displayed little variation (6.8 to 7.8). Measurements for fixed, normal and cirrhotic tissues indicated that the nonlinearity parameter does not depend strongly on pathology. However, the values for fixed tissues were somewhat higher than those of the fresh tissues.

Shock waves raised by explosions in space as sources of ultra-high-energy cosmic rays

NASA Astrophysics Data System (ADS)

Kichigin, Gennadiy

2015-03-01

The paper discusses the possibility of particle acceleration up to ultrahigh energies in the relativistic waves generated by various explosive processes in the interstellar medium. We propose to use the surfatron mechanism of acceleration (surfing) of charged particles trapped in the front of relativistic waves as a generator of high-energy cosmic rays (CRs). Conditions under which surfing in these waves can be made are studied thoroughly. Ultra-high-energy CRs (up to 10^20 eV) are shown to be obtained due to the surfing in the relativistic plane and spherical waves. Surfing is supposed to take place in nonlinear Langmuir waves excited by powerful electromagnetic radiation or relativistic beams of charged particles, as well as in strong shock waves generated by relativistic jets or spherical formations that expand fast (fireballs).

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.

Analytical study of exact solutions of the nonlinear Korteweg-de Vries equation with space-time fractional derivatives

NASA Astrophysics Data System (ADS)

Liu, Jiangen; Zhang, Yufeng

2018-01-01

This paper gives an analytical study of dynamic behavior of the exact solutions of nonlinear Korteweg-de Vries equation with space-time local fractional derivatives. By using the improved (G‧ G )-expansion method, the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solutions and soliton-like solutions, are obtained for the first time. They can better help us further understand the physical phenomena and provide a strong basis. Meanwhile, some solutions are presented through 3D-graphs.

Nonlinear symmetry breaking in photometamaterials

NASA Astrophysics Data System (ADS)

Gorlach, Maxim A.; Dobrykh, Dmitry A.; Slobozhanyuk, Alexey P.; Belov, Pavel A.; Lapine, Mikhail

2018-03-01

We design and analyze theoretically photometamaterials with each meta-atom containing both photodiode and light-emitting diode. Illumination of the photodiode by the light-emitting diode gives rise to an additional optical feedback within each unit cell, which strongly affects resonant properties and nonlinear response of the meta-atom. In particular, we demonstrate that inversion symmetry breaking occurs upon a certain threshold magnitude of the incident wave intensity resulting in an abrupt emergence of second-harmonic generation, which was not originally available, as well as in the reduced third-harmonic signal.

Nonlinear Wave propagation at sediment layers

NASA Astrophysics Data System (ADS)

Tsuda, K.; Archuleta, R. J.; O'Connell, D. R.; Bonilla, F. L.

2002-12-01

Data from some large earthquakes, such as the 2000 Tottoriken-Seibu earthquake, the 1995 Kobe earthquake, and 1994 Northridge earthquake have reinforced the importance of the effect of surface soil on seismic waves. This is especially true of the Tottoriken-Seibu earthquake where the damage from the liquefaction of surface soil was very severe. The mechanism of the liquefaction of soil is understood as the result of the nonlinear soil behavior-the pore water pressure build up-during the strong shaking. The model to explain the mechanics of pore water pressure build up has been proposed by many studies. In this study, we tried to predict the pore water pressure based on the constitutive model proposed by Iai et al. (1992). This model has been already applied to predict nonlinear soil behavior by Bonilla (2000) whose simulated results showed good agreement with the laboratory data in the VELACS program. We have applied this method to simulate ground motions at Jackson Lake Dam, Wyoming. We constructed a 140 m one-dimensional shear-wave velocity/depth profile for the sediment layers. The water table is at 2 m depth. The elastic material properties are based on in situ measurements. However, the parameters needed for the nonlinear response are taken from generic data for similar materials. To check for consistency we have constructed liquefaction resistance curves using a range of parameters that will be assumed for the soil column. These curves are compared with measured point values of the liquefaction resistance. To estimate the response at Jackson Lake Dam we have used strong motion records-JMA records from the 1995 Kobe earthquake and the Pleasant Valley Pumping Plant records from the 1983 Coalinga earthquake-as input motions at 140 m depth. We have also used synthetic ground motions computed from scenario earthquakes that might occur on the Teton Fault, very close to the dam. In the case of the synthetic input motions, the calculated shear strain approaches 20% in the sand layer. The material between 0 and 10 m shows maximum strain of about 1%, which still produces an increase in the fundamental period of the layer as well as a deamplification of the amplitude of the seismic waves.

Large Spin-Wave Bullet in a Ferrimagnetic Insulator Driven by the Spin Hall Effect

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

Jungfleisch, M. B.; Zhang, W.; Sklenar, J.

2016-02-01

Due to its transverse nature, spin Hall effects (SHE) provide the possibility to excite and detect spin currents and magnetization dynamics even in magnetic insulators. Magnetic insulators are outstanding materials for the investigation of nonlinear phenomena and for novel low power spintronics applications because of their extremely low Gilbert damping. Here, we report on the direct imaging of electrically driven spin-torque ferromagnetic resonance (ST-FMR) in the ferrimagnetic insulator Y 3Fe 5O 12 based on the excitation and detection by SHEs. The driven spin dynamics in Y 3Fe 5O 12 is directly imaged by spatially-resolved microfocused Brillouin light scattering (BLS) spectroscopy.more » Previously, ST-FMR experiments assumed a uniform precession across the sample, which is not valid in our measurements. A strong spin-wave localization in the center of the sample is observed indicating the formation of a nonlinear, self-localized spin-wave `bullet'.« less

Ionospheric total electron content seismo-perturbation after Japan's March 11, 2011, M=9.0 Tohoku earthquake under a geomagnetic storm; a nonlinear principal component analysis

NASA Astrophysics Data System (ADS)

Lin, Jyh-Woei

2012-10-01

Nonlinear principal component analysis (NLPCA) is implemented to analyze the spatial pattern of total electron content (TEC) anomalies 3 hours after Japan's Tohoku earthquake that occurred at 05:46:23 on 11 March, 2011 (UTC) ( M w =9). A geomagnetic storm was in progress at the time of the earthquake. NLPCA and TEC data processing were conducted on the global ionospheric map (GIM) for the time between 08:30 to 09:30 UTC, about 3 hours after this devastating earthquake and ensuing tsunami. Analysis results show stark earthquake-associated TEC anomalies that are widespread, and appear to have been induced by two acoustic gravity waves due to strong shaking (vertical acoustic wave) and the generation of the tsunami (horizontal Rayleigh mode gravity wave). The TEC anomalies roughly fit the initial mainshock and movement of the tsunami. Observation of the earthquake-associated TEC anomalies does not appear to be affected by a contemporaneous geomagnetic storm.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Manipulating acoustic wave reflection by a nonlinear elastic metasurface

NASA Astrophysics Data System (ADS)

Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent

2018-03-01

The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.

Chirped solitary pulses for a nonic nonlinear Schrödinger equation on a continuous-wave background

NASA Astrophysics Data System (ADS)

Triki, Houria; Porsezian, K.; Choudhuri, Amitava; Dinda, P. Tchofo

2016-06-01

A class of derivative nonlinear Schrödinger equation with cubic-quintic-septic-nonic nonlinear terms describing the propagation of ultrashort optical pulses through a nonlinear medium with higher-order Kerr responses is investigated. An intensity-dependent chirp ansatz is adopted for solving the two coupled amplitude-phase nonlinear equations of the propagating wave. We find that the dynamics of field amplitude in this system is governed by a first-order nonlinear ordinary differential equation with a tenth-degree nonlinear term. We demonstrate that this system allows the propagation of a very rich variety of solitary waves (kink, dark, bright, and gray solitary pulses) which do not coexist in the conventional nonlinear systems that have appeared so far in the literature. The stability of the solitary wave solution under some violation on the parametric conditions is investigated. Moreover, we show that, unlike conventional systems, the nonlinear Schrödinger equation considered here meets the special requirements for the propagation of a chirped solitary wave on a continuous-wave background, involving a balance among group velocity dispersion, self-steepening, and higher-order nonlinearities of different nature.

Continuous-wave optical parametric oscillators on their way to the terahertz range

NASA Astrophysics Data System (ADS)

Sowade, Rosita; Breunig, Ingo; Kiessling, Jens; Buse, Karsten

2010-02-01

Continuous-wave optical parametric oscillators (OPOs) are known to be working horses for spectroscopy in the near- and mid-infrared. However, strong absorption in nonlinear media like lithium niobate complicates the generation of far-infrared light. This absorption leads to pump thresholds vastly exceeding the power of standard pump lasers. Our first approach was, therefore, to combine the established technique of photomixing with optical parametric oscillators. Here, two OPOs provide one wave each, with a tunable difference frequency. These waves are combined to a beat signal as a source for photomixers. Terahertz radiation between 0.065 and 1.018 THz is generated with powers in the order of nanowatts. To overcome the upper frequency limit of the opto-electronic photomixers, terahertz generation has to rely entirely on optical methods. Our all-optical approach, getting around the high thresholds for terahertz generation, is based on cascaded nonlinear processes: the resonantly enhanced signal field, generated in the primary parametric process, is intense enough to act as the pump for a secondary process, creating idler waves with frequencies in the terahertz regime. The latter ones are monochromatic and tunable with detected powers of more than 2 μW at 1.35 THz. Thus, continuous-wave optical parametric oscillators have entered the field of terahertz photonics.

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

PubMed Central

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

2015-01-01

Regular wave-induced behaviour of a floating stationary two-dimensional body with a moonpool is studied. The focus is on resonant piston-mode motion in the moonpool and rigid-body motions. Dedicated two-dimensional experiments have been performed. Two numerical hybrid methods, which have previously been applied to related problems, are further developed. Both numerical methods couple potential and viscous flow. The semi-nonlinear hybrid method uses linear free-surface and body-boundary conditions. The other one uses fully nonlinear free-surface and body-boundary conditions. The harmonic polynomial cell method solves the Laplace equation in the potential flow domain, while the finite volume method solves the Navier–Stokes equations in the viscous flow domain near the body. Results from the two codes are compared with the experimental data. The nonlinear hybrid method compares well with the data, while certain discrepancies are observed for the semi-nonlinear method. In particular, the roll motion is over-predicted by the semi-nonlinear hybrid method. Error sources in the semi-nonlinear hybrid method are discussed. The moonpool strongly affects heave motions in a frequency range around the piston-mode resonance frequency of the moonpool. No resonant water motions occur in the moonpool at the piston-mode resonance frequency. Instead large moonpool motions occur at a heave natural frequency associated with small damping near the piston-mode resonance frequency. PMID:25512594

Constraints on Nonlinear and Stochastic Growth Theories for Type 3 Solar Radio Bursts from the Corona to 1 AU

NASA Technical Reports Server (NTRS)

Cairns, Iver H.; Robinson, P. A.

1998-01-01

Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostatic (ES) decay processes, or stochastic growth physics to preserve the electron beam, limit the levels of Langmuir-like waves driven by the beam, and produce wave spectra capable of coupling nonlinearly to generate the observed radio emission. Theoretical constraints exist on the wavenumbers and relative sizes of the wave bandwidth and nonlinear growth rate for which Langmuir waves are subject to modulational instability and the parametric and random phase versions of ES decay. A constraint also exists on whether stochastic growth theory (SGT) is appropriate. These constraints are evaluated here using the beam, plasma, and wave properties (1) observed in specific interplanetary type III sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by power-law models based on interplanetary observations. It is found that the Langmuir waves driven directly by the beam have wavenumbers that are almost always too large for modulational instability but are appropriate to ES decay. Even for waves scattered to lower wavenumbers (by ES decay, for instance), the wave bandwidths are predicted to be too large and the nonlinear growth rates too small for modulational instability to occur for the specific interplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exceptions are for very rare, unusually intense, narrowband wave packets, predominantly close to the Sun, and for the front portion of very fast beams traveling through unusually dilute, cold solar wind plasmas. Similar arguments demonstrate that the ES decay should proceed almost always as a random phase process rather than a parametric process, with similar exceptions. These results imply that it is extremely rare for modulational instability or parametric decay to proceed in type III sources at any heliocentric distance: theories for type III bursts based on modulational instability or parametric decay are therefore not viable in general. In contrast, the constraint on SGT can be satisfied and random phase ES decay can proceed at all heliocentric distances under almost all circumstances. (The contrary circumstances involve unusually slow, broad beams moving through unusually hot regions of the Corona.) The analyses presented here strongly justify extending the existing SGT-based model for interplanetary type III bursts (which includes SGT physics, random phase ES decay, and specific electromagnetic emission mechanisms) into a general theory for type III bursts from the corona to beyond 1 AU. This extended theory enjoys strong theoretical support, explains the characteristics of specific interplanetary type III bursts very well, and can account for the detailed dynamic spectra of type III bursts from the lower corona and solar wind.

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

NASA Astrophysics Data System (ADS)

Dorfman, S. E.; Carter, T. A.; Pribyl, P.; Tripathi, S.; Van Compernolle, B.; Vincena, S. T.; Sydora, R. D.

2013-12-01

Alfvén waves, a fundamental mode of magnetized plasmas, are ubiquitous in space plasmas. While the linear behavior of these waves has been extensively studied [1], non-linear effects are important in many real systems, including the solar corona and solar wind. In particular, a parametric decay process in which a large amplitude Alfvén wave decays into an ion acoustic wave and backward propagating Alfvén wave may play an important role in the coronal heating problem. Specifically, the decay of large-amplitude Alfvén waves propagating outward from the photosphere could lead to heating of the corona by the daughter ion acoustic modes [2]. As direct observational evidence of parametric decay is limited [3], laboratory experiments may play an important role in validating simple theoretical predictions and aiding in the interpretation of space measurements. Recent counter-propagating Alfvén wave experiments in the Large Plasma Device (LAPD) have recorded the first laboratory observation of the Alfvén-acoustic mode coupling at the heart of this parametric decay instability [4]. A resonance in the beat wave response produced by the two launched Alfvén waves is observed and is identified as a damped ion acoustic mode based on the measured dispersion relation. Other properties of the interaction including the spatial profile of the beat mode and response amplitude are also consistent with theoretical predictions for a three-wave interaction driven by a nonlinear ponderomotive force. Strong damping observed after the pump Alfvén waves are turned off is under investigation; a novel ion acoustic wave launcher is under development to launch the mode directly for damping studies. New experiments also aim to identify decay instabilities from a single large-amplitude Alfvén wave. In conjunction with these experiments, gyrokinetic simulation efforts are underway to scope out the relevant parameter space. [1] W. Gekelman, et. al., Phys. Plasmas 18, 055501 (2011). [2] F. Pruneti, F and M. Velli, ESA Spec. Pub. 404, 623 (1997). [3] S. R. Spangler, et. al., Phys. Plasmas 4, 846 (1997). [4] S. Dorfman and T. Carter, Phys. Rev. Lett. 110, 195001 (2013).

Three-dimensional site response at KiK-net downhole arrays

USGS Publications Warehouse

Thompson, Eric M.; Tanaka, Yasuo; Baise, Laurie G.; Kayen, Robert E.

2010-01-01

Ground motions at two Kiban-Kyoshin Network (KiK-net) strong motion downhole array sites in Hokkaido, Japan (TKCH08 in Taiki and TKCH05 in Honbetsu) illustrate the importance of three-dimensional (3D) site effects. These sites recorded the M8.0 2003 Tokachi-Oki earthquake, with recorded accelerations above 0.4 g at both sites as well as numerous ground motions from smaller events. Weak ground motions indicate that site TKCH08 is well modeled with the assumption of plane SH waves traveling through a 1D medium (SH1D), while TKCH05 is characteristic of a poor fit to the SH1D theoretical response. We hypothesized that the misfit at TKCH05results from the heterogeneity of the subsurface. To test this hypothesis, we measured four S-wave velocity profiles in the vicinity (< 300 m) of each site with the spectral analysis of surface waves (SASW) method. This KiK-net site pair is ideal for assessing the relative importance of 3D site effects and nonlinear site effects. The linear ground motions at TKCH05 isolate the 3D site effects, as we hypothesized from the linear ground motions and confirmed with our subsequent SASW surveys. The Tokachi-Oki time history at TKCH08 isolates the effects of nonlinearity from spatial heterogeneity because the 3D effects are negligible. The Tokachi-Oki time history at TKCH05 includes both nonlinear and 3D site effects. Comparisons of the accuracy of the SH1D model predictions of these surface time histories from the downhole time histories indicates that the 3D site effects are at least as important as nonlinear effects in this case. The errors associated with the assumption of a 1D medium and 1D wave propagation will be carried into a nonlinear analysis that relies on these same assumptions. Thus, the presence of 3D effects should be ruled out prior to a 1D nonlinear analysis. The SH1D residuals show that 3D effects can be mistaken for nonlinear effects.

Calculation of Seismic Waves from Explosions with Tectonic Stresses and Topography

NASA Astrophysics Data System (ADS)

Stevens, J. L.; O'Brien, M.

2017-12-01

We investigate the effects of explosion depth, tectonic stresses and topography on seismic waves from underground nuclear explosions. We perform three-dimensional nonlinear calculations of an explosion at several depths in the topography of the North Korean test site. We also perform a large number of two-dimensional axisymmetric calculations of explosions at depths from 150 to 1000 meters in four earth structures, with compressive and tensile tectonic stresses and with no tectonic stresses. We use the representation theorem to propagate the results of these calculations and calculate seismic waves at regional and teleseismic distances. We find that P-waves are not strongly affected by any of these effects because the initial downgoing P-wave is unaffected by interaction with the free surface. Surface waves, however, are strongly affected by all of these effects. There is an optimal depth at which surface waves are maximized at the base of a mountain and at or slightly below normal containment depth. At deeper depths, increasing overburden pressure reduces the surface waves. At shallower depths, interaction with the free surface reduces the surface waves. For explosions inside a mountain, displacement of the sides of the mountain reduces surface waves. Compressive prestress reduces surface waves substantially, while tensile prestress increases surface waves. The North Korean explosions appear to be at an optimal depth, in a region of extension, and beneath a mountain, all of which increase surface wave amplitudes.

X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity

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

Balyan, M. K., E-mail: mbalyan@ysu.am

The two-wave dynamical diffraction in the Laue geometry has been theoretically considered for a plane X-ray wave in a crystal with a third-order nonlinear response to the external field. An analytical solution to the problem stated is found for certain diffraction conditions. A nonlinear pendulum effect is analyzed. The nonlinear extinction length is found to depend on the incident-wave intensity. A pendulum effect of a new type is revealed: the intensities of the transmitted and diffracted waves periodically depend on the incidentwave intensity at a fixed crystal thickness. The rocking curves and Borrmann nonlinear effect are numerically calculated.

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.

Transfer and dissipation of energy during wave group propagation on a gentle beach slope

NASA Astrophysics Data System (ADS)

Padilla, Enrique M.; Alsina, José M.

2017-08-01

The propagation of bichromatic wave groups over a constant 1:100 beach slope and the influence of the group modulation is presented. The modulation is controlled by varying the group frequency, fg, which is shown to remarkably affect the energy transfer to high and low frequency components. The growth of the high frequency (hf) wave skewness increases when fg decreases. This is explained by nonlinear coupling between the primary frequencies, which results in a larger growth of hf components as fg decreases, causing the hf waves to break earlier. Due to high spatial resolution, wave tracking has provided an accurate measurement of the varying breakpoint. These breaking locations are very well described (R2>0.91) by the wave-height to effective-depth ratio (γ). However, for any given Iribarren number, this γ is shown to increase with fg. Therefore, a modified Iribarren number is proposed to include the grouping structure, leading to a considerable improvement in reproducing the measured γ-values. Within the surf zone, the behavior of the Incident Long Wave also depends on the group modulation. For low fg conditions, the lf wave decays only slightly by transferring energy back to the hf wave components. However, for high fg wave conditions, strong dissipation of low frequency (lf) components occurs close to the shoreline associated with lf wave breaking. This mechanism is explained by the growth of the lf wave height, induced partly by the self-self interaction of fg, and partly by the nonlinear coupling between the primary frequencies and fg.

Directional asymmetry of the nonlinear wave phenomena in a three-dimensional granular phononic crystal under gravity.

PubMed

Merkel, A; Tournat, V; Gusev, V

2014-08-01

We report the experimental observation of the gravity-induced asymmetry for the nonlinear transformation of acoustic waves in a noncohesive granular phononic crystal. Because of the gravity, the contact precompression increases with depth inducing space variations of not only the linear and nonlinear elastic moduli but also of the acoustic wave dissipation. We show experimentally and explain theoretically that, in contrast to symmetric propagation of linear waves, the amplitude of the nonlinearly self-demodulated wave depends on whether the propagation of the waves is in the direction of the gravity or in the opposite direction. Among the observed nonlinear processes, we report frequency mixing of the two transverse-rotational modes belonging to the optical band of vibrations and propagating with negative phase velocities, which results in the excitation of a longitudinal wave belonging to the acoustic band of vibrations and propagating with positive phase velocity. We show that the measurements of the gravity-induced asymmetry in the nonlinear acoustic phenomena can be used to compare the in-depth distributions of the contact nonlinearity and of acoustic absorption.

Fatigue crack detection by nonlinear spectral correlation with a wideband input

NASA Astrophysics Data System (ADS)

Liu, Peipei; Sohn, Hoon

2017-04-01

Due to crack-induced nonlinearity, ultrasonic wave can distort, create accompanying harmonics, multiply waves of different frequencies, and, under resonance conditions, change resonance frequencies as a function of driving amplitude. All these nonlinear ultrasonic features have been widely studied and proved capable of detecting fatigue crack at its very early stage. However, in noisy environment, the nonlinear features might be drown in the noise, therefore it is difficult to extract those features using a conventional spectral density function. In this study, nonlinear spectral correlation is defined as a new nonlinear feature, which considers not only nonlinear modulations in ultrasonic waves but also spectral correlation between the nonlinear modulations. The proposed nonlinear feature is associated with the following two advantages: (1) stationary noise in the ultrasonic waves has little effect on nonlinear spectral correlation; and (2) the contrast of nonlinear spectral correlation between damage and intact conditions can be enhanced simply by using a wideband input. To validate the proposed nonlinear feature, micro fatigue cracks are introduced to aluminum plates by repeated tensile loading, and the experiment is conducted using surface-mounted piezoelectric transducers for ultrasonic wave generation and measurement. The experimental results confirm that the nonlinear spectral correlation can successfully detect fatigue crack with a higher sensitivity than the classical nonlinear coefficient.

Nonlinear coherent structures of Alfvén wave in a collisional plasma

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

Jana, Sayanee; Chakrabarti, Nikhil; Ghosh, Samiran

2016-07-15

The Alfvén wave dynamics is investigated in the framework of two-fluid approach in a compressible collisional magnetized plasma. In the finite amplitude limit, the dynamics of the nonlinear Alfvén wave is found to be governed by a modified Korteweg-de Vries Burgers equation (mKdVB). In this mKdVB equation, the electron inertia is found to act as a source of dispersion, and the electron-ion collision serves as a dissipation. The collisional dissipation is eventually responsible for the Burgers term in mKdVB equation. In the long wavelength limit, this weakly nonlinear Alfvén wave is shown to be governed by a damped nonlinear Schrödingermore » equation. Furthermore, these nonlinear equations are analyzed by means of analytical calculation and numerical simulation to elucidate the various aspects of the phase-space dynamics of the nonlinear wave. Results reveal that nonlinear Alfvén wave exhibits the dissipation mediated shock, envelope, and breather like structures. Numerical simulations also predict the formation of dissipative Alfvénic rogue wave, giant breathers, and rogue wave holes. These results are discussed in the context of the space plasma.« less

Drift waves, intense parallel electric fields, and turbulence associated with asymmetric magnetic reconnection at the magnetopause

NASA Astrophysics Data System (ADS)

Ergun, R. E.; Chen, L.-J.; Wilder, F. D.; Ahmadi, N.; Eriksson, S.; Usanova, M. E.; Goodrich, K. A.; Holmes, J. C.; Sturner, A. P.; Malaspina, D. M.; Newman, D. L.; Torbert, R. B.; Argall, M. R.; Lindqvist, P.-A.; Burch, J. L.; Webster, J. M.; Drake, J. F.; Price, L.; Cassak, P. A.; Swisdak, M.; Shay, M. A.; Graham, D. B.; Strangeway, R. J.; Russell, C. T.; Giles, B. L.; Dorelli, J. C.; Gershman, D.; Avanov, L.; Hesse, M.; Lavraud, B.; Le Contel, O.; Retino, A.; Phan, T. D.; Goldman, M. V.; Stawarz, J. E.; Schwartz, S. J.; Eastwood, J. P.; Hwang, K.-J.; Nakamura, R.; Wang, S.

2017-04-01

Observations of magnetic reconnection at Earth's magnetopause often display asymmetric structures that are accompanied by strong magnetic field (B) fluctuations and large-amplitude parallel electric fields (E||). The B turbulence is most intense at frequencies above the ion cyclotron frequency and below the lower hybrid frequency. The B fluctuations are consistent with a thin, oscillating current sheet that is corrugated along the electron flow direction (along the X line), which is a type of electromagnetic drift wave. Near the X line, electron flow is primarily due to a Hall electric field, which diverts ion flow in asymmetric reconnection and accompanies the instability. Importantly, the drift waves appear to drive strong parallel currents which, in turn, generate large-amplitude ( 100 mV/m) E|| in the form of nonlinear waves and structures. These observations suggest that turbulence may be common in asymmetric reconnection, penetrate into the electron diffusion region, and possibly influence the magnetic reconnection process.

High-accuracy power series solutions with arbitrarily large radius of convergence for the fractional nonlinear Schrödinger-type equations

NASA Astrophysics Data System (ADS)

Khawaja, U. Al; Al-Refai, M.; Shchedrin, Gavriil; Carr, Lincoln D.

2018-06-01

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These effective descriptions thus appear commonly in physical and mathematical modeling. We present a new series method providing systematic controlled accuracy for solutions of fractional nonlinear differential equations, including the fractional nonlinear Schrödinger equation and the fractional nonlinear diffusion equation. The method relies on spatially iterative use of power series expansions. Our approach permits an arbitrarily large radius of convergence and thus solves the typical divergence problem endemic to power series approaches. In the specific case of the fractional nonlinear Schrödinger equation we find fractional generalizations of cnoidal waves of Jacobi elliptic functions as well as a fractional bright soliton. For the fractional nonlinear diffusion equation we find the combination of fractional and nonlinear effects results in a more strongly localized solution which nevertheless still exhibits power law tails, albeit at a much lower density.

Stability of matter-wave solitons in optical lattices

NASA Astrophysics Data System (ADS)

Ali, Sk. Golam; Roy, S. K.; Talukdar, B.

2010-08-01

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ1) is less than that of the LOL (V0) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ1 > V0, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ1 < V0. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.

Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides.

PubMed

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

2013-01-01

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

Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy

NASA Astrophysics Data System (ADS)

Gninzanlong, Carlos Lawrence; Ndjomatchoua, Frank Thomas; Tchawoua, Clément

2018-04-01

The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.

Guided wave opto-acoustic device

DOEpatents

Jarecki, Jr., Robert L.; Rakich, Peter Thomas; Camacho, Ryan; Shin, Heedeuk; Cox, Jonathan Albert; Qiu, Wenjun; Wang, Zheng

2016-02-23

The various technologies presented herein relate to various hybrid phononic-photonic waveguide structures that can exhibit nonlinear behavior associated with traveling-wave forward stimulated Brillouin scattering (forward-SBS). The various structures can simultaneously guide photons and phonons in a suspended membrane. By utilizing a suspended membrane, a substrate pathway can be eliminated for loss of phonons that suppresses SBS in conventional silicon-on-insulator (SOI) waveguides. Consequently, forward-SBS nonlinear susceptibilities are achievable at about 3000 times greater than achievable with a conventional waveguide system. Owing to the strong phonon-photon coupling achievable with the various embodiments, potential application for the various embodiments presented herein cover a range of radiofrequency (RF) and photonic signal processing applications. Further, the various embodiments presented herein are applicable to applications operating over a wide bandwidth, e.g. 100 MHz to 50 GHz or more.

Non-autonomous multi-rogue waves for spin-1 coupled nonlinear Gross-Pitaevskii equation and management by external potentials.

PubMed

Li, Li; Yu, Fajun

2017-09-06

We investigate non-autonomous multi-rogue wave solutions in a three-component(spin-1) coupled nonlinear Gross-Pitaevskii(GP) equation with varying dispersions, higher nonlinearities, gain/loss and external potentials. The similarity transformation allows us to relate certain class of multi-rogue wave solutions of the spin-1 coupled nonlinear GP equation to the solutions of integrable coupled nonlinear Schrödinger(CNLS) equation. We study the effect of time-dependent quadratic potential on the profile and dynamic of non-autonomous rogue waves. With certain requirement on the backgrounds, some non-autonomous multi-rogue wave solutions exhibit the different shapes with two peaks and dip in bright-dark rogue waves. Then, the managements with external potential and dynamic behaviors of these solutions are investigated analytically. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers and super-fluids.

Method to improve optical parametric oscillator beam quality

DOEpatents

Smith, Arlee V.; Alford, William J.; Bowers, Mark S.

2003-11-11

A method to improving optical parametric oscillator (OPO) beam quality having an optical pump, which generates a pump beam at a pump frequency greater than a desired signal frequency, a nonlinear optical medium oriented so that a signal wave at the desired signal frequency and a corresponding idler wave are produced when the pump beam (wave) propagates through the nonlinear optical medium, resulting in beam walk off of the signal and idler waves, and an optical cavity which directs the signal wave to repeatedly pass through the nonlinear optical medium, said optical cavity comprising an equivalently even number of non-planar mirrors that produce image rotation on each pass through the nonlinear optical medium. Utilizing beam walk off where the signal wave and said idler wave have nonparallel Poynting vectors in the nonlinear medium and image rotation, a correlation zone of distance equal to approximately .rho.L.sub.crystal is created which, through multiple passes through the nonlinear medium, improves the beam quality of the OPO output.

Optical parametric osicllators with improved beam quality

DOEpatents

Smith, Arlee V.; Alford, William J.

2003-11-11

An optical parametric oscillator (OPO) having an optical pump, which generates a pump beam at a pump frequency greater than a desired signal frequency, a nonlinear optical medium oriented so that a signal wave at the desired signal frequency and a corresponding idler wave are produced when the pump beam (wave) propagates through the nonlinear optical medium, resulting in beam walk off of the signal and idler waves, and an optical cavity which directs the signal wave to repeatedly pass through the nonlinear optical medium, said optical cavity comprising an equivalently even number of non-planar mirrors that produce image rotation on each pass through the nonlinear optical medium. Utilizing beam walk off where the signal wave and said idler wave have nonparallel Poynting vectors in the nonlinear medium and image rotation, a correlation zone of distance equal to approximately .rho.L.sub.crystal is created which, through multiple passes through the nonlinear medium, improves the beam quality of the OPO output.

Torsional Alfvén Waves in a Dipolar Magnetic Field

NASA Astrophysics Data System (ADS)

Nataf, H. C.; Tigrine, Z.; Cardin, P.; Schaeffer, N.

2017-12-01

The discovery of torsional Alfvén waves in the Earth's core (Gillet et al, 2010) is a strong motivation for investigating the properties of these waves. Here, we report on the first experimental study of such waves. Alfvén waves are difficult to excite and observe in liquid metals because of their high magnetic diffusivity. Nevertheless, we obtained clear signatures of such diffusive waves in our DTS experiment. In this setup, some 40 liters of liquid sodium are contained between a ro = 210 mm-radius stainless steel outer shell, and a ri = 74 mm-radius copper inner sphere. Both spherical boundaries can rotate independently around a common vertical axis. The inner sphere shells a strong permanent magnet, which produces a nearly dipolar magnetic field whose intensity falls from 175 mT at ri to 8 mT at ro in the equatorial plane. We excite Alfvén waves in the liquid sodium by applying a sudden jerk of the inner sphere. To study the effect of global rotation, which leads to the formation of geostrophic torsional Alfvén waves, we spin the experiment at rotation rates fo = fi up to 15 Hz. The Alfvén wave produces a clear azimuthal magnetic signal on magnetometers installed in a sleeve inside the fluid. We also probe the associated azimuthal velocity field using ultrasound Doppler velocimetry. Electric potentials at the surface of the outer sphere turn out to be very revealing as well. In parallel, we use the XSHELLS magnetohydrodynamics spherical code to model torsional Alfvén waves in the experimental conditions, and beyond. We explore both linear and non-linear regimes. We observe a strong excitation of inertial waves in the equatorial plane, where the wave transits from a region of strong magnetic field to a region dominated by rotation (see figure of meridian map of azimuthal velocity). These novel observations should help deciphering the dynamics of Alfvén waves in planetary cores.

Rogue events in the group velocity horizon.

PubMed

Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Mahnke, Christoph; Mitschke, Fedor; Steinmeyer, Günter

2012-01-01

The concept of rogue waves arises from a mysterious and potentially calamitous phenomenon of oceanic surfaces. There is mounting evidence that they are actually commonplace in a variety of different physical settings. A set of defining criteria has been advanced; this set is of great generality and therefore applicable to a wide class of systems. The question arises naturally whether there are generic mechanisms responsible for extreme events in different systems. Here we argue that under suitable circumstances nonlinear interaction between weak and strong waves results in intermittent giant waves with all the signatures of rogue waves. To obtain these circumstances only a few basic conditions must be met. Then reflection of waves at the so-called group-velocity horizon occurs. The connection between rogue waves and event horizons, seemingly unrelated physical phenomena, is identified as a feature common in many different physical systems.

Sediment transport under wave groups: Relative importance between nonlinear waveshape and nonlinear boundary layer streaming

USGS Publications Warehouse

Yu, X.; Hsu, T.-J.; Hanes, D.M.

2010-01-01

Sediment transport under nonlinear waves in a predominately sheet flow condition is investigated using a two-phase model. Specifically, we study the relative importance between the nonlinear waveshape and nonlinear boundary layer streaming on cross-shore sand transport. Terms in the governing equations because of the nonlinear boundary layer process are included in this one-dimensional vertical (1DV) model by simplifying the two-dimensional vertical (2DV) ensemble-averaged two-phase equations with the assumption that waves propagate without changing their form. The model is first driven by measured time series of near-bed flow velocity because of a wave group during the SISTEX99 large wave flume experiment and validated with the measured sand concentration in the sheet flow layer. Additional studies are then carried out by including and excluding the nonlinear boundary layer terms. It is found that for the grain diameter (0.24 mm) and high-velocity skewness wave condition considered here, nonlinear waveshape (e.g., skewness) is the dominant mechanism causing net onshore transport and nonlinear boundary layer streaming effect only causes an additional 36% onshore transport. However, for conditions of relatively low-wave skewness and a stronger offshore directed current, nonlinear boundary layer streaming plays a more critical role in determining the net transport. Numerical experiments further suggest that the nonlinear boundary layer streaming effect becomes increasingly important for finer grain. When the numerical model is driven by measured near-bed flow velocity in a more realistic surf zone setting, model results suggest nonlinear boundary layer processes may nearly double the onshore transport purely because of nonlinear waveshape. Copyright 2010 by the American Geophysical Union.

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.

Nonlinear optical waves with the second Painleve transcendent shape of envelope in Kerr media

NASA Astrophysics Data System (ADS)

Shcherbakov, Alexandre S.; Tepichin Rodriguez, Eduardo; Sanchez Sanchez, Mauro

2004-05-01

Nonlinear optical wave packets with the second Painleve transcendent shape of envelope are revealed in Kerr media, manifesting weakly focusing cubic nonlinearity, square-law dispersion, and linear losses. When the state of nonlinear optical transmission is realized, two possible types of boundary conditions turn out to be satisfied for these wave packets. The propagation of initially unchirped optical wave packets under consideration could be supported by lossless medium in both normal and anomalous dispersion regimes. At the same time initially chirped optical waves with the second Painleve transcendent shape in low-loss medium and need matching the magnitude of optical losses by the dispersion and nonlinear properties of that medium.

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.

Evolution of basic equations for nearshore wave field

PubMed Central

ISOBE, Masahiko

2013-01-01

In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680

Experimental observation of steady inertial wave turbulence in deep rotating flows

NASA Astrophysics Data System (ADS)

Yarom, Ehud; Sharon, Eran

2015-11-01

We present experimental evidence of inertial wave turbulence in deep rotating fluid. Experiments were performed in a rotating cylindrical water tank, where previous work showed statistics similar to 2D turbulence (specifically an inverse energy cascade). Using Fourier analysis of high resolution data in both space (3D) and time we show that most of the energy of a steady state flow is contained around the inertial wave dispersion relation. The nonlinear interaction between the waves is manifested by the widening of the time spectrum around the dispersion relation. We show that as the Rossby number increases so does the spectrum width, with a strong dependence on wave number. Our results suggest that in some parameters range, rotating turbulence velocity field can be represented as a field of interacting waves (wave turbulence). Such formalism may provide a better understanding of the flow statistics. This work was supported by the Israel Science Foundation, Grant No. 81/12.

Nonlinear CARS measurement of nitrogen vibrational and rotational temperatures behind hypervelocity strong shock wave

NASA Astrophysics Data System (ADS)

Osada, Takashi; Endo, Youichi; Kanazawa, Chikara; Ota, Masanori; Maeno, Kazuo

2009-02-01

The hypervelocity strong shock waves are generated, when the space vehicles reenter the atmosphere from space. Behind the shock wave radiative and non-equilibrium flow is generated in front of the surface of the space vehicle. Many studies have been reported to investigate the phenomena for the aerospace exploit and reentry. The research information and data on the high temperature flows have been available to the rational heatproof design of the space vehicles. Recent development of measurement techniques with laser systems and photo-electronics now enables us to investigate the hypervelocity phenomena with greatly advanced accuracy. In this research strong shock waves are generated in low-density gas to simulate the reentry range gas flow with a free-piston double-diaphragm shock tube, and CARS (Coherent Anti-stokes Raman Spectroscopy) measurement method is applied to the hypervelocity flows behind the shock waves, where spectral signals of high space/time resolution are acquired. The CARS system consists of YAG and dye lasers, a spectroscope, and a CCD camera system. We obtain the CARS signal spectrum data by this special time-resolving experiment, and the vibrational and rotational temperatures of N2 are determined by fitting between the experimental spectroscopic profile data and theoretically estimated spectroscopic data.

Interaction of strong converging shock wave with SF6 gas bubble

NASA Astrophysics Data System (ADS)

Liang, Yu; Zhai, ZhiGang; Luo, XiSheng

2018-06-01

Interaction of a strong converging shock wave with an SF6 gas bubble is studied, focusing on the effects of shock intensity and shock shape on interface evolution. Experimentally, the converging shock wave is generated by shock dynamics theory and the gas bubble is created by soap film technique. The post-shock flow field is captured by a schlieren photography combined with a high-speed video camera. Besides, a three-dimensional program is adopted to provide more details of flow field. After the strong converging shock wave impact, a wide and pronged outward jet, which differs from that in planar shock or weak converging shock condition, is derived from the downstream interface pole. This specific phenomenon is considered to be closely associated with shock intensity and shock curvature. Disturbed by the gas bubble, the converging shocks approaching the convergence center have polygonal shapes, and the relationship between shock intensity and shock radius verifies the applicability of polygonal converging shock theory. Subsequently, the motion of upstream point is discussed, and a modified nonlinear theory considering rarefaction wave and high amplitude effects is proposed. In addition, the effects of shock shape on interface morphology and interface scales are elucidated. These results indicate that the shape as well as shock strength plays an important role in interface evolution.

Nonlinear Landau damping in the ionosphere

NASA Technical Reports Server (NTRS)

Kiwamoto, Y.; Benson, R. F.

1978-01-01

A model is presented to explain the non-resonant waves which give rise to the diffuse resonance observed near 3/2 f sub H by the Alouette and ISIS topside sounders, where f sub H is the ambient electron cyclotron frequency. In a strictly linear analysis, these instability driven waves will decay due to Landau damping on a time scale much shorter than the observed time duration of the diffuse resonance. Calculations of the nonlinear wave particle coupling coefficients, however, indicate that the diffuse resonance wave can be maintained by the nonlinear Landau damping of the sounder stimulated 2f sub H wave. The time duration of the diffuse resonance is determined by the transit time of the instability generated and nonlinearly maintained diffuse resonance wave from the remote short lived hot region back to the antenna. The model is consistent with the Alouette/ISIS observations, and clearly demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.

Spectral dynamics of THz pulses generated by two-color laser filaments in air: the role of Kerr nonlinearities and pump wavelength.

PubMed

Nguyen, A; González de Alaiza Martínez, P; Déchard, J; Thiele, I; Babushkin, I; Skupin, S; Bergé, L

2017-03-06

We theoretically and numerically study the influence of both instantaneous and Raman-delayed Kerr nonlinearities as well as a long-wavelength pump in the terahertz (THz) emissions produced by two-color femtosecond filaments in air. Although the Raman-delayed nonlinearity induced by air molecules weakens THz generation, four-wave mixing is found to impact the THz spectra accumulated upon propagation via self-, cross-phase modulations and self-steepening. Besides, using the local current theory, we show that the scaling of laser-to-THz conversion efficiency with the fundamental laser wavelength strongly depends on the relative phase between the two colors, the pulse duration and shape, rendering a universal scaling law impossible. Scaling laws in powers of the pump wavelength may only provide a rough estimate of the increase in the THz yield. We confront these results with comprehensive numerical simulations of strongly focused pulses and of filaments propagating over meter-range distances.

Optical measurement of the weak non-linearity in the eardrum vibration response to auditory stimuli

NASA Astrophysics Data System (ADS)

Aerts, Johan

The mammalian hearing organ consists of the external ear (auricle and ear canal) followed by the middle ear (eardrum and ossicles) and the inner ear (cochlea). Its function is to convert the incoming sound waves and convert them into nerve pulses which are processed in the final stage by the brain. The main task of the external and middle ear is to concentrate the incoming sound waves on a smaller surface to reduce the loss that would normally occur in transmission from air to inner ear fluid. In the past it has been shown that this is a linear process, thus without serious distortions, for sound waves going up to pressures of 130 dB SPL (˜90 Pa). However, at large pressure changes up to several kPa, the middle ear movement clearly shows non-linear behaviour. Thus, it is possible that some small non-linear distortions are also present in the middle ear vibration at lower sound pressures. In this thesis a sensitive measurement set-up is presented to detect this weak non-linear behaviour. Essentially, this set-up consists of a loud-speaker which excites the middle ear, and the resulting vibration is measured with an heterodyne vibrometer. The use of specially designed acoustic excitation signals (odd random phase multisines) enables the separation of the linear and non-linear response. The application of this technique on the middle ear demonstrates that there are already non-linear distortions present in the vibration of the middle ear at a sound pressure of 93 dB SPL. This non-linear component also grows strongly with increasing sound pressure. Knowledge of this non-linear component can contribute to the improvement of modern hearing aids, which operate at higher sound pressures where the non-linearities could distort the signal considerably. It is also important to know the contribution of middle ear non-linearity to otoacoustic emissions. This are non-linearities caused by the active feedback amplifier in the inner ear, and can be detected in the external and middle ear. These signals are used for diagnostic purposes, and therefore it is important to have an estimate the non-linear middle ear contribution to these emissions.

Nonlinear electrostatic solitary waves in electron-positron plasmas

NASA Astrophysics Data System (ADS)

Lazarus, I. J.; Bharuthram, R.; Moolla, S.; Singh, S. V.; Lakhina, G. S.

2016-02-01

The generation of nonlinear electrostatic solitary waves (ESWs) is explored in a magnetized four component two-temperature electron-positron plasma. Fluid theory is used to derive a set of nonlinear equations for the ESWs, which propagate obliquely to an external magnetic field. The electric field structures are examined for various plasma parameters and are shown to yield sinusoidal, sawtooth and bipolar waveforms. It is found that an increase in the densities of the electrons and positrons strengthen the nonlinearity while the periodicity and nonlinearity of the wave increases as the cool-to-hot temperature ratio increases. Our results could be useful in understanding nonlinear propagation of waves in astrophysical environments and related laboratory experiments.

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.

From solitons to rogue waves in nonlinear left-handed metamaterials.

PubMed

Shen, Yannan; Kevrekidis, P G; Veldes, G P; Frantzeskakis, D J; DiMarzio, D; Lan, X; Radisic, V

2017-03-01

In the present work, we explore soliton and roguelike wave solutions in the transmission line analog of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltage-dependent, symmetric capacitance motivated by recently developed ferroelectric barium strontium titanate thin-film capacitor designs. We develop both the corresponding nonlinear dynamical lattice and its reduction via a multiple scales expansion to a nonlinear Schrödinger (NLS) model for the envelope of a given carrier wave. The reduced model can feature either a focusing or a defocusing nonlinearity depending on the frequency (wave number) of the carrier. We then consider the robustness of different types of solitary waves of the reduced model within the original nonlinear left-handed medium. We find that both bright and dark solitons persist in a suitable parametric regime, where the reduction to the NLS model is valid. Additionally, for suitable initial conditions, we observe a rogue wave type of behavior that differs significantly from the classic Peregrine rogue wave evolution, including most notably the breakup of a single Peregrine-like pattern into solutions with multiple wave peaks. Finally, we touch upon the behavior of generalized members of the family of the Peregrine solitons, namely, Akhmediev breathers and Kuznetsov-Ma solitons, and explore how these evolve in the left-handed transmission line.

Electronic transmission in non-linear potential profile of GaAs/AlxGa1-xAs biased quantum well structure

NASA Astrophysics Data System (ADS)

Meghoufel, F. Z.; Bentata, S.; Terkhi, S.; Bendahma, F.; Cherid, S.

2013-05-01

We study the effect of the nonlinearity on electrons transmission properties in a double barriers structure GaAs/AlxGa1-xAs superlattices. The nonlinearity is introduced as an effective potential in the Schrödinger equation and translates the electronic Colombian repulsion. We have used the transfer matrix formalism and the plane wave functions approximation to solve numerically the equation and calculate the electronic transmission coefficient. We have shown the occurrence of two allowed states within the same well instead of a single, translating the presence of two resonant states at two different energies. The first allowed state intensity strongly decreases with increasing the nonlinear parameter, whereas the second one called the degeneracy state increases. Both the two states evolve towards higher resonances energies.

Review of mixing length estimates and effects of toroidicity in a fluid model for turbulent transport in tokamaks

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

Weiland, J., E-mail: elfjw@chalmers.se

2016-05-15

Basic aspects of turbulent transport in toroidal magnetized plasmas are discussed. In particular the fluid closure has strong effects on zonal flows which are needed to create an absorbing boundary for long wave lengths and also to obtain the Dimits nonlinear upshift. The fluid resonance in the energy equation is found to be instrumental for generating the L–H transition, the spin-up of poloidal rotation in internal transport barriers, as well as the nonlinear Dimits upshift. The difference between the linearly fastest growing mode number and the corresponding longer nonlinear correlation length is also addressed. It is found that the Kadomtsevmore » mixing length result is consistent with the non-Markovian diagonal limit of the transport at the nonlinearly obtained correlation length.« less

The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface

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

Chabchoub, A., E-mail: achabchoub@swin.edu.au; Kibler, B.; Finot, C.

2015-10-15

The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. amore » nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.« less

Non-reciprocal geometric wave diode by engineering asymmetric shapes of nonlinear materials.

PubMed

Li, Nianbei; Ren, Jie

2014-08-29

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports.

Kinetic Simulations of the Interruption of Large-Amplitude Shear-Alfvén Waves in a High- β Plasma

DOE PAGES

Squire, J.; Kunz, M. W.; Quataert, E.; ...

2017-10-12

Using two-dimensional hybrid-kinetic simulations, we explore the nonlinear “interruption” of standing and traveling shear-Alfvén waves in collisionless plasmas. Interruption involves a self-generated pressure anisotropy removing the restoring force of a linearly polarized Alfvénic perturbation, and occurs for wave amplitudes δB ⊥/B 0≳β –1/2 (where β is the ratio of thermal to magnetic pressure). We use highly elongated domains to obtain maximal scale separation between the wave and the ion gyroscale. For standing waves above the amplitude limit, we find that the large-scale magnetic field of the wave decays rapidly. The dynamics are strongly affected by the excitation of oblique firehosemore » modes, which transition into long-lived parallel fluctuations at the ion gyroscale and cause significant particle scattering. Traveling waves are damped more slowly, but are also influenced by small-scale parallel fluctuations created by the decay of firehose modes. Our results demonstrate that collisionless plasmas cannot support linearly polarized Alfvén waves above δB ⊥/B 0~β –1/2. Here, they also provide a vivid illustration of two key aspects of low-collisionality plasma dynamics: (i) the importance of velocity-space instabilities in regulating plasma dynamics at high β, and (ii) how nonlinear collisionless processes can transfer mechanical energy directly from the largest scales into thermal energy and microscale fluctuations, without the need for a scale-by-scale turbulent cascade.« less

Kinetic Simulations of the Interruption of Large-Amplitude Shear-Alfvén Waves in a High- β Plasma

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

Squire, J.; Kunz, M. W.; Quataert, E.

Using two-dimensional hybrid-kinetic simulations, we explore the nonlinear “interruption” of standing and traveling shear-Alfvén waves in collisionless plasmas. Interruption involves a self-generated pressure anisotropy removing the restoring force of a linearly polarized Alfvénic perturbation, and occurs for wave amplitudes δB ⊥/B 0≳β –1/2 (where β is the ratio of thermal to magnetic pressure). We use highly elongated domains to obtain maximal scale separation between the wave and the ion gyroscale. For standing waves above the amplitude limit, we find that the large-scale magnetic field of the wave decays rapidly. The dynamics are strongly affected by the excitation of oblique firehosemore » modes, which transition into long-lived parallel fluctuations at the ion gyroscale and cause significant particle scattering. Traveling waves are damped more slowly, but are also influenced by small-scale parallel fluctuations created by the decay of firehose modes. Our results demonstrate that collisionless plasmas cannot support linearly polarized Alfvén waves above δB ⊥/B 0~β –1/2. Here, they also provide a vivid illustration of two key aspects of low-collisionality plasma dynamics: (i) the importance of velocity-space instabilities in regulating plasma dynamics at high β, and (ii) how nonlinear collisionless processes can transfer mechanical energy directly from the largest scales into thermal energy and microscale fluctuations, without the need for a scale-by-scale turbulent cascade.« less

Development of attenuation and diffraction corrections for linear and nonlinear Rayleigh surface waves radiating from a uniform line source

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

Jeong, Hyunjo, E-mail: hjjeong@wku.ac.kr; Cho, Sungjong; Zhang, Shuzeng

2016-04-15

In recent studies with nonlinear Rayleigh surface waves, harmonic generation measurements have been successfully employed to characterize material damage and microstructural changes, and found to be sensitive to early stages of damage process. A nonlinearity parameter of Rayleigh surface waves was derived and frequently measured to quantify the level of damage. The accurate measurement of the nonlinearity parameter generally requires making corrections for beam diffraction and medium attenuation. These effects are not generally known for nonlinear Rayleigh waves, and therefore not properly considered in most of previous studies. In this paper, the nonlinearity parameter for a Rayleigh surface wave ismore » defined from the plane wave displacement solutions. We explicitly define the attenuation and diffraction corrections for fundamental and second harmonic Rayleigh wave beams radiated from a uniform line source. Attenuation corrections are obtained from the quasilinear theory of plane Rayleigh wave equations. To obtain closed-form expressions for diffraction corrections, multi-Gaussian beam (MGB) models are employed to represent the integral solutions derived from the quasilinear theory of the full two-dimensional wave equation without parabolic approximation. Diffraction corrections are presented for a couple of transmitter-receiver geometries, and the effects of making attenuation and diffraction corrections are examined through the simulation of nonlinearity parameter determination in a solid sample.« less

Spectro-spatial analysis of wave packet propagation in nonlinear acoustic metamaterials

NASA Astrophysics Data System (ADS)

Zhou, W. J.; Li, X. P.; Wang, Y. S.; Chen, W. Q.; Huang, G. L.

2018-01-01

The objective of this work is to analyze wave packet propagation in weakly nonlinear acoustic metamaterials and reveal the interior nonlinear wave mechanism through spectro-spatial analysis. The spectro-spatial analysis is based on full-scale transient analysis of the finite system, by which dispersion curves are generated from the transmitted waves and also verified by the perturbation method (the L-P method). We found that the spectro-spatial analysis can provide detailed information about the solitary wave in short-wavelength region which cannot be captured by the L-P method. It is also found that the optical wave modes in the nonlinear metamaterial are sensitive to the parameters of the nonlinear constitutive relation. Specifically, a significant frequency shift phenomenon is found in the middle-wavelength region of the optical wave branch, which makes this frequency region behave like a band gap for transient waves. This special frequency shift is then used to design a direction-biased waveguide device, and its efficiency is shown by numerical simulations.

Controllable rogue waves in the nonautonomous nonlinear system with a linear potential

NASA Astrophysics Data System (ADS)

Dai, C. Q.; Zheng, C. L.; Zhu, H. P.

2012-04-01

Based on the similarity transformation connected the nonautonomous nonlinear Schrödinger equation with the autonomous nonlinear Schrödinger equation, we firstly derive self-similar rogue wave solutions (rational solutions) for the nonautonomous nonlinear system with a linear potential. Then, we investigate the controllable behaviors of one-rogue wave, two-rogue wave and rogue wave triplets in a soliton control system. Our results demonstrate that the propagation behaviors of rogue waves, including postpone, sustainment, recurrence and annihilation, can be manipulated by choosing the relation between the maximum value of the effective propagation distance Z m and the parameter Z 0. Moreover, the excitation time of controllable rogue waves is decided by the parameter T 0.

Nonlinear fractional waves at elastic interfaces

NASA Astrophysics Data System (ADS)

Kappler, Julian; Shrivastava, Shamit; Schneider, Matthias F.; Netz, Roland R.

2017-11-01

We derive the nonlinear fractional surface wave equation that governs compression waves at an elastic interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective thickness of the bulk layer that is coupled to the interface is frequency dependent. The nonlinearity arises from the nonlinear dependence of the interface compressibility on the local compression, which is obtained from experimental measurements and reflects a phase transition at the interface. Numerical solutions of our nonlinear fractional theory reproduce several experimental key features of surface waves in phospholipid monolayers at the air-water interface without freely adjustable fitting parameters. In particular, the propagation distance of the surface wave abruptly increases at a threshold excitation amplitude. The wave velocity is found to be of the order of 40 cm/s in both experiments and theory and slightly increases as a function of the excitation amplitude. Nonlinear acoustic switching effects in membranes are thus shown to arise purely based on intrinsic membrane properties, namely, the presence of compressibility nonlinearities that accompany phase transitions at the interface.

Modeling Boulder Transport by Smooth Particle Hydrodynamics

NASA Astrophysics Data System (ADS)

Karpytchev, M.

2017-12-01

Large coastal boulders are often believed to have been transported by strong tsunami andstorm waves. Understanding and quantifying the boulder transport processes is, therefore,crucial for evaluation of strength and timing of the past tsunamis and storms. Over the last10-15 year, a series of studies have obtained estimates of basic wave parameters neededto set in motion a boulder of given size, shape and mass by using simplified paramaterizationsof fluid-particle interactions. Although, parameterizing the principal hydraulic forces drivingboulder transport was succefull in reproducing effects of several historical tsunamis, someimportant details about initiation of boulder motion and the contribution of coastal wavetransformations as well as of suspended sediment to enhancing coastal currents are still lacking.These essentially non-linear processes can be particularly important for distingushing, in everyparticular case, whether it is a storm wave or a tsunami (or both) that was capable to transportspecific boulder to a given site.In this study, we employ the Smooth Particle Hydrodynamics (SPH) method in orderto get new insights on interaction of waves with boulders in the nearshore area.We first compare the SPH predictions with available laboratory experiments and thenexplore the effects of realistic 3D coastal bathymetry, non-linear behaviour of coastal waves,boulders shape and the impact of bedload and suspended sediment on dislodgement and initiationof boulder transport.

Two-dimensional solitary waves and periodic waves on coupled nonlinear electrical transmission lines

NASA Astrophysics Data System (ADS)

Wang, Heng; Zheng, Shuhua

2017-06-01

By using the dynamical system approach, the exact travelling wave solutions for a system of coupled nonlinear electrical transmission lines are studied. Based on this method, the bifurcations of phase portraits of a dynamical system are given. The two-dimensional solitary wave solutions and periodic wave solutions on coupled nonlinear transmission lines are obtained. With the aid of Maple, the numerical simulations are conducted for solitary wave solutions and periodic wave solutions to the model equation. The results presented in this paper improve upon previous studies.

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.

Electron plasma wave filamentation in the kinetic regime

NASA Astrophysics Data System (ADS)

Lushnikov, Pavel; Rose, Harvey; Silantyev, Denis

2016-10-01

We consider nonlinear electron plasma wave (EPW) dynamics in the kinetic wavenumber regime, 0.25 < kλD < 0.45 , which is typical for current high temperature laser-plasma interaction experiments, where k is the EPW wavenumber and λD is the electron Debye length. In this kinetic regime, EPW frequency reduction due to electron trapping may dominate the ponderomotive frequency shift. Previous 3D PIC simulations showed that the trapped electron EPW filamentation instability can saturate stimulated Raman backscatter by reducing the EPWs coherence but multidimensional Vlasov simulations [1] are needed to address that saturation in details. We performed nonlinear, non-equilibrium 2D Vlasov simulations to study the EPW filamentation. The initial conditions are created either by external forcing or by constructing the appropriate 1D travelling Bernstein-Greene-Kruskal (BGK) mode. Transverse perturbations of any of these initial conditions grow with time eventually producing strongly nonlinear filamentation followed by plasma turbulence. We compared these simulations with the theoretical results on growth rates of the transverse instability BGK mode showing the satisfactory agreement. Supported by the New Mexico Consortium and NSF DMS-1412140.

Experimental investigation of the effect of pump incoherence on nonlinear pump spectral broadening and continuous-wave supercontinuum generation

NASA Astrophysics Data System (ADS)

Martin-Lopez, S.; Carrasco-Sanz, A.; Corredera, P.; Abrardi, L.; Hernanz, M. L.; Gonzalez-Herraez, M.

2006-12-01

The development of high-power cw fiber lasers has triggered a great interest in the phenomena of nonlinear pump spectral broadening and cw supercontinuum generation. These effects have very convenient applications in Raman amplification, optical fiber metrology, and fiber sensing. In particular, it was recently shown that pump incoherence has a strong impact in these processes. We study experimentally the effect of pump incoherence in nonlinear pump spectral broadening and cw supercontinuum generation in optical fibers. We show that under certain experimental conditions an optimum degree of pump incoherence yields the best performance in the broadening process. We qualitatively explain these results, and we point out that these results may have important implications in cw supercontinuum optimization.

Growth of ring ripple in a collisionless plasma in relativistic-ponderomotive regime and its effect on stimulated Raman backscattering process

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

Rawat, Priyanka; Purohit, Gunjan, E-mail: gunjan75@gmail.com; Gauniyal, Rakhi

A theoretical and numerical study has been made of the propagation of a ring rippled laser beam in collisionless plasma with dominant relativistic ponderomotive nonlinearity and its effect on the excitation of electron plasma wave and stimulated Raman backscattering process. The growth of ring ripple, riding on an intense Gaussian laser beam in plasma has also been studied. A paraxial-ray and WKB approximation has been invoked to understand the nature of propagation of the ring rippled Gaussian laser beam in plasma, electron plasma wave and back reflectivity under the influence of both nonlinearities. The growth rate and focusing of amore » ring rippled beam is found to be considerably affected by the power of the main beam and the phase angle between the electric vectors of the main beam and the ring ripple. It has also been observed that the focusing is released by the coupling of relativistic and ponderomotive nonlinearities, which significantly affected the dynamics of the excitation of electron plasma wave and back reflectivity of stimulated Raman scattering (SRS). Due to the strong coupling between ring rippled laser beam and the excited electron plasma wave, back reflectivity of SRS is enhanced. It has been observed from the computational results that the effect of the increased intensity leads to suppression of SRS back reflectivity. The results have been presented for established laser and plasma parameters.« less

Nonlinear low frequency (LF) waves - Comets and foreshock phenomena

NASA Technical Reports Server (NTRS)

Tsurutani, Bruce T.

1991-01-01

A review is conducted of LF wave nonlinear properties at comets and in the earth's foreshock, engaging such compelling questions as why there are no cometary cyclotron waves, the physical mechanism responsible for 'dispersive whiskers', and the character of a general description of linear waves. Attention is given to the nonlinear properties of LF waves, whose development is illustrated by examples of waves and their features at different distances from the comet, as well as by computer simulation results. Also discussed is a curious wave mode detected from Comet Giacobini-Zinner, both at and upstream of the bow shock/wave.

Acoustic wave propagation and intensity fluctuations in shallow water 2006 experiment

NASA Astrophysics Data System (ADS)

Luo, Jing

Fluctuations of low frequency sound propagation in the presence of nonlinear internal waves during the Shallow Water 2006 experiment are analyzed. Acoustic waves and environmental data including on-board ship radar images were collected simultaneously before, during, and after a strong internal solitary wave packet passed through a source-receiver acoustic track. Analysis of the acoustic wave signals shows temporal intensity fluctuations. These fluctuations are affected by the passing internal wave and agrees well with the theory of the horizontal refraction of acoustic wave propagation in shallow water. The intensity focusing and defocusing that occurs in a fixed source-receiver configuration while internal wave packet approaches and passes the acoustic track is addressed in this thesis. Acoustic ray-mode theory is used to explain the modal evolution of broadband acoustic waves propagating in a shallow water waveguide in the presence of internal waves. Acoustic modal behavior is obtained from the data through modal decomposition algorithms applied to data collected by a vertical line array of hydrophones. Strong interference patterns are observed in the acoustic data, whose main cause is identified as the horizontal refraction referred to as the horizontal Lloyd mirror effect. To analyze this interference pattern, combined Parabolic Equation model and Vertical-mode horizontal-ray model are utilized. A semi-analytic formula for estimating the horizontal Lloyd mirror effect is developed.

Mixing of ultrasonic Lamb waves in thin plates with quadratic nonlinearity.

PubMed

Li, Feilong; Zhao, Youxuan; Cao, Peng; Hu, Ning

2018-07-01

This paper investigates the propagation of Lamb waves in thin plates with quadratic nonlinearity by one-way mixing method using numerical simulations. It is shown that an A 0 -mode wave can be generated by a pair of S 0 and A 0 mode waves only when mixing condition is satisfied, and mixing wave signals are capable of locating the damage zone. Additionally, it is manifested that the acoustic nonlinear parameter increases linearly with quadratic nonlinearity but monotonously with the size of mixing zone. Furthermore, because of frequency deviation, the waveform of the mixing wave changes significantly from a regular diamond shape to toneburst trains. Copyright © 2018 Elsevier B.V. All rights reserved.

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

PubMed

Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

2014-01-01

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

Self-organization of large-scale ULF electromagnetic wave structures in their interaction with nonuniform zonal winds in the ionospheric E region

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

Aburjania, G. D.; Chargazia, Kh. Z.

A study is made of the generation and subsequent linear and nonlinear evolution of ultralow-frequency planetary electromagnetic waves in the E region of a dissipative ionosphere in the presence of a nonuniform zonal wind (a sheared flow). Hall currents flowing in the E region and such permanent global factors as the spatial nonuniformity of the geomagnetic field and of the normal component of the Earth's angular velocity give rise to fast and slow planetary-scale electromagnetic waves. The efficiency of the linear amplification of planetary electromagnetic waves in their interaction with a nonuniform zonal wind is analyzed. When there are shearedmore » flows, the operators of linear problems are non-self-conjugate and the corresponding eigenfunctions are nonorthogonal, so the canonical modal approach is poorly suited for studying such motions and it is necessary to utilize the so-called nonmodal mathematical analysis. It is shown that, in the linear evolutionary stage, planetary electromagnetic waves efficiently extract energy from the sheared flow, thereby substantially increasing their amplitude and, accordingly, energy. The criterion for instability of a sheared flow in an ionospheric medium is derived. As the shear instability develops and the perturbation amplitude grows, a nonlinear self-localization mechanism comes into play and the process ends with the self-organization of nonlinear, highly localized, solitary vortex structures. The system thus acquires a new degree of freedom, thereby providing a new way for the perturbation to evolve in a medium with a sheared flow. Depending on the shape of the sheared flow velocity profile, nonlinear structures can be either purely monopole vortices or vortex streets against the background of the zonal wind. The accumulation of such vortices can lead to a strongly turbulent state in an ionospheric medium.« less

Simulation of Self-consistent Radio Wave Artificial Ionospheric Turbulence Pumping and Damping

NASA Astrophysics Data System (ADS)

Kochetov, Andrey

The numerical simulations of the action of self-consistent incident powerful electromagnetic wave absorption arising in the regions of artificial plasma turbulence excitation at formation, saturation and relaxation stages of turbulent structures (Kochetov, A.V., Mironov, V.A., Te-rina, G.I., Bubukina V. N, Physica D, Nonlinear phenomena, 2001, 152-153, 723) to reflection index dynamics are carried out. The nonlinear Schrüdinger equation in inhomogeneous plasma layer with incident electromagnetic wave pumping and backscattered radiation damping (Ko-chetov, et al, Adv. Space Res., 2002, 29, 1369 and 2006, 38, 2490) is extended with the imagi-nary part of plasma dielectric constant (volume damping), which is should be taken into account in strong electromagnetic field plasma regions and results the energy transformation from elec-tromagnetic waves to plasma ones at resonance interaction (D.V. Shapiro, V.I. Shevchenko, in Handbook of Plasma Physics 2, eds. A.A Galeev, R.N. Sudan. Elsevier, Amsterdam, 1984). The volume damping reproduces the basic energy transformation peculiarities: hard excitation, nonlinearity, hysteresis (A.V. Kochetov, E. Mjoelhus, Proc. of IV Intern. Workshop "SMP", Ed. A.G. Litvak, Vol.2, N. Novgorod, 2000, 491). Computer modeling demonstrates that the amplitude and period of reflection index oscillations at the formation stage slowly depend on damping parameters of turbulent plasma regions. The transformation from complicated: quasi-periodic and chaotic dynamics, to quasi-stationary regimes is shown at the saturation stage. Transient processes time becomes longer if the incident wave amplitude and nonlinear plasma response increase, but damping decreases. It is obtained that the calculated reflection and absorption index dynamics at the beginning of the saturation stage agrees qualitatively to the experimental results for ionosphere plasma modification study (Thide B., E.N. Sergeev, S.M. Grach, et. al., Phys. Rev. Lett., 2005, 95, 255002). The work was supported in part by RFBR grant 09-02-01150-a.

Effect of a relative phase of waves constituting the initial perturbation and the wave interference on the dynamics of strong-shock-driven Richtmyer-Meshkov flows

NASA Astrophysics Data System (ADS)

Pandian, Arun; Stellingwerf, Robert F.; Abarzhi, Snezhana I.

2017-07-01

While it is a common wisdom that initial conditions influence the evolution of the Richtmyer-Meshkov instability (RMI), the research in this area is focused primarily on the effects of the wavelength and amplitude of the interface perturbation. The information has hitherto largely ignored the influences on RMI dynamics of the relative phase of waves constituting a multiwave initial perturbation and the interference of the perturbation waves. In this work we systematically study the influence of the relative phase and the interference of waves constituting a multiwave initial perturbation on a strong-shock-driven Richtmyer-Meshkov unstable interface separating ideal fluids with contrast densities. We apply group theory analysis and smoothed particle hydrodynamics numerical simulations. For verification and validation of the simulations, qualitative and quantitative comparisons are performed with rigorous zeroth-order, linear, and nonlinear theories as well as with gas dynamics experiments achieving good agreement. For a sample case of a two-wave (two-mode) initial perturbation we select the first-wave amplitude enabling the maximum initial growth rate of the RMI and we vary the second-wave amplitude from 1% to 100% of the first-wave amplitude. We also vary the relative phase of the first and second waves and consider the in-phase, the antiphase and the random-phase cases. We find that the relative phase and the interference of waves are important factors of RMI dynamics influencing qualitatively and quantitatively the symmetry, morphology, and growth rate of the Richtmyer-Meshkov unstable interface, as well as the order and disorder in strong-shock-driven RMI.

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.

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

PubMed

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

2015-01-28

Regular wave-induced behaviour of a floating stationary two-dimensional body with a moonpool is studied. The focus is on resonant piston-mode motion in the moonpool and rigid-body motions. Dedicated two-dimensional experiments have been performed. Two numerical hybrid methods, which have previously been applied to related problems, are further developed. Both numerical methods couple potential and viscous flow. The semi-nonlinear hybrid method uses linear free-surface and body-boundary conditions. The other one uses fully nonlinear free-surface and body-boundary conditions. The harmonic polynomial cell method solves the Laplace equation in the potential flow domain, while the finite volume method solves the Navier-Stokes equations in the viscous flow domain near the body. Results from the two codes are compared with the experimental data. The nonlinear hybrid method compares well with the data, while certain discrepancies are observed for the semi-nonlinear method. In particular, the roll motion is over-predicted by the semi-nonlinear hybrid method. Error sources in the semi-nonlinear hybrid method are discussed. The moonpool strongly affects heave motions in a frequency range around the piston-mode resonance frequency of the moonpool. No resonant water motions occur in the moonpool at the piston-mode resonance frequency. Instead large moonpool motions occur at a heave natural frequency associated with small damping near the piston-mode resonance frequency. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

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.

Nonlinear Waves In A Stenosed Elastic Tube Filled With Viscous Fluid: Forced Perturbed Korteweg-De Vries Equation

NASA Astrophysics Data System (ADS)

Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee

In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.

Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).

PubMed

Hess, Peter; Lomonosov, Alexey M; Mayer, Andreas P

2014-01-01

The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented. Copyright © 2013 Elsevier B.V. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials

PubMed Central

Li, Nianbei; Ren, Jie

2014-01-01

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports. PMID:25169668

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations.

PubMed

Slunyaev, A; Pelinovsky, E; Sergeeva, A; Chabchoub, A; Hoffmann, N; Onorato, M; Akhmediev, N

2013-07-01

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

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).

Double-Diffusive Convection at Low Prandtl Number

NASA Astrophysics Data System (ADS)

Garaud, Pascale

2018-01-01

This work reviews present knowledge of double-diffusive convection at low Prandtl number obtained using direct numerical simulations, in both the fingering regime and the oscillatory regime. Particular emphasis is given to modeling the induced turbulent mixing and its impact in various astrophysical applications. The nonlinear saturation of fingering convection at low Prandtl number usually drives small-scale turbulent motions whose transport properties can be predicted reasonably accurately using a simple semi-analytical model. In some instances, large-scale internal gravity waves can be excited by a collective instability and eventually cause layering. The nonlinear saturation of oscillatory double-diffusive convection exhibits much more complex behavior. Weakly stratified systems always spontaneously transition into layered convection associated with very efficient mixing. More strongly stratified systems remain dominated by weak wave turbulence unless they are initialized into a layered state. The effects of rotation, shear, lateral gradients, and magnetic fields are briefly discussed.

Turbulence and wave particle interactions in solar-terrestrial plasmas

NASA Technical Reports Server (NTRS)

Dulk, G. A.

1982-01-01

Theoretical modelling of two dimensional compressible convection in the Sun shows that convective flows can extend over many pressure scale heights without the nonlinear motions becoming supersonic, and that compressional work arising from pressure fluctuations can be comparable to that by buoyancy forces. These results are contrary to what was supposed in prevailing mixing length models for solar convection, and they imply a much greater degree of organized flow extending over the full depth of the convection zone. The nonlinear penetration of motions into the stable region below the convection zone was emphasized. These compressible flows are dominated by downward directed plumes in the unstable zone. Their strong penetration into the region of stable stratification below excites a broad spectrum of internal gravity waves there, and these in turn feed back upon the convection in the unstable zone to produce a rich time dependence.

Monitoring stress related velocity variation in concrete with a 2 x 10(-5) relative resolution using diffuse ultrasound.

PubMed

Larose, Eric; Hall, Stephen

2009-04-01

Ultrasonic waves propagating in solids have stress-dependent velocities. The relation between stress (or strain) and velocity forms the basis of non-linear acoustics. In homogeneous solids, conventional time-of-flight techniques have measured this dependence with spectacular precision. In heterogeneous media such as concrete, the direct (ballistic) wave around 500 kHz is strongly attenuated and conventional techniques are less efficient. In this manuscript, the effect of weak stress changes on the late arrivals constituting the acoustic diffuse coda is tracked. A resolution of 2 x 10(-5) in relative velocity change is attained which corresponds to a sensitivity to stress change of better than 50 kPa. Therefore, the technique described here provides an original way to measure the non-linear parameter with stress variations on the order of tens of kPa.

Uniform shock waves in disordered granular matter.

PubMed

Gómez, Leopoldo R; Turner, Ari M; Vitelli, Vincenzo

2012-10-01

The confining pressure P is perhaps the most important parameter controlling the properties of granular matter. Strongly compressed granular media are, in many respects, simple solids in which elastic perturbations travel as ordinary phonons. However, the speed of sound in granular aggregates continuously decreases as the confining pressure decreases, completely vanishing at the jamming-unjamming transition. This anomalous behavior suggests that the transport of energy at low pressures should not be dominated by phonons. In this work we use simulations and theory to show how the response of granular systems becomes increasingly nonlinear as pressure decreases. In the low-pressure regime the elastic energy is found to be mainly transported through nonlinear waves and shocks. We numerically characterize the propagation speed, shape, and stability of these shocks and model the dependence of the shock speed on pressure and impact intensity by a simple analytical approach.

Good vibrations: Controlling light with sound (Conference Presentation)

NASA Astrophysics Data System (ADS)

Eggleton, Benjamin J.; Choudhary, Amol

2016-10-01

One of the surprises of nonlinear optics, is that light may interact strongly with sound. Intense laser light literally "shakes" the glass in optical fibres, exciting acoustic waves (sound) in the fibre. Under the right conditions, it leads to a positive feedback loop between light and sound termed "Stimulated Brillouin Scattering," or simply SBS. This nonlinear interaction can amplify or filter light waves with extreme precision in frequency which makes it uniquely suited to solve key problems in the fields of defence, biomedicine, wireless communications, spectroscopy and imaging. We have achieved the first demonstration of SBS in compact chip-scale structures, carefully designed so that the optical fields and the acoustic fields are simultaneously confined and guided. This new platform has opened a range of new functionalities that are being applied in communications and defence with breathtaking performance and compactness. My talk will introduce this new field and review our progress and achievements, including silicon based optical phononic processor.

Boundary enhanced effects on the existence of quadratic solitons

NASA Astrophysics Data System (ADS)

Chen, Manna; Zhang, Ting; Li, Wenjie; Lu, Daquan; Guo, Qi; Hu, Wei

2018-05-01

We investigate, both analytically and numerically, the boundary enhanced effects exerted on the quadratic solitons consisting of fundamental waves and oscillatory second harmonics in the presence of boundary conditions. The nonlocal analogy predicts that the soliton for fundamental wave is supported by the balance between equivalent nonlinear confinement and diffraction (or dispersion). Under Snyder and Mitchell's strongly nonlocal approximation, we obtain the analytical soliton solutions both with and without the boundary conditions to show the impact of boundary conditions. We can distinguish explicitly the nonlinear confinement between the second harmonic mutual interaction and the enhanced effects caused by remote boundaries. Those boundary enhanced effects on the existence of solitons can be positive or negative, which depend on both sample size and nonlocal parameter. The piecewise existence regime of solitons can be explained analytically. The analytical soliton solutions are verified by the numerical ones and the discrepancy between them is also discussed.

Saturation mechanisms of backward stimulated Raman scattering in a one-dimensional geometry

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

Friou, A.; Bénisti, D.; Gremillet, L.

2013-10-15

In this paper, we investigate the saturation mechanisms of backward stimulated Raman scattering (BSRS) induced by nonlinear kinetic effects. In particular, we stress the importance of accounting for both the nonlinear frequency shift of the electron plasma wave and the growth of sidebands, in order to understand what stops the coherent growth of Raman scattering. Using a Bernstein-Greene-Kruskal approach, we provide an estimate for the maximum amplitude reached by a BSRS-driven plasma wave after the phase of monotonic growth. This estimate is in very good agreement with the results from kinetic simulations of stimulated Raman scattering using both a Vlasovmore » and a Particle in Cell code. Our analysis, which may be generalized to a multidimensional geometry, should provide a means to estimate the limits of backward Raman amplification or the effectiveness of strategies that aim at strongly reducing Raman reflectivity in a fusion plasma.« less

Rogue events in the group velocity horizon

PubMed Central

Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Mahnke, Christoph; Mitschke, Fedor; Steinmeyer, Günter

2012-01-01

The concept of rogue waves arises from a mysterious and potentially calamitous phenomenon of oceanic surfaces. There is mounting evidence that they are actually commonplace in a variety of different physical settings. A set of defining criteria has been advanced; this set is of great generality and therefore applicable to a wide class of systems. The question arises naturally whether there are generic mechanisms responsible for extreme events in different systems. Here we argue that under suitable circumstances nonlinear interaction between weak and strong waves results in intermittent giant waves with all the signatures of rogue waves. To obtain these circumstances only a few basic conditions must be met. Then reflection of waves at the so-called group-velocity horizon occurs. The connection between rogue waves and event horizons, seemingly unrelated physical phenomena, is identified as a feature common in many different physical systems. PMID:23152941

Turbulence and Biological Productivity at Dongsha Reef in the S. China Sea.

NASA Astrophysics Data System (ADS)

St Laurent, L.

2016-02-01

The combination of the Kuroshio Current, strong tides, topography, and stratification make the South China Sea one of the most energetic energy cascade environments in the global ocean. Internal waves generated in the Luzon Strait emit into the South China Sea as solitons, and propagate until they dissipate along the continental shelves of China and Vietnam. The abrupt conversion of solitons to nonlinear wave trains occurs as the waves pass onto the Dongsha Plateau. The Dongsha Reef at the center of the Plateau is directly in the path of the incoming waves. A measurement program during 2015 documented the energetic turbulence that results as internal waves collide with the Reef. Glider based measurements of microstructure and optical properties showed that turbulent mixing and transport are correlated to biological productivity. It is speculated that the existence of the Reef itself is the result of the breaking internal waves, which moderate the temperature and nutrient levels.

Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Grelu, Philippe; Mihalache, Dumitru

2017-11-01

This review is dedicated to recent progress in the active field of rogue waves, with an emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector, and multidimensional integrable nonlinear systems. We first give a brief outline of the historical background of the rogue wave research, including referring to relevant up-to-date experimental results. Then we present an in-depth discussion of the scalar rogue waves within two different integrable frameworks—the infinite nonlinear Schrödinger (NLS) hierarchy and the general cubic-quintic NLS equation, considering both the self-focusing and self-defocusing Kerr nonlinearities. We highlight the concept of chirped Peregrine solitons, the baseband modulation instability as an origin of rogue waves, and the relation between integrable turbulence and rogue waves, each with illuminating examples confirmed by numerical simulations. Later, we recur to the vector rogue waves in diverse coupled multicomponent systems such as the long-wave short-wave equations, the three-wave resonant interaction equations, and the vector NLS equations (alias Manakov system). In addition to their intriguing bright-dark dynamics, a series of other peculiar structures, such as coexisting rogue waves, watch-hand-like rogue waves, complementary rogue waves, and vector dark three sisters, are reviewed. Finally, for practical considerations, we also remark on higher-dimensional rogue waves occurring in three closely-related (2  +  1)D nonlinear systems, namely, the Davey-Stewartson equation, the composite (2  +  1)D NLS equation, and the Kadomtsev-Petviashvili I equation. As an interesting contrast to the peculiar X-shaped light bullets, a concept of rogue wave bullets intended for high-dimensional systems is particularly put forward by combining contexts in nonlinear optics.

Wave-Kinetic Simulations of the Nonlinear Generation of Electromagnetic VLF Waves through Velocity Ring Instabilities

NASA Astrophysics Data System (ADS)

Ganguli, G.; Crabtree, C. E.; Rudakov, L.; Mithaiwala, M.

2014-12-01

Velocity ring instabilities are a common naturally occuring magnetospheric phenomenon that can also be generated by man made ionospheric experiments. These instabilities are known to generate lower-hybrid waves, which generally cannot propagte out of the source region. However, nonlinear wave physics can convert these linearly driven electrostatic lower-hybrid waves into electromagnetic waves that can escape the source region. These nonlinearly generated waves can be an important source of VLF turbulence that controls the trapped electron lifetime in the radiation belts. We develop numerical solutions to the wave-kinetic equation in a periodic box including the effects of nonlinear (NL) scattering (nonlinear Landau damping) of Lower-hybrid waves giving the evolution of the wave-spectra in wavenumber space. Simultaneously we solve the particle diffusion equation of both the background plasma particles and the ring ions, due to both linear and nonlinear Landau resonances. At initial times for cold ring ions, an electrostatic beam mode is excited, while the kinetic mode is stable. As the instability progresses the ring ions heat, the beam mode is stabilized, and the kinetic mode destabilizes. When the amplitude of the waves becomes sufficient the lower-hybrid waves are scattered (by either nearly unmagnetized ions or magnetized electrons) into electromagnetic magnetosonic waves [Ganguli et al 2010]. The effect of NL scattering is to limit the amplitude of the waves, slowing down the quasilinear relaxation time and ultimately allowing more energy from the ring to be liberated into waves [Mithaiwala et al. 2011]. The effects of convection out of the instability region are modeled, additionally limiting the amplitude of the waves, allowing further energy to be liberated from the ring [Scales et al., 2012]. Results are compared to recent 3D PIC simulations [Winske and Duaghton 2012].

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

NASA Astrophysics Data System (ADS)

Hasanian, Mostafa; Lissenden, Cliff J.

2018-04-01

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

Ultrasound shear wave simulation based on nonlinear wave propagation and Wigner-Ville Distribution analysis

NASA Astrophysics Data System (ADS)

Bidari, Pooya Sobhe; Alirezaie, Javad; Tavakkoli, Jahan

2017-03-01

This paper presents a method for modeling and simulation of shear wave generation from a nonlinear Acoustic Radiation Force Impulse (ARFI) that is considered as a distributed force applied at the focal region of a HIFU transducer radiating in nonlinear regime. The shear wave propagation is simulated by solving the Navier's equation from the distributed nonlinear ARFI as the source of the shear wave. Then, the Wigner-Ville Distribution (WVD) as a time-frequency analysis method is used to detect the shear wave at different local points in the region of interest. The WVD results in an estimation of the shear wave time of arrival, its mean frequency and local attenuation which can be utilized to estimate medium's shear modulus and shear viscosity using the Voigt model.

Generation mechanisms of fundamental rogue wave spatial-temporal structure.

PubMed

Ling, Liming; Zhao, Li-Chen; Yang, Zhan-Ying; Guo, Boling

2017-08-01

We discuss the generation mechanism of fundamental rogue wave structures in N-component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the N-component coupled nonlinear Schrödinger equation. Furthermore, our results show that N-component coupled nonlinear Schrödinger systems may possess N different fundamental rogue wave patterns at most. These results can be extended to evaluate the type and number of fundamental rogue wave structure in other coupled nonlinear systems.

Signatures of Nonlinear Waves in Coronal Plumes and Holes

NASA Technical Reports Server (NTRS)

Ofman, Leon

1999-01-01

In recent Ultraviolet Coronagraph Spectrometer/Solar and Heliospheric Observatory (UVCS/SOHO) White Light Channel (WLC) observations we found quasi-periodic variations in the polarized brightness (pB) in the polar coronal holes at heliocentric distances of 1.9-2.45 solar radii. The motivation for the observation is the 2.5D Magnetohydrodynamics (MHD) model of solar wind acceleration by nonlinear waves, that predicts compressive fluctuations in coronal holes. To help identify the waves observed with the UVCS/WLC we model the propagation and dissipation of slow magnetosonic waves in polar plumes using 1D MHD code in spherical geometry, We find that the slow waves nonlinearly steepen in the gravitationally stratified plumes. The nonlinear steepening of the waves leads to enhanced dissipation due to compressive viscosity at the wave-fronts.

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics

NASA Astrophysics Data System (ADS)

Horikis, Theodoros P.; Frantzeskakis, Dimitrios J.

2017-06-01

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in 2 +1 dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming Y -, X -, and H -shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters.

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics.

PubMed

Horikis, Theodoros P; Frantzeskakis, Dimitrios J

2017-06-16

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in 2+1 dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming Y-, X-, and H-shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters.

Interaction of solitons for obliquely propagating magnetoacoustic waves in stellar atmosphere

NASA Astrophysics Data System (ADS)

Jahangir, R.; Masood, W.; Siddiq, M.; Batool, Nazia

2016-12-01

We study here the nonlinear oblique propagation of magnetoacoustic waves in dense plasmas with degenerate electrons by deriving Kadomtsev-Petviashvili (KP) equation for small but finite amplitude perturbations. The two soliton interaction has been studied by finding the solution of the KP equation using the Hirota bilinear formalism. For illustrative purposes, we have used the plasma parameters typically found in white dwarf stars for both the fast and slow modes of magnetoacoustic waves. It has been observed that the soliton interaction in the fast and slow modes is strongly influenced by the predominant and weak dispersive coefficients of the KP equation. The single soliton behavior has also been explained for the fast and slow magnetoacoustic modes.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Wu, Xiao-Yu; Sun, Yan

2018-02-01

Under investigation in this paper is the higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials which can be applied in the nonlinear optics, hydrodynamics, plasma physics and Bose-Einstein condensation. Based on the Kadomtsev-Petviashvili hierarchy reduction, we construct the Nth order rogue wave-like solutions in terms of the Gramian under the integrable constraint. With the help of the analytic and graphic analysis, we exhibit the first-, second- and third-order rogue wave-like solutions through the different dispersion, nonlinearity and linear potential coefficients. We find that only if the dispersion and nonlinearity coefficients are proportional to each other, heights of the background of those rogue waves maintain unchanged with time increasing. Due to the existence of complex parameters, such nonautonomous rogue waves in the higher-order cases have more complex features than those in the lower.

Observation of strong stimulated photorefractive scattering and self-pumped phase conjugation in LiNbO3:Mg in the ultraviolet

NASA Astrophysics Data System (ADS)

Qiao, Haijun; Tomita, Yasuo; Xu, Jingjun; Wu, Qiang; Zhang, Guoquan; Zhang, Guangyin

2005-09-01

We report on the observation of diffusion-dominant photorefraction and light-induced nonlinear forward and backward scattering in highly Mg-doped LiNbO3 at 351 nm. We also demonstrate what we believe to be the first continuous-wave self-pumped phase conjugation via stimulated photorefractive backscattering in the ultraviolet.

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

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

Ruban, V. P., E-mail: ruban@itp.ac.ru

2015-05-15

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of roguemore » wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.« less

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.

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.

Violent transient sloshing-wave interaction with a baffle in a three-dimensional numerical tank

NASA Astrophysics Data System (ADS)

Xue, Mi-An; Zheng, Jinhai; Lin, Pengzhi; Xiao, Zhong

2017-08-01

A finite difference model for solving Navier Stokes equations with turbulence taken into account is used to investigate viscous liquid sloshing-wave interaction with baffles in a tank. The volume-of-fluid and virtual boundary force methods are employed to simulate free surface flow interaction with structures. A liquid sloshing experimental apparatus was established to evaluate the accuracy of the proposed model, as well as to study nonlinear sloshing in a prismatic tank with the baffles. Damping effects of sloshing in a rectangular tank with bottom-mounted vertical baffles and vertical baffles touching the free surface are studied numerically and experimentally. Good agreement is obtained between the present numerical results and experimental data. The numerical results match well with the current experimental data for strong nonlinear sloshing with large free surface slopes. The reduction in sloshing-wave elevation and impact pressure induced by the bottom-mounted vertical baffle and the vertical baffle touching the free surface is estimated by varying the external excitation frequency and the location and height of the vertical baffle under horizontal excitation.

Marine natural hazards in coastal zone: observations, analysis and modelling (Plinius Medal Lecture)

NASA Astrophysics Data System (ADS)

Didenkulova, Ira

2010-05-01

Giant surface waves approaching the coast frequently cause extensive coastal flooding, destruction of coastal constructions and loss of lives. Such waves can be generated by various phenomena: strong storms and cyclones, underwater earthquakes, high-speed ferries, aerial and submarine landslides. The most famous examples of such events are the catastrophic tsunami in the Indian Ocean, which occurred on 26 December 2004 and hurricane Katrina (28 August 2005) in the Atlantic Ocean. The huge storm in the Baltic Sea on 9 January 2005, which produced unexpectedly long waves in many areas of the Baltic Sea and the influence of unusually high surge created by long waves from high-speed ferries, should also be mentioned as examples of regional marine natural hazards connected with extensive runup of certain types of waves. The processes of wave shoaling and runup for all these different marine natural hazards (tsunami, coastal freak waves, ship waves) are studied based on rigorous solutions of nonlinear shallow-water theory. The key and novel results presented here are: i) parameterization of basic formulas for extreme runup characteristics for bell-shape waves, showing that they weakly depend on the initial wave shape, which is usually unknown in real sea conditions; ii) runup analysis of periodic asymmetric waves with a steep front, as such waves are penetrating inland over large distances and with larger velocities than symmetric waves; iii) statistical analysis of irregular wave runup demonstrating that wave nonlinearity nearshore does not influence on the probability distribution of the velocity of the moving shoreline and its moments, and influences on the vertical displacement of the moving shoreline (runup). Wave runup on convex beaches and in narrow bays, which allow abnormal wave amplification is also discussed. Described analytical results are used for explanation of observed extreme runup of tsunami, freak (sneaker) waves and ship waves on different coasts along different bottom profiles.

Nonlinear theory for axisymmetric self-similar two-dimensional oscillations of electrons in cold plasma with constant proton background

NASA Astrophysics Data System (ADS)

Osherovich, V. A.; Fainberg, J.

2018-01-01

We consider simultaneous oscillations of electrons moving both along the axis of symmetry and also in the direction perpendicular to the axis. We derive a system of three nonlinear ordinary differential equations which describe self-similar oscillations of cold electrons in a constant proton density background (np = n0 = constant). These three equations represent an exact class of solutions. For weak nonlinear conditions, the frequency spectra of electric field oscillations exhibit split frequency behavior at the Langmuir frequency ωp0 and its harmonics, as well as presence of difference frequencies at low spectral values. For strong nonlinear conditions, the spectra contain peaks at frequencies with values ωp0(n +m √{2 }) , where n and m are integer numbers (positive and negative). We predict that both spectral types (weak and strong) should be observed in plasmas where axial symmetry may exist. To illustrate possible applications of our theory, we present a spectrum of electric field oscillations observed in situ in the solar wind by the WAVES experiment on the Wind spacecraft during the passage of a type III solar radio burst.

Local defect resonance (LDR): A route to highly efficient thermosonic and nonlinear ultrasonic NDT

NASA Astrophysics Data System (ADS)

Solodov, Igor

2014-02-01

The concept of LDR is based on the fact that inclusion of a defect leads to a local drop of rigidity for a certain mass of the material that should manifest in a particular characteristic frequency of the defect. A frequency match between the driving ultrasonic wave and this characteristic frequency provides an efficient energy pumping from the wave directly into the defect. For simulated and realistic defects in various materials the LDR-induced local resonance increase in the vibration amplitude averages up to ˜ (20-40 dB). Due to a strong resonance amplification of the local vibrations, the LDR-driven defects manifest a profound nonlinearity even at moderate ultrasonic excitation level. The nonlinearity combined with resonance results in efficient generation of the higher harmonics and is also used as a filter/amplifier in the frequency mixing mode of nonlinear NDT. The LDR high-Q thermal response enables to realize a frequency-selective imaging with an opportunity to distinguish between different defects by changing the driving frequency. The LDR-thermosonics requires much lower acoustic power to activate defects that makes it possible to avoid high-power ultrasonic instrumentation and proceed to a noncontact ultrasonic thermography by using air-coupled ultrasonic excitation.

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

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

Neutron star merger GW170817 strongly constrains doubly coupled bigravity

NASA Astrophysics Data System (ADS)

Akrami, Yashar; Brax, Philippe; Davis, Anne-Christine; Vardanyan, Valeri

2018-06-01

We study the implications of the recent detection of gravitational waves emitted by a pair of merging neutron stars and their electromagnetic counterpart, events GW170817 and GRB170817A, on the viability of the doubly coupled bimetric models of cosmic evolution, where the two metrics couple directly to matter through a composite, effective metric. We demonstrate that the bounds on the speed of gravitational waves place strong constraints on the doubly coupled models, forcing either the two metrics to be proportional at the background level or the models to become singly coupled. Proportional backgrounds are particularly interesting as they provide stable cosmological solutions with phenomenologies equivalent to that of Λ CDM at the background level as well as for linear perturbations, while nonlinearities are expected to show deviations from the standard model.

Investigation of scaling characteristics for defining design environments due to transient ground winds and near-field, nonlinear acoustic fields

NASA Technical Reports Server (NTRS)

Shih, C. C.

1973-01-01

In order to establish a foundation of scaling laws for the highly nonlinear waves associated with the launch vehicle, the basic knowledge of the relationships among the paramaters pertinent to the energy dissipation process associated with the propagation of nonlinear pressure waves in thermoviscous media is required. The problem of interest is to experimentally investigate the temporal and spacial velocity profiles of fluid flow in a 3-inch open-end pipe of various lengths, produced by the propagation of nonlinear pressure waves for various diaphragm burst pressures of a pressure wave generator. As a result, temporal and spacial characteristics of wave propagation for a parametric set of nonlinear pressure waves in the pipe containing air under atmospheric conditions were determined. Velocity measurements at five sections along the pipes of up to 210 ft. in length were made with hot-film anemometers for five pressure waves produced by a piston. The piston was derived with diaphragm burst pressures at 20, 40, 60, 80 and 100 psi in the driver chamber of the pressure wave generator.

Altimeter Observations of Baroclinic Oceanic Inertia-Gravity Wave Turbulence

NASA Technical Reports Server (NTRS)

Glazman, R. E.; Cheng, B.

1996-01-01

For a wide range of nonlinear wave processes - from capillary to planetary waves - theory predicts the existence of Kolmogorov-type spectral cascades of energy and other conserved quantities occuring via nonlinear resonant wave-wave interactions. So far, observations of wave turbulence (WT) have been limited to small-scale processes such as surface gravity and capillary-gravity waves.

3D numerical simulation of the long range propagation of acoustical shock waves through a heterogeneous and moving medium

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

Luquet, David; Marchiano, Régis; Coulouvrat, François, E-mail: francois.coulouvrat@upmc.fr

2015-10-28

Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength,more » the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D aspect, the code was massively parallelized using the single program, multiple data paradigm with the Message Passing Interfaces (MPI) for distributed memory architectures. This allows us to handle problems in the order of a thousand billion mesh points in the four dimensions (3 dimensions of space plus time). The validity of the method has been thoroughly evaluated on many cases with known solutions: linear piston, scattering of plane wave by a heterogeneous sphere, propagation in a waveguide with a shear flow, scattering by a finite amplitude vortex and nonlinear propagation in a thermoviscous medium. This validation process allows for a detailed assessment of the advantages and limitations of the method. Finally, applications to atmospheric propagation of shock waves will be presented.« less

3D numerical simulation of the long range propagation of acoustical shock waves through a heterogeneous and moving medium

NASA Astrophysics Data System (ADS)

Luquet, David; Marchiano, Régis; Coulouvrat, François

2015-10-01

Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D aspect, the code was massively parallelized using the single program, multiple data paradigm with the Message Passing Interfaces (MPI) for distributed memory architectures. This allows us to handle problems in the order of a thousand billion mesh points in the four dimensions (3 dimensions of space plus time). The validity of the method has been thoroughly evaluated on many cases with known solutions: linear piston, scattering of plane wave by a heterogeneous sphere, propagation in a waveguide with a shear flow, scattering by a finite amplitude vortex and nonlinear propagation in a thermoviscous medium. This validation process allows for a detailed assessment of the advantages and limitations of the method. Finally, applications to atmospheric propagation of shock waves will be presented.

Rogue wave solutions for the infinite integrable nonlinear Schrödinger equation hierarchy.

PubMed

Ankiewicz, A; Akhmediev, N

2017-07-01

We present rogue wave solutions of the integrable nonlinear Schrödinger equation hierarchy with an infinite number of higher-order terms. The latter include higher-order dispersion and higher-order nonlinear terms. In particular, we derive the fundamental rogue wave solutions for all orders of the hierarchy, with exact expressions for velocities, phase, and "stretching factors" in the solutions. We also present several examples of exact solutions of second-order rogue waves, including rogue wave triplets.

Optical rogue waves for the inhomogeneous generalized nonlinear Schrödinger equation.

PubMed

Loomba, Shally; Kaur, Harleen

2013-12-01

We present optical rogue wave solutions for a generalized nonlinear Schrodinger equation by using similarity transformation. We have predicted the propagation of rogue waves through a nonlinear optical fiber for three cases: (i) dispersion increasing (decreasing) fiber, (ii) periodic dispersion parameter, and (iii) hyperbolic dispersion parameter. We found that the rogue waves and their interactions can be tuned by properly choosing the parameters. We expect that our results can be used to realize improved signal transmission through optical rogue waves.

Observation of ion acoustic multi-Peregrine solitons in multicomponent plasma with negative ions

NASA Astrophysics Data System (ADS)

Pathak, Pallabi; Sharma, Sumita K.; Nakamura, Y.; Bailung, H.

2017-12-01

The evolution of the multi-Peregrine soliton is investigated in a multicomponent plasma and found to be critically dependent on the initial bound state. Formation and splitting of Peregrine soliton, broadening of the frequency spectra provide clear evidence of nonlinear-dispersive focusing due to modulational instability, a generic mechanism for rogue wave formation in which amplitude and phase modulation grow as a result of interplay between nonlinearity and anomalous dispersion. We have shown that initial perturbation parameters (amplitude & temporal length) critically determine the number of solitons evolution. It is also found that a sufficiently long wavelength perturbation of high amplitude invoke strong nonlinearity to generate a supercontinuum state. Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT) analysis of the experimental time series data clearly indicate the spatio-temporal localization and spectral broadening. We consider a model based on the frame work of Nonlinear Schrodinger equation (NLSE) to explain the experimental observations.

Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation

PubMed Central

Jing, Yun; Tao, Molei; Clement, Greg T.

2011-01-01

A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green’s function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed. PMID:21302985

The Effect of Crack Orientation on the Nonlinear Interaction of a P-wave with an S-wave

DOE PAGES

TenCate, J. A.; Malcolm, A. E.; Feng, X.; ...

2016-06-06

Cracks, joints, fluids, and other pore-scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore-scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presencemore » and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low-amplitude P wave probe by a high-amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.« less

NONLINEAR REFLECTION PROCESS OF LINEARLY POLARIZED, BROADBAND ALFVÉN WAVES IN THE FAST SOLAR WIND

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

Shoda, M.; Yokoyama, T., E-mail: shoda@eps.s.u-tokyo.ac.jp

2016-04-01

Using one-dimensional numerical simulations, we study the elementary process of Alfvén wave reflection in a uniform medium, including nonlinear effects. In the linear regime, Alfvén wave reflection is triggered only by the inhomogeneity of the medium, whereas in the nonlinear regime, it can occur via nonlinear wave–wave interactions. Such nonlinear reflection (backscattering) is typified by decay instability. In most studies of decay instabilities, the initial condition has been a circularly polarized Alfvén wave. In this study we consider a linearly polarized Alfvén wave, which drives density fluctuations by its magnetic pressure force. For generality, we also assume a broadband wavemore » with a red-noise spectrum. In the data analysis, we decompose the fluctuations into characteristic variables using local eigenvectors, thus revealing the behaviors of the individual modes. Different from the circular-polarization case, we find that the wave steepening produces a new energy channel from the parent Alfvén wave to the backscattered one. Such nonlinear reflection explains the observed increasing energy ratio of the sunward to the anti-sunward Alfvénic fluctuations in the solar wind with distance against the dynamical alignment effect.« less

Second-harmonic generation in shear wave beams with different polarizations

NASA Astrophysics Data System (ADS)

Spratt, Kyle S.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2015-10-01

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

Transition from geostrophic turbulence to inertia-gravity waves in the atmospheric energy spectrum.

PubMed

Callies, Jörn; Ferrari, Raffaele; Bühler, Oliver

2014-12-02

Midlatitude fluctuations of the atmospheric winds on scales of thousands of kilometers, the most energetic of such fluctuations, are strongly constrained by the Earth's rotation and the atmosphere's stratification. As a result of these constraints, the flow is quasi-2D and energy is trapped at large scales—nonlinear turbulent interactions transfer energy to larger scales, but not to smaller scales. Aircraft observations of wind and temperature near the tropopause indicate that fluctuations at horizontal scales smaller than about 500 km are more energetic than expected from these quasi-2D dynamics. We present an analysis of the observations that indicates that these smaller-scale motions are due to approximately linear inertia-gravity waves, contrary to recent claims that these scales are strongly turbulent. Specifically, the aircraft velocity and temperature measurements are separated into two components: one due to the quasi-2D dynamics and one due to linear inertia-gravity waves. Quasi-2D dynamics dominate at scales larger than 500 km; inertia-gravity waves dominate at scales smaller than 500 km.

Transition from geostrophic turbulence to inertia–gravity waves in the atmospheric energy spectrum

PubMed Central

Callies, Jörn; Ferrari, Raffaele; Bühler, Oliver

2014-01-01

Midlatitude fluctuations of the atmospheric winds on scales of thousands of kilometers, the most energetic of such fluctuations, are strongly constrained by the Earth’s rotation and the atmosphere’s stratification. As a result of these constraints, the flow is quasi-2D and energy is trapped at large scales—nonlinear turbulent interactions transfer energy to larger scales, but not to smaller scales. Aircraft observations of wind and temperature near the tropopause indicate that fluctuations at horizontal scales smaller than about 500 km are more energetic than expected from these quasi-2D dynamics. We present an analysis of the observations that indicates that these smaller-scale motions are due to approximately linear inertia–gravity waves, contrary to recent claims that these scales are strongly turbulent. Specifically, the aircraft velocity and temperature measurements are separated into two components: one due to the quasi-2D dynamics and one due to linear inertia–gravity waves. Quasi-2D dynamics dominate at scales larger than 500 km; inertia–gravity waves dominate at scales smaller than 500 km. PMID:25404349

Exact result in strong wave turbulence of thin elastic plates

NASA Astrophysics Data System (ADS)

Düring, Gustavo; Krstulovic, Giorgio

2018-02-01

An exact result concerning the energy transfers between nonlinear waves of a thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the 4/5 -Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity, and the Airy stress function of a plate, is proven to be equal to -ɛ ℓ , where ℓ is a length scale in the inertial range at which the increments are evaluated and ɛ the energy dissipation rate. Numerical data confirm this law. In addition, a useful definition of the energy fluxes in Fourier space is introduced and proven numerically to be flat in the inertial range. The exact results derived in this Rapid Communication are valid for both weak and strong wave turbulence. They could be used as a theoretical benchmark of new wave-turbulence theories and to develop further analogies with hydrodynamical turbulence.

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.

Nonlinear surface waves at ferrite-metamaterial waveguide structure

NASA Astrophysics Data System (ADS)

Hissi, Nour El Houda; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Shabat, Mohammed Musa; Atangana, Jacques

2016-09-01

A new ferrite slab made of a metamaterial (MTM), surrounded by a nonlinear cover cladding and a ferrite substrate, was shown to support unusual types of electromagnetic surface waves. We impose the boundary conditions to derive the dispersion relation and others necessary to formulate the proposed structure. We analyse the dispersion properties of the nonlinear surface waves and we calculate the associated propagation index and the film-cover interface nonlinearity. In the calculation, several sets of the permeability of the MTM are considered. Results show that the waves behaviour depends on the values of the permeability of the MTM, the thickness of the waveguide and the film-cover interface nonlinearity. It is also shown that the use of the singular solutions to the electric field equation allows to identify several new properties of surface waves which do not exist in conventional waveguide.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures.

PubMed

Khusnutdinova, Karima R; Samsonov, Alexander M; Zakharov, Alexey S

2009-05-01

We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

Simulations of kinetic electrostatic electron nonlinear (KEEN) waves with variable velocity resolution grids and high-order time-splitting

NASA Astrophysics Data System (ADS)

Afeyan, Bedros; Casas, Fernando; Crouseilles, Nicolas; Dodhy, Adila; Faou, Erwan; Mehrenberger, Michel; Sonnendrücker, Eric

2014-10-01

KEEN waves are non-stationary, nonlinear, self-organized asymptotic states in Vlasov plasmas. They lie outside the precepts of linear theory or perturbative analysis, unlike electron plasma waves or ion acoustic waves. Steady state, nonlinear constructs such as BGK modes also do not apply. The range in velocity that is strongly perturbed by KEEN waves depends on the amplitude and duration of the ponderomotive force generated by two crossing laser beams, for instance, used to drive them. Smaller amplitude drives manage to devolve into multiple highly-localized vorticlets, after the drive is turned off, and may eventually succeed to coalesce into KEEN waves. Fragmentation once the drive stops, and potential eventual remerger, is a hallmark of the weakly driven cases. A fully formed (more strongly driven) KEEN wave has one dominant vortical core. But it also involves fine scale complex dynamics due to shedding and merging of smaller vortical structures with the main one. Shedding and merging of vorticlets are involved in either case, but at different rates and with different relative importance. The narrow velocity range in which one must maintain sufficient resolution in the weakly driven cases, challenges fixed velocity grid numerical schemes. What is needed is the capability of resolving locally in velocity while maintaining a coarse grid outside the highly perturbed region of phase space. We here report on a new Semi-Lagrangian Vlasov-Poisson solver based on conservative non-uniform cubic splines in velocity that tackles this problem head on. An additional feature of our approach is the use of a new high-order time-splitting scheme which allows much longer simulations per computational effort. This is needed for low amplitude runs. There, global coherent structures take a long time to set up, such as KEEN waves, if they do so at all. The new code's performance is compared to uniform grid simulations and the advantages are quantified. The birth pains associated with weakly driven KEEN waves are captured in these simulations. Canonical KEEN waves with ample drive are also treated using these advanced techniques. They will allow the efficient simulation of KEEN waves in multiple dimensions, which will be tackled next, as well as generalizations to Vlasov-Maxwell codes. These are essential for pursuing the impact of KEEN waves in high energy density plasmas and in inertial confinement fusion applications. More generally, one needs a fully-adaptive grid-in-phase-space method which could handle all small vorticlet dynamics whether pealing off or remerging. Such fully adaptive grids would have to be computed sparsely in order to be viable. This two-velocity grid method is a concrete and fruitful step in that direction. Contribution to the Topical Issue "Theory and Applications of the Vlasov Equation", edited by Francesco Pegoraro, Francesco Califano, Giovanni Manfredi and Philip J. Morrison.

Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides

PubMed Central

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

2013-01-01

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

Globally aligned states and hydrodynamic traffic jams in confined suspensions of active asymmetric particles.

PubMed

Lefauve, Adrien; Saintillan, David

2014-02-01

Strongly confined active liquids are subject to unique hydrodynamic interactions due to momentum screening and lubricated friction by the confining walls. Using numerical simulations, we demonstrate that two-dimensional dilute suspensions of fore-aft asymmetric polar swimmers in a Hele-Shaw geometry can exhibit a rich variety of novel phase behaviors depending on particle shape, including coherent polarized density waves with global alignment, persistent counterrotating vortices, density shocks and rarefaction waves. We also explain these phenomena using a linear stability analysis and a nonlinear traffic flow model, both derived from a mean-field kinetic theory.

A novel nonlinear damage resonance intermodulation effect for structural health monitoring

NASA Astrophysics Data System (ADS)

Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele

2017-04-01

This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Consistent nonlinear deterministic and stochastic evolution equations for deep to shallow water wave shoaling

NASA Astrophysics Data System (ADS)

Vrecica, Teodor; Toledo, Yaron

2015-04-01

One-dimensional deterministic and stochastic evolution equations are derived for the dispersive nonlinear waves while taking dissipation of energy into account. The deterministic nonlinear evolution equations are formulated using operational calculus by following the approach of Bredmose et al. (2005). Their formulation is extended to include the linear and nonlinear effects of wave dissipation due to friction and breaking. The resulting equation set describes the linear evolution of the velocity potential for each wave harmonic coupled by quadratic nonlinear terms. These terms describe the nonlinear interactions between triads of waves, which represent the leading-order nonlinear effects in the near-shore region. The equations are translated to the amplitudes of the surface elevation by using the approach of Agnon and Sheremet (1997) with the correction of Eldeberky and Madsen (1999). The only current possibility for calculating the surface gravity wave field over large domains is by using stochastic wave evolution models. Hence, the above deterministic model is formulated as a stochastic one using the method of Agnon and Sheremet (1997) with two types of stochastic closure relations (Benney and Saffman's, 1966, and Hollway's, 1980). These formulations cannot be applied to the common wave forecasting models without further manipulation, as they include a non-local wave shoaling coefficients (i.e., ones that require integration along the wave rays). Therefore, a localization method was applied (see Stiassnie and Drimer, 2006, and Toledo and Agnon, 2012). This process essentially extracts the local terms that constitute the mean nonlinear energy transfer while discarding the remaining oscillatory terms, which transfer energy back and forth. One of the main findings of this work is the understanding that the approximated non-local coefficients behave in two essentially different manners. In intermediate water depths these coefficients indeed consist of rapidly oscillating terms, but as the water depth becomes shallow they change to an exponential growth (or decay) behavior. Hence, the formerly used localization technique cannot be justified for the shallow water region. A new formulation is devised for the localization in shallow water, it approximates the nonlinear non-local shoaling coefficient in shallow water and matches it to the one fitting to the intermediate water region. This allows the model behavior to be consistent from deep water to intermediate depths and up to the shallow water regime. Various simulations of the model were performed for the cases of intermediate, and shallow water, overall the model was found to give good results in both shallow and intermediate water depths. The essential difference between the shallow and intermediate nonlinear shoaling physics is explained via the dominating class III Bragg resonances phenomenon. By inspecting the resonance conditions and the nature of the dispersion relation, it is shown that unlike in the intermediate water regime, in shallow water depths the formation of resonant interactions is possible without taking into account bottom components. References Agnon, Y. & Sheremet, A. 1997 Stochastic nonlinear shoaling of directional spectra. J. Fluid Mech. 345, 79-99. Benney, D. J. & Saffman, P. G. 1966 Nonlinear interactions of random waves. Proc. R. Soc. Lond. A 289, 301-321. Bredmose, H., Agnon, Y., Madsen, P.A. & Schaffer, H.A. 2005 Wave transformation models with exact second-order transfer. European J. of Mech. - B/Fluids 24 (6), 659-682. Eldeberky, Y. & Madsen, P. A. 1999 Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves. Coastal Engineering 38, 1-24. Kaihatu, J. M. & Kirby, J. T. 1995 Nonlinear transformation of waves in infinite water depth. Phys. Fluids 8, 175-188. Holloway, G. 1980 Oceanic internal waves are not weak waves. J. Phys. Oceanogr. 10, 906-914. Stiassnie, M. & Drimer, N. 2006 Prediction of long forcing waves for harbor agitation studies. J. of waterways, port, coastal and ocean engineering 132(3), 166-171. Toledo, Y. & Agnon, Y. 2012 Stochastic evolution equations with localized nonlinear shoaling coefficients. European J. of Mech. - B/Fluids 34, 13-18.

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.

Planning for coordinated space and ground-based ionospheric modification experiments

NASA Technical Reports Server (NTRS)

Lee, M. C.; Burke, William J.; Carlson, Herbert C.; Heckscher, John L.; Kossey, Paul A.; Weber, E. J.; Kuo, S. P.

1990-01-01

The planning and conduction of coordinated space and ground-based ionospheric modification experiments are discussed. The purpose of these experiments is to discuss: (1) the nonlinear VLF wave interaction with the ionospheric plasmas; and (2) the nonlinear propagation of VLF waves in the HF-modified ionosphere. It is expected that the HF-induced ionospheric density striations can render the nonlinear mode conversion of VLF waved into lower hybrid waves. Lower hybrid waves can also be excited parametrically by the VLF waves in the absence of the density striations if the VLF waves are intense enough. Laboratory experiments are planned for crosschecking the results obtained from the field experiments.

Excitations of breathers and rogue wave in the Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Qi, Jian-Wen; Duan, Liang; Yang, Zhan-Ying; Yang, Wen-Li

2018-01-01

We study the excitations of breathers and rogue wave in a classical Heisenberg spin chain with twist interaction, which is governed by a fourth-order integrable nonlinear Schrödinger equation. The dynamics of these waves have been extracted from an exact solution. In particular, the corresponding existence conditions based on the parameters of perturbation wave number K, magnon number N, background wave vector ks and amplitude c are presented explicitly. Furthermore, the characteristics of magnetic moment distribution corresponding to these nonlinear waves are also investigated in detail. Finally, we discussed the state transition of three types nonlinear localized waves under the different excitation conditions.

NONLINEAR OPTICAL EFFECTS AND FIBER OPTICS: Theory of four-wave mixing in photorefractive media when the response of a medium is nonlinear in respect of the modulation parameter

NASA Astrophysics Data System (ADS)

Zozulya, A. A.

1988-12-01

A theoretical model is constructed for four-wave mixing in a photorefractive crystal where a transmission grating is formed by the drift-diffusion nonlinearity mechanism in the absence of an external electrostatic field and the response of the medium is nonlinear in respect of the modulation parameter. A comparison is made with a model in which the response of the medium is linear in respect of the modulation parameter. Theoretical models of four-wave and two-wave mixing are also compared with experiments.

Effect of higher order nonlinearity, directionality and finite water depth on wave statistics: Comparison of field data and numerical simulations

NASA Astrophysics Data System (ADS)

Fernández, Leandro; Monbaliu, Jaak; Onorato, Miguel; Toffoli, Alessandro

2014-05-01

This research is focused on the study of nonlinear evolution of irregular wave fields in water of arbitrary depth by comparing field measurements and numerical simulations.It is now well accepted that modulational instability, known as one of the main mechanisms for the formation of rogue waves, induces strong departures from Gaussian statistics. However, whereas non-Gaussian properties are remarkable when wave fields follow one direction of propagation over an infinite water depth, wave statistics only weakly deviate from Gaussianity when waves spread over a range of different directions. Over finite water depth, furthermore, wave instability attenuates overall and eventually vanishes for relative water depths as low as kh=1.36 (where k is the wavenumber of the dominant waves and h the water depth). Recent experimental results, nonetheless, seem to indicate that oblique perturbations are capable of triggering and sustaining modulational instability even if kh<1.36. In this regard, the aim of this research is to understand whether the combined effect of directionality and finite water depth has a significant effect on wave statistics and particularly on the occurrence of extremes. For this purpose, numerical experiments have been performed solving the Euler equation of motion with the Higher Order Spectral Method (HOSM) and compared with data of short crested wave fields for different sea states observed at the Lake George (Australia). A comparative analysis of the statistical properties (i.e. density function of the surface elevation and its statistical moments skewness and kurtosis) between simulations and in-situ data provides a confrontation between the numerical developments and real observations in field conditions.

Laser-Plasma Instabilities by Avoiding the Strong Ion Landau Damping Limit: The Central Role of Statistical, Ultrafast, Nonlinear Optical Laser Techniques (SUNOL)

NASA Astrophysics Data System (ADS)

Afeyan, Bedros; Hüller, Stefan; Montgomery, David; Moody, John; Froula, Dustin; Hammer, James; Jones, Oggie; Amendt, Peter

2014-10-01

In mid-Z and high-Z plasmas, it is possible to control crossed bean energy transfer (CBET) and subsequently occurring single or multiple beam instabilities such as Stimulated Raman Scattering (SRS) by novel means. These new techniques are inoperative when the ion acoustic waves are in their strong damping limit, such as occurs in low Z plasmas with comparable electron and ion temperatures. For mid-Z plasmas, such as Z = 10, and near the Mach 1 surface, the strong coupling regime (SCR) can be exploited for LPI mitigation. While at higher Z values, it is thermal filamentation in conjunction with nonlocal heat transport that are useful to exploit. In both these settings, the strategy is to induce laser hot spot intensity dependent, and thus spatially dependent, frequency shifts to the ion acoustic waves in the transient response of wave-wave interactions. The latter is achieved by the on-off nature of spike trains of uneven duration and delay, STUD pulses. The least taxing use of STUD pulses is to modulate the beams at the 10 ps time scale and to choose which crossing beams are overlapping in time and which are not. Work supported by a grant from the DOE NNSA-OFES joint program on HEDP

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.

Effect of Forcing Function on Nonlinear Acoustic Standing Waves

NASA Technical Reports Server (NTRS)

Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce

2003-01-01

Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.

Linear and Nonlinear Coupling of Electrostatic Drift and Acoustic Perturbations in a Nonuniform Bi-Ion Plasma with Non-Maxwellian Electrons

NASA Astrophysics Data System (ADS)

Ali, Gul-e.; Ahmad, Ali; Masood, W.; Mirza, Arshad M.

2017-12-01

Linear and nonlinear coupling of drift and ion acoustic waves are studied in a nonuniform magnetized plasma comprising of Oxygen and Hydrogen ions with nonthermal distribution of electrons. It has been observed that different ratios of ion number densities and kappa and Cairns distributed electrons significantly modify the linear dispersion characteristics of coupled drift-ion acoustic waves. In the nonlinear regime, KdV (for pure drift waves) and KP (for coupled drift-ion acoustic waves) like equations have been derived to study the nonlinear evolution of drift solitary waves in one and two dimensions. The dependence of drift solitary structures on different ratios of ion number densities and nonthermal distribution of electrons has also been explored in detail. It has been found that the ratio of the diamagnetic drift velocity to the velocity of the nonlinear structure determines the existence regimes for the drift solitary waves. The present investigation may be beneficial to understand the formation of solitons in the ionospheric F-region.

The role of nonlinear critical layers in boundary layer transition

NASA Technical Reports Server (NTRS)

Goldstein, M.E.

1995-01-01

Asymptotic methods are used to describe the nonlinear self-interaction between pairs of oblique instability modes that eventually develops when initially linear spatially growing instability waves evolve downstream in nominally two-dimensional laminar boundary layers. The first nonlinear reaction takes place locally within a so-called 'critical layer', with the flow outside this layer consisting of a locally parallel mean flow plus a pair of oblique instability waves - which may or may not be accompanied by an associated plane wave. The amplitudes of these waves, which are completely determined by nonlinear effects within the critical layer, satisfy either a single integro-differential equation or a pair of integro-differential equations with quadratic to quartic-type nonlinearities. The physical implications of these equations are discussed.

Waves: Internal Tides

NASA Technical Reports Server (NTRS)

Ray, Richard D.

1999-01-01

Oceanic internal tides are internal waves with tidal periodicities. They are ubiquitous throughout the ocean, although generally more pronounced near large bathymetric features such as mid-ocean ridges and continental slopes. The internal vertical displacements associated with these waves can be extraordinarily large. Near some shelf breaks where the surface tides are strong, internal displacements (e.g., of an isothermal surface) can exceed 200 meters. Displacements of 10 meters in the open ocean are not uncommon. The associated current velocities are usually comparable to or larger than the currents of the surface tide. On continental shelves internal tides can occasionally generate packets of internal solitons, which are detectable in remote sensing imagery. Other common nonlinear features are generation of higher harmonics (e.g., 6-hr waves) and wave breaking. Internal tides are known to be an important energy source for mixing of shelf waters. Recent research suggests that they may also be a significant energy source for deep-ocean mixing.

Observation of self-excited acoustic vortices in defect-mediated dust acoustic wave turbulence.

PubMed

Tsai, Ya-Yi; I, Lin

2014-07-01

Using the self-excited dust acoustic wave as a platform, we demonstrate experimental observation of self-excited fluctuating acoustic vortex pairs with ± 1 topological charges through spontaneous waveform undulation in defect-mediated turbulence for three-dimensional traveling nonlinear longitudinal waves. The acoustic vortex pair has helical waveforms with opposite chirality around the low-density hole filament pair in xyt space (the xy plane is the plane normal to the wave propagation direction). It is generated through ruptures of sequential crest surfaces and reconnections with their trailing ruptured crest surfaces. The initial rupture is originated from the amplitude reduction induced by the formation of the kinked wave crest strip with strong stretching through the undulation instability. Increasing rupture causes the separation of the acoustic vortex pair after generation. A similar reverse process is followed for the acoustic vortex annihilating with the opposite-charged acoustic vortex from the same or another pair generation.

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

Ro, Stephen; Matzner, Christopher D., E-mail: ro@astro.utoronto.ca

Wave-driven outflows and non-disruptive explosions have been implicated in pre-supernova outbursts, supernova impostors, luminous blue variable eruptions, and some narrow-line and superluminous supernovae. To model these events, we investigate the dynamics of stars set in motion by strong acoustic pulses and wave trains, focusing on nonlinear wave propagation, shock formation, and an early phase of the development of a weak shock. We identify the shock formation radius, showing that a heuristic estimate based on crossing characteristics matches an exact expansion around the wave front and verifying both with numerical experiments. Our general analytical condition for shock formation applies to one-dimensionalmore » motions within any static environment, including both eruptions and implosions. We also consider the early phase of shock energy dissipation. We find that waves of super-Eddington acoustic luminosity always create shocks, rather than damping by radiative diffusion. Therefore, shock formation is integral to super-Eddington outbursts.« less

Prefrontal bore mixing

NASA Astrophysics Data System (ADS)

van Haren, Hans; Duineveld, Gerard; de Stigter, Henko

2017-09-01

Rainbow Ridge, a 1950 m deep upthrusted ultramafic block along the axis of the Mid-Atlantic Ridge, has an active hydrothermal vent system at 2400 m on its western slope. However, within 1 km from the vent excessive temperatures are barely measurable, probably due to strong turbulent mixing. This mixing is studied here using a 400 m long high-resolution temperature sensor array moored with a 600 m ranging 75 kHz acoustic Doppler current profiler. Rich internal wave turbulence was recorded, characterized by 100-200 m upshoots and >200 m large overturning in particular near the end of the warming phase of the up and down moving tide. These highly nonlinear internal waves of tides interacting with buoyancy frequency waves extend up to 400 m above the sloping bottom of the ridge. While a turbulent "bottom boundary layer" could barely be defined, the more intense turbulence higher up in the water column is suggested to lead to the strong dispersion of the hydrothermal plume.

Near-Resonant Raman Amplification in the Rotational Quantum Wave Packets of Nitrogen Molecular Ions Generated by Strong Field Ionization

NASA Astrophysics Data System (ADS)

Liu, Zhaoxiang; Yao, Jinping; Chen, Jinming; Xu, Bo; Chu, Wei; Cheng, Ya

2018-02-01

The generation of laserlike narrow bandwidth emissions from nitrogen molecular ions (N2+ ) generated in intense near- and mid infrared femtosecond laser fields has aroused much interest because of the mysterious physics underlying such a phenomenon. Here, we perform a pump-probe measurement on the nonlinear interaction of rotational quantum wave packets of N2+ generated in midinfrared (e.g., at a wavelength centered at 1580 nm) femtosecond laser fields with an ultrashort probe pulse whose broad spectrum overlaps both P - and R -branch rotational transition lines between the electronic states N2+(B2Σu+,v'=0 ) and N2+(X2Σg+,v =0 ) . The results indicate the occurrence of highly efficient near-resonant stimulated Raman scattering in the quantum wave packets of N2+ ions generated in strong laser fields in the midinfrared region, of which the underlying mechanism is different from that of the air lasers generated in atmospheric environment when pumping with 800 nm intense pulses.

Prognostic characteristics of the lowest-mode internal waves in the Sea of Okhotsk

NASA Astrophysics Data System (ADS)

Kurkin, Andrey; Kurkina, Oxana; Zaytsev, Andrey; Rybin, Artem; Talipova, Tatiana

2017-04-01

The nonlinear dynamics of short-period internal waves on ocean shelves is well described by generalized nonlinear evolutionary models of Korteweg - de Vries type. Parameters of these models such as long wave propagation speed, nonlinear and dispersive coefficients can be calculated using hydrological data (sea water density stratification), and therefore have geographical and seasonal variations. The internal wave parameters for the basin of the Sea of Okhotsk are computed on a base of recent version of hydrological data source GDEM V3.0. Geographical and seasonal variability of internal wave characteristics is investigated. It is shown that annually or seasonally averaged data can be used for linear parameters. The nonlinear parameters are more sensitive to temporal averaging of hydrological data and detailed data are preferable to use. The zones for nonlinear parameters to change their signs (so-called "turning points") are selected. Possible internal waveforms appearing in the process of internal tide transformation including the solitary waves changing polarities are simulated for the hydrological conditions in the Sea of Okhotsk shelf to demonstrate different scenarios of internal wave adjustment, transformation, refraction and cylindrical divergence.

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.

Periodic waves in fiber Bragg gratings

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

Chow, K. W.; Merhasin, Ilya M.; Malomed, Boris A.

2008-02-15

We construct two families of exact periodic solutions to the standard model of fiber Bragg grating (FBG) with Kerr nonlinearity. The solutions are named ''sn'' and ''cn'' waves, according to the elliptic functions used in their analytical representation. The sn wave exists only inside the FBG's spectral bandgap, while waves of the cn type may only exist at negative frequencies ({omega}<0), both inside and outside the bandgap. In the long-wave limit, the sn and cn families recover, respectively, the ordinary gap solitons, and (unstable) antidark and dark solitons. Stability of the periodic solutions is checked by direct numerical simulations and,more » in the case of the sn family, also through the calculation of instability growth rates for small perturbations. Although, rigorously speaking, all periodic solutions are unstable, a subfamily of practically stable sn waves, with a sufficiently large spatial period and {omega}>0, is identified. However, the sn waves with {omega}<0, as well as all cn solutions, are strongly unstable.« less

Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion.

PubMed

Morichetti, Francesco; Canciamilla, Antonio; Ferrari, Carlo; Samarelli, Antonio; Sorel, Marc; Melloni, Andrea

2011-01-01

Wave mixing inside optical resonators, while experiencing a large enhancement of the nonlinear interaction efficiency, suffers from strong bandwidth constraints, preventing its practical exploitation for processing broad-band signals. Here we show that such limits are overcome by the new concept of travelling-wave resonant four-wave mixing (FWM). This approach combines the efficiency enhancement provided by resonant propagation with a wide-band conversion process. Compared with conventional FWM in bare waveguides, it exhibits higher robustness against chromatic dispersion and propagation loss, while preserving transparency to modulation formats. Travelling-wave resonant FWM has been demonstrated in silicon-coupled ring resonators and was exploited to realize a 630-μm-long wavelength converter operating over a wavelength range wider than 60 nm and with 28-dB gain with respect to a bare waveguide of the same physical length. Full compatibility of the travelling-wave resonant FWM with optical signal processing applications has been demonstrated through signal retiming and reshaping at 10 Gb s(-1).

Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion

PubMed Central

Morichetti, Francesco; Canciamilla, Antonio; Ferrari, Carlo; Samarelli, Antonio; Sorel, Marc; Melloni, Andrea

2011-01-01

Wave mixing inside optical resonators, while experiencing a large enhancement of the nonlinear interaction efficiency, suffers from strong bandwidth constraints, preventing its practical exploitation for processing broad-band signals. Here we show that such limits are overcome by the new concept of travelling-wave resonant four-wave mixing (FWM). This approach combines the efficiency enhancement provided by resonant propagation with a wide-band conversion process. Compared with conventional FWM in bare waveguides, it exhibits higher robustness against chromatic dispersion and propagation loss, while preserving transparency to modulation formats. Travelling-wave resonant FWM has been demonstrated in silicon-coupled ring resonators and was exploited to realize a 630-μm-long wavelength converter operating over a wavelength range wider than 60 nm and with 28-dB gain with respect to a bare waveguide of the same physical length. Full compatibility of the travelling-wave resonant FWM with optical signal processing applications has been demonstrated through signal retiming and reshaping at 10 Gb s−1 PMID:21540838

Lagrangian methods in nonlinear plasma wave interaction

NASA Technical Reports Server (NTRS)

Crawford, F. W.

1980-01-01

Analysis of nonlinear plasma wave interactions is usually very complicated, and simplifying mathematical approaches are highly desirable. The application of averaged-Lagrangian methods offers a considerable reduction in effort, with improved insight into synchronism and conservation (Manley-Rowe) relations. This chapter indicates how suitable Lagrangian densities have been defined, expanded, and manipulated to describe nonlinear wave-wave and wave-particle interactions in the microscopic, macroscopic and cold plasma models. Recently, further simplifications have been introduced by the use of techniques derived from Lie algebra. These and likely future developments are reviewed briefly.

Propagation of a finite-amplitude elastic pulse in a bar of Berea sandstone: A detailed look at the mechanisms of classical nonlinearity, hysteresis, and nonequilibrium dynamics: Nonlinear propagation of elastic pulse

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

Remillieux, Marcel C.; Ulrich, T. J.; Goodman, Harvey E.

Here, we study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a non-contact scanning 3D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classicalmore » nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We then show that the numerical resolution of the 1D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. But, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which not only quantifies classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.« less

Propagation of a finite-amplitude elastic pulse in a bar of Berea sandstone: A detailed look at the mechanisms of classical nonlinearity, hysteresis, and nonequilibrium dynamics: Nonlinear propagation of elastic pulse

DOE PAGES

Remillieux, Marcel C.; Ulrich, T. J.; Goodman, Harvey E.; ...

2017-10-18

Here, we study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a non-contact scanning 3D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classicalmore » nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We then show that the numerical resolution of the 1D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. But, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which not only quantifies classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.« less

A Locally Generated High-Mode Nonlinear Internal Wave Detected on the Shelf of the Northern South China Sea From Marine Seismic Observations

NASA Astrophysics Data System (ADS)

Tang, Qunshu; Xu, Min; Zheng, Chan; Xu, Xing; Xu, Jiang

2018-02-01

In this work, a secondary nonlinear internal wave (NIW) on the continental shelf of the northern South China Sea is investigated using high-resolution seismic imaging and joint inversion of water structure properties combined with in situ hydrographic observations. It is an extraordinary wave combination with two mode-2 NIWs and one elevated NIW occurring within a short distance of 2 km. The most energetic part of the NIW could be regarded as a mode-2 NIW in the upper layer between 40 and 120 m depth. The vertical particle velocity of ˜41 cm/s may exceed the critical value of wave breaking and thus collapse the strong stratification followed by a series of processes including internal wave breaking, overturning, Kelvin-Helmholtz instability, stratification splitting, and eventual restratification. Among these processes, the shear-induced Kelvin-Helmholtz instability is directly imaged using the seismic method for the first time. The stratification splitting and restratification show that the unstable stage lasts only for a few hours and spans several kilometers. It is a new observation that the elevated NIW could be generated in a deepwater region (as deep as ˜370 m). Different from the periodical NIWs originating from the Luzon Strait, this secondary NIW is most likely generated locally, at the continental shelf break during ebb tide.

Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-09-01

Nonlinear two-dimensional Kadomtsev-Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech-tanh, sinh-cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.

Inverse four-wave-mixing and self-parametric amplification effect in optical fibre

PubMed Central

Turitsyn, Sergei K.; Bednyakova, Anastasia E.; Fedoruk, Mikhail P.; Papernyi, Serguei B.; Clements, Wallace R.L.

2015-01-01

An important group of nonlinear processes in optical fibre involves the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and self-action of the propagating optical field (self-phase modulation and modulation instability). Here, we present a new nonlinear self-action effect, self-parametric amplification (SPA), which manifests itself as optical spectrum narrowing in normal dispersion fibre, leading to very stable propagation with a distinctive spectral distribution. The narrowing results from an inverse four-wave mixing, resembling an effective parametric amplification of the central part of the spectrum by energy transfer from the spectral tails. SPA and the observed stable nonlinear spectral propagation with random temporal waveform can find applications in optical communications and high power fibre lasers with nonlinear intra-cavity dynamics. PMID:26345290

Nonlinear ultrasonic imaging with X wave

NASA Astrophysics Data System (ADS)

Du, Hongwei; Lu, Wei; Feng, Huanqing

2009-10-01

X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.

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.

Amplification of nonlinear surface waves by wind

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

Leblanc, Stephane

2007-10-15

A weakly nonlinear analysis is conducted to study the evolution of slowly varying wavepackets with small but finite amplitudes, that evolve at the interface between air and water under the effect of wind. In the inviscid assumption, wave envelopes are governed by cubic nonlinear Schroedinger or Davey-Stewartson equations forced by a linear term corresponding to Miles' mechanism of wave generation. Under fair wind, it is shown that Stokes waves grow exponentially and that Benjamin-Feir instability becomes explosive.