Nonlinear Scattering of VLF Waves in the Radiation Belts

NASA Astrophysics Data System (ADS)

Crabtree, Chris; Rudakov, Leonid; Ganguli, Guru; Mithaiwala, Manish

2014-10-01

Electromagnetic VLF waves, such as whistler mode waves, control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering. Since the pitch-angle scattering rate is a strong function of the wave properties, a solid understanding of VLF wave sources and propagation in the magnetosphere is critical to accurately calculate electron lifetimes. Nonlinear scattering (Nonlinear Landau Damping) is a mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation, and has not been accounted for in previous models of radiation belt dynamics. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Recent results show that the threshold for nonlinear scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear scattering can then dramatically alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al. 2012]. By considering these effects, the lifetimes of electrons can be dramatically reduced. This work is supported by the Naval Research Laboratory base program.

Nonlinear Hysteretic Torsional Waves

NASA Astrophysics Data System (ADS)

Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.

2015-07-01

We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

Solitary Waves, Periodic Peakons and Pseudo-Peakons of the Nonlinear Acoustic Wave Model in Rotating Magnetized Plasma

NASA Astrophysics Data System (ADS)

Li, Jibin

The dynamical model of the nonlinear acoustic wave in rotating magnetized plasma is governed by a partial differential equation system. Its traveling system is a singular traveling wave system of first class depending on two parameters. By using the bifurcation theory and method of dynamical systems and the theory of singular traveling wave systems, in this paper, we show that there exist parameter groups such that this singular system has pseudo-peakons, periodic peakons and compactons as well as different solitary wave solutions.

Nonlinear excited waves on the interventricular septum

NASA Astrophysics Data System (ADS)

Bekki, Naoaki; Harada, Yoshifumi; Kanai, Hiroshi

2012-11-01

Using a novel ultrasonic noninvasive imaging method, we observe some phase singularities in propagating excited waves on a human cardiac interventricular septum (IVS) for a healthy young male. We present a possible physical model explaining one-dimensional dynamics of phase singularities in nonlinearly excited waves on the IVS. We show that at least one of the observed phase singularities in the excited waves on the IVS can be explained by the Bekki-Nozaki hole solution of the complex Ginzburg-Landau equation without any adjustable parameters. We conclude that the complex Ginzburg-Landau equation is such a suitable model for one-dimensional dynamics of cardiac phase singularities in nonlinearly excited waves on the IVS.

Comparison of heaving buoy and oscillating flap wave energy converters

NASA Astrophysics Data System (ADS)

Abu Bakar, Mohd Aftar; Green, David A.; Metcalfe, Andrew V.; Najafian, G.

2013-04-01

Waves offer an attractive source of renewable energy, with relatively low environmental impact, for communities reasonably close to the sea. Two types of simple wave energy converters (WEC), the heaving buoy WEC and the oscillating flap WEC, are studied. Both WECs are considered as simple energy converters because they can be modelled, to a first approximation, as single degree of freedom linear dynamic systems. In this study, we estimate the response of both WECs to typical wave inputs; wave height for the buoy and corresponding wave surge for the flap, using spectral methods. A nonlinear model of the oscillating flap WEC that includes the drag force, modelled by the Morison equation is also considered. The response to a surge input is estimated by discrete time simulation (DTS), using central difference approximations to derivatives. This is compared with the response of the linear model obtained by DTS and also validated using the spectral method. Bendat's nonlinear system identification (BNLSI) technique was used to analyze the nonlinear dynamic system since the spectral analysis was only suitable for linear dynamic system. The effects of including the nonlinear term are quantified.

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

NASA Astrophysics Data System (ADS)

Gupta, Samit Kumar

2018-03-01

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

Decoupling nonclassical nonlinear behavior of elastic wave types

DOE PAGES

Remillieux, Marcel C.; Guyer, Robert A.; Payan, Cedric; ...

2016-03-01

In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. As a result, this could lead to furthermore » understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.« less

Nonlinear Wave Propagation

DTIC Science & Technology

2009-02-09

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

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.

Nonlinear amplification of coherent waves in media with soliton-type refractive index pattern.

PubMed

Bugaychuk, S; Conte, R

2012-08-01

We derive the complex Ginzburg-Landau equation for the dynamical self-diffraction of optical waves in a nonlinear cavity. The case of the reflection geometry of wave interaction as well as a medium that possesses the cubic nonlinearity (including a local and a nonlocal nonlinear responses) and the relaxation is considered. A stable localized spatial structure in the form of a "dark" dissipative soliton is formed in the cavity in the steady state. The envelope of the intensity pattern, as well as of the dynamical grating amplitude, takes the shape of a tanh function. The obtained complex Ginzburg-Landau equation describes the dynamics of this envelope; at the same time, the evolution of this spatial structure changes the parameters of the output waves. New effects are predicted in this system due to the transformation of the dissipative soliton which takes place during the interaction of a pulse with a continuous wave, such as retention of the pulse shape during the transmission of impulses in a long nonlinear cavity, and giant amplification of a seed pulse, which takes energy due to redistribution of the pump continuous energy into the signal.

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.

Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis

ERIC Educational Resources Information Center

Jeffrey, Alan

1971-01-01

The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

Aspects of wave turbulence in preheating

NASA Astrophysics Data System (ADS)

Crespo, José A.; de Oliveira, H. P.

2014-06-01

In this work we have studied the nonlinear preheating dynamics of several inflationary models. It is well established that after a linear stage of preheating characterized by the parametric resonance, the nonlinear dynamics becomes relevant driving the system towards turbulence. Wave turbulence is the appropriated description of this phase since the matter contents are fields instead of usual fluids. Turbulence develops due to the nonlinear interations of waves, here represented by the small inhomogeneities of the scalar fields. We present relevant aspects of wave turbulence such as the Kolmogorov-Zakharov spectrum in frequency and wave number that indicates the energy transfer through scales. From the power spectrum of the matter energy density we were able to estimate the temperature of the thermalized system.

Nonlinear dynamics of toroidal Alfvén eigenmodes in presence of tearing modes

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Rogue-wave pattern transition induced by relative frequency.

PubMed

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

2014-08-01

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

Modulational instability, beak-shaped rogue waves, multi-dark-dark solitons and dynamics in pair-transition-coupled nonlinear Schrödinger equations.

PubMed

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

2017-07-01

The integrable coupled nonlinear Schrödinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N -fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial-temporal distribution structures including triangular, pentagonal, 'claw-like' and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.

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

Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

NASA Astrophysics Data System (ADS)

Fontanela, F.; Grolet, A.; Salles, L.; Chabchoub, A.; Hoffmann, N.

2018-01-01

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics.

Dynamics of unstable sound waves in a non-equilibrium medium at the nonlinear stage

NASA Astrophysics Data System (ADS)

Khrapov, Sergey; Khoperskov, Alexander

2018-03-01

A new dispersion equation is obtained for a non-equilibrium medium with an exponential relaxation model of a vibrationally excited gas. We have researched the dependencies of the pump source and the heat removal on the medium thermodynamic parameters. The boundaries of sound waves stability regions in a non-equilibrium gas have been determined. The nonlinear stage of sound waves instability development in a vibrationally excited gas has been investigated within CSPH-TVD and MUSCL numerical schemes using parallel technologies OpenMP-CUDA. We have obtained a good agreement of numerical simulation results with the linear perturbations dynamics at the initial stage of the sound waves growth caused by instability. At the nonlinear stage, the sound waves amplitude reaches the maximum value that leads to the formation of shock waves system.

Emergent geometries and nonlinear-wave dynamics in photon fluids.

PubMed

Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D

2016-03-22

Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.

Emergent geometries and nonlinear-wave dynamics in photon fluids

NASA Astrophysics Data System (ADS)

Marino, F.; Maitland, C.; Vocke, D.; Ortolan, A.; Faccio, D.

2016-03-01

Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.

Nonlinear Tides in Close Binary Systems

NASA Astrophysics Data System (ADS)

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

2012-06-01

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

Nonlinear elasticity in rocks: A comprehensive three-dimensional description

DOE PAGES

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

2017-07-17

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

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

NASA Astrophysics Data System (ADS)

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

1996-01-01

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

Nonlinear dynamic analysis of traveling wave-type ultrasonic motors.

PubMed

Nakagawa, Yosuke; Saito, Akira; Maeno, Takashi

2008-03-01

In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.

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.

Nonlinear Internal Waves on the Inner Shelf: Observations Using a Distributed Temperature Sensing (DTS) System.

NASA Astrophysics Data System (ADS)

Davis, K. A.; Reid, E. C.; Cohen, A. L.

2016-02-01

Internal waves propagating across the continental slope and shelf are transformed by the competing effects of nonlinear steepening and dispersive spreading, forming nonlinear internal waves (NLIWs) that can penetrate onto the shallow inner shelf, often appearing in the form of bottom-propagating nonlinear internal bores or boluses. NLIWs play a significant role in nearshore dynamics with baroclinic current amplitudes on the order of that of wind- and surface wave-driven flows and rapid temperature changes on the order of annual ranges. In June 2014 we used a Distributed Temperature Sensing (DTS) system to give a continuous cross-shelf view of nonlinear internal wave dynamics on the forereef of Dongsha Atoll, a coral reef in the northern South China Sea. A DTS system measures temperature continuously along the length of an optical fiber, resolving meter-to-kilometer spatial scales. This unique view of cross-shelf temperature structure made it possible to observe internal wave reflection, variable propagation speed across the shelf, bolus formation and dissipation. Additionally, we used the DTS data to track internal waves across the shallow fore reef and onto the reef flat and to quantify spatial patterns in temperature variability. Shoaling internal waves are an important process affecting physical variability and water properties on the reef.

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

PubMed

Kourakis, I; Shukla, P K

2005-07-01

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

A nonlinear steady model for moist hydrostatic mountain waves

NASA Technical Reports Server (NTRS)

Barcilon, A.; Fitzjarrald, D.

1985-01-01

The dynamics of hydrostatic gravity waves generated by the passage of a steady, stably stratified, moist flow over a two-dimensional topography is considered. Coriolis effects are neglected. The cloud region is determined by the dynamics, and within that region the Brunt-Vaisala frequency takes on a value smaller than the outside value. In both the dry and cloudy regions the Brunt-Vaisala frequency is constant with height. The moist layer is considered to be either next to the mountain or at midlevels and to be deep enough so that an entire cloud forms in that layer. The nonlinearity in the flow and lower boundary affects the dynamics of these waves and wave drag. The latter is found to depend upon: (1) the location of the moist layer with respect to the ground, (2) the amount of moisture, (3) the degree of nonlinearity and (4) the departure from symmetry in the bottom topography.

Rogue wave modes for a derivative nonlinear Schrödinger model.

PubMed

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

2014-03-01

Rogue waves in fluid dynamics and optical waveguides are unexpectedly large displacements from a background state, and occur in the nonlinear Schrödinger equation with positive linear dispersion in the regime of positive cubic nonlinearity. Rogue waves of a derivative nonlinear Schrödinger equation are calculated in this work as a long-wave limit of a breather (a pulsating mode), and can occur in the regime of negative cubic nonlinearity if a sufficiently strong self-steepening nonlinearity is also present. This critical magnitude is shown to be precisely the threshold for the onset of modulation instabilities of the background plane wave, providing a strong piece of evidence regarding the connection between a rogue wave and modulation instability. The maximum amplitude of the rogue wave is three times that of the background plane wave, a result identical to that of the Peregrine breather in the classical nonlinear Schrödinger equation model. This amplification ratio and the resulting spectral broadening arising from modulation instability correlate with recent experimental results of water waves. Numerical simulations in the regime of marginal stability are described.

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.

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.

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

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

NASA Astrophysics Data System (ADS)

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

2012-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Unimodal dynamical systems: Comparison principles, spreading speeds and travelling waves

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming; Wu, Jianhong

Reaction diffusion equations with delayed nonlinear reaction terms are used as prototypes to motivate an appropriate abstract formulation of dynamical systems with unimodal nonlinearity. For such non-monotone dynamical systems, we develop a general comparison principle and show how this general comparison principle, coupled with some existing results for monotone dynamical systems, can be used to establish results on the asymptotic speeds of spread and travelling waves. We illustrate our main results by an integral equation which includes a nonlocal delayed reaction diffusion equation and a nonlocal delayed lattice differential system in an unbounded domain, with the non-monotone nonlinearities including the Ricker birth function and the Mackey-Glass hematopoiesis feedback.

Control of propagation of spatially localized polariton wave packets in a Bragg mirror with embedded quantum wells

NASA Astrophysics Data System (ADS)

Sedova, I. E.; Chestnov, I. Yu.; Arakelian, S. M.; Kavokin, A. V.; Sedov, E. S.

2018-01-01

We considered the nonlinear dynamics of Bragg polaritons in a specially designed stratified semiconductor structure with embedded quantum wells, which possesses a convex dispersion. The model for the ensemble of single periodically arranged quantum wells coupled with the Bragg photon fields has been developed. In particular, the generalized Gross-Pitaevskii equation with the non-parabolic dispersion has been obtained for the Bragg polariton wave function. We revealed a number of dynamical regimes for polariton wave packets resulting from competition of the convex dispersion and the repulsive nonlinearity effects. Among the regimes are spreading, breathing and soliton propagation. When the control parameters including the exciton-photon detuning, the matter-field coupling and the nonlinearity are manipulated, the dynamical regimes switch between themselves.

Nonlinear Problems in Fluid Dynamics and Inverse Scattering

DTIC Science & Technology

1993-05-31

nonlinear Kadomtsev - Petviashvili (KP) equations , have solutions which will become infinite in finite time. This phenomenon is sometimes referred to as...40 (November 1992). 4 7. Wave Collapse and Instability of Solitary Waves of a Generalized Nonlinear Kaoiomtsev- Petviashvili Equation , X.P. Wang, M.J...words) The inverse scattering of a class of differential-difference equations and multidimensional operators has been constructed. Solutions of nonlinear

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.

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

Integrable pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Ling, Liming; Zhao, Li-Chen

2015-08-01

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

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

Lee, Wonjung; Kovacic, Gregor; Cai, David

Using the (1+1)D Majda-McLaughlin-Tabak model as an example, we present an extension of the wave turbulence (WT) theory to systems with strong nonlinearities. We demonstrate that nonlinear wave interactions renormalize the dynamics, leading to (i) a possible destruction of scaling structures in the bare wave systems and a drastic deformation of the resonant manifold even at weak nonlinearities, and (ii) creation of nonlinear resonance quartets in wave systems for which there would be no resonances as predicted by the linear dispersion relation. Finally, we derive an effective WT kinetic equation and show that our prediction of the renormalized Rayleigh-Jeans distributionmore » is in excellent agreement with the simulation of the full wave system in equilibrium.« less

Propagation of flexural waves in inhomogeneous plates exhibiting hysteretic nonlinearity: Nonlinear acoustic black holes.

PubMed

Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua

2015-08-01

Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping. Copyright © 2015 Elsevier B.V. All rights reserved.

Characteristics of the solitary waves and rogue waves with interaction phenomena in a (2 + 1)-dimensional Breaking Soliton equation

NASA Astrophysics Data System (ADS)

Hossen, Md. Belal; Roshid, Harun-Or; Ali, M. Zulfikar

2018-05-01

Under inquisition in this paper is a (2 + 1)-dimensional Breaking Soliton equation, which can describe various nonlinear scenarios in fluid dynamics. Using the Bell polynomials, some proficient auxiliary functions are offered to apparently construct its bilinear form and corresponding soliton solutions which are different from the previous literatures. Moreover, a direct method is used to construct its rogue wave and solitary wave solutions using particular auxiliary function with the assist of bilinear formalism. Finally, the interactions between solitary waves and rogue waves are offered with a complete derivation. These results enhance the variety of the dynamics of higher dimensional nonlinear wave fields related to mathematical physics and engineering.

Nonlinear Light Dynamics in Multi-Core Structures

DTIC Science & Technology

2017-02-27

be generated in continuous- discrete optical media such as multi-core optical fiber or waveguide arrays; localisation dynamics in a continuous... discrete nonlinear system. Detailed theoretical analysis is presented of the existence and stability of the discrete -continuous light bullets using a very...and pulse compression using wave collapse (self-focusing) energy localisation dynamics in a continuous- discrete nonlinear system, as implemented in a

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

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

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

2014-07-15

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

High-order rogue waves in vector nonlinear Schrödinger equations.

PubMed

Ling, Liming; Guo, Boling; Zhao, Li-Chen

2014-04-01

We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber.

Covariances and spectra of the kinematics and dynamics of nonlinear waves

NASA Technical Reports Server (NTRS)

Tung, C. C.; Huang, N. E.

1985-01-01

Using the Stokes waves as a model of nonlinear waves and considering the linear component as a narrow-band Gaussian process, the covariances and spectra of velocity and acceleration components and pressure for points in the vicinity of still water level were derived taking into consideration the effects of free surface fluctuations. The results are compared with those obtained earlier using linear Gaussian waves.

Hydroelastic response of a floating runway to cnoidal waves

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

Ertekin, R. C., E-mail: ertekin@hawaii.edu; Xia, Dingwu

2014-02-15

The hydroelastic response of mat-type Very Large Floating Structures (VLFSs) to severe sea conditions, such as tsunamis and hurricanes, must be assessed for safety and survivability. An efficient and robust nonlinear hydroelastic model is required to predict accurately the motion of and the dynamic loads on a VLFS due to such large waves. We develop a nonlinear theory to predict the hydroelastic response of a VLFS in the presence of cnoidal waves and compare the predictions with the linear theory that is also developed here. This hydroelastic problem is formulated by directly coupling the structure with the fluid, by usemore » of the Level I Green-Naghdi theory for the fluid motion and the Kirchhoff thin plate theory for the runway. The coupled fluid structure system, together with the appropriate jump conditions are solved in two-dimensions by the finite-difference method. The numerical model is used to study the nonlinear response of a VLFS to storm waves which are modeled by use of the cnoidal-wave theory. Parametric studies show that the nonlinearity of the waves is very important in accurately predicting the dynamic bending moment and wave run-up on a VLFS in high seas.« less

Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Yang, H. Q.

1989-01-01

The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

Classical black holes: the nonlinear dynamics of curved spacetime.

PubMed

Thorne, Kip S

2012-08-03

Numerical simulations have revealed two types of physical structures, made from curved spacetime, that are attached to black holes: tendexes, which stretch or squeeze anything they encounter, and vortexes, which twist adjacent inertial frames relative to each other. When black holes collide, their tendexes and vortexes interact and oscillate (a form of nonlinear dynamics of curved spacetime). These oscillations generate gravitational waves, which can give kicks up to 4000 kilometers per second to the merged black hole. The gravitational waves encode details of the spacetime dynamics and will soon be observed and studied by the Laser Interferometer Gravitational Wave Observatory and its international partners.

Classical Black Holes: The Nonlinear Dynamics of Curved Spacetime

NASA Astrophysics Data System (ADS)

Thorne, Kip S.

2012-08-01

Numerical simulations have revealed two types of physical structures, made from curved spacetime, that are attached to black holes: tendexes, which stretch or squeeze anything they encounter, and vortexes, which twist adjacent inertial frames relative to each other. When black holes collide, their tendexes and vortexes interact and oscillate (a form of nonlinear dynamics of curved spacetime). These oscillations generate gravitational waves, which can give kicks up to 4000 kilometers per second to the merged black hole. The gravitational waves encode details of the spacetime dynamics and will soon be observed and studied by the Laser Interferometer Gravitational Wave Observatory and its international partners.

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.

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.

Nonlinear excitations for the positron acoustic shock waves in dissipative nonextensive electron-positron-ion plasmas

NASA Astrophysics Data System (ADS)

Saha, Asit

2017-03-01

Positron acoustic shock waves (PASHWs) in unmagnetized electron-positron-ion (e-p-i) plasmas consisting of mobile cold positrons, immobile positive ions, q-nonextensive distributed electrons, and hot positrons are studied. The cold positron kinematic viscosity is considered and the reductive perturbation technique is used to derive the Burgers equation. Applying traveling wave transformation, the Burgers equation is transformed to a one dimensional dynamical system. All possible vector fields corresponding to the dynamical system are presented. We have analyzed the dynamical system with the help of potential energy, which helps to identify the stability and instability of the equilibrium points. It is found that the viscous force acting on cold mobile positron fluid is a source of dissipation and is responsible for the formation of the PASHWs. Furthermore, fully nonlinear arbitrary amplitude positron acoustic waves are also studied applying the theory of planar dynamical systems. It is also observed that the fundamental features of the small amplitude and arbitrary amplitude PASHWs are significantly affected by the effect of the physical parameters q e , q h , μ e , μ h , σ , η , and U. This work can be useful to understand the qualitative changes in the dynamics of nonlinear small amplitude and fully nonlinear arbitrary amplitude PASHWs in solar wind, ionosphere, lower part of magnetosphere, and auroral acceleration regions.

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.

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.

Dispersive shock waves in Bose-Einstein condensates and nonlinear nano-oscillators in ferromagnetic thin films

NASA Astrophysics Data System (ADS)

Hoefer, Mark A.

This thesis examines nonlinear wave phenomena, in two physical systems: a Bose-Einstein condensate (BEC) and thin film ferromagnets where the magnetization dynamics are excited by the spin momentum transfer (SMT) effect. In the first system, shock waves generated by steep gradients in the BEC wavefunction are shown to be of the disperse type. Asymptotic and averaging methods are used to determine shock speeds and structure in one spatial dimension. These results are compared with multidimensional numerical simulations and experiment showing good, qualitative agreement. In the second system, a model of magnetization dynamics due to SMT is presented. Using this model, nonlinear oscillating modes---nano-oscillators---are found numerically and analytically using perturbative methods. These results compare well with experiment. A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with laboratory experiments show that three and two-dimensional approximations are in excellent agreement and one dimensional approximations are in qualitative agreement. The interaction of two DSWs is investigated analytically and numerically. Using one dimensional DSW theory it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves. A nonlinear mathematical model of spin-wave excitation using a point contact in a thin ferromagnetic film is introduced. This work incorporates a recently proposed spin-torque contribution to classical magnetodynamic theory with a variable coefficient terra in the magnetic torque equation. Large-amplitude magnetic solitary waves are computed, which help explain recent spin-torque experiments. Numerical simulations of the full nonlinear model predict excitation frequencies in excess of 0.2 THz for contact diameters smaller than 6 nm. Simulations also predict a saturation and red shift of the frequency at currents large enough to invert the magnetization tinder the point contact. In the weak nonlinear limit, the theory is approximated by a cubic complex Ginzburg-Landau type equation. The mode's nonlinear frequency shift is found by use of perturbation techniques, whose results agree with those of direct numerical simulations.

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.

Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

NASA Astrophysics Data System (ADS)

Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

2018-06-01

Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

Nonlinear waves of a nonlocal modified KdV equation in the atmospheric and oceanic dynamical system

NASA Astrophysics Data System (ADS)

Tang, Xiao-yan; Liang, Zu-feng; Hao, Xia-zhi

2018-07-01

A new general nonlocal modified KdV equation is derived from the nonlinear inviscid dissipative and equivalent barotropic vorticity equation in a β-plane. The nonlocal property is manifested in the shifted parity and delayed time reversal symmetries. Exact solutions of the nonlocal modified KdV equation are obtained including periodic waves, kink waves, solitary waves, kink- and/or anti-kink-cnoidal periodic wave interaction solutions, which can be utilized to describe various two-place and time-delayed correlated events. As an illustration, a special approximate solution is applied to theoretically capture the salient features of two correlated dipole blocking events in atmospheric dynamical systems.

Nonlinear hydrodynamic stability and transition; Proceedings of the IUTAM Symposium, Nice, France, Sept. 3-7, 1990

NASA Astrophysics Data System (ADS)

Theoretical and experimental research on nonlinear hydrodynamic stability and transition is presented. Bifurcations, amplitude equations, pattern in experiments, and shear flows are considered. Particular attention is given to bifurcations of plane viscous fluid flow and transition to turbulence, chaotic traveling wave covection, chaotic behavior of parametrically excited surface waves in square geometry, amplitude analysis of the Swift-Hohenberg equation, traveling wave convection in finite containers, focus instability in axisymmetric Rayleigh-Benard convection, scaling and pattern formation in flowing sand, dynamical behavior of instabilities in spherical gap flows, and nonlinear short-wavelength Taylor vortices. Also discussed are stability of a flow past a two-dimensional grid, inertia wave breakdown in a precessing fluid, flow-induced instabilities in directional solidification, structure and dynamical properties of convection in binary fluid mixtures, and instability competition for convecting superfluid mixtures.

Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications

NASA Astrophysics Data System (ADS)

Ali, Asghar; Seadawy, Aly R.; Lu, Dianchen

2018-05-01

The aim of this article is to construct some new traveling wave solutions and investigate localized structures for fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) water wave dynamical equation. The simple equation method (SEM) and the modified simple equation method (MSEM) are applied in this paper to construct the analytical traveling wave solutions of AKNS equation. The different waves solutions are derived by assigning special values to the parameters. The obtained results have their importance in the field of physics and other areas of applied sciences. All the solutions are also graphically represented. The constructed results are often helpful for studying several new localized structures and the waves interaction in the high-dimensional models.

Nonlinear Dust Acoustic Waves in a Magnetized Dusty Plasma with Trapped and Superthermal Electrons

NASA Astrophysics Data System (ADS)

Ahmadi, Abrishami S.; Nouri, Kadijani M.

2014-06-01

In this work, the effects of superthermal and trapped electrons on the oblique propagation of nonlinear dust-acoustic waves in a magnetized dusty (complex) plasma are investigated. The dynamic of electrons is simulated by the generalized Lorentzian (κ) distribution function (DF). The dust grains are cold and their dynamics are simulated by hydrodynamic equations. Using the standard reductive perturbation technique (RPT) a nonlinear modified Korteweg-de Vries (mKdV) equation is derived. Two types of solitary waves; fast and slow dust acoustic solitons, exist in this plasma. Calculations reveal that compressive solitary structures are likely to propagate in this plasma where dust grains are negatively (or positively) charged. The properties of dust acoustic solitons (DASs) are also investigated numerically.

On Hokusai's Great wave off Kanagawa: localization, linearity and a rogue wave in sub-Antarctic waters.

PubMed

Dudley, J M; Sarano, V; Dias, F

2013-06-20

The Hokusai woodcut entitled The great wave off Kanagawa has been interpreted as an unusually large storm wave, likely to be classed as a rogue wave, and possibly generated from nonlinear wave dynamics (J. H. E. Cartwright and H. Nakamura, Notes Rec. R. Soc. 63 , 119-135 (2009)). In this paper, we present a complementary discussion of this hypothesis, discussing in particular how linear and nonlinear mechanisms can both contribute to the emergence of rogue wave events. By making reference to the Great wave 's simultaneous transverse and longitudinal localization, we show that the purely linear mechanism of directional focusing also predicts characteristics consistent with those of the Great wave . In addition, we discuss the properties of a particular rogue wave photographed on the open ocean in sub-Antarctic waters, which shows two-dimensional localization and breaking dynamics remarkably similar to Hokusai's depiction in the woodcut.

On Hokusai's Great wave off Kanagawa: localization, linearity and a rogue wave in sub-Antarctic waters

PubMed Central

Dudley, J. M.; Sarano, V.; Dias, F.

2013-01-01

The Hokusai woodcut entitled The great wave off Kanagawa has been interpreted as an unusually large storm wave, likely to be classed as a rogue wave, and possibly generated from nonlinear wave dynamics (J. H. E. Cartwright and H. Nakamura, Notes Rec. R. Soc. 63, 119–135 (2009)). In this paper, we present a complementary discussion of this hypothesis, discussing in particular how linear and nonlinear mechanisms can both contribute to the emergence of rogue wave events. By making reference to the Great wave's simultaneous transverse and longitudinal localization, we show that the purely linear mechanism of directional focusing also predicts characteristics consistent with those of the Great wave. In addition, we discuss the properties of a particular rogue wave photographed on the open ocean in sub-Antarctic waters, which shows two-dimensional localization and breaking dynamics remarkably similar to Hokusai's depiction in the woodcut. PMID:24687148

Rogue waves: from nonlinear Schrödinger breather solutions to sea-keeping test.

PubMed

Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco

2013-01-01

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.

Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test

PubMed Central

Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco

2013-01-01

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship. PMID:23405086

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

On solitons: the biomolecular nonlinear transmission line models with constant and time variable coefficients

NASA Astrophysics Data System (ADS)

Raza, Nauman; Murtaza, Isma Ghulam; Sial, Sultan; Younis, Muhammad

2018-07-01

The article studies the dynamics of solitons in electrical microtubule ? model, which describes the propagation of waves in nonlinear dynamical system. Microtubules are not only a passive support of a cell but also they have highly dynamic structures involved in cell motility, intracellular transport and signaling. The underlying model has been considered with constant and variable coefficients of time function. The solitary wave ansatz has been applied successfully to extract these solitons. The corresponding integrability criteria, also known as constraint conditions, naturally emerge from the analysis of these models.

Dispersive solitary wave solutions of Kadomtsev-Petviashvili and modified Kadomtsev-Petviashvili dynamical equations in unmagnetized dust plasma

NASA Astrophysics Data System (ADS)

Seadawy, A. R.; El-Rashidy, K.

2018-03-01

The Kadomtsev-Petviashvili (KP) and modified KP equations are two of the most universal models in nonlinear wave theory, which arises as a reduction of system with quadratic nonlinearity which admit weakly dispersive waves. The generalized extended tanh method and the F-expansion method are used to derive exact solitary waves solutions of KP and modified KP equations. The region of solutions are displayed graphically.

Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model

NASA Astrophysics Data System (ADS)

Panajotov, Krassimir; Clerc, Marcel G.; Tlidi, Mustapha

2017-06-01

Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height. Contribution to the Topical Issue "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

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

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.

Freak waves in random oceanic sea states.

PubMed

Onorato, M; Osborne, A R; Serio, M; Bertone, S

2001-06-18

Freak waves are very large, rare events in a random ocean wave train. Here we study their generation in a random sea state characterized by the Joint North Sea Wave Project spectrum. We assume, to cubic order in nonlinearity, that the wave dynamics are governed by the nonlinear Schrödinger (NLS) equation. We show from extensive numerical simulations of the NLS equation how freak waves in a random sea state are more likely to occur for large values of the Phillips parameter alpha and the enhancement coefficient gamma. Comparison with linear simulations is also reported.

High-order rogue waves of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Liu, Wei

2017-10-01

High-order rogue wave solutions of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin-Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

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.

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.

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.

Localization of intense electromagnetic waves in a relativistically hot plasma.

PubMed

Shukla, P K; Eliasson, B

2005-02-18

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

Coupling nonlinear optical waves to photoreactive and phase-separating soft matter: Current status and perspectives

NASA Astrophysics Data System (ADS)

Biria, Saeid; Morim, Derek R.; An Tsao, Fu; Saravanamuttu, Kalaichelvi; Hosein, Ian D.

2017-10-01

Nonlinear optics and polymer systems are distinct fields that have been studied for decades. These two fields intersect with the observation of nonlinear wave propagation in photoreactive polymer systems. This has led to studies on the nonlinear dynamics of transmitted light in polymer media, particularly for optical self-trapping and optical modulation instability. The irreversibility of polymerization leads to permanent capture of nonlinear optical patterns in the polymer structure, which is a new synthetic route to complex structured soft materials. Over time more intricate polymer systems are employed, whereby nonlinear optical dynamics can couple to nonlinear chemical dynamics, opening opportunities for self-organization. This paper discusses the work to date on nonlinear optical pattern formation processes in polymers. A brief overview of nonlinear optical phenomenon is provided to set the stage for understanding their effects. We review the accomplishments of the field on studying nonlinear waveform propagation in photopolymerizable systems, then discuss our most recent progress in coupling nonlinear optical pattern formation to polymer blends and phase separation. To this end, perspectives on future directions and areas of sustained inquiry are provided. This review highlights the significant opportunity in exploiting nonlinear optical pattern formation in soft matter for the discovery of new light-directed and light-stimulated materials phenomenon, and in turn, soft matter provides a platform by which new nonlinear optical phenomenon may be discovered.

General high-order breathers and rogue waves in the (3 + 1) -dimensional KP-Boussinesq equation

NASA Astrophysics Data System (ADS)

Sun, Baonan; Wazwaz, Abdul-Majid

2018-11-01

In this work, we investigate the (3 + 1) -dimensional KP-Boussinesq equation, which can be used to describe the nonlinear dynamic behavior in scientific and engineering applications. We derive general high-order soliton solutions by using the Hirota's bilinear method combined with the perturbation expansion technique. We also obtain periodic solutions comprising of high-order breathers, periodic line waves, and mixed solutions consisting of breathers and periodic line waves upon selecting particular parameter constraints of the obtained soliton solutions. Furthermore, smooth rational solutions are generated by taking a long wave limit of the soliton solutions. These smooth rational solutions include high-order rogue waves, high-order lumps, and hybrid solutions consisting of lumps and line rogue waves. To better understand the dynamical behaviors of these solutions, we discuss some illustrative graphical analyses. It is expected that our results can enrich the dynamical behavior of the (3 + 1) -dimensional nonlinear evolution equations of other forms.

Several reverse-time integrable nonlocal nonlinear equations: Rogue-wave solutions

NASA Astrophysics Data System (ADS)

Yang, Bo; Chen, Yong

2018-05-01

A study of rogue-wave solutions in the reverse-time nonlocal nonlinear Schrödinger (NLS) and nonlocal Davey-Stewartson (DS) equations is presented. By using Darboux transformation (DT) method, several types of rogue-wave solutions are constructed. Dynamics of these rogue-wave solutions are further explored. It is shown that the (1 + 1)-dimensional fundamental rogue-wave solutions in the reverse-time NLS equation can be globally bounded or have finite-time blowing-ups. It is also shown that the (2 + 1)-dimensional line rogue waves in the reverse-time nonlocal DS equations can be bounded for all space and time or develop singularities in critical time. In addition, the multi- and higher-order rogue waves exhibit richer structures, most of which have no counterparts in the corresponding local nonlinear equations.

Nonlinear Dynamics of a Diffusing Interface

NASA Technical Reports Server (NTRS)

Duval, Walter M. B.

2001-01-01

Excitation of two miscible-viscous liquids inside a bounded enclosure in a microgravity environment has shown the evolution of quasi-stationary waves of various modes for a range of parameters. We examine computationally the nonlinear dynamics of the system as the interface breakup and bifurcates to resonance structures typified by the Rayleigh-Taylor instability mechanism. Results show that when the mean steady field is much smaller than the amplitude of the sinusoidal excitation, the system behaves linearly, and growth of quasi-stationary waves occurs through the Kelvin-Helmholtz instability mechanism. However, as the amplitude of excitation increases, nonlinearity occurs through subharmonic bifurcation prior to broadband chaos.

Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics: Building Blocks for a Higher Order Method

DTIC Science & Technology

2006-09-30

equation known as the Kadomtsev - Petviashvili (KP) equation ): (ηt + coηx +αηηx + βη )x +γηyy = 0 (4) where γ = co / 2 . The KdV equation ...using the spectral formulation of the Kadomtsev - Petviashvili equation , a standard equation for nonlinear, shallow water wave dynamics that is a... Petviashvili and nonlinear Schroedinger equations and higher order corrections have been developed as prerequisites to coding the Boussinesq and Euler

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

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

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

Stability of nonlinear waves and patterns and related topics

NASA Astrophysics Data System (ADS)

Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn

2018-04-01

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

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.

Breather Rogue Waves in Random Seas

NASA Astrophysics Data System (ADS)

Wang, J.; Ma, Q. W.; Yan, S.; Chabchoub, A.

2018-01-01

Rogue or freak waves are extreme wave events that have heights exceeding 8 times the standard deviation of surrounding waves and emerge, for instance, in the ocean as well as in other physical dispersive wave guides, such as in optical fibers. One effective and convenient way to model such an extreme dynamics in laboratory environments within a controlled framework as well as for short process time and length scales is provided through the breather formalism. Breathers are pulsating localized structures known to model extreme waves in several nonlinear dispersive media in which the initial underlying process is assumed to be narrow banded. On the other hand, several recent studies suggest that breathers can also persist in more complex environments, such as in random seas, beyond the attributed physical limitations. In this work, we study the robustness of the Peregrine breather (PB) embedded in Joint North Sea Wave Project (JONSWAP) configurations using fully nonlinear hydrodynamic numerical simulations in order to validate its practicalness for ocean engineering applications. We provide a specific range for both the spectral bandwidth of the dynamical process as well as the background wave steepness and, thus, quantify the applicability of the PB in modeling rogue waves in realistic oceanic conditions. Our results may motivate analogous studies in fields of physics such as optics and plasma to quantify the limitations of exact weakly nonlinear models, such as solitons and breathers, within the framework of the fully nonlinear governing equations of the corresponding medium.

Nonlinear travelling waves in rotating Hagen–Poiseuille flow

NASA Astrophysics Data System (ADS)

Pier, Benoît; Govindarajan, Rama

2018-03-01

The dynamics of viscous flow through a rotating pipe is considered. Small-amplitude stability characteristics are obtained by linearizing the Navier–Stokes equations around the base flow and solving the resulting eigenvalue problems. For linearly unstable configurations, the dynamics leads to fully developed finite-amplitude perturbations that are computed by direct numerical simulations of the complete Navier–Stokes equations. By systematically investigating all linearly unstable combinations of streamwise wave number k and azimuthal mode number m, for streamwise Reynolds numbers {{Re}}z ≤slant 500 and rotational Reynolds numbers {{Re}}{{Ω }} ≤slant 500, the complete range of nonlinear travelling waves is obtained and the associated flow fields are characterized.

Nonlinear dynamics of electromagnetic turbulence in a nonuniform magnetized plasma

NASA Astrophysics Data System (ADS)

Shukla, P. K.; Mirza, Arshad M.; Faria, R. T.

1998-03-01

By using the hydrodynamic electron response with fixed (kinetic) ions along with Poisson's equation as well as Ampère's law, a system of nonlinear equations for low-frequency (in comparison with the electron gyrofrequency) long-(short-) wavelength electromagnetic waves in a nonuniform resistive magnetoplasma has been derived. The plasma contains equilibrium density gradient and sheared equilibrium plasma flows. In the linear limit, local dispersion relations are obtained and analyzed. It is found that sheared equilibrium flows can cause instability of Alfvén-like electromagnetic waves even in the absence of a density gradient. Furthermore, it is shown that possible stationary solutions of the nonlinear equations without dissipation can be represented in the form of various types of vortices. On the other hand, the temporal behavior of our nonlinear dissipative systems without the equilibrium density inhomogeneity can be described by the generalized Lorenz equations which admit chaotic trajectories. The density inhomogeneity may lead to even qualitative changes in the chaotic dynamics. The results of our investigation should be useful in understanding the linear and nonlinear properties of nonthermal electromagnetic waves in space and laboratory plasmas.

NONLINEAR AND FIBER OPTICS: Transient stimulated thermal scattering in a field of quasiplanar counterpropagating pump beams

NASA Astrophysics Data System (ADS)

Arutyunov, Yu A.; Bagan, A. A.; Gerasimov, V. B.; Golyanov, A. V.; Ogluzdin, Valerii E.; Sugrobov, V. A.; Khizhnyak, A. I.

1990-04-01

Theoretical analyses and experimental studies are made of transient stimulated thermal scattering in a thermal nonlinear medium subjected to a field of counterpropagating quasiplane waves. The equations for the counterpropagating four-beam interaction are solved analytically for pairwise counterpropagating scattered waves using the constant pump wave intensity approximation. The conditions for the occurrence of an absolute instability of the scattered waves are determined and the angular dependence of their increment is obtained; these results are in good agreement with experimental data. An investigation is reported of the dynamics of spiky lasing in a laser with resonators coupled by a dynamic hologram in which stimulated thermal scattering is a source of radiation initiating lasing in the system as a whole.

The Dynamics and Evolution of Poles and Rogue Waves for Nonlinear Schrödinger Equations*

NASA Astrophysics Data System (ADS)

Chiu, Tin Lok; Liu, Tian Yang; Chan, Hiu Ning; Wing Chow, Kwok

2017-09-01

Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schrödinger (NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.

Spectra of KeV Protons Related to Ion-Cyclotron Wave Packets

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Sibeck, D. G.; Tel'Nikhin, A. A.; Kronberg, T. K.

2017-01-01

We use the Fokker-Planck-Kolmogorov equation to study the statistical aspects of stochastic dynamics of the radiation belt (RB) protons driven by nonlinear electromagnetic ion-cyclotron (EMIC) wave packets. We obtain the spectra of keV protons scattered by these waves that showsteeping near the gyroresonance, the signature of resonant wave-particle interaction that cannot be described by a simple power law. The most likely mechanism for proton precipitation events in RBs is shown to be nonlinear wave-particle interaction, namely, the scattering of RB protons into the loss cone by EMIC waves.

Dynamic response signatures of a scaled model platform for floating wind turbines in an ocean wave basin

PubMed Central

Jaksic, V.; O'Shea, R.; Cahill, P.; Murphy, J.; Mandic, D. P.; Pakrashi, V.

2015-01-01

Understanding of dynamic behaviour of offshore wind floating substructures is extremely important in relation to design, operation, maintenance and management of floating wind farms. This paper presents assessment of nonlinear signatures of dynamic responses of a scaled tension-leg platform (TLP) in a wave tank exposed to different regular wave conditions and sea states characterized by the Bretschneider, the Pierson–Moskowitz and the JONSWAP spectra. Dynamic responses of the TLP were monitored at different locations using load cells, a camera-based motion recognition system and a laser Doppler vibrometer. The analysis of variability of the TLP responses and statistical quantification of their linearity or nonlinearity, as non-destructive means of structural monitoring from the output-only condition, remains a challenging problem. In this study, the delay vector variance (DVV) method is used to statistically study the degree of nonlinearity of measured response signals from a TLP. DVV is observed to create a marker estimating the degree to which a change in signal nonlinearity reflects real-time behaviour of the structure and also to establish the sensitivity of the instruments employed to these changes. The findings can be helpful in establishing monitoring strategies and control strategies for undesirable levels or types of dynamic response and can help to better estimate changes in system characteristics over the life cycle of the structure. PMID:25583866

Multicomponent long-wave-short-wave resonance interaction system: Bright solitons, energy-sharing collisions, and resonant solitons.

PubMed

Sakkaravarthi, K; Kanna, T; Vijayajayanthi, M; Lakshmanan, M

2014-11-01

We consider a general multicomponent (2+1)-dimensional long-wave-short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlevé analysis. Then we construct the exact bright multisoliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.

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

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

Shallow near-fault material self organizes so it is just nonlinear in typical strong shaking

NASA Astrophysics Data System (ADS)

Sleep, N. H.

2011-12-01

Cracking within shallow compliant fault zones self-organizes so that strong dynamic stresses marginally exceed the elastic limit. To the first order, the compliant material experiences strain boundary conditions imposed by underlying stiffer rock. A major strike-slip fault yields simple dimensional relations. The near-field velocity pulse is essentially a Love wave. The dynamic strain is the ratio of the measured particle velocity over the deep S-wave velocity. The shallow dynamic stress is this quantity times the local shear modulus. I obtain the equilibrium shear modulus by starting a sequence of earthquakes with intact stiff rock surrounding the shallow fault zone. The imposed dynamic strain in stiff rock causes Coulomb failure and leaves cracks in it wake. Cracked rock is more compliant than the original intact rock. Each subsequent event causes more cracking until the rock becomes compliant enough that it just reaches its elastic limit. Further events maintain the material at the shear modulus where it just fails. Analogously, shallow damaged regolith forms with its shear modulus and S-wave velocity increasing with depth so it just reaches failure during typical strong shaking. The 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. The equilibrium shear modulus and S-wave velocity depend only modestly on the effective coefficient of internal friction.

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

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

Ruiz, Daniel

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

Observation of a group of dark rogue waves in a telecommunication optical fiber

NASA Astrophysics Data System (ADS)

Baronio, F.; Frisquet, B.; Chen, S.; Millot, G.; Wabnitz, S.; Kibler, B.

2018-01-01

Over the past decade, the rogue wave debate has stimulated the comparison of predictions and observations among different branches of wave physics, particularly between hydrodynamics and optics, in situations where analogous dynamical behaviors can be identified, thanks to the use of common universal models. Although the scalar nonlinear Schrödinger equation (NLSE) has constantly played a central role for rogue wave investigations, moving beyond the standard NLSE model is relevant and needful for describing more general classes of physical systems and applications. In this direction, the coupled NLSEs are known to play a pivotal role for the understanding of the complex wave dynamics in hydrodynamics and optics. Benefiting from the advanced technology of high-speed telecommunication-grade components, and relying on a careful design of the nonlinear propagation of orthogonally polarized optical pump waves in a randomly birefringent telecom fiber, this work explores, both theoretically and experimentally, the rogue wave dynamics governed by such coupled NLSEs. We report, for the first time, the evidence of a group of three dark rogue waves, the so-called dark three-sister rogue waves, where experiments, numerics, and analytics show a very good consistency.

Nonlinear attenuation of S-waves and Love waves within ambient rock

NASA Astrophysics Data System (ADS)

Sleep, Norman H.; Erickson, Brittany A.

2014-04-01

obtain scaling relationships for nonlinear attenuation of S-waves and Love waves within sedimentary basins to assist numerical modeling. These relationships constrain the past peak ground velocity (PGV) of strong 3-4 s Love waves from San Andreas events within Greater Los Angeles, as well as the maximum PGV of future waves that can propagate without strong nonlinear attenuation. During each event, the shaking episode cracks the stiff, shallow rock. Over multiple events, this repeated damage in the upper few hundred meters leads to self-organization of the shear modulus. Dynamic strain is PGV divided by phase velocity, and dynamic stress is strain times the shear modulus. The frictional yield stress is proportional to depth times the effective coefficient of friction. At the eventual quasi-steady self-organized state, the shear modulus increases linearly with depth allowing inference of past typical PGV where rock over the damaged depth range barely reaches frictional failure. Still greater future PGV would cause frictional failure throughout the damaged zone, nonlinearly attenuating the wave. Assuming self-organization has taken place, estimated maximum past PGV within Greater Los Angeles Basins is 0.4-2.6 m s-1. The upper part of this range includes regions of accumulating sediments with low S-wave velocity that may have not yet compacted, rather than having been damaged by strong shaking. Published numerical models indicate that strong Love waves from the San Andreas Fault pass through Whittier Narrows. Within this corridor, deep drawdown of the water table from its currently shallow and preindustrial levels would nearly double PGV of Love waves reaching Downtown Los Angeles.

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.

Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Nonlinear ring resonator: spatial pattern generation

NASA Astrophysics Data System (ADS)

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

2000-03-01

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

Nonlinear wave propagation in discrete and continuous systems

NASA Astrophysics Data System (ADS)

Rothos, V. M.

2016-09-01

In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.

Green-Naghdi dynamics of surface wind waves in finite depth

NASA Astrophysics Data System (ADS)

Manna, M. A.; Latifi, A.; Kraenkel, R. A.

2018-04-01

The Miles’ quasi laminar theory of waves generation by wind in finite depth h is presented. In this context, the fully nonlinear Green-Naghdi model equation is derived for the first time. This model equation is obtained by the non perturbative Green-Naghdi approach, coupling a nonlinear evolution of water waves with the atmospheric dynamics which works as in the classic Miles’ theory. A depth-dependent and wind-dependent wave growth γ is drawn from the dispersion relation of the coupled Green-Naghdi model with the atmospheric dynamics. Different values of the dimensionless water depth parameter δ = gh/U 1, with g the gravity and U 1 a characteristic wind velocity, produce two families of growth rate γ in function of the dimensionless theoretical wave-age c 0: a family of γ with h constant and U 1 variable and another family of γ with U 1 constant and h variable. The allowed minimum and maximum values of γ in this model are exhibited.

Nonlinear ship waves and computational fluid dynamics

PubMed Central

MIYATA, Hideaki; ORIHARA, Hideo; SATO, Yohei

2014-01-01

Research works undertaken in the first author’s laboratory at the University of Tokyo over the past 30 years are highlighted. Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design. Based on these findings, a multitude of the Computational Fluid Dynamic (CFD) techniques have been developed over this period, and are highlighted in this paper. The TUMMAC code has been developed for wave problems, based on a rectangular grid system, while the WISDAM code treats both wave and viscous flow problems in the framework of a boundary-fitted grid system. These two techniques are able to cope with almost all fluid dynamical problems relating to ships, including the resistance, ship’s motion and ride-comfort issues. Consequently, the two codes have contributed significantly to the progress in the technology of ship design, and now form an integral part of the ship-designing process. PMID:25311139

Stability of nonlinear waves and patterns and related topics.

PubMed

Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn

2018-04-13

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties.This article is part of the theme issue 'Stability of nonlinear waves and patterns and related topics'. © 2018 The Author(s).

A new mathematical approach for shock-wave solution in a dusty plasma

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

Das, G.C.; Dwivedi, C.B.; Talukdar, M.

1997-12-01

The problem of nonlinear Burger equation in a plasma contaminated with heavy dust grains has been revisited. As discussed earlier [C. B. Dwivedi and B. P. Pandey, Phys. Plasmas {bold 2}, 9 (1995)], the Burger equation originates due to dust charge fluctuation dynamics. A new alternate mathematical approach based on a simple traveling wave formalism has been applied to find out the solution of the derived Burger equation, and the method recovers the known shock-wave solution. This technique, although having its own limitation, predicts successfully the salient features of the weak shock-wave structure in a dusty plasma with dust chargemore » fluctuation dynamics. It is emphasized that this approach of the traveling wave formalism is being applied for the first time to solve the nonlinear wave equation in plasmas. {copyright} {ital 1997 American Institute of Physics.}« less

Self-consistent Langmuir waves in resonantly driven thermal plasmas

NASA Astrophysics Data System (ADS)

Lindberg, R. R.; Charman, A. E.; Wurtele, J. S.

2007-12-01

The longitudinal dynamics of a resonantly driven Langmuir wave are analyzed in the limit that the growth of the electrostatic wave is slow compared to the bounce frequency. Using simple physical arguments, the nonlinear distribution function is shown to be nearly invariant in the canonical particle action, provided both a spatially uniform term and higher-order spatial harmonics are included along with the fundamental in the longitudinal electric field. Requirements of self-consistency with the electrostatic potential yield the basic properties of the nonlinear distribution function, including a frequency shift that agrees closely with driven, electrostatic particle simulations over a range of temperatures. This extends earlier work on nonlinear Langmuir waves by Morales and O'Neil [G. J. Morales and T. M. O'Neil, Phys. Rev. Lett. 28, 417 (1972)] and Dewar [R. L. Dewar, Phys. Plasmas 15, 712 (1972)], and could form the basis of a reduced kinetic treatment of plasma dynamics for accelerator applications or Raman backscatter.

Millimeter-wave interconnects for microwave-frequency quantum machines

NASA Astrophysics Data System (ADS)

Pechal, Marek; Safavi-Naeini, Amir H.

2017-10-01

Superconducting microwave circuits form a versatile platform for storing and manipulating quantum information. A major challenge to further scalability is to find approaches for connecting these systems over long distances and at high rates. One approach is to convert the quantum state of a microwave circuit to optical photons that can be transmitted over kilometers at room temperature with little loss. Many proposals for electro-optic conversion between microwave and optics use optical driving of a weak three-wave mixing nonlinearity to convert the frequency of an excitation. Residual absorption of this optical pump leads to heating, which is problematic at cryogenic temperatures. Here we propose an alternative approach where a nonlinear superconducting circuit is driven to interconvert between microwave-frequency (7 ×109 Hz) and millimeter-wave-frequency photons (3 ×1011 Hz). To understand the potential for quantum state conversion between microwave and millimeter-wave photons, we consider the driven four-wave mixing quantum dynamics of nonlinear circuits. In contrast to the linear dynamics of the driven three-wave mixing converters, the proposed four-wave mixing converter has nonlinear decoherence channels that lead to a more complex parameter space of couplings and pump powers that we map out. We consider physical realizations of such converter circuits by deriving theoretically the upper bound on the maximum obtainable nonlinear coupling between any two modes in a lossless circuit, and synthesizing an optimal circuit based on realistic materials that saturates this bound. Our proposed circuit dissipates less than 10-9 times the energy of current electro-optic converters per qubit. Finally, we outline the quantum link budget for optical, microwave, and millimeter-wave connections, showing that our approach is viable for realizing interconnected quantum processors for intracity or quantum data center environments.

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 .

Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques.

PubMed

Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J

2017-11-01

The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

Elastic Nonlinear Response in Granular Media Under Resonance Conditions

NASA Astrophysics Data System (ADS)

Jia, X.; Johnson, P. A.

2004-12-01

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

Nonlinear coherent structures in granular crystals

NASA Astrophysics Data System (ADS)

Chong, C.; Porter, Mason A.; Kevrekidis, P. G.; Daraio, C.

2017-10-01

The study of granular crystals, which are nonlinear metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures—which include traveling solitary waves, dispersive shock waves, and discrete breathers—have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research to date has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.

Salient features of solitary waves in dusty plasma under the influence of Coriolis force

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

Das, G. C.; Nag, Apratim; Department of Physics, G. C. College, Silchar-788004

The main interest is to study the nonlinear acoustic wave in rotating dusty plasma augmented through the derivation of a modified Sagdeev potential equation. Small rotation causes the interaction of Coriolis force in the dynamical system, and leads to the complexity in the derivation of the nonlinear wave equation. As a result, the finding of solitary wave propagation in dusty plasma ought to be of merit. However, the nonlinear wave equation has been successfully solved by the use of the hyperbolic method. Main emphasis has been given to the changes on the evolution and propagation of soliton, and the variationmore » caused by the dusty plasma constituents as well as by the Coriolis force have been highlighted. Some interesting nonlinear wave behavior has been found which can be elaborately studied for the interest of laboratory and space plasmas. Further, to support the theoretical investigations, numeric plasma parameters have been taken for finding the inherent features of solitons.« less

Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser.

PubMed

Peng, Junsong; Tarasov, Nikita; Sugavanam, Srikanth; Churkin, Dmitry

2016-09-19

We report for the first time, rogue waves generation in a mode-locked fiber laser that worked in multiple-soliton state in which hundreds of solitons occupied the whole laser cavity. Using real-time spatio-temporal intensity dynamics measurements, it is unveiled that nonlinear soliton collision accounts for the formation of rogue waves in this laser state. The nature of interactions between solitons are also discussed. Our observation may suggest similar formation mechanisms of rogue waves in other systems.

Evidence of negative-index refraction in nonlinear chemical waves.

PubMed

Yuan, Xujin; Wang, Hongli; Ouyang, Qi

2011-05-06

The negative index of refraction of nonlinear chemical waves has become a recent focus in nonlinear dynamics researches. Theoretical analysis and computer simulations have predicted that the negative index of refraction can occur on the interface between antiwaves and normal waves in a reaction-diffusion (RD) system. However, no experimental evidence has been found so far. In this Letter, we report our experimental design in searching for such a phenomenon in a chlorite-iodide-malonic acid (CIMA) reaction. Our experimental results demonstrate that competition between waves and antiwaves at their interface determines the fate of the wave interaction. The negative index of refraction was only observed when the oscillation frequency of a normal wave is significantly smaller than that of the antiwave. All experimental results were supported by simulations using the Lengyel-Epstein RD model which describes the CIMA reaction-diffusion system.

Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma

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

Ghosh, Samiran, E-mail: sran_g@yahoo.com; Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in

2016-08-15

The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.

ONR Ocean Wave Dynamics Workshop

NASA Astrophysics Data System (ADS)

In anticipation of the start (in Fiscal Year 1988) of a new Office of Naval Research (ONR) Accelerated Research Initiative (ARI) on Ocean Surface Wave Dynamics, a workshop was held August 5-7, 1986, at Woods Hole, Mass., to discuss new ideas and directions of research. This new ARI on Ocean Surface Wave Dynamics is a 5-year effort that is organized by the ONR Physical Oceanography Program in cooperation with the ONR Fluid Mechanics Program and the Physical Oceanography Branch at the Naval Ocean Research and Development Activity (NORDA). The central theme is improvement of our understanding of the basic physics and dynamics of surface wave phenomena, with emphasis on the following areas: precise air-sea coupling mechanisms,dynamics of nonlinear wave-wave interaction under realistic environmental conditions,wave breaking and dissipation of energy,interaction between surface waves and upper ocean boundary layer dynamics, andsurface statistical and boundary layer coherent structures.

Coexisting rogue waves within the (2+1)-component long-wave-short-wave resonance.

PubMed

Chen, Shihua; Soto-Crespo, Jose M; Grelu, Philippe

2014-09-01

The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics.

Nonlinear Dynamics and Quantum Transport in Small Systems

DTIC Science & Technology

2012-02-22

2.3 Nonlinear wave and chaos in optical metamaterials 2.3.1 Transient chaos in optical metamaterials We investigated the dynamics of light rays in two...equations can be modeled by a set of ordinary differential equations for light rays . We found that transient chaotic dynamics, hyperbolic or nonhyperbolic...are common in optical metamaterial systems. Due to the analogy between light- ray dynamics in metamaterials and the motion of light and matter as

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.

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.

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.

Dynamic response signatures of a scaled model platform for floating wind turbines in an ocean wave basin.

PubMed

Jaksic, V; O'Shea, R; Cahill, P; Murphy, J; Mandic, D P; Pakrashi, V

2015-02-28

Understanding of dynamic behaviour of offshore wind floating substructures is extremely important in relation to design, operation, maintenance and management of floating wind farms. This paper presents assessment of nonlinear signatures of dynamic responses of a scaled tension-leg platform (TLP) in a wave tank exposed to different regular wave conditions and sea states characterized by the Bretschneider, the Pierson-Moskowitz and the JONSWAP spectra. Dynamic responses of the TLP were monitored at different locations using load cells, a camera-based motion recognition system and a laser Doppler vibrometer. The analysis of variability of the TLP responses and statistical quantification of their linearity or nonlinearity, as non-destructive means of structural monitoring from the output-only condition, remains a challenging problem. In this study, the delay vector variance (DVV) method is used to statistically study the degree of nonlinearity of measured response signals from a TLP. DVV is observed to create a marker estimating the degree to which a change in signal nonlinearity reflects real-time behaviour of the structure and also to establish the sensitivity of the instruments employed to these changes. The findings can be helpful in establishing monitoring strategies and control strategies for undesirable levels or types of dynamic response and can help to better estimate changes in system characteristics over the life cycle of the structure. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

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

PubMed

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

2016-04-29

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

Nonlinear dynamics and anisotropic structure of rotating sheared turbulence.

PubMed

Salhi, A; Jacobitz, F G; Schneider, K; Cambon, C

2014-01-01

Homogeneous turbulence in rotating shear flows is studied by means of pseudospectral direct numerical simulation and analytical spectral linear theory (SLT). The ratio of the Coriolis parameter to shear rate is varied over a wide range by changing the rotation strength, while a constant moderate shear rate is used to enable significant contributions to the nonlinear interscale energy transfer and to the nonlinear intercomponental redistribution terms. In the destabilized and neutral cases, in the sense of kinetic energy evolution, nonlinearity cannot saturate the growth of the largest scales. It permits the smallest scale to stabilize by a scale-by-scale quasibalance between the nonlinear energy transfer and the dissipation spectrum. In the stabilized cases, the role of rotation is mainly nonlinear, and interacting inertial waves can affect almost all scales as in purely rotating flows. In order to isolate the nonlinear effect of rotation, the two-dimensional manifold with vanishing spanwise wave number is revisited and both two-component spectra and single-point two-dimensional energy components exhibit an important effect of rotation, whereas the SLT as well as the purely two-dimensional nonlinear analysis are unaffected by rotation as stated by the Proudman theorem. The other two-dimensional manifold with vanishing streamwise wave number is analyzed with similar tools because it is essential for any shear flow. Finally, the spectral approach is used to disentangle, in an analytical way, the linear and nonlinear terms in the dynamical equations.

Nonlinear dynamics of a two-dimensional Wigner solid on superfluid helium

NASA Astrophysics Data System (ADS)

Monarkha, Yu. P.

2018-04-01

Nonlinear dynamics and transport properties of a 2D Wigner solid (WS) on the free surface of superfluid helium are theoretically studied. The analysis is nonperturbative in the amplitude of the WS velocity. An anomalous nonlinear response of the liquid helium surface to the oscillating motion of the WS is shown to appear when the driving frequency is close to subharmonics of the frequency of a capillary wave (ripplon) whose wave vector coincides with a reciprocal-lattice vector. As a result, the effective mass of surface dimples formed under electrons and the kinetic friction acquire sharp anomalies in the low-frequency range, which affects the mobility and magnetoconductivity of the WS. The results obtained here explain a variety of experimental observations reported previously.

Saturation of energetic-particle-driven geodesic acoustic modes due to wave-particle nonlinearity

NASA Astrophysics Data System (ADS)

Biancalani, A.; Chavdarovski, I.; Qiu, Z.; Bottino, A.; Del Sarto, D.; Ghizzo, A.; Gürcan, Ö.; Morel, P.; Novikau, I.

2017-12-01

The nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic modes (EGAM) is investigated here. A numerical analysis with the global gyrokinetic particle-in-cell code ORB5 is performed, and the results are interpreted with the analytical theory, in close comparison with the theory of the beam-plasma instability. Only axisymmetric modes are considered, with a nonlinear dynamics determined by wave-particle interaction. Quadratic scalings of the saturated electric field with respect to the linear growth rate are found for the case of interest. As a main result, the formula for the saturation level is provided. Near the saturation, we observe a transition from adiabatic to non-adiabatic dynamics, i.e. the frequency chirping rate becomes comparable to the resonant EP bounce frequency. The numerical analysis is performed here with electrostatic simulations with circular flux surfaces, and kinetic effects of the electrons are neglected.

Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay.

PubMed

Akimenko, Vitalii; Anguelov, Roumen

2017-12-01

In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtained system is studied both theoretically and numerically. Three different regimes of population dynamics for asymptotically stable states of autonomous systems are obtained in numerical experiments for the different initial values of population density. The quasi-periodical travelling wave solutions are studied numerically for the autonomous system with the different values of time delays and for the system with oscillating death rate and birth modulus. In both cases it is observed three types of travelling wave solutions: harmonic oscillations, pulse sequence and single pulse.

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

PubMed

Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

2014-01-01

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

Nonlinear dynamics near the stability margin in rotating pipe flow

NASA Technical Reports Server (NTRS)

Yang, Z.; Leibovich, S.

1991-01-01

The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and the entire marginal stability boundary is explored. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a traveling wave. The envelope of the wave system is governed by a complex Ginzburg-Landau equation. The Ginzburg-Landau equation admits Stokes waves, which correspond to standing modulations of the linear traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.

Solitary waves in dimer binary collision model

NASA Astrophysics Data System (ADS)

Ahsan, Zaid; Jayaprakash, K. R.

2017-01-01

Solitary wave propagation in nonlinear diatomic (dimer) chains is a very interesting topic of research in the study of nonlinear lattices. Such waves were recently found to be supported by the essentially nonlinear granular lattice and Toda lattice. An interesting aspect of this discovery is attributed to the realization of a spectrum of the mass ratio (the only system parameter governing the dynamics) that supports the propagation of such waves corresponding to the considered interaction potential. The objective of this exposition is to explore solitary wave propagation in the dimer binary collision (BC) model. Interestingly, the dimer BC model supports solitary wave propagation at a discrete spectrum of mass ratios similar to those observed in granular and Toda dimers. Further, we report a qualitative and one-to-one correspondence between the spectrum of the mass ratio corresponding to the dimer BC model and those corresponding to granular and Toda dimer chains.

Fundamentals of Plasma Physics

NASA Astrophysics Data System (ADS)

Bellan, Paul M.

2008-07-01

Preface; 1. Basic concepts; 2. The Vlasov, two-fluid, and MHD models of plasma dynamics; 3. Motion of a single plasma particle; 4. Elementary plasma waves; 5. Streaming instabilities and the Landau problem; 6. Cold plasma waves in a magnetized plasma; 7. Waves in inhomogeneous plasmas and wave energy relations; 8. Vlasov theory of warm electrostatic waves in a magnetized plasma; 9. MHD equilibria; 10. Stability of static MHD equilibria; 11. Magnetic helicity interpreted and Woltjer-Taylor relaxation; 12. Magnetic reconnection; 13. Fokker-Planck theory of collisions; 14. Wave-particle nonlinearities; 15. Wave-wave nonlinearities; 16. Non-neutral plasmas; 17. Dusty plasmas; Appendix A. Intuitive method for vector calculus identities; Appendix B. Vector calculus in orthogonal curvilinear coordinates; Appendix C. Frequently used physical constants and formulae; Bibliography; References; Index.

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions.

PubMed

Kanna, T; Sakkaravarthi, K; Tamilselvan, K

2013-12-01

We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.

Exploring Wave-Wave Interactions in a General Circulation Model

NASA Astrophysics Data System (ADS)

Nystrom, Virginia; Gasperini, Federico; Forbes, Jeffrey M.; Hagan, Maura E.

2018-01-01

Nonlinear interactions involving Kelvin waves with (periods, zonal wave numbers) = (3.7d, s =- 1) (UFKW1) and = (2.4d, s =- 1) (UFKW2) and s = 0 and s = 1 quasi 9 day waves (Q9DW) with diurnal tides DW1, DW2, DW3, DE2, and DE3 are explored within a National Center for Atmospheric Research (NCAR) thermosphere-ionosphere-mesosphere electrodynamics general circulation model (TIME-GCM) simulation driven at its ˜30 km lower boundary by interpolated 3-hourly output from Modern-Era Retrospective Analysis for Research and Applications (MERRA). The existence of nonlinear wave-wave interactions between the above primary waves is determined by the presence of secondary waves (SWs) with frequencies and zonal wave numbers that are the sums and differences of those of the primary (interacting) waves. Focus is on 10-21 April 2009, when the nontidal dynamics in the mesosphere-lower thermosphere (MLT) region is dominated by UFKW and when identification of SW is robust. Fifteen SWs are identified in all. An interesting triad is identified involving UFKW1, DE3, and a secondary UFKW4 = (1.5d, s =- 2): The UFKW1-DE3 interaction produces UFKW4, the UFKW4-DE3 interaction produces UFKW1, and the UFKW1 interaction with UFKW4 produces DE3. At 120 km the dynamic range of the reconstructed latitude-longitude zonal wind field due to all of the SW is roughly half that of the primary waves, which produced them. This suggests that nonlinear wave-wave interactions could significantly modify the way that the lower atmosphere couples with the ionosphere.

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.

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

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1977-01-01

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

Computational study of nonlinear plasma waves. [plasma simulation model applied to electrostatic waves in collisionless plasma

NASA Technical Reports Server (NTRS)

Matsuda, Y.

1974-01-01

A low-noise plasma simulation model is developed and applied to a series of linear and nonlinear problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. It is demonstrated that use of the hybrid simulation model allows economical studies to be carried out in both the linear and nonlinear regimes with better quantitative results, for comparable computing time, than can be obtained by conventional particle simulation models, or direct solution of the Vlasov equation. The characteristics of the hybrid simulation model itself are first investigated, and it is shown to be capable of verifying the theoretical linear dispersion relation at wave energy levels as low as .000001 of the plasma thermal energy. Having established the validity of the hybrid simulation model, it is then used to study the nonlinear dynamics of monochromatic wave, sideband instability due to trapped particles, and satellite growth.

Nonlinear internal waves in the Gulf of Guinea: observations and modeling

NASA Astrophysics Data System (ADS)

Baquet, Emeric; Pichon, Annick; Raynaud, Stephane; Carton, Xavier

2017-04-01

Nonlinear internal waves are known hazards to offshore operations. They have been observed at different locations around the world and have been studied for a long time in Southeast Asia. However in West Africa, they are less documented. This research presents original data of currentmeters in northeastern part of the Gulf of Guinea, in the vicinity of offshore oil platforms. Nonlinear internal waves were observed. Their characteristics were determined under the assumptions of the weakly nonlinear and non-hydrostatic Korteweg-de Vries equation. Their directions of propagation were studied to determine generation zones. The monthly distribution was shown to assess seasonal variability. Their main generation mechanism was the barotropic tides over the shelf break, but other processes were at work too. The seasonal variability due to the monsoon, river discharges also played a part in the nonlinear internal wave dynamics. Since several processes, of different time and space scales, are at work, interactions between them must be investigated. Thus, a two-layered numerical model was used to reproduce nonlinear internal waves. Sensitivity experiments were made, in order to investigate the balance between nonlinearities, Coriolis and non-hydrostatic dispersions. The impact of non-uniform bathymetry and the presence of another flow in addition to the tides were also tested.

Electronic transport in disordered chains with saturable nonlinearity

NASA Astrophysics Data System (ADS)

dos Santos, J. L. L.; Nguyen, Ba Phi; de Moura, F. A. B. F.

2015-10-01

In this work we study numerically the dynamics of an initially localized wave packet in one-dimensional disordered chains with saturable nonlinearity. By using the generalized discrete nonlinear Schrödinger equation, we calculate two different physical quantities as a function of time, which are the participation number and the mean square displacement from the excitation site. From detailed numerical analysis, we find that the saturable nonlinearity can promote a sub-diffusive spreading of the wave packet even in the presence of diagonal disorder for a long time. In addition, we also investigate the effect of the saturated nonlinearity for initial times of the electronic evolution thus showing the possibility of mobile breather-like modes.

Electronegative nonlinear oscillating modes in plasmas

NASA Astrophysics Data System (ADS)

Panguetna, Chérif Souleman; Tabi, Conrad Bertrand; Kofané, Timoléon Crépin

2018-02-01

The emergence of nonlinear modulated waves is addressed in an unmagnetized electronegative plasma made of Boltzmann electrons, Boltzmann negative ions and cold mobile positive ions. The reductive perturbation method is used to reduce the dynamics of the whole system to a cubic nonlinear Schrödinger equation, whose the nonlinear and dispersion coefficients, P and Q, are function of the negative ion parameters, namely the negative ion concentration ratio (α) and the electron-to-negative ion temperature ratio (σn). It is observed that these parameters importantly affect the formation of modulated ion-acoustic waves, either as exact solutions or via the activation of modulational instability. Especially, the theory of modulational instability is used to show the correlation between the parametric analysis and the formation of modulated solitons, obtained here as bright envelopes and kink-wave solitons.

Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation

NASA Astrophysics Data System (ADS)

Wen, Xiao-Yong; Zhang, Guoqiang

2018-01-01

Under investigation in this paper is the Kundu equation, which may be used to describe the propagation process of ultrashort optical pulses in nonlinear optics. The modulational instability of the plane-wave for the possible reason of the formation of the rogue wave (RW) is studied for the system. Based on our proposed generalized perturbation (n,N - n)-fold Darboux transformation (DT), some new higher-order implicit RW solutions in terms of determinants are obtained by means of the generalized perturbation (1,N - 1)-fold DT, when choosing different special parameters, these results will reduce to the RW solutions of the Kaup-Newell (KN) equation, Chen-Lee-Liu (CLL) equation and Gerjikov-Ivanov (GI) equation, respectively. The relevant wave structures are shown graphically, which display abundant interesting wave structures. The dynamical behaviors and propagation stability of the first-order and second-order RW solutions are discussed by using numerical simulations, the higher-order nonlinear terms for the Kundu equation have an impact on the propagation instability of the RW. The method can also be extended to find the higher-order RW or rational solutions of other integrable nonlinear equations.

THE DYNAMICAL GENERATION OF CURRENT SHEETS IN ASTROPHYSICAL PLASMA TURBULENCE

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

Howes, Gregory G.

2016-08-20

Turbulence profoundly affects particle transport and plasma heating in many astrophysical plasma environments, from galaxy clusters to the solar corona and solar wind to Earth's magnetosphere. Both fluid and kinetic simulations of plasma turbulence ubiquitously generate coherent structures, in the form of current sheets, at small scales, and the locations of these current sheets appear to be associated with enhanced rates of dissipation of the turbulent energy. Therefore, illuminating the origin and nature of these current sheets is critical to identifying the dominant physical mechanisms of dissipation, a primary aim at the forefront of plasma turbulence research. Here, we presentmore » evidence from nonlinear gyrokinetic simulations that strong nonlinear interactions between counterpropagating Alfvén waves, or strong Alfvén wave collisions, are a natural mechanism for the generation of current sheets in plasma turbulence. Furthermore, we conceptually explain this current sheet development in terms of the nonlinear dynamics of Alfvén wave collisions, showing that these current sheets arise through constructive interference among the initial Alfvén waves and nonlinearly generated modes. The properties of current sheets generated by strong Alfvén wave collisions are compared to published observations of current sheets in the Earth's magnetosheath and the solar wind, and the nature of these current sheets leads to the expectation that Landau damping of the constituent Alfvén waves plays a dominant role in the damping of turbulently generated current sheets.« less

Glimpses of Kolmogorov's spectral energy dynamics in nonlinear acoustic waves

NASA Astrophysics Data System (ADS)

Gupta, Prateek; Scalo, Carlo

2017-11-01

Gupta, Lodato, and Scalo (AIAA 2017) have demonstrated the existence of an equilibrium spectral energy cascade in shock waves formed as a result of continued modal thermoacoustic amplification consistent with Kolmogorov's theory for high-Reynolds-number hydrodynamic turbulence. In this talk we discuss the derivation of a perturbation energy density norm that guarantees energy conservation during the nonlinear wave steepening process, analogous to inertial subrange turbulent energy cascade dynamics. The energy cascade is investigated via a bi-spectral analysis limited to wave-numbers and frequencies lower than the ones associated with the shock, analogous to the viscous dissipation length scale in turbulence. The proposed norm is derived by recombining second-order nonlinear acoustic equations and is positive definite; moreover, it decays to zero in the presence of viscous dissipation and is hence classifiable as a Lyapunov function of acoustic perturbation variables. The cumulative energy spectrum wavenumber distribution demonstrates a -3/2 decay law in the inertial range. The governing equation for the thus-derived energy norm highlights terms responsible for energy cascade towards higher harmonics, analogous to vortex stretching terms in hydrodynamic turbulence.

Laboratory tests of short intense envelope solitons

NASA Astrophysics Data System (ADS)

Slunyaev, A.; Clauss, G. F.; Klein, M.; Onorato, M.

2012-04-01

Stability of short intense nonlinear wave groups propagating over deep water is tested in laboratory runs which are performed in the facility of the Technical University of Berlin. The strongly nonlinear simulation of quasi-steady nonlinear wave groups within the framework of the Euler equations is used to generate the surface elevation time series at a border of the water tank. Besides, the exact analytic solution of the nonlinear Schrodinger equation is used for this purpose. The time series is then transformed to a wave maker signal with use of a designed transfer algorithm. Wave group propagation along the tank was recorded by 4 distant gauges and by an array of 6 densely situated gauges. This setup allows to consider the wave evolution from 10 to 85 m from the wave maker, and to obtain the wave envelope shape directly from the instrumental data. In the experiments wave groups were characterized by the steepness values up to kAcr < 0.32 and kAtr < 0.24, where k is the mean wavenumber, Acr is the crest amplitude, and Atr is the trough amplitude; and the maximum local wave slope was up to 0.34. Wave breaking phenomenon was not observed in the experiments. Different mean wave numbers and wave groups of different intensities were considered. In some cases the wave groups exhibit noticeable radiation in the course of propagation, though the groups are not dispersed fully. The effect of finite water depth is found to be significant on the wave group stability. Intense wave groups have shorter time of adjustment, what in some sense may help them to manifest their individuality clearer. The experimental tests confirm recent numerical simulations of fully nonlinear equations, where very steep stable single and interacting nonlinear wave groups were reported [1-3]. The quasi-stationary wave groups observed in numerical and laboratory experiments are strongly nonlinear analogues of the nonlinear Schrodinger envelope solitons. The results emphasize the importance of long-living nonlinear wave groups in dynamics of intense sea waves. [1] V.E. Zakharov, A.I. Dyachenko, A.O. Prokofiev, Eur. J. Mech. B / Fluids 25, 677 (2006). [2] A.I. Dyachenko, V.E. Zakharov, JETP Lett. 88, 307 (2008). [3] A.V. Slunyaev, JETP 109, 676 (2009).

Spectra of Baroclinic Inertia-Gravity Wave Turbulence

NASA Technical Reports Server (NTRS)

Glazman, Roman E.

1996-01-01

Baroclinic inertia-gravity (IG) waves form a persistent background of thermocline depth and sea surface height oscillations. They also contribute to the kinetic energy of horizontal motions in the subsurface layer. Measured by the ratio of water particle velocity to wave phase speed, the wave nonlinearity may be rather high. Given a continuous supply of energy from external sources, nonlinear wave-wave interactions among IG waves would result in inertial cascades of energy, momentum, and wave action. Based on a recently developed theory of wave turbulence in scale-dependent systems, these cascades are investigated and IG wave spectra are derived for an arbitrary degree of wave nonlinearity. Comparisons with satellite-altimetry-based spectra of surface height variations and with energy spectra of horizontal velocity fluctuations show good agreement. The well-known spectral peak at the inertial frequency is thus explained as a result of the inverse cascade. Finally, we discuss a possibility of inferring the internal Rossby radius of deformation and other dynamical properties of the upper thermocline from the spectra of SSH (sea surface height) variations based on altimeter measurements.

Global solutions and finite time blow-up for fourth order nonlinear damped wave equation

NASA Astrophysics Data System (ADS)

Xu, Runzhang; Wang, Xingchang; Yang, Yanbing; Chen, Shaohua

2018-06-01

In this paper, we study the initial boundary value problem and global well-posedness for a class of fourth order wave equations with a nonlinear damping term and a nonlinear source term, which was introduced to describe the dynamics of a suspension bridge. The global existence, decay estimate, and blow-up of solution at both subcritical (E(0) < d) and critical (E(0) = d) initial energy levels are obtained. Moreover, we prove the blow-up in finite time of solution at the supercritical initial energy level (E(0) > 0).

Numerical modelling of nonlinear full-wave acoustic propagation

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

Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx

2015-10-28

The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on amore » GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.« less

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.

PubMed

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-04-08

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

PubMed Central

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-01-01

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves. PMID:24711719

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Nonlinear Gap Junctions Enable Long-Distance Propagation of Pulsating Calcium Waves in Astrocyte Networks

PubMed Central

Goldberg, Mati; De Pittà, Maurizio; Volman, Vladislav; Berry, Hugues; Ben-Jacob, Eshel

2010-01-01

A new paradigm has recently emerged in brain science whereby communications between glial cells and neuron-glia interactions should be considered together with neurons and their networks to understand higher brain functions. In particular, astrocytes, the main type of glial cells in the cortex, have been shown to communicate with neurons and with each other. They are thought to form a gap-junction-coupled syncytium supporting cell-cell communication via propagating Ca2+ waves. An identified mode of propagation is based on cytoplasm-to-cytoplasm transport of inositol trisphosphate (IP3) through gap junctions that locally trigger Ca2+ pulses via IP3-dependent Ca2+-induced Ca2+ release. It is, however, currently unknown whether this intracellular route is able to support the propagation of long-distance regenerative Ca2+ waves or is restricted to short-distance signaling. Furthermore, the influence of the intracellular signaling dynamics on intercellular propagation remains to be understood. In this work, we propose a model of the gap-junctional route for intercellular Ca2+ wave propagation in astrocytes. Our model yields two major predictions. First, we show that long-distance regenerative signaling requires nonlinear coupling in the gap junctions. Second, we show that even with nonlinear gap junctions, long-distance regenerative signaling is favored when the internal Ca2+ dynamics implements frequency modulation-encoding oscillations with pulsating dynamics, while amplitude modulation-encoding dynamics tends to restrict the propagation range. As a result, spatially heterogeneous molecular properties and/or weak couplings are shown to give rise to rich spatiotemporal dynamics that support complex propagation behaviors. These results shed new light on the mechanisms implicated in the propagation of Ca2+ waves across astrocytes and the precise conditions under which glial cells may participate in information processing in the brain. PMID:20865153

Validating simple dynamical simulations of the unitary Fermi gas

NASA Astrophysics Data System (ADS)

Forbes, Michael McNeil; Sharma, Rishi

2014-10-01

We present a comparison between simulated dynamics of the unitary fermion gas using the superfluid local density approximation (SLDA) and a simplified bosonic model, the extended Thomas-Fermi (ETF) with a unitary equation of state. Small-amplitude fluctuations have similar dynamics in both theories for frequencies far below the pair-breaking threshold and wave vectors much smaller than the Fermi momentum. The low-frequency linear responses in both match well for surprisingly large wave vectors, even up to the Fermi momentum. For nonlinear dynamics such as vortex generation, the ETF provides a semiquantitative description of SLDA dynamics as long as the fluctuations do not have significant power near the pair-breaking threshold; otherwise the dynamics of the ETF cannot be trusted. Nonlinearities in the ETF tend to generate high-frequency fluctuations, and with no normal component to remove this energy from the superfluid, features such as vortex lattices cannot relax and crystallize as they do in the SLDA.

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.

Nonlinear properties of small amplitude dust ion acoustic solitary waves

NASA Astrophysics Data System (ADS)

Ghosh, Samiran; Sarkar, S.; Khan, Manoranjan; Gupta, M. R.

2000-09-01

In this paper some nonlinear characteristics of small amplitude dust ion acoustic solitary wave in three component dusty plasma consisting of electrons, ions, and dust grains have been studied. Simultaneously, the charge fluctuation dynamics of the dust grains under the assumption that the dust charging time scale is much smaller than the dust hydrodynamic time scale has been considered here. The ion dust collision has also been incorporated. It has been seen that a damped Korteweg-de Vries (KdV) equation governs the nonlinear dust ion acoustic wave. The damping arises due to ion dust collision, under the assumption that the ion hydrodynamical time scale is much smaller than that of the ion dust collision. Numerical investigations reveal that the dust ion acoustic wave admits only a positive potential, i.e., compressive soliton.

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

NASA Astrophysics Data System (ADS)

Schmidt, Patrick; Ó Náraigh, Lennon; Lucquiaud, Mathieu; Valluri, Prashant

2016-04-01

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

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

Schmidt, Patrick; Lucquiaud, Mathieu; Valluri, Prashant, E-mail: prashant.valluri@ed.ac.uk

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analysesmore » based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.« less

On the Connection Between Microbursts and Nonlinear Electronic Structures in Planetary Radiation Belts

NASA Technical Reports Server (NTRS)

Osmane, Adnane; Wilson, Lynn B., III; Blum, Lauren; Pulkkinen, Tuija I.

2016-01-01

Using a dynamical-system approach, we have investigated the efficiency of large-amplitude whistler waves for causing microburst precipitation in planetary radiation belts by modeling the microburst energy and particle fluxes produced as a result of nonlinear wave-particle interactions. We show that wave parameters, consistent with large amplitude oblique whistlers, can commonly generate microbursts of electrons with hundreds of keV-energies as a result of Landau trapping. Relativistic microbursts (greater than 1 MeV) can also be generated by a similar mechanism, but require waves with large propagation angles Theta (sub k)B greater than 50 degrees and phase-speeds v(sub phi) greater than or equal to c/9. Using our result for precipitating density and energy fluxes, we argue that holes in the distribution function of electrons near the magnetic mirror point can result in the generation of double layers and electron solitary holes consistent in scales (of the order of Debye lengths) to nonlinear structures observed in the radiation belts by the Van Allen Probes. Our results indicate a relationship between nonlinear electrostatic and electromagnetic structures in the dynamics of planetary radiation belts and their role in the cyclical production of energetic electrons (E greater than or equal to 100 keV) on kinetic timescales, which is much faster than previously inferred.

Nonequilibrium Precondensation of Classical Waves in Two Dimensions Propagating through Atomic Vapors

NASA Astrophysics Data System (ADS)

Šantić, Neven; Fusaro, Adrien; Salem, Sabeur; Garnier, Josselin; Picozzi, Antonio; Kaiser, Robin

2018-02-01

The nonlinear Schrödinger equation, used to describe the dynamics of quantum fluids, is known to be valid not only for massive particles but also for the propagation of light in a nonlinear medium, predicting condensation of classical waves. Here we report on the initial evolution of random waves with Gaussian statistics using atomic vapors as an efficient two dimensional nonlinear medium. Experimental and theoretical analysis of near field images reveal a phenomenon of nonequilibrium precondensation, characterized by a fast relaxation towards a precondensate fraction of up to 75%. Such precondensation is in contrast to complete thermalization to the Rayleigh-Jeans equilibrium distribution, requiring prohibitive long interaction lengths.

Nonlinear dynamics of global atmospheric and Earth system processes

NASA Technical Reports Server (NTRS)

Saltzman, Barry

1993-01-01

During the past eight years, we have been engaged in a NASA-supported program of research aimed at establishing the connection between satellite signatures of the earth's environmental state and the nonlinear dynamics of the global weather and climate system. Thirty-five publications and four theses have resulted from this work, which included contributions in five main areas of study: (1) cloud and latent heat processes in finite-amplitude baroclinic waves; (2) application of satellite radiation data in global weather analysis; (3) studies of planetary waves and low-frequency weather variability; (4) GCM studies of the atmospheric response to variable boundary conditions measurable from satellites; and (5) dynamics of long-term earth system changes. Significant accomplishments from the three main lines of investigation pursued during the past year are presented and include the following: (1) planetary atmospheric waves and low frequency variability; (2) GCM studies of the atmospheric response to changed boundary conditions; and (3) dynamics of long-term changes in the global earth system.

Energy dynamics in a simulation of LAPD turbulence

NASA Astrophysics Data System (ADS)

Friedman, B.; Carter, T. A.; Umansky, M. V.; Schaffner, D.; Dudson, B.

2012-10-01

Energy dynamics calculations in a 3D fluid simulation of drift wave turbulence in the linear Large Plasma Device [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] illuminate processes that drive and dissipate the turbulence. These calculations reveal that a nonlinear instability dominates the injection of energy into the turbulence by overtaking the linear drift wave instability that dominates when fluctuations about the equilibrium are small. The nonlinear instability drives flute-like (k∥=0) density fluctuations using free energy from the background density gradient. Through nonlinear axial wavenumber transfer to k∥≠0 fluctuations, the nonlinear instability accesses the adiabatic response, which provides the requisite energy transfer channel from density to potential fluctuations as well as the phase shift that causes instability. The turbulence characteristics in the simulations agree remarkably well with experiment. When the nonlinear instability is artificially removed from the system through suppressing k∥=0 modes, the turbulence develops a coherent frequency spectrum which is inconsistent with experimental data. This indicates the importance of the nonlinear instability in producing experimentally consistent turbulence.

Kalman filter control of a model of spatiotemporal cortical dynamics

PubMed Central

Schiff, Steven J; Sauer, Tim

2007-01-01

Recent advances in Kalman filtering to estimate system state and parameters in nonlinear systems have offered the potential to apply such approaches to spatiotemporal nonlinear systems. We here adapt the nonlinear method of unscented Kalman filtering to observe the state and estimate parameters in a computational spatiotemporal excitable system that serves as a model for cerebral cortex. We demonstrate the ability to track spiral wave dynamics, and to use an observer system to calculate control signals delivered through applied electrical fields. We demonstrate how this strategy can control the frequency of such a system, or quench the wave patterns, while minimizing the energy required for such results. These findings are readily testable in experimental applications, and have the potential to be applied to the treatment of human disease. PMID:18310806

Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrödinger equation.

PubMed

Wen, Xiao-Yong; Yang, Yunqing; Yan, Zhenya

2015-07-01

In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc., and may be useful to study the physical mechanism of multirogue waves in optics. The dynamical behaviors of these multi-rogue-wave solutions are illustrated using numerical simulations. The same Darboux matrix can also be used to investigate the Gerjikov-Ivanov equation such that its multi-rogue-wave solutions and their wave structures are also found. The method can also be extended to find multi-rogue-wave solutions of other nonlinear integrable equations.

Magnetosonic shock wave in collisional pair-ion plasma

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

Adak, Ashish, E-mail: ashish-adak@yahoo.com; Khan, Manoranjan, E-mail: mkhan.ju@gmail.com; Sikdar, Arnab, E-mail: arnabs.ju@gmail.com

2016-06-15

Nonlinear propagation of magnetosonic shock wave has been studied in collisional magnetized pair-ion plasma. The masses of both ions are same but the temperatures are slightly different. Two fluid model has been taken to describe the model. Two different modes of the magnetosonic wave have been obtained. The dynamics of the nonlinear magnetosonic wave is governed by the Korteweg-de Vries Burgers' equation. It has been shown that the ion-ion collision is the source of dissipation that causes the Burgers' term which is responsible for the shock structures in equal mass pair-ion plasma. The numerical investigations reveal that the magnetosonic wavemore » exhibits both oscillatory and monotonic shock structures depending on the strength of the dissipation. The nonlinear wave exhibited the oscillatory shock wave for strong magnetic field (weak dissipation) and monotonic shock wave for weak magnetic field (strong dissipation). The results have been discussed in the context of the fullerene pair-ion plasma experiments.« less

Effect of Second-Order and Fully Nonlinear Wave Kinematics on a Tension-Leg-Platform Wind Turbine in Extreme Wave Conditions: Preprint

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

Robertson, Amy N; Jonkman, Jason; Pegalajar-Jurado, Antonio

In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equation for the hydrodynamic forcing. The wave kinematics are computed from either theoretical or measured signals of free-surface elevation. The numerical results from each model are compared to results from wave basin tests on a scaled prototype. The comparison shows that sub and superharmonic responses can be introduced by second-order and fully nonlinear wave kinematics. The response at themore » wave frequency range is better reproduced when kinematics are generated from the measured surface elevation. In the future, the numerical response may be further improved by replacing the global, constant damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping.« less

Effect of Second-Order and Fully Nonlinear Wave Kinematics on a Tension-Leg-Platform Wind Turbine in Extreme Wave Conditions

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

Robertson, Amy N; Jonkman, Jason; Pegalajar-Jurado, Antonio

In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equation for the hydrodynamic forcing. The wave kinematics are computed from either theoretical or measured signals of free-surface elevation. The numerical results from each model are compared to results from wave basin tests on a scaled prototype. The comparison shows that sub and superharmonic responses can be introduced by second-order and fully nonlinear wave kinematics. The response at themore » wave frequency range is better reproduced when kinematics are generated from the measured surface elevation. In the future, the numerical response may be further improved by replacing the global, constant damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping.« less

The application of the constants of motion to nonlinear stationary waves in complex plasmas: a unified fluid dynamic viewpoint

NASA Astrophysics Data System (ADS)

McKenzie, J. F.; Dubinin, E.; Sauer, K.; Doyle, T. B.

2004-08-01

Perturbation reductive procedures, as used to analyse various weakly nonlinear plasma waves (solitons and periodic waves), normally lead to the dynamical system being described by KdV, Burgers' or a nonlinear Schrödinger-type equation, with properties that can be deduced from an array of mathematical techniques. Here we develop a fully nonlinear theory of one-dimensional stationary plasma waves, which elucidates the common nature of various diverse wave phenomena. This is accomplished by adopting an essentially fluid dynamic viewpoint. In this unified treatment the constants of the motion (for mass, momentum and energy) lead naturally to the construction of the wave structure equations. It is shown, for example, that electrostatic, Hall magnetohydrodynamic and ion cyclotron acoustic nonlinear waves all obey first-order differential equations of the same generic type for the longitudinal flow field of the wave. The equilibrium points, which define the soliton amplitude, are given by the compressive and/or rarefactive roots of a total plasma ‘energy’ or ‘momentum’ function characterizing the wave type. This energy function, which is an algebraic combination of the Bernoulli momentum and energy functions for the longitudinal flow field, is the fluid dynamic counterpart of the pseudo-potentials, which are characteristic of system structure equations formulated in other than fluid variables. Another general feature of the structure equation is the phenomenon of choked flow, which occurs when the flow speed becomes sonic. It is this trans-sonic property that limits the soliton amplitudes and defines the critical collective Mach numbers of the waves. These features are also obtained in multi-component plasmas where, for example, in a bi-ion plasma, momentum exchanges between protons and heavier ions are mediated by the Maxwell magnetic stresses. With a suitable generalization of the concept of a sonic point in a bi-ion system and the corresponding choked flow feature, the wave structures, although now more complicated, can also be understood within this overall fluid framework. Particularly useful tools in this context are the momentum hodograph (an algebraic relation between the bi-ion speeds and the electron speed, or magnetic field, which follows from the conservation of mass, momentum and charge-neutrality) and a generalized Bernoulli energy density for each species. Analysis shows that the bi-ion solitons are essentially compressive, but contain the remarkable feature of the presence of a proton rarefactive core. A new type of soliton, called an ‘oscilliton’ because embedded spatial oscillations are superimposed on the classical soliton, is also described and discussed. A necessary condition for the existence of this type of wave is that the linear phase velocity must exhibit an extremum where the phase speed matches the group speed. The remarkable properties of this wave are illustrated for the case of both whistler waves and bi-ion waves where, for the latter, the requisite condition is met near the cross-over frequencies. In the case of the whistler oscilliton, which propagates at speeds in excess of one half of the Alfvén speed (based on the electrons), an analytic solution has been constructed through a phase-portrait integral of the system in which the proton and electron dynamics must be placed on the same footing. The relevance of the different wave structures to diverse space environments is briefly discussed in relation to recently available high-time and spatial resolution data from satellite observations.

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.

The nonlinear wave equation for higher harmonics in free-electron lasers

NASA Technical Reports Server (NTRS)

Colson, W. B.

1981-01-01

The nonlinear wave equation and self-consistent pendulum equation are generalized to describe free-electron laser operation in higher harmonics; this can significantly extend their tunable range to shorter wavelengths. The dynamics of the laser field's amplitude and phase are explored for a wide range of parameters using families of normalized gain curves applicable to both the fundamental and harmonics. The electron phase-space displays the fundamental physics driving the wave, and this picture is used to distinguish between the effects of high gain and Coulomb forces.

Wave theory of turbulence in compressible media

NASA Technical Reports Server (NTRS)

Kentzer, C. P.

1975-01-01

An acoustical theory of turbulence was developed to aid in the study of the generation of sound in turbulent flows. The statistical framework adopted is a quantum-like wave dynamical formulation in terms of complex distribution functions. This formulation results in nonlinear diffusion-type transport equations for the probability densities of the five modes of wave propagation: two vorticity modes, one entropy mode, and two acoustic modes. This system of nonlinear equations is closed and complete. The technique of analysis was chosen such that direct applications to practical problems can be obtained with relative ease.

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

NASA Astrophysics Data System (ADS)

Shen, Yanfeng

2017-04-01

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

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.

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.

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.

Statistical properties of nonlinear one-dimensional wave fields

NASA Astrophysics Data System (ADS)

Chalikov, D.

2005-06-01

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

Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses.

PubMed

Chen, Yong; Yan, Zhenya; Mihalache, Dumitru; Malomed, Boris A

2017-04-28

Since the parity-time-([Formula: see text]-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with [Formula: see text]-symmetric potentials have been investigated. However, previous studies of [Formula: see text]-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized [Formula: see text]-symmetric Scarf-II potentials. The broken linear [Formula: see text] symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than [Formula: see text]-symmetric ones, but feature similar properties. Our results may suggest new experiments for [Formula: see text]-symmetric nonlinear waves in nonlinear nonuniform optical media.

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 criterion for pure pair-ion plasmas and the role of quasineutrality in nonlinear dynamics

NASA Astrophysics Data System (ADS)

Saleem, H.

2007-01-01

A criterion is presented to decide whether a produced plasma can be called a pure pair-ion plasma or not. The theory is discussed in the light of recent experiments which claim that a pure pair-ion fullerene (C60±) plasma has been produced. It is also shown that the ion acoustic wave is replaced by the pair ion convective cell (PPCC) mode as the electron density becomes vanishingly small in a magnetized plasma comprised of positive and negative ions. The nonlinear dynamics of pure pair plasmas is described by two coupled equations which have no analog in electron-ion plasmas. In a stationary frame, it becomes similar to the Hasegawa-Mima equation but does not contain drift waves and ion acoustic waves.

Geometrodynamics: the nonlinear dynamics of curved spacetime

NASA Astrophysics Data System (ADS)

Scheel, M. A.; Thorne, K. S.

2014-04-01

We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of spacetime curvature near singularities, the instability of black strings in five spacetime dimensions, and the collision of four-dimensional black holes. We also discuss the prospects for further discoveries in geometrodynamics via observations of gravitational waves.

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.

Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System

NASA Astrophysics Data System (ADS)

Li, Hailiang; Wang, Yi; Yang, Tong; Zhong, Mingying

2018-04-01

The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133-179, 2004) and Liu et al. (Physica D 188:178-192, 2004), we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665-725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.

Controlling rogue waves in inhomogeneous Bose-Einstein condensates.

PubMed

Loomba, Shally; Kaur, Harleen; Gupta, Rama; Kumar, C N; Raju, Thokala Soloman

2014-05-01

We present the exact rogue wave solutions of the quasi-one-dimensional inhomogeneous Gross-Pitaevskii equation by using similarity transformation. Then, by employing the exact analytical solutions we have studied the controllable behavior of rogue waves in the Bose-Einstein condensates context for the experimentally relevant systems. Additionally, we have also investigated the nonlinear tunneling of rogue waves through a conventional hyperbolic barrier and periodic barrier. We have found that, for the conventional nonlinearity barrier case, rogue waves are localized in space and time and get amplified near the barrier, while for the dispersion barrier case rogue waves are localized in space and propagating in time and their amplitude is reduced at the barrier location. In the case of the periodic barrier, the interesting dynamical features of rogue waves are obtained and analyzed analytically.

Refraction of dispersive shock waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khodorovskii, V. V.; Leszczyszyn, A. M.

2012-09-01

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave, often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of the defocusing nonlinear Schrödinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem.

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

PubMed

Krafft, C; Volokitin, A

2013-05-01

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

KAM Tori for 1D Nonlinear Wave Equationswith Periodic Boundary Conditions

NASA Astrophysics Data System (ADS)

Chierchia, Luigi; You, Jiangong

In this paper, one-dimensional (1D) nonlinear wave equations with periodic boundary conditions are considered; V is a periodic smooth or analytic function and the nonlinearity f is an analytic function vanishing together with its derivative at u≡0. It is proved that for ``most'' potentials V(x), the above equation admits small-amplitude periodic or quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system. The proof is based on an infinite dimensional KAM theorem which allows for multiple normal frequencies.

Traveling wave and soliton solutions of coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients.

PubMed

Zhong, Wei-Ping; Belić, Milivoj

2010-10-01

Exact traveling wave and soliton solutions, including the bright-bright and dark-dark soliton pairs, are found for the system of two coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients, by employing the homogeneous balance principle and the F-expansion technique. A kind of shape-changing soliton collision is identified in the system. The collision is essentially elastic between the two solitons with opposite velocities. Our results demonstrate that the dynamics of solitons can be controlled by selecting the diffraction, nonlinearity, and gain coefficients.

Nonlinear structures and anomalous transport in partially magnetized E×B plasmas

DOE PAGES

Janhunen, Salomon; Smolyakov, Andrei; Chapurin, Oleksandr; ...

2017-12-29

Nonlinear dynamics of the electron-cyclotron instability driven by the electron E x B current in a crossed electric and magnetic field is studied. In the nonlinear regime, the instability proceeds by developing a large amplitude coherent wave driven by the energy input from the fundamental cyclotron resonance. Further evolution shows the formation of the long wavelength envelope akin to the modulational instability. Simultaneously, the ion density shows the development of a high-k content responsible for wave focusing and sharp peaks on the periodic cnoidal wave structure. Here, it is shown that the anomalous electron transport (along the direction of themore » applied electric field) is dominated by the long wavelength part of the turbulent spectrum.« less

High-frequency solitons in media with induced scattering from damped low-frequency waves with nonuniform dispersion and nonlinearity

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

Aseeva, N. V., E-mail: vtyutin@hse.ru; Gromov, E. M.; Tyutin, V. V.

2015-12-15

The dynamics of high-frequency field solitons is considered using the extended nonhomogeneous nonlinear Schrödinger equation with induced scattering from damped low-frequency waves (pseudoinduced scattering). This scattering is a 3D analog of the stimulated Raman scattering from temporal spatially homogeneous damped low-frequency modes, which is well known in optics. Spatial inhomogeneities of secondorder linear dispersion and cubic nonlinearity are also taken into account. It is shown that the shift in the 3D spectrum of soliton wavenumbers toward the short-wavelength region is due to nonlinearity increasing in coordinate and to decreasing dispersion. Analytic results are confirmed by numerical calculations.

Weakly nonlinear dynamics of near-CJ detonation waves

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

Bdzil, J.B.; Klein, R.

1993-01-01

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature aremore » running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.« less

Weakly nonlinear dynamics of near-CJ detonation waves

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

Bdzil, J.B.; Klein, R.

1993-02-01

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature aremore » running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.« less

Periodic Peakons, Pseudo-Peakons and Compactons of Ion-Acoustic Wave Model in Electronegative Plasmas with Electrons Featuring Tsallis Distribution

NASA Astrophysics Data System (ADS)

Li, Jibin

The dynamical model of the nonlinear ion-acoustic oscillations is governed by a partial differential equation system. Its traveling system is just a singular traveling wave system of first class depending on four parameters. By using the method of dynamical systems and the theory of singular traveling wave systems, in this paper, we show that there exist parameter groups such that this singular system has pseudo-peakons, periodic peakons and compactons as well as kink and anti-kink wave solutions.

Nonlinear effects associated with fast magnetosonic waves and turbulent magnetic amplification in laboratory and astrophysical plasmas

NASA Astrophysics Data System (ADS)

Tiwary, PremPyari; Sharma, Swati; Sharma, Prachi; Singh, Ram Kishor; Uma, R.; Sharma, R. P.

2016-12-01

This paper presents the spatio-temporal evolution of magnetic field due to the nonlinear coupling between fast magnetosonic wave (FMSW) and low frequency slow Alfvén wave (SAW). The dynamical equations of finite frequency FMSW and SAW in the presence of ponderomotive force of FMSW (pump wave) has been presented. Numerical simulation has been carried out for the nonlinear coupled equations of finite frequency FMSW and SAW. A systematic scan of the nonlinear behavior/evolution of the pump FMSW has been done for one of the set of parameters chosen in this paper, using the coupled dynamical equations. Filamentation of fast magnetosonic wave has been considered to be responsible for the magnetic turbulence during the laser plasma interaction. The results show that the formation and growth of localized structures depend on the background magnetic field but the order of amplification does not get affected by the magnitude of the background magnetic field. In this paper, we have shown the relevance of our model for two different parameters used in laboratory and astrophysical phenomenon. We have used one set of parameters pertaining to experimental observations in the study of fast ignition of laser fusion and hence studied the turbulent structures in stellar environment. The other set corresponds to the study of magnetic field amplification in the clumpy medium surrounding the supernova remnant Cassiopeia A. The results indicate considerable randomness in the spatial structure of the magnetic field profile in both the cases and gives a sufficient indication of turbulence. The turbulent spectra have been studied and the break point has been found around k which is consistent with the observations in both the cases. The nonlinear wave-wave interaction presented in this paper may be important in understanding the turbulence in the laboratory as well as the astrophysical phenomenon.

One-dimensional optical wave turbulence: Experiment and theory

NASA Astrophysics Data System (ADS)

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

2012-05-01

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

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.

The Effect of Surface Topography on the Nonlinear Dynamics of Rossby Waves

NASA Technical Reports Server (NTRS)

Abarzhi, S. I.; Desjardins, O.; Pitsch, H.

2003-01-01

Boussinesq convection in rotating systems attracts a sustained attention of the fluid dynamics community, because it has intricate non-linear dynamics (Cross & Hohenberg 1993) and plays an important role in geophysical and astrophysical applications, such as the motion of the liquid outer core of Earth, the Red Spot in Jupiter, the giant cells in the Sun etc. (Alridge et al. 1990). A fundamental distinction between the real geo- and astrophysical problems and the idealized laboratory studies is that natural systems are inhomogeneous (Alridge et al. 1990). Heterogeneities modulate the flow and influence significantly the dynamics of convective patterns (Alridge et al. 1990; Hide 1971). The effect of modulations on pattern formation and transition to turbulence in Boussinesq convection is far from being completely understood (Cross & Hohenberg 1993; Aranson & Kramer 2002). It is generally accepted that in the liquid outer core of the Earth the transport of the angular momentum and internal heat occurs via thermal Rossby waves (Zhang et al. 2001; Kuang & Bloxham 1999). These waves been visualized in laboratory experiments in rotating liquid-filled spheres and concentric spherical shells (Zhang et al. 2001; Kuang & Bloxham 1999). The basic dynamical features of Rossby waves have been reproduced in a cylindrical annulus, a system much simpler than the spherical ones (Busse & Or 1986; Or & Busse 1987). For convection in a cylindrical annulus, the fluid motion is two-dimensional, and gravity is replaced by a centrifugal force, (Busse & Or 1986; Or & Busse 1987). Hide (1971) has suggested that the momentum and heat transport in the core might be influenced significantly by so-called bumps, which are heterogeneities on the mantle-core boundary. To model the effect of surface topography on the transport of momentum and energy in the liquid outer core of the Earth, Bell & Soward (1996), Herrmann & Busse (1998) and Westerburg & Busse (2001) have studied the nonlinear dynamics of thermal Rossby waves in a cylindrical annulus with azimuthally modulated height.

(2 + 1)-dimensional bright optical solitons in metamaterials with Kerr, power and parabolic law nonlinearities

NASA Astrophysics Data System (ADS)

Boubir, Badreddine

2018-06-01

In this paper, we investigate the dynamics of bright optical solitons in nonlinear metamaterials governed by a (2 + 1)-dimensional nonlinear Schrödinger equation. Three types of nonlinearities have been considered, Kerr law, power law and parabolic law. We based on the solitary wave ansatz method to find these optical soliton solutions. All necessary parametric conditions for their existence are driven.

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.

Research on ponderomotive driven Vlasov–Poisson system in electron acoustic wave parametric region

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

Xiao, C. Z.; Huang, T. W.; Liu, Z. J.

2014-03-15

Theoretical analysis and corresponding 1D Particle-in-Cell (PIC) simulations of ponderomotive driven Vlasov–Poisson system in electron acoustic wave (EAW) parametric region are demonstrated. Theoretical analysis identifies that under the resonant condition, a monochromatic EAW can be excited when the wave number of the drive ponderomotive force satisfies 0.26≲k{sub d}λ{sub D}≲0.53. If k{sub d}λ{sub D}≲0.26, nonlinear superposition of harmonic waves can be resonantly excited, called kinetic electrostatic electron nonlinear waves. Numerical simulations have demonstrated these wave excitation and evolution dynamics, in consistence with the theoretical predictions. The physical nature of these two waves is supposed to be interaction of harmonic waves, andmore » their similar phase space properties are also discussed.« less

Quantitative theory of driven nonlinear brain dynamics.

PubMed

Roberts, J A; Robinson, P A

2012-09-01

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

Modeling dynamic acousto-elastic testing experiments: validation and perspectives.

PubMed

Gliozzi, A S; Scalerandi, M

2014-10-01

Materials possessing micro-inhomogeneities often display a nonlinear response to mechanical solicitations, which is sensitive to the confining pressure acting on the sample. Dynamic acoustoelastic testing allows measurement of the instantaneous variations in the elastic modulus due to the change of the dynamic pressure induced by a low-frequency wave. This paper shows that a Preisach-Mayergoyz space based hysteretic multi-state elastic model provides an explanation for experimental observations in consolidated granular media and predicts memory and nonlinear effects comparable to those measured in rocks.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Application of Nonlinear Elastic Resonance Spectroscopy For Damage Detection In Concrete: An Interesting Story

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

Byers, Loren W.; Ten Cate, James A.; Johnson, Paul A.

2012-06-28

Nonlinear resonance ultrasound spectroscopy experiments conducted on concrete cores, one chemically and mechanically damaged by alkali-silica reactivity, and one undamaged, show that this material displays highly nonlinear wave behavior, similar to many other damaged materials. They find that the damaged sample responds more nonlinearly, manifested by a larger resonant peak and modulus shift as a function of strain amplitude. The nonlinear response indicates that there is a hysteretic influence in the stress-strain equation of state. Further, as in some other materials, slow dynamics are present. The nonlinear response they observe in concrete is an extremely sensitive indicator of damage. Ultimately,more » nonlinear wave methods applied to concrete may be used to guide mixing, curing, or other production techniques, in order to develop materials with particular desired qualities such as enhanced strength or chemical resistance, and to be used for damage inspection.« less

SMALL-SCALE SOLAR WIND TURBULENCE DUE TO NONLINEAR ALFVÉN WAVES

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

Kumar, Sanjay; Moon, Y.-J.; Sharma, R. P., E-mail: sanjaykumar@khu.ac.kr

We present an evolution of wave localization and magnetic power spectra in solar wind plasma using kinetic Alfvén waves (AWs) and fast AWs. We use a two-fluid model to derive the dynamical equations of these wave modes and then numerically solve these nonlinear dynamical equations to analyze the power spectra and wave localization at different times. The ponderomotive force associated with the kinetic AW (or pump) is responsible for the wave localization, and these thin slabs (or sheets) become more chaotic as the system evolves with time until the modulational instability (or oscillating two-stream instability) saturates. From our numerical results,more » we notice a steepening of the spectra from the inertial range (k{sup −1.67}) to the dispersion range (k{sup −3.0}). The steepening of the spectra could be described as the energy transference from longer to smaller scales. The formation of complex magnetic thin slabs and the change of the spectral index may be considered to be the main reason for the charged particles acceleration in solar wind plasma.« less

Self-Organized Lattices of Nonlinear Optochemical Waves in Photopolymerizable Fluids: The Spontaneous Emergence of 3-D Order in a Weakly Correlated System.

PubMed

Ponte, Matthew R; Hudson, Alexander D; Saravanamuttu, Kalaichelvi

2018-03-01

Many of the extraordinary three-dimensional architectures that pattern our physical world emerge from complex nonlinear systems or dynamic populations whose individual constituents are only weakly correlated to each other. Shoals of fish, murmuration behaviors in birds, congestion patterns in traffic, and even networks of social conventions are examples of spontaneous pattern formation, which cannot be predicted from the properties of individual elements alone. Pattern formation at a different scale has been observed or predicted in weakly correlated systems including superconductors, atomic gases near Bose Einstein condensation, and incoherent optical fields. Understanding pattern formation in nonlinear weakly correlated systems, which are often unified through mathematical expression, could pave intelligent self-organizing pathways to functional materials, architectures, and computing technologies. However, it is experimentally difficult to directly visualize the nonlinear dynamics of pattern formation in most populations-especially in three dimensions. Here, we describe the collective behavior of large populations of nonlinear optochemical waves, which are poorly correlated in both space and time. The optochemical waves-microscopic filaments of white light entrapped within polymer channels-originate from the modulation instability of incandescent light traveling in photopolymerizable fluids. By tracing the three-dimensional distribution of optical intensity in the nascent polymerizing system, we find that populations of randomly distributed, optochemical waves synergistically and collectively shift in space to form highly ordered lattices of specific symmetries. These, to our knowledge, are the first three-dimensionally periodic structures to emerge from a system of weakly correlated waves. Their spontaneous formation in an incoherent and effectively chaotic field is counterintuitive, but the apparent contradiction of known behaviors of light including the laws of optical interference can be explained through the soliton-like interactions of optochemical waves with nearest neighbors. Critically, this work casts fundamentally new insight into the collective behaviors of poorly correlated nonlinear waves in higher dimensions and provides a rare, accessible platform for further experimental studies of these previously unexplored behaviors. Furthermore, it defines a self-organization paradigm that, unlike conventional counterparts, could generate polymer microstructures with symmetries spanning all the Bravais lattices.

Solitary waves and nonlinear dynamic coherent structures in magnetic metamaterials

NASA Astrophysics Data System (ADS)

Tankeyev, A. P.; Smagin, V. V.; Borich, M. A.; Zhuravlev, A. S.

2009-03-01

Within the framework of the extended nonlinear Schrödinger equation (ENSE), two types of nonlinear states of magnetization in a ferromagnet-dielectric-metal metamagnetic structure have been obtained and investigated. These states have an internal structure; e.g., a periodic sequence of compound solitons is formed by kink-antikink pairs (shock waves), and coherent periodic breather structures are formed by “bright” quasi-solitons. Conditions have been found under which the envelope of these states is described by a modified Korteweg-de Vries (mKdV) equation. It is shown that the compound solitons are described by an mKdV equation with repulsion, and the breather structures, by an mKdV equation with attraction. It is shown also that the characteristic properties of the solutions are determined by the sign of the group-velocity dispersion rather than by the sign of the group velocity itself. The results obtained can be used for searching new nonlinear dynamic coherent structures, e.g., compound solitons and breathers in high-dispersion magnetic metamaterials.

Nonlinear dynamic phenomena in the space shuttle thermal protection system

NASA Technical Reports Server (NTRS)

Housner, J. M.; Edighoffer, H. H.; Park, K. C.

1981-01-01

The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.

Non-Linear Dynamics and Emergence in Laboratory Fusion Plasmas

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

Hnat, B.

2011-09-22

Turbulent behaviour of laboratory fusion plasma system is modelled using extended Hasegawa-Wakatani equations. The model is solved numerically using finite difference techniques. We discuss non-linear effects in such a system in the presence of the micro-instabilities, specifically a drift wave instability. We explore particle dynamics in different range of parameters and show that the transport changes from diffusive to non-diffusive when large directional flows are developed.

Nonlinear and Stochastic Dynamics in the Heart

PubMed Central

Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.

2014-01-01

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems. PMID:25267872

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

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

Simple waves in a two-component Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Ivanov, S. K.; Kamchatnov, A. M.

2018-04-01

We study the dynamics of so-called simple waves in a two-component Bose-Einstein condensate. The evolution of the condensate is described by Gross-Pitaevskii equations which can be reduced for these simple wave solutions to a system of ordinary differential equations which coincide with those derived by Ovsyannikov for the two-layer fluid dynamics. We solve the Ovsyannikov system for two typical situations of large and small difference between interspecies and intraspecies nonlinear interaction constants. Our analytic results are confirmed by numerical simulations.

Simple determinant representation for rogue waves of the nonlinear Schrödinger equation.

PubMed

Ling, Liming; Zhao, Li-Chen

2013-10-01

We present a simple representation for arbitrary-order rogue wave solution and a study on the trajectories of them explicitly. We find that the trajectories of two valleys on whole temporal-spatial distribution all look "X" -shaped for rogue waves. Additionally, we present different types of high-order rogue wave structures, which could be helpful towards realizing the complex dynamics of rogue waves.

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

NASA Astrophysics Data System (ADS)

Wallen, Samuel P.

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

Characteristics of solitary waves, quasiperiodic solutions, homoclinic breather solutions and rogue waves in the generalized variable-coefficient forced Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Zou, Li

2017-12-01

In this paper, the generalized variable-coefficient forced Kadomtsev-Petviashvili (gvcfKP) equation is investigated, which can be used to characterize the water waves of long wavelength relating to nonlinear restoring forces. Using a dependent variable transformation and combining the Bell’s polynomials, we accurately derive the bilinear expression for the gvcfKP equation. By virtue of bilinear expression, its solitary waves are computed in a very direct method. By using the Riemann theta function, we derive the quasiperiodic solutions for the equation under some limitation factors. Besides, an effective way can be used to calculate its homoclinic breather waves and rogue waves, respectively, by using an extended homoclinic test function. We hope that our results can help enrich the dynamical behavior of the nonlinear wave equations with variable-coefficient.

Model of anisotropic nonlinearity in self-defocusing photorefractive media.

PubMed

Barsi, C; Fleischer, J W

2015-09-21

We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.

Nonlinear vibrations analysis of rotating drum-disk coupling structure

NASA Astrophysics Data System (ADS)

Chaofeng, Li; Boqing, Miao; Qiansheng, Tang; Chenyang, Xi; Bangchun, Wen

2018-04-01

A dynamic model of a coupled rotating drum-disk system with elastic support is developed in this paper. By considering the effects of centrifugal and Coriolis forces as well as rotation-induced hoop stress, the governing differential equation of the drum-disk is derived by Donnell's shell theory. The nonlinear amplitude-frequency characteristics of coupled structure are studied. The results indicate that the natural characteristics of the coupling structure are sensitive to the supporting stiffness of the disk, and the sensitive range is affected by rotating speeds. The circumferential wave numbers can affect the characteristics of the drum-disk structure. If the circumferential wave number n = 1 , the vibration response of the drum keeps a stable value under an unbalanced load of the disk, there is no coupling effect if n ≠ 1 . Under the excitation, the nonlinear hardening characteristics of the forward traveling wave are more evident than that of the backward traveling wave. Moreover, because of the coupling effect of the drum and the disk, the supporting stiffness of the disk has certain effect on the nonlinear characteristics of the forward and backward traveling waves. In addition, small length-radius and thickness-radius ratios have a significant effect on the nonlinear characteristics of the coupled structure, which means nonlinear shell theory should be adopted to design rotating drum's parameter for its specific structural parameters.

Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin

NASA Astrophysics Data System (ADS)

Baronio, Fabio; Wabnitz, Stefan; Kodama, Yuji

2016-04-01

There is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave solutions of the (2 +1 )D nonlinear Schrödinger equation. Dark lumps represent multidimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2 +1 )D shallow water Kadomtsev-Petviashvili model, inheriting their complex interaction properties. This finding opens a novel path for the excitation and control of optical spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave phenomena.

Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin.

PubMed

Baronio, Fabio; Wabnitz, Stefan; Kodama, Yuji

2016-04-29

There is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave solutions of the (2+1)D nonlinear Schrödinger equation. Dark lumps represent multidimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2+1)D shallow water Kadomtsev-Petviashvili model, inheriting their complex interaction properties. This finding opens a novel path for the excitation and control of optical spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave phenomena.

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

NASA Astrophysics Data System (ADS)

Dikandé, Alain M.; Voma Titafan, J.; Essimbi, B. Z.

2017-10-01

The transition dynamics from continuous-wave to pulse regimes of operation for a generic model of passively mode-locked lasers with saturable absorbers, characterized by an active medium with non-Kerr nonlinearity, are investigated analytically and numerically. The system is described by a complex Ginzburg-Landau equation with a general m:n saturable nonlinearity (i.e {I}m/{(1+{{Γ }}I)}n, where I is the field intensity and m and n are two positive numbers), coupled to a two-level gain equation. An analysis of stability of continuous waves, following the modulational instability approach, provides a global picture of the self-starting dynamics in the system. The analysis reveals two distinct routes depending on values of the couple (m, n), and on the dispersion regime: in the normal dispersion regime, when m = 2 and n is arbitrary, the self-starting requires positive values of the fast saturable absorber and nonlinearity coefficients, but negative values of these two parameters for the family with m = 0. However, when the spectral filter is negative, the laser can self-start for certain values of the input field and the nonlinearity saturation coefficient Γ. The present work provides a general map for the self-starting mechanisms of rare-earth doped figure-eight fiber lasers, as well as Kerr-lens mode-locked solid-state lasers.

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.

Single-shot observation of optical rogue waves in integrable turbulence using time microscopy

PubMed Central

Suret, Pierre; Koussaifi, Rebecca El; Tikan, Alexey; Evain, Clément; Randoux, Stéphane; Szwaj, Christophe; Bielawski, Serge

2016-01-01

Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear Schrödinger equation such as fundamental solitons or solitons on finite background can be generated by launching periodic, specifically designed coherent waves in optical fibres. It is an open fundamental question to know whether these coherent structures can emerge from the nonlinear propagation of random waves. However the typical sub-picosecond timescale prevented—up to now—time-resolved observations of the awaited dynamics. Here, we report temporal ‘snapshots' of random light using a specially designed ‘time-microscope'. Ultrafast structures having peak powers much larger than the average optical power are generated from the propagation of partially coherent waves in optical fibre and are recorded with 250 femtoseconds resolution. Our experiment demonstrates the central role played by ‘breather-like' structures such as the Peregrine soliton in the emergence of heavy-tailed statistics in integrable turbulence. PMID:27713416

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.

Internal Gravity Waves Forced by an Isolated Mountain

NASA Astrophysics Data System (ADS)

Nikitina, L.; Campbell, L.

2009-12-01

Density-stratified fluid flow over topography such as mountains, hills and ridges may give rise to internal gravity waves which transport and distribute energy away from their source and have profound effects on the general circulation of the atmosphere and ocean. Much of our knowledge of internal gravity wave dynamics has been acquired from theoretical studies involving mathematical analyses of simplified forms of the governing equations, as well as numerical simulations at varying levels of approximation. In this study, both analytical and numerical methods are used to examine the nonlinear dynamics of gravity waves forced by an isolated mountain. The topography is represented by a lower boundary condition on a two-dimensional rectangular domain and the waves are represented as a perturbation to the background shear flow, thus allowing the use of weakly-nonlinear and multiple-scale asymptotic analyzes. The waves take the form of a packet, localized in the horizontal direction and comprising a continuous spectrum of horizontal wavenumbers centered at zero. For horizontally-localized wave packets, such as those forced by a mountain range with multiple peaks, there are generally two horizontal scales, the fast (short) scale which is defined by the oscillations within the packet and the slow (large) scale which is defined by the horizontal extent of the packet. In the case of an isolated mountain that we examine here, the multiple-scaling procedure is simplified by the absence of a fast spatial scale. The problem is governed by two small parameters that define the height and width of the mountain and approximate solutions are derived in terms of these parameters. Numerical solutions are also carried out to simulate nonlinear critical-level interactions such as the transfer of energy to the background flow by the wave packet, wave reflection and static instability and, eventually, wave breaking leading to turbulence. It is found that for waves forced by an isolated mountain the time frame within which these nonlinear effects become significant depends on both the mountain height and width and that they begin to occur at least an order of magnitude later and the configuration thus remains stable longer than in the case of waves forced by a mountain range of equivalent height.

Optimal Control of a Surge-Mode WEC in Random Waves

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

Chertok, Allan; Ceberio, Olivier; Staby, Bill

2016-08-30

The objective of this project was to develop one or more real-time feedback and feed-forward (MPC) control algorithms for an Oscillating Surge Wave Converter (OSWC) developed by RME called SurgeWEC™ that leverages recent innovations in wave energy converter (WEC) control theory to maximize power production in random wave environments. The control algorithms synthesized innovations in dynamic programming and nonlinear wave dynamics using anticipatory wave sensors and localized sensor measurements; e.g. position and velocity of the WEC Power Take Off (PTO), with predictive wave forecasting data. The result was an advanced control system that uses feedback or feed-forward data from anmore » array of sensor channels comprised of both localized and deployed sensors fused into a single decision process that optimally compensates for uncertainties in the system dynamics, wave forecasts, and sensor measurement errors.« less

Direct measurement of nonlinear dispersion relation for water surface waves

NASA Astrophysics Data System (ADS)

Magnus Arnesen Taklo, Tore; Trulsen, Karsten; Elias Krogstad, Harald; Gramstad, Odin; Nieto Borge, José Carlos; Jensen, Atle

2013-04-01

The linear dispersion relation for water surface waves is often taken for granted for the interpretation of wave measurements. High-resolution spatiotemporal measurements suitable for direct validation of the linear dispersion relation are on the other hand rarely available. While the imaging of the ocean surface with nautical radar does provide the desired spatiotemporal coverage, the interpretation of the radar images currently depends on the linear dispersion relation as a prerequisite, (Nieto Borge et al., 2004). Krogstad & Trulsen (2010) carried out numerical simulations with the nonlinear Schrödinger equation and its generalizations demonstrating that the nonlinear evolution of wave fields may render the linear dispersion relation inadequate for proper interpretation of observations, the reason being that the necessary domain of simultaneous coverage in space and time would allow significant nonlinear evolution. They found that components above the spectral peak can have larger phase and group velocities than anticipated by linear theory, and that the spectrum does not maintain a thin dispersion surface. We have run laboratory experiments and accurate numerical simulations designed to have sufficient resolution in space and time to deduce the dispersion relation directly. For a JONSWAP spectrum we find that the linear dispersion relation can be appropriate for the interpretation of spatiotemporal measurements. For a Gaussian spectrum with narrower bandwidth we find that the dynamic nonlinear evolution in space and time causes the directly measured dispersion relation to deviate from the linear dispersion surface in good agreement with our previous numerical predictions. This work has been supported by RCN grant 214556/F20. Krogstad, H. E. & Trulsen, K. (2010) Interpretations and observations of ocean wave spectra. Ocean Dynamics 60:973-991. Nieto Borge, J. C., Rodríguez, G., Hessner, K., Izquierdo, P. (2004) Inversion of marine radar images for surface wave analysis. J. Atmos. Ocean. Tech. 21:1291-1300.

V.A.Robsman: Nonlinear Testing and Building Industry

NASA Astrophysics Data System (ADS)

Rudenko, Oleg V.

2006-05-01

This talk is devoted to the memory of outstanding scientist and engineer Vadim A. Robsman who died in January 2005. Dr.Robsman was the Honored Builder of Russia. He developed and applied new methods of nondestructive testing of buildings, bridges, power plants and other building units. At the same time, he published works on fundamental problems of acoustics and nonlinear dynamics. In particular, he suggested a new equation of the 4-th order continuing the series of basic equations of nonlinear wave theory (Burgers Eq.: 2-nd order, Korteveg - de Vries Eq.: 3-rd order) and found exact solutions for high-intensity waves in scattering media.

Nonlinear spatial evolution of inviscid instabilities on hypersonic boundary layers

NASA Technical Reports Server (NTRS)

Wundrow, David W.

1996-01-01

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

Head-on collision of the second mode internal solitary waves

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Numerical investigation of bubble nonlinear dynamics characteristics

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

Shi, Jie, E-mail: shijie@hrbeu.edu.cn; Yang, Desen; Shi, Shengguo

2015-10-28

The complicated dynamical behaviors of bubble oscillation driven by acoustic wave can provide favorable conditions for many engineering applications. On the basis of Keller-Miksis model, the influences of control parameters, including acoustic frequency, acoustic pressure and radius of gas bubble, are discussed by utilizing various numerical analysis methods, Furthermore, the law of power spectral variation is studied. It is shown that the complicated dynamic behaviors of bubble oscillation driven by acoustic wave, such as bifurcation and chaos, further the stimulated scattering processes are revealed.

Wave-vortex interactions in the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Guo, Yuan; Bühler, Oliver

2014-02-01

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

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

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)

Field measurements of the linear and nonlinear shear moduli of cemented alluvium using dynamically loaded surface footings

NASA Astrophysics Data System (ADS)

Park, Kwangsoo

In this dissertation, a research effort aimed at development and implementation of a direct field test method to evaluate the linear and nonlinear shear modulus of soil is presented. The field method utilizes a surface footing that is dynamically loaded horizontally. The test procedure involves applying static and dynamic loads to the surface footing and measuring the soil response beneath the loaded area using embedded geophones. A wide range in dynamic loads under a constant static load permits measurements of linear and nonlinear shear wave propagation from which shear moduli and associated shearing strains are evaluated. Shear wave velocities in the linear and nonlinear strain ranges are calculated from time delays in waveforms monitored by geophone pairs. Shear moduli are then obtained using the shear wave velocities and the mass density of a soil. Shear strains are determined using particle displacements calculated from particle velocities measured at the geophones by assuming a linear variation between geophone pairs. The field test method was validated by conducting an initial field experiment at sandy site in Austin, Texas. Then, field experiments were performed on cemented alluvium, a complex, hard-to-sample material. Three separate locations at Yucca Mountain, Nevada were tested. The tests successfully measured: (1) the effect of confining pressure on shear and compression moduli in the linear strain range and (2) the effect of strain on shear moduli at various states of stress in the field. The field measurements were first compared with empirical relationships for uncemented gravel. This comparison showed that the alluvium was clearly cemented. The field measurements were then compared to other independent measurements including laboratory resonant column tests and field seismic tests using the spectral-analysis-of-surface-waves method. The results from the field tests were generally in good agreement with the other independent test results, indicating that the proposed method has the ability to directly evaluate complex material like cemented alluvium in the field.

Self-Consistent Frequency Sweeping of TAE mode

NASA Astrophysics Data System (ADS)

Wang, Ge

2012-03-01

We have extended our intuitive Toroidal Alfven Wave (TAE) model [1] for describing spontaneous frequency sweeping by a destabilizing component of energetic particles. Now a fully developed self-consistent description for frequency sweeping of an isolated TAE mode has been developed. As in [1], we use the Rosenbluth, Berk,Van Dam tip theory [2], valid for low beta, large aspect ratio, circular tokamaks, to describe the evolution of the TAE wave equation. The wave is coupled to the particle dynamics that uses the Berk, Breizman, Ye map model [3] to construct the particle/wave Lagrangian associated with a phase space dependent mode structure. Then together with the appropriate Vlasov equation for describing the particle dynamics, a set of equations determining the dynamics of the system has been formulated. Adiabatic solutions have been obtained and work is underway in simulating the exact nonlinear dynamics. A status report of our results will be given at the meeting. [4pt] [1] G. Wang and H. L. Berk, Communication in Nonlinear Science and Numerical Simulation 17, 2179 (2012) [0pt] [2] M. N. Rosenbluth,; H. L. Berk, J. Van Dam and D. M. Lingberg, Phys. Rev. Lett. 68, 596 (1992). [0pt] [3] Berk, H.L.; Breizman, B.N.; Ye, H. In: Physics of Fluids B 51993, 1506 (1993)

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.

Semirational rogue waves for the three-coupled fourth-order nonlinear Schrödinger equations in an alpha helical protein

NASA Astrophysics Data System (ADS)

Du, Zhong; Tian, Bo; Qu, Qi-Xing; Chai, Han-Peng; Wu, Xiao-Yu

2017-12-01

Investigated in this paper are the three-coupled fourth-order nonlinear Schrödinger equations, which describe the dynamics of alpha helical protein with the interspine coupling at the higher order. We show that the representation of the Lax pair with Expressions (42) -(45) in Ref. [25] is not correct, because the three-coupled fourth-order nonlinear Schrödinger equations can not be reproduced by the Lax pair with Expressions (42) -(45) in Ref. [25] through the compatibility condition. Therefore, we recalculate the Lax pair. Based on the recalculated Lax pair, we construct the generalized Darboux transformation, and derive the first- and second-order semirational solutions. Through such solutions, dark-bright-bright soliton, breather-breather-bright soliton, breather soliton and rogue waves are analyzed. It is found that the rogue waves in the three components are mutually proportional. Moreover, three types of the semirational rogue waves consisting of the rogue waves and solitons are presented: (1) consisting of the first-order rogue wave and one soliton; (2) consisting of the first-order rogue wave and two solitons; (3) consisting of the second-order rogue wave and two solitons.

Formation of rogue waves from a locally perturbed condensate.

PubMed

Gelash, A A

2018-02-01

The one-dimensional focusing nonlinear Schrödinger equation (NLSE) on an unstable condensate background is the fundamental physical model that can be applied to study the development of modulation instability (MI) and formation of rogue waves. The complete integrability of the NLSE via inverse scattering transform enables the decomposition of the initial conditions into elementary nonlinear modes: breathers and continuous spectrum waves. The small localized condensate perturbations (SLCP) that grow as a result of MI have been of fundamental interest in nonlinear physics for many years. Here, we demonstrate that Kuznetsov-Ma and superregular NLSE breathers play the key role in the dynamics of a wide class of SLCP. During the nonlinear stage of MI development, collisions of these breathers lead to the formation of rogue waves. We present new scenarios of rogue wave formation for randomly distributed breathers as well as for artificially prepared initial conditions. For the latter case, we present an analytical description based on the exact expressions found for the space-phase shifts that breathers acquire after collisions with each other. Finally, the presence of Kuznetsov-Ma and superregular breathers in arbitrary-type condensate perturbations is demonstrated by solving the Zakharov-Shabat eigenvalue problem with high numerical accuracy.

Formation of rogue waves from a locally perturbed condensate

NASA Astrophysics Data System (ADS)

Gelash, A. Â. A.

2018-02-01

The one-dimensional focusing nonlinear Schrödinger equation (NLSE) on an unstable condensate background is the fundamental physical model that can be applied to study the development of modulation instability (MI) and formation of rogue waves. The complete integrability of the NLSE via inverse scattering transform enables the decomposition of the initial conditions into elementary nonlinear modes: breathers and continuous spectrum waves. The small localized condensate perturbations (SLCP) that grow as a result of MI have been of fundamental interest in nonlinear physics for many years. Here, we demonstrate that Kuznetsov-Ma and superregular NLSE breathers play the key role in the dynamics of a wide class of SLCP. During the nonlinear stage of MI development, collisions of these breathers lead to the formation of rogue waves. We present new scenarios of rogue wave formation for randomly distributed breathers as well as for artificially prepared initial conditions. For the latter case, we present an analytical description based on the exact expressions found for the space-phase shifts that breathers acquire after collisions with each other. Finally, the presence of Kuznetsov-Ma and superregular breathers in arbitrary-type condensate perturbations is demonstrated by solving the Zakharov-Shabat eigenvalue problem with high numerical accuracy.

Design of materials configurations for enhanced phononic and electronic properties

NASA Astrophysics Data System (ADS)

Daraio, Chiara

The discovery of novel nonlinear dynamic and electronic phenomena is presented for the specific cases of granular materials and carbon nanotubes. This research was conducted for designing and constructing optimized macro-, micro- and nano-scale structural configurations of materials, and for studying their phononic and electronic behavior. Variation of composite arrangements of granular elements with different elastic properties in a linear chain-of-sphere, Y-junction or 3-D configurations led to a variety of novel phononic phenomena and interesting physical properties, which can be potentially useful for security, communications, mechanical and biomedical engineering applications. Mechanical and electronic properties of carbon nanotubes with different atomic arrangements and microstructures were also investigated. Electronic properties of Y-junction configured carbon nanotubes exhibit an exciting transistor switch behavior which is not seen in linear configuration nanotubes. Strongly nonlinear materials were designed and fabricated using novel and innovative concepts. Due to their unique strongly nonlinear and anisotropic nature, novel wave phenomena have been discovered. Specifically, violations of Snell's law were detected and a new mechanism of wave interaction with interfaces between NTPCs (Nonlinear Tunable Phononic Crystals) was established. Polymer-based systems were tested for the first time, and the tunability of the solitary waves speed was demonstrated. New materials with transformed signal propagation speed in the manageable range of 10-100 m/s and signal amplitude typical for audible speech have been developed. The enhancing of the mitigation of solitary and shock waves in 1-D chains were demonstrated and a new protective medium was designed for practical applications. 1-D, 2-D and 3-D strongly nonlinear system have been investigated providing a broad impact on the whole area of strongly nonlinear wave dynamics and creating experimental basis for new theories and models. Potential applications include (1) designing of a sound scrambler/decoder for secure voice communications, (2) improving invisibility of submarine to acoustic detection signal, (3) noise and shock wave mitigation for protection of vibration sensitive devices such as head mounted vision devices, (4) drastic compression of acoustic signals into centimeter regime impulses for artificial ear implants, hearing aid and devices for ease of conversion to electronic signals and processing, and acoustic delay lines for communication applications.

Nonlinear wave interactions in shallow water magnetohydrodynamics of astrophysical plasma

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

Klimachkov, D. A., E-mail: klimachkovdmitry@gmail.com; Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru

2016-05-15

The rotating magnetohydrodynamic flows of a thin layer of astrophysical and space plasmas with a free surface in a vertical external magnetic field are considered in the shallow water approximation. The presence of a vertical external magnetic field changes significantly the dynamics of wave processes in an astrophysical plasma, in contrast to a neutral fluid and a plasma layer in an external toroidal magnetic field. There are three-wave nonlinear interactions in the case under consideration. Using the asymptotic method of multiscale expansions, we have derived nonlinear equations for the interaction of wave packets: three magneto- Poincare waves, three magnetostrophic waves,more » two magneto-Poincare and one magnetostrophic waves, and two magnetostrophic and one magneto-Poincare waves. The existence of decay instabilities and parametric amplification is predicted. We show that a magneto-Poincare wave decays into two magneto-Poincare waves, a magnetostrophic wave decays into two magnetostrophic waves, a magneto-Poincare wave decays into one magneto-Poincare and one magnetostrophic waves, and a magnetostrophic wave decays into one magnetostrophic and one magneto-Poincare waves. There are the following parametric amplification mechanisms: the parametric amplification of magneto-Poincare waves, the parametric amplification of magnetostrophic waves, the amplification of a magneto-Poincare wave in the field of a magnetostrophic wave, and the amplification of a magnetostrophic wave in the field of a magneto-Poincare wave. The instability growth rates and parametric amplification factors have been found for the corresponding processes.« less

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.

Formation of rarefaction waves in origami-based metamaterials

NASA Astrophysics Data System (ADS)

Yasuda, H.; Chong, C.; Charalampidis, E. G.; Kevrekidis, P. G.; Yang, J.

2016-04-01

We investigate the nonlinear wave dynamics of origami-based metamaterials composed of Tachi-Miura polyhedron (TMP) unit cells. These cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometrical configurations or initial folded conditions. We assemble these TMP cells into a cluster of origami-based metamaterials, and we theoretically model and numerically analyze their wave transmission mechanism under external impact. Numerical simulations show that origami-based metamaterials can provide a prototypical platform for the formation of nonlinear coherent structures in the form of rarefaction waves, which feature a tensile wavefront upon the application of compression to the system. We also demonstrate the existence of numerically exact traveling rarefaction waves in an effective lumped-mass model. Origami-based metamaterials can be highly useful for mitigating shock waves, potentially enabling a wide variety of engineering applications.

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.

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

NASA Astrophysics Data System (ADS)

Benoit, Michel

2017-04-01

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

High amplitude nonlinear acoustic wave driven flow fields in cylindrical and conical resonators.

PubMed

Antao, Dion Savio; Farouk, Bakhtier

2013-08-01

A high fidelity computational fluid dynamic model is used to simulate the flow, pressure, and density fields generated in a cylindrical and a conical resonator by a vibrating end wall/piston producing high-amplitude standing waves. The waves in the conical resonator are found to be shock-less and can generate peak acoustic overpressures that exceed the initial undisturbed pressure by two to three times. A cylindrical (consonant) acoustic resonator has limitations to the output response observed at one end when the opposite end is acoustically excited. In the conical geometry (dissonant acoustic resonator) the linear acoustic input is converted to high energy un-shocked nonlinear acoustic output. The model is validated using past numerical results of standing waves in cylindrical resonators. The nonlinear nature of the harmonic response in the conical resonator system is further investigated for two different working fluids (carbon dioxide and argon) operating at various values of piston amplitude. The high amplitude nonlinear oscillations observed in the conical resonator can potentially enhance the performance of pulse tube thermoacoustic refrigerators and these conical resonators can be used as efficient mixers.

Numerical study of nonlinear full wave acoustic propagation

NASA Astrophysics Data System (ADS)

Velasco-Segura, Roberto; Rendon, Pablo L.

2013-11-01

With the aim of describing nonlinear acoustic phenomena, a form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A CLAWPACK based, 2D finite-volume method using Roe's linearization has been implemented to obtain numerically the solution of the proposed equations. In order to validate the code, two different tests have been performed: one against a special Taylor shock-like analytic solution, the other against published results on a HIFU system, both with satisfactory results. The code is written for parallel execution on a GPU and improves performance by a factor of over 50 when compared to the standard CLAWPACK Fortran code. This code can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from modest models of diagnostic and therapeutic HIFU, parametric acoustic arrays, to acoustic wave guides. A couple of examples will be presented showing shock formation and oblique interaction. DGAPA PAPIIT IN110411, PAEP UNAM 2013.

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.

Nonlinear optics of fibre event horizons.

PubMed

Webb, Karen E; Erkintalo, Miro; Xu, Yiqing; Broderick, Neil G R; Dudley, John M; Genty, Goëry; Murdoch, Stuart G

2014-09-17

The nonlinear interaction of light in an optical fibre can mimic the physics at an event horizon. This analogue arises when a weak probe wave is unable to pass through an intense soliton, despite propagating at a different velocity. To date, these dynamics have been described in the time domain in terms of a soliton-induced refractive index barrier that modifies the velocity of the probe. Here we complete the physical description of fibre-optic event horizons by presenting a full frequency-domain description in terms of cascaded four-wave mixing between discrete single-frequency fields, and experimentally demonstrate signature frequency shifts using continuous wave lasers. Our description is confirmed by the remarkable agreement with experiments performed in the continuum limit, reached using ultrafast lasers. We anticipate that clarifying the description of fibre event horizons will significantly impact on the description of horizon dynamics and soliton interactions in photonics and other systems.

Nonlinear dynamics of global atmospheric and Earth-system processes

NASA Technical Reports Server (NTRS)

Saltzman, Barry; Ebisuzaki, Wesley; Maasch, Kirk A.; Oglesby, Robert; Pandolfo, Lionel

1990-01-01

Researchers are continuing their studies of the nonlinear dynamics of global weather systems. Sensitivity analyses of large-scale dynamical models of the atmosphere (i.e., general circulation models i.e., GCM's) were performed to establish the role of satellite-signatures of soil moisture, sea surface temperature, snow cover, and sea ice as crucial boundary conditions determining global weather variability. To complete their study of the bimodality of the planetary wave states, they are using the dynamical systems approach to construct a low-order theoretical explanation of this phenomenon. This work should have important implications for extended range forecasting of low-frequency oscillations, elucidating the mechanisms for the transitions between the two wave modes. Researchers are using the methods of jump analysis and attractor dimension analysis to examine the long-term satellite records of significant variables (e.g., long wave radiation, and cloud amount), to explore the nature of mode transitions in the atmosphere, and to determine the minimum number of equations needed to describe the main weather variations with a low-order dynamical system. Where feasible they will continue to explore the applicability of the methods of complex dynamical systems analysis to the study of the global earth-system from an integrative viewpoint involving the roles of geochemical cycling and the interactive behavior of the atmosphere, hydrosphere, and biosphere.

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

PubMed

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

2009-04-24

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

Dynamics of ultraharmonic resonances in spiral galaxies

NASA Technical Reports Server (NTRS)

Artymowicz, Pawel; Lubow, Stephen H.

1992-01-01

The mildly nonlinear response of a fluid disk with pressure, viscosity, and self-gravity to spiral stellar forcing is considered as a model of the interstellar medium in spiral galaxies. Nonlinear effects are analyzed through a quasi-linear flow analysis ordered by successive powers of a dimensionless spiral perturbing force, which is the ratio of imposed nonaxisymmetric gravitational to axisymmetric gravitational forces. Waves with mn arms are launched from a position where the wavenumber of a free wave matches n times the wavenumber of the spiral forcing. The launched short wave in the gas is an interarm feature that is more tightly wrapped than the stellar wave. The gas wave extracts energy and angular momentum from the stellar wave, causing it to damp. The application of the results to the stellar disk alone reveals even stronger damping, as stars undergo Landau damping of the short wave. For parameters in M81, damping times are less than 10 exp 9 yr.

Dark and grey compressional dispersive Alfven solitons in plasmas

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

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

2011-06-15

The amplitude modulation of compressional dispersive Alfven (CDA) waves in a low-{beta} plasma is considered. It is shown that the dynamics of modulated CDA waves is governed by a cubic nonlinear Schroedinger equation, which depicts the formation of a dark/grey envelope CDA soliton.

A dynamical model of plasma turbulence in the solar wind

PubMed Central

Howes, G. G.

2015-01-01

A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfvén waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfvén waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature. PMID:25848075

Propagation of 3D internal gravity wave beams in a slowly varying stratification

NASA Astrophysics Data System (ADS)

Fan, Boyu; Akylas, T. R.

2017-11-01

The time-mean flows induced by internal gravity wave beams (IGWB) with 3D variations have been shown to have dramatic implications for long-term IGWB dynamics. While uniform stratifications are convenient both theoretically and in the laboratory, stratifications in the ocean can vary by more than an order of magnitude over the ocean depth. Here, in view of this fact, we study the propagation of a 3D IGWB in a slowly varying stratification. We assume that the stratification varies slowly relative to the local variations in the wave profile. In the 2D case, the IGWB bends in response to the changing stratification, but nonlinear effects are minor even in the finite amplitude regime. For a 3D IGWB, in addition to bending, we find that nonlinearity results in the transfer of energy from waves to a large-scale time-mean flow associated with the mean potential vorticity, similar to IGWB behavior in a uniform stratification. In a weakly nonlinear setting, we derive coupled evolution equations that govern this process. We also use these equations to determine the stability properties of 2D IGWB to 3D perturbations. These findings indicate that 3D effects may be relevant and possibly fundamental to IGWB dynamics in nature. Supported by NSF Grant DMS-1512925.

Mechanical energy fluctuations in granular chains: the possibility of rogue fluctuations or waves.

PubMed

Han, Ding; Westley, Matthew; Sen, Surajit

2014-09-01

The existence of rogue or freak waves in the ocean has been known for some time. They have been reported in the context of optical lattices and the financial market. We ask whether such waves are generic to late time behavior in nonlinear systems. In that vein, we examine the dynamics of an alignment of spherical elastic beads held within fixed, rigid walls at zero precompression when they are subjected to sufficiently rich initial conditions. Here we define such waves generically as unusually large energy fluctuations that sustain for short periods of time. Our simulations suggest that such unusually large fluctuations ("hot spots") and occasional series of such fluctuations through space and time ("rogue fluctuations") are likely to exist in the late time dynamics of the granular chain system at zero dissipation. We show that while hot spots are common in late time evolution, rogue fluctuations are seen in purely nonlinear systems (i.e., no precompression) at late enough times. We next show that the number of such fluctuations grows exponentially with increasing nonlinearity whereas rogue fluctuations decrease superexponentially with increasing precompression. Dissipation-free granular alignment systems may be possible to realize as integrated circuits and hence our observations may potentially be testable in the laboratory.

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.

Some special solutions to the Hyperbolic NLS equation

NASA Astrophysics Data System (ADS)

Vuillon, Laurent; Dutykh, Denys; Fedele, Francesco

2018-04-01

The Hyperbolic Nonlinear SCHRöDINGER equation (HypNLS) arises as a model for the dynamics of three-dimensional narrow-band deep water gravity waves. In this study, the symmetries and conservation laws of this equation are computed. The PETVIASHVILI method is then exploited to numerically compute bi-periodic time-harmonic solutions of the HypNLS equation. In physical space they represent non-localized standing waves. Non-trivial spatial patterns are revealed and an attempt is made to describe them using symbolic dynamics and the language of substitutions. Finally, the dynamics of a slightly perturbed standing wave is numerically investigated by means a highly accurate FOURIER solver.

Theory and observation of electromagnetic ion cyclotron triggered emissions in the magnetosphere

NASA Astrophysics Data System (ADS)

Omura, Yoshiharu; Pickett, Jolene; Grison, Benjamin; Santolik, Ondrej; Dandouras, Iannis; Engebretson, Mark; Décréau, Pierrette M. E.; Masson, Arnaud

2010-07-01

We develop a nonlinear wave growth theory of electromagnetic ion cyclotron (EMIC) triggered emissions observed in the inner magnetosphere. We first derive the basic wave equations from Maxwell's equations and the momentum equations for the electrons and ions. We then obtain equations that describe the nonlinear dynamics of resonant protons interacting with an EMIC wave. The frequency sweep rate of the wave plays an important role in forming the resonant current that controls the wave growth. Assuming an optimum condition for the maximum growth rate as an absolute instability at the magnetic equator and a self-sustaining growth condition for the wave propagating from the magnetic equator, we obtain a set of ordinary differential equations that describe the nonlinear evolution of a rising tone emission generated at the magnetic equator. Using the physical parameters inferred from the wave, particle, and magnetic field data measured by the Cluster spacecraft, we determine the dispersion relation for the EMIC waves. Integrating the differential equations numerically, we obtain a solution for the time variation of the amplitude and frequency of a rising tone emission at the equator. Assuming saturation of the wave amplitude, as is found in the observations, we find good agreement between the numerical solutions and the wave spectrum of the EMIC triggered emissions.

Experimental Chaos - Proceedings of the 3rd Conference

NASA Astrophysics Data System (ADS)

Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep

1996-10-01

The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina

Selected Problems in Nonlinear Dynamics and Sociophysics

NASA Astrophysics Data System (ADS)

Westley, Alexandra Renee

This Ph.D. dissertation focuses on a collection of problems on the dynamical behavior of nonlinear many-body systems, drawn from two substantially different areas. First, the dynamical behavior seen in strongly nonlinear lattices such as in the Fermi-Pasta-Ulam-Tsingou (FPUT) system (part I) and second, time evolution behavior of interacting living objects which can be broadly considered as sociophysics systems (part II). The studies on FPUT-like systems will comprise of five chapters, dedicated to the properties of solitary and anti-solitary waves in the system, how localized nonlinear excitations decay and spread throughout these lattices, how two colliding solitary waves can precipitate highly localized and stable excitations, a possible alternative way to view these localized excitations through Duffing oscillators, and finally an exploration of parametric resonance in an FPUT-like lattice. Part II consists of two problems in the context of sociophysics. I use molecular dynamics inspired simulations to study the size and the stability of social groups of chimpanzees (such as those seen in central Africa) and compare the results with existing observations on the stability of chimpanzee societies. Secondly, I use an agent-based model to simulate land battles between an intelligent army and an insurgency when both have access to equally powerful weaponry. The study considers genetic algorithm based adaptive strategies to infer the strategies needed for the intelligent army to win the battles.

Theoretical and experimental evidence of non-symmetric doubly localized rogue waves.

PubMed

He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin

2014-11-08

We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water.

Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

PubMed Central

He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin

2014-01-01

We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water. PMID:25383023

Study of critical behavior in concrete during curing by application of dynamic linear and nonlinear means.

PubMed

Lacouture, Jean-Christoph; Johnson, Paul A; Cohen-Tenoudji, Frederic

2003-03-01

The monitoring of both linear and nonlinear elastic properties of a high performance concrete during curing is presented by application of compressional and shear waves. To follow the linear elastic behavior, both compressional and shear waves are used in wide band pulse echo mode. Through the value of the complex reflection coefficient between the cell material (Lucite) and the concrete within the cell, the elastic moduli are calculated. Simultaneously, the transmission of a continuous compressional sine wave at progressively increasing drive levels permits us to calculate the nonlinear properties by extracting the harmonics amplitudes of the signal. Information regarding the chemical evolution of the concrete based upon the reaction of hydration of cement is obtained by monitoring the temperature inside the sample. These different types of measurements are linked together to interpret the critical behavior.

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.

Nonlinear vibration and radiation from a panel with transition to chaos induced by acoustic waves

NASA Technical Reports Server (NTRS)

Maestrello, Lucio; Frendi, Abdelkader; Brown, Donald E.

1992-01-01

The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling) and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance, bifurcation is diffused and difficult to maintain, thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on aluminum panel and using a graphite epoxy panel having the same size and weight. Good agreement is obtained between the experimental and numerical results.

Geometrically induced nonlinear dynamics in one-dimensional lattices

NASA Astrophysics Data System (ADS)

Hamilton, Merle D.; de Alcantara Bonfim, O. F.

2006-03-01

We present a lattice model consisting of a single one-dimensional chain, where the masses are interconnected by linear springs and allowed to move in a horizontal direction only, as in a monorail. In the transverse direction each mass is also attached to two other linear springs, one on each side of the mass. The ends of these springs are kept at fixed positions. The nonlinearity in the model arises from the geometric constraints imposed on the motion of the masses, as well as from the configuration of the springs, where in the transverse direction the springs are either in the extended or compressed state depending on the position of the masses. Under these conditions we show that solitary waves are present in the system. In the long wavelength limit an analytic solution for these nonlinear waves is found. Numerical integrations of the equations of motion in the full system are also performed to analyze the conditions for the existence and stability of the nonlinear waves.

Vector semirational rogue waves and modulation instability for the coupled higher-order nonlinear Schrödinger equations in the birefringent optical fibers.

PubMed

Sun, Wen-Rong; Liu, De-Yin; Xie, Xi-Yang

2017-04-01

We report the existence and properties of vector breather and semirational rogue-wave solutions for the coupled higher-order nonlinear Schrödinger equations, which describe the propagation of ultrashort optical pulses in birefringent optical fibers. Analytic vector breather and semirational rogue-wave solutions are obtained with Darboux dressing transformation. We observe that the superposition of the dark and bright contributions in each of the two wave components can give rise to complicated breather and semirational rogue-wave dynamics. We show that the bright-dark type vector solitons (or breather-like vector solitons) with nonconstant speed interplay with Akhmediev breathers, Kuznetsov-Ma solitons, and rogue waves. By adjusting parameters, we note that the rogue wave and bright-dark soliton merge, generating the boomeron-type bright-dark solitons. We prove that the rogue wave can be excited in the baseband modulation instability regime. These results may provide evidence of the collision between the mixed ultrashort soliton and rogue wave.

Coherent Two-Dimensional Terahertz Magnetic Resonance Spectroscopy of Collective Spin Waves.

PubMed

Lu, Jian; Li, Xian; Hwang, Harold Y; Ofori-Okai, Benjamin K; Kurihara, Takayuki; Suemoto, Tohru; Nelson, Keith A

2017-05-19

We report a demonstration of two-dimensional (2D) terahertz (THz) magnetic resonance spectroscopy using the magnetic fields of two time-delayed THz pulses. We apply the methodology to directly reveal the nonlinear responses of collective spin waves (magnons) in a canted antiferromagnetic crystal. The 2D THz spectra show all of the third-order nonlinear magnon signals including magnon spin echoes, and 2-quantum signals that reveal pairwise correlations between magnons at the Brillouin zone center. We also observe second-order nonlinear magnon signals showing resonance-enhanced second-harmonic and difference-frequency generation. Numerical simulations of the spin dynamics reproduce all of the spectral features in excellent agreement with the experimental 2D THz spectra.

Dust ion-acoustic shock waves in magnetized pair-ion plasma with kappa distributed electrons

NASA Astrophysics Data System (ADS)

Kaur, B.; Singh, M.; Saini, N. S.

2018-01-01

We have performed a theoretical and numerical analysis of the three dimensional dynamics of nonlinear dust ion-acoustic shock waves (DIASWs) in a magnetized plasma, consisting of positive and negative ion fluids, kappa distributed electrons, immobile dust particulates along with positive and negative ion kinematic viscosity. By employing the reductive perturbation technique, we have derived the nonlinear Zakharov-Kuznetsov-Burgers (ZKB) equation, in which the nonlinear forces are balanced by dissipative forces (associated with kinematic viscosity). It is observed that the characteristics of DIASWs are significantly affected by superthermality of electrons, magnetic field strength, direction cosines, dust concentration, positive to negative ions mass ratio and viscosity of positive and negative ions.

Three-dimensional instability of standing waves

NASA Astrophysics Data System (ADS)

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

2003-12-01

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

Nonplanar KdV and KP equations for quantum electron-positron-ion plasma

NASA Astrophysics Data System (ADS)

Dutta, Debjit

2015-12-01

Nonlinear quantum ion-acoustic waves with the effects of nonplanar cylindrical geometry, quantum corrections, and transverse perturbations are studied. By using the standard reductive perturbation technique, a cylindrical Kadomtsev-Petviashvili equation for ion-acoustic waves is derived by incorporating quantum-mechanical effects. The quantum-mechanical effects via quantum diffraction and quantum statistics and the role of transverse perturbations in cylindrical geometry on the dynamics of this wave are studied analytically. It is found that the dynamics of ion-acoustic solitary waves (IASWs) is governed by a three-dimensional cylindrical Kadomtsev-Petviashvili equation (CKPE). The results could help in a theoretical analysis of astrophysical and laser produced plasmas.

A nonlinear dynamics for the scalar field in Randers spacetime

NASA Astrophysics Data System (ADS)

Silva, J. E. G.; Maluf, R. V.; Almeida, C. A. S.

2017-03-01

We investigate the properties of a real scalar field in the Finslerian Randers spacetime, where the local Lorentz violation is driven by a geometrical background vector. We propose a dynamics for the scalar field by a minimal coupling of the scalar field and the Finsler metric. The coupling is intrinsically defined on the Randers spacetime, and it leads to a non-canonical kinetic term for the scalar field. The nonlinear dynamics can be split into a linear and nonlinear regimes, which depend perturbatively on the even and odd powers of the Lorentz-violating parameter, respectively. We analyze the plane-waves solutions and the modified dispersion relations, and it turns out that the spectrum is free of tachyons up to second-order.

Dissipative tunnelling by means of scaled trajectories

NASA Astrophysics Data System (ADS)

Mousavi, S. V.; Miret-Artés, S.

2018-06-01

Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schrödinger-Langevin or Kostin quantum-classical transition wave equation is used and applied resulting in a scaled differential equation of motion. A Gaussian wave packet solution to the resulting scaled Kostin nonlinear equation is assumed and compared to the same solution for the scaled linear Caldirola-Kanai equation. The resulting scaled trajectories are obtained at different dynamical regimes and friction cases, showing the gradual decoherence process in this open dynamics. Theoretical results show that the transmission probabilities are always higher in the Kostin approach than in the Caldirola-Kanai approach in the presence or not of an external electric field. This discrepancy should be understood due to the presence of an environment since the corresponding open dynamics should be governed by nonlinear quantum equations, whereas the second approach is issued from an effective Hamiltonian within a linear theory.

Nonlinear Dynamical Analysis of Fibrillation

NASA Astrophysics Data System (ADS)

Kerin, John A.; Sporrer, Justin M.; Egolf, David A.

2013-03-01

The development of spatiotemporal chaotic behavior in heart tissue, termed fibrillation, is a devastating, life-threatening condition. The chaotic behavior of electrochemical signals, in the form of spiral waves, causes the muscles of the heart to contract in an incoherent manner, hindering the heart's ability to pump blood. We have applied the mathematical tools of nonlinear dynamics to large-scale simulations of a model of fibrillating heart tissue to uncover the dynamical modes driving this chaos. By studying the evolution of Lyapunov vectors and exponents over short times, we have found that the fibrillating tissue is sensitive to electrical perturbations only in narrow regions immediately in front of the leading edges of spiral waves, especially when these waves collide, break apart, or hit the edges of the tissue sample. Using this knowledge, we have applied small stimuli to areas of varying sensitivity. By studying the evolution of the effects of these perturbations, we have made progress toward controlling the electrochemical patterns associated with heart fibrillation. This work was supported by the U.S. National Science Foundation (DMR-0094178) and Research Corporation.

Formation of rarefaction waves in origami-based metamaterials

DOE PAGES

Yasuda, H.; Chong, C.; Charalampidis, E. G.; ...

2016-04-15

Here, we investigate the nonlinear wave dynamics of origami-based metamaterials composed of Tachi-Miura polyhedron (TMP) unit cells. These cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometrical configurations or initial folded conditions. We assemble these TMP cells into a cluster of origami-based metamaterials, and we theoretically model and numerically analyze their wave transmission mechanism under external impact. Numerical simulations show that origami-based metamaterials can provide a prototypical platform for the formation of nonlinear coherent structures in the form of rarefaction waves, which feature a tensile wavefront upon the application of compression to the system.more » We also demonstrate the existence of numerically exact traveling rarefaction waves in an effective lumped-mass model. Origami-based metamaterials can be highly useful for mitigating shock waves, potentially enabling a wide variety of engineering applications.« less

Single-mode dispersive waves and soliton microcomb dynamics

PubMed Central

Yi, Xu; Yang, Qi-Fan; Zhang, Xueyue; Yang, Ki Youl; Li, Xinbai; Vahala, Kerry

2017-01-01

Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power as a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. Here, a limiting case is studied in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton induces hysteresis behaviour in the soliton's spectral and temporal properties. Also, an operating point of enhanced repetition-rate stability occurs through balance of dispersive-wave recoil and Raman-induced soliton-self-frequency shift. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications. PMID:28332495

Cylindrical dust acoustic solitary waves with transverse perturbations in quantum dusty plasmas

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

Mushtaq, A.

2007-11-15

The nonlinear quantum dust acoustic waves with effects of nonplanar cylindrical geometry, quantum corrections, and transverse perturbations are studied. By using the perturbation method, a cylindrical Kadomtsev-Petviashvili equation for dust acoustic waves is derived by incorporating quantum-mechanical effects. The quantum-mechanical effects via quantum diffraction and quantum statistics, and the role of transverse perturbations in cylindrical geometry on the dynamics of this wave, are studied both analytically and numerically.

Nonlinear dynamics of shells conveying pulsatile flow with pulse-wave propagation. Theory and numerical results for a single harmonic pulsation

NASA Astrophysics Data System (ADS)

Tubaldi, Eleonora; Amabili, Marco; Païdoussis, Michael P.

2017-05-01

In deformable shells conveying pulsatile flow, oscillatory pressure changes cause local movements of the fluid and deformation of the shell wall, which propagate downstream in the form of a wave. In biomechanics, it is the propagation of the pulse that determines the pressure gradient during the flow at every location of the arterial tree. In this study, a woven Dacron aortic prosthesis is modelled as an orthotropic circular cylindrical shell described by means of the Novozhilov nonlinear shell theory. Flexible boundary conditions are considered to simulate connection with the remaining tissue. Nonlinear vibrations of the shell conveying pulsatile flow and subjected to pulsatile pressure are investigated taking into account the effects of the pulse-wave propagation. For the first time in literature, coupled fluid-structure Lagrange equations of motion for a non-material volume with wave propagation in case of pulsatile flow are developed. The fluid is modeled as a Newtonian inviscid pulsatile flow and it is formulated using a hybrid model based on the linear potential flow theory and considering the unsteady viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. Contributions of pressure and velocity propagation are also considered in the pressure drop along the shell and in the pulsatile frictional traction on the internal wall in the axial direction. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior of a pressurized Dacron aortic graft conveying blood flow. A pulsatile time-dependent blood flow model is considered by applying the first harmonic of the physiological waveforms of velocity and pressure during the heart beating period. Geometrically nonlinear vibration response to pulsatile flow and transmural pulsatile pressure, considering the propagation of pressure and velocity changes inside the shell, is here presented via frequency-response curves, time histories, bifurcation diagrams and Poincaré maps. It is shown that traveling waves of pressure and velocity cause a delay in the radial displacement of the shell at different values of the axial coordinate. The effect of different pulse wave velocities is also studied. Comparisons with the corresponding ideal case without wave propagation (i.e. with the same pulsatile velocity and pressure at any point of the shell) are here discussed. Bifurcation diagrams of Poincaré maps obtained from direct time integration have been used to study the system in the spectral neighborhood of the fundamental natural frequency. By increasing the forcing frequency, the response undergoes very complex nonlinear dynamics (chaos, amplitude modulation and period-doubling bifurcation), here deeply investigated.

Modulated heavy nucleus-acoustic waves and associated rogue waves in a degenerate relativistic quantum plasma system

NASA Astrophysics Data System (ADS)

Sultana, S.; Islam, S.; Mamun, A. A.; Schlickeiser, R.

2018-01-01

A theoretical and numerical investigation has been carried out on amplitude modulated heavy nucleus-acoustic envelope solitons (HNAESs) in a degenerate relativistic quantum plasma (DRQP) system containing relativistically degenerate electrons and light nuclei, and non-degenerate mobile heavy nuclei. The cubic nonlinear Schrödinger equation, describing the nonlinear dynamics of the heavy nucleus-acoustic waves (HNAWs), is derived by employing a multi-scale perturbation technique. The dispersion relation for the HNAWs is derived, and the criteria for the occurrence of modulational instability of the HNAESs are analyzed. The localized structures (viz., envelope solitons and associated rogue waves) are found to be formed in the DRQP system under consideration. The basic features of the amplitude modulated HNAESs and associated rogue waves formed in realistic DRQP systems are briefly discussed.

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

Yasuda, H.; Chong, C.; Charalampidis, E. G.

Here, we investigate the nonlinear wave dynamics of origami-based metamaterials composed of Tachi-Miura polyhedron (TMP) unit cells. These cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometrical configurations or initial folded conditions. We assemble these TMP cells into a cluster of origami-based metamaterials, and we theoretically model and numerically analyze their wave transmission mechanism under external impact. Numerical simulations show that origami-based metamaterials can provide a prototypical platform for the formation of nonlinear coherent structures in the form of rarefaction waves, which feature a tensile wavefront upon the application of compression to the system.more » We also demonstrate the existence of numerically exact traveling rarefaction waves in an effective lumped-mass model. Origami-based metamaterials can be highly useful for mitigating shock waves, potentially enabling a wide variety of engineering applications.« less

Phase transition of traveling waves in bacterial colony pattern

NASA Astrophysics Data System (ADS)

Wakano, Joe Yuichiro; Komoto, Atsushi; Yamaguchi, Yukio

2004-05-01

Depending on the growth condition, bacterial colonies can exhibit different morphologies. Many previous studies have used reaction diffusion equations to reproduce spatial patterns. They have revealed that nonlinear reaction term can produce diverse patterns as well as nonlinear diffusion coefficient. Typical reaction term consists of nutrient consumption, bacterial reproduction, and sporulation. Among them, the functional form of sporulation rate has not been biologically investigated. Here we report experimentally measured sporulation rate. Then, based on the result, a reaction diffusion model is proposed. One-dimensional simulation showed the existence of traveling wave solution. We study the wave form as a function of the initial nutrient concentration and find two distinct types of solution. Moreover, transition between them is very sharp, which is analogous to phase transition. The velocity of traveling wave also shows sharp transition in nonlinear diffusion model, which is consistent with the previous experimental result. The phenomenon can be explained by separatrix in reaction term dynamics. Results of two-dimensional simulation are also shown and discussed.

Nonlinear Vibrations, Stability, and Dynamics of Structures and Mechanisms Conference (4th) Held in Blacksburg, Virginia on June 7-11, 1992

DTIC Science & Technology

1992-11-01

Subharmonic Forced Traveling Waves in a Thin Perfect Circular Disk T. A. Nayfeh and A. F. Vakakis, University of Illinois at Urbana -Champaign, Urbana ...of Illinois at Urbana -Champaign, Urbana , IL and J. Awrejcewicz, The University of Tokyo, Tokyo, JAPAN 0830-1010 On the Nonlinear Parametric Excitation...and A. F. Vakakis, University of Illinois at Urbana -Champaign, Urbana , IL Thursday, June 11 Session 15. Multibody Dynamics I/ Chairmen: G. Anderson

Nonlinear shear wave interaction at a frictional interface: energy dissipation and generation of harmonics.

PubMed

Meziane, A; Norris, A N; Shuvalov, A L

2011-10-01

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface. © 2011 Acoustical Society of America

Geometric interpretation of four-wave mixing

NASA Astrophysics Data System (ADS)

Ott, J. R.; Steffensen, H.; Rottwitt, K.; McKinstrie, C. J.

2013-10-01

The nonlinear phenomenon of four-wave mixing (FWM) is investigated using a method, where, without the need of calculus, both phase and amplitudes of the mixing fields are visualized simultaneously, giving a complete overview of the FWM dynamics. This is done by introducing a set of Stokes-like coordinates of the electric fields, which reduce the FWM dynamics to a closed two-dimensional surface, similar to the Bloch sphere of quantum electrodynamics or the Pointcaré sphere in polarization dynamics. The coordinates are chosen so as to use the gauge invariance symmetries of the FWM equations which also give the conservation of action flux known as the Manley-Rowe relations. This reduces the dynamics of FWM to the one-dimensional intersection between the closed two-dimensional surface and the phase-plane given by the conserved Hamiltonian. The analysis is advantageous for visualizing phase-dependent FWM phenomena which are found in a large variety of nonlinear systems and even in various optical communication schemes.

Localized waves in three-component coupled nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Xu, Tao; Chen, Yong

2016-09-01

We study the generalized Darboux transformation to the three-component coupled nonlinear Schrödinger equation. First- and second-order localized waves are obtained by this technique. In first-order localized wave, we get the interactional solutions between first-order rogue wave and one-dark, one-bright soliton respectively. Meanwhile, the interactional solutions between one-breather and first-order rogue wave are also given. In second-order localized wave, one-dark-one-bright soliton together with second-order rogue wave is presented in the first component, and two-bright soliton together with second-order rogue wave are gained respectively in the other two components. Besides, we observe second-order rogue wave together with one-breather in three components. Moreover, by increasing the absolute values of two free parameters, the nonlinear waves merge with each other distinctly. These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system. Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things, China (Grant No. ZF1213).

Numerical tools to predict the environmental loads for offshore structures under extreme weather conditions

NASA Astrophysics Data System (ADS)

Wu, Yanling

2018-05-01

In this paper, the extreme waves were generated using the open source computational fluid dynamic (CFD) tools — OpenFOAM and Waves2FOAM — using linear and nonlinear NewWave input. They were used to conduct the numerical simulation of the wave impact process. Numerical tools based on first-order (with and without stretching) and second-order NewWave are investigated. The simulation to predict force loading for the offshore platform under the extreme weather condition is implemented and compared.

Topological approximation of the nonlinear Anderson model

NASA Astrophysics Data System (ADS)

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport.

Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions

NASA Astrophysics Data System (ADS)

Khajehtourian, Romik

Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium. The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium. In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The extended method, which is based on a standard transfer-matrix formulation augmented with a nonlinear enrichment at the constitutive material level, yields an approximate band structure that is accurate to an amplitude that is roughly one eighth of the unit cell length. This approach represents a new paradigm for examining the balance between periodicity and nonlinearity in shaping the nature of wave motion.

Characterizing Droplet Formation from Non-Linear Slosh in a Propellant Tank

NASA Technical Reports Server (NTRS)

Brodnick, Jacob; Yang, Hong; West, Jeffrey

2015-01-01

The Fluid Dynamics Branch (ER42) at the Marshall Space Flight Center (MSFC) was tasked with characterizing the formation and evolution of liquid droplets resulting from nonlinear propellant slosh in a storage tank. Lateral excitation of propellant tanks can produce high amplitude nonlinear slosh waves through large amplitude excitations and or excitation frequencies near a resonance frequency of the tank. The high amplitude slosh waves become breaking waves upon attaining a certain amplitude or encountering a contracting geometry such as the upper dome section of a spherical tank. Inherent perturbations in the thinning regions of breaking waves result in alternating regions of high and low pressure within the fluid. Droplets form once the force from the local pressure differential becomes larger than the force maintaining the fluid interface shape due to surface tension. Droplets released from breaking waves in a pressurized tank may lead to ullage collapse given the appropriate conditions due to the increased liquid surface area and thus heat transfer between the fluids. The goal of this project is to create an engineering model that describes droplet formation as a function of propellant slosh for use in the evaluation of ullage collapse during a sloshing event. The Volume of Fluid (VOF) model in the production level Computational Fluid Dynamics (CFD) code Loci-Stream was used to predict droplet formation from breaking waves with realistic surface tension characteristics. Various excitation frequencies and amplitudes were investigated at multiple fill levels for a single storage tank to create the engineering model of droplet formation from lateral propellant slosh.

Drift dust acoustic soliton in the presence of field-aligned sheared flow and nonextensivity effects

NASA Astrophysics Data System (ADS)

Shah, AttaUllah; Mushtaq, A.; Farooq, M.; Khan, Aurangzeb; Aman-ur-Rehman

2018-05-01

Low frequency electrostatic dust drift acoustic (DDA) waves are studied in an inhomogeneous dust magnetoplasma comprised of dust components of opposite polarity, Boltzmannian ions, and nonextensive distributed electrons. The magnetic-field-aligned dust sheared flow drives the electrostatic drift waves in the presence of ions and electrons. The sheared flow decreases or increases the frequency of the DDA wave, mostly depending on its polarity. The conditions of instability for this mode, with nonextensivity and dust streaming effects, are discussed. The nonlinear dynamics is then investigated for the DDA wave by deriving the Koeteweg-deVries (KdV) nonlinear equation. The KdV equation yields an electrostatic structure in the form of a DDA soliton. The relevancy of the work to laboratory four component dusty plasmas is illustrated.

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

PubMed

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

2011-04-01

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

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.

Blobs and drift wave dynamics

DOE PAGES

Zhang, Yanzeng; Krasheninnikov, S. I.

2017-09-29

The modified Hasegawa-Mima equation retaining all nonlinearities is investigated from the point of view of the formation of blobs. The linear analysis shows that the amplitude of the drift wave packet propagating in the direction of decreasing background plasma density increases and eventually saturates due to nonlinear effects. Nonlinear modification of the time averaged plasma density profile results in the formation of large amplitude modes locked in the radial direction, but still propagating in the poloidal direction, which resembles the experimentally observed chain of blobs propagating in the poloidal direction. Such specific density profiles, causing the locking of drift waves,more » could form naturally at the edge of tokamak due to a neutral ionization source. Thus, locked modes can grow in situ due to plasma instabilities, e.g., caused by finite resistivity. Furthermore, the modulation instability (in the poloidal direction) of these locked modes can result in a blob-like burst of plasma density.« less

Nonlinear softening of unconsolidated granular earth materials

NASA Astrophysics Data System (ADS)

Lieou, Charles K. C.; Daub, Eric G.; Guyer, Robert A.; Johnson, Paul A.

2017-09-01

Unconsolidated granular earth materials exhibit softening behavior due to external perturbations such as seismic waves, namely, the wave speed and elastic modulus decrease upon increasing the strain amplitude above dynamics strains of about 10-6 under near-surface conditions. In this letter, we describe a theoretical model for such behavior. The model is based on the idea that shear transformation zones—clusters of grains that are loose and susceptible to contact changes, particle displacement, and rearrangement—are responsible for plastic deformation and softening of the material. We apply the theory to experiments on simulated fault gouge composed of glass beads and demonstrate that the theory predicts nonlinear resonance shifts, reduction of the P wave modulus, and attenuation, in agreement with experiments. The theory thus offers insights on the nature of nonlinear elastic properties of a granular medium and potentially into phenomena such as triggering on earthquake faults.

Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability

PubMed Central

Närhi, Mikko; Wetzel, Benjamin; Billet, Cyril; Toenger, Shanti; Sylvestre, Thibaut; Merolla, Jean-Marc; Morandotti, Roberto; Dias, Frederic; Genty, Goëry; Dudley, John M.

2016-01-01

Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose–Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics. PMID:27991513

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.

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.

Fast and accurate modeling of nonlinear pulse propagation in graded-index multimode fibers.

PubMed

Conforti, Matteo; Mas Arabi, Carlos; Mussot, Arnaud; Kudlinski, Alexandre

2017-10-01

We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists of a 1+1D generalized nonlinear Schrödinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics.

Stationary states of extended nonlinear Schrödinger equation with a source

NASA Astrophysics Data System (ADS)

Borich, M. A.; Smagin, V. V.; Tankeev, A. P.

2007-02-01

Structure of nonlinear stationary states of the extended nonlinear Schrödinger equation (ENSE) with a source has been analyzed with allowance for both third-order and nonlinearity dispersion. A new class of particular solutions (solitary waves) of the ENSe has been obtained. The scenario of the destruction of these states under the effect of an external perturbation has been investigated analytically and numerically. The results obtained can be used to interpret experimental data on the weakly nonlinear dynamics of the magnetostatic envelope in heterophase ferromagnet-insulator-metal, metal-insulator-ferromagnet-insulator-metal, and other similar structures and upon the simulation of nonlinear processes in optical systems.

Middle Atmosphere Dynamics with Gravity Wave Interactions in the Numerical Spectral Model: Tides and Planetary Waves

NASA Technical Reports Server (NTRS)

Mayr, Hans G.; Mengel, J. G.; Chan, K. L.; Huang, F. T.

2010-01-01

As Lindzen (1981) had shown, small-scale gravity waves (GW) produce the observed reversals of the zonal-mean circulation and temperature variations in the upper mesosphere. The waves also play a major role in modulating and amplifying the diurnal tides (DT) (e.g., Waltersheid, 1981; Fritts and Vincent, 1987; Fritts, 1995a). We summarize here the modeling studies with the mechanistic numerical spectral model (NSM) with Doppler spread parameterization for GW (Hines, 1997a, b), which describes in the middle atmosphere: (a) migrating and non-migrating DT, (b) planetary waves (PW), and (c) global-scale inertio gravity waves. Numerical experiments are discussed that illuminate the influence of GW filtering and nonlinear interactions between DT, PW, and zonal mean variations. Keywords: Theoretical modeling, Middle atmosphere dynamics, Gravity wave interactions, Migrating and non-migrating tides, Planetary waves, Global-scale inertio gravity waves.

Three-wave resonant interactions: Multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics

NASA Astrophysics Data System (ADS)

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

2018-03-01

We investigate three-wave resonant interactions through both the generalized Darboux transformation method and numerical simulations. Firstly, we derive a simple multi-dark-dark-dark-soliton formula through the generalized Darboux transformation. Secondly, we use the matrix analysis method to avoid the singularity of transformed potential functions and to find the general nonsingular breather solutions. Moreover, through a limit process, we deduce the general rogue wave solutions and give a classification by their dynamics including bright, dark, four-petals, and two-peaks rogue waves. Ever since the coexistence of dark soliton and rogue wave in non-zero background, their interactions naturally become a quite appealing topic. Based on the N-fold Darboux transformation, we can derive the explicit solutions to depict their interactions. Finally, by performing extensive numerical simulations we can predict whether these dark solitons and rogue waves are stable enough to propagate. These results can be available for several physical subjects such as fluid dynamics, nonlinear optics, solid state physics, and plasma physics.

Breather-to-soliton transformation rules in the hierarchy of nonlinear Schrödinger equations.

PubMed

Chowdury, Amdad; Krolikowski, Wieslaw

2017-06-01

We study the exact first-order soliton and breather solutions of the integrable nonlinear Schrödinger equations hierarchy up to fifth order. We reveal the underlying physical mechanism which transforms a breather into a soliton. Furthermore, we show how the dynamics of the Akhmediev breathers which exist on a constant background as a result of modulation instability, is connected with solitons on a zero background. We also demonstrate that, while a first-order rogue wave can be directly transformed into a soliton, higher-order rogue wave solutions become rational two-soliton solutions with complex collisional structure on a background. Our results will have practical implications in supercontinuum generation, turbulence, and similar other complex nonlinear scenarios.

Acceleration Wave Propagation in Hyperelastic Rods of Variable Cross-Section.

DTIC Science & Technology

1981-07-01

direction of propagation. Many authors have considered both static and dynamic problems for such materials, of whom we mention only Antman [2] and... Antman and Jordan [3] who studied the Kirchhoff problem for nonlinearly elastic rods and qualitative properties in general, Jeffrey and Teymur [4] and...Jeffrey and Suhubi [5] who considered shock wave formation and acceleration wave propagation through periodically layered media, and Antman and Liu [6

Frequency clusters in self-excited dust density waves

NASA Astrophysics Data System (ADS)

Menzel, Kristoffer O.; Arp, Oliver; Piel, Alexander

2010-11-01

Self-excited dust density waves were studied under microgravity conditions. Their non-sinusoidal shape and high degrees of modulation suggests that nonlinear effects play an important role in their spatio-temporal dynamics. The resulting complex wave pattern is analyzed in great detail by means of the Hilbert transform, which provides instantaneous wave attributes, such as the phase and the frequency. Our analysis showed that the spatial frequency distribution of the DDWs is usually not constant over the dust cloud. In contrast, the wave field is divided into regions of different but almost constant frequencies [1]. The boundaries of these so-called frequency clusters coincide with the locations of phase defects in the wave field. It is found that the size of the clusters depends on the strength of spatial gradients in the plasma parameters. We attribute the formation of frequency clusters to synchronization phenomena as a consequence of the nonlinear character of the wave.[1] K. O. Menzel, O. Arp, A.Piel, Phys. Rev. Lett. 104, 235002 (2010)

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.

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.

Modulation instability and dissipative rogue waves in ion-beam plasma: Roles of ionization, recombination, and electron attachment

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

Guo, Shimin, E-mail: gsm861@126.com; Mei, Liquan, E-mail: lqmei@mail.xjtu.edu.cn

The amplitude modulation of ion-acoustic waves is investigated in an unmagnetized plasma containing positive ions, negative ions, and electrons obeying a kappa-type distribution that is penetrated by a positive ion beam. By considering dissipative mechanisms, including ionization, negative-positive ion recombination, and electron attachment, we introduce a comprehensive model for the plasma with the effects of sources and sinks. Via reductive perturbation theory, the modified nonlinear Schrödinger equation with a dissipative term is derived to govern the dynamics of the modulated waves. The effect of the plasma parameters on the modulation instability criterion for the modified nonlinear Schrödinger equation is numericallymore » investigated in detail. Within the unstable region, first- and second-order dissipative ion-acoustic rogue waves are present. The effect of the plasma parameters on the characteristics of the dissipative rogue waves is also discussed.« less

Multi-operational tuneable Q-switched mode-locking Er fibre laser

NASA Astrophysics Data System (ADS)

Qamar, F. Z.

2018-01-01

A wavelength-spacing tuneable, Q-switched mode-locking (QML) erbium-doped fibre laser based on non-linear polarization rotation controlled by four waveplates and a cube polarizer is proposed. A mode-locked pulse train using two quarter-wave plates and a half-wave plate (HWP) is obtained first, and then an extra HWP is inserted into the cavity to produce different operation regimes. The evolutions of temporal and spectral dynamics with different orientation angles of the extra HWP are investigated. A fully modulated stable QML pulse train is observed experimentally. This is, to the author’s best knowledge, the first experimental work reporting QML operation without adding an extra saturable absorber inside the laser cavity. Multi-wavelength pulse laser operation, multi-pulse train continuous-wave mode-locking operation and pulse-splitting operations are also reported at certain HWP angles. The observed operational dynamics are interpreted as a mutual interaction of dispersion, non-linear effect and insertion loss. This work provides a new mechanism for fabricating cheap tuneable multi-wavelength lasers with QML pulses.

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

Quantum effects on compressional Alfven waves in compensated semiconductors

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

Amin, M. R.

2015-03-15

Amplitude modulation of a compressional Alfven wave in compensated electron-hole semiconductor plasmas is considered in the quantum magnetohydrodynamic regime in this paper. The important ingredients of this study are the inclusion of the particle degeneracy pressure, exchange-correlation potential, and the quantum diffraction effects via the Bohm potential in the momentum balance equations of the charge carriers. A modified nonlinear Schrödinger equation is derived for the evolution of the slowly varying amplitude of the compressional Alfven wave by employing the standard reductive perturbation technique. Typical values of the parameters for GaAs, GaSb, and GaN semiconductors are considered in analyzing the linearmore » and nonlinear dispersions of the compressional Alfven wave. Detailed analysis of the modulation instability in the long-wavelength regime is presented. For typical parameter ranges of the semiconductor plasmas and at the long-wavelength regime, it is found that the wave is modulationally unstable above a certain critical wavenumber. Effects of the exchange-correlation potential and the Bohm potential in the wave dynamics are also studied. It is found that the effect of the Bohm potential may be neglected in comparison with the effect of the exchange-correlation potential in the linear and nonlinear dispersions of the compressional Alfven wave.« less

Do the freak waves exist in soliton gas?

NASA Astrophysics Data System (ADS)

Shurgalina, Ekaterina; Pelinovsky, Efim

2016-04-01

The possibility of short-lived anomalous large waves (rogue waves) in soliton gas in the frameworks of integrable models like the Korteweg - de Vries - type equations is studied. It is shown that the dynamics of heteropolar soliton gas differs sufficiently from the dynamics of unipolar soliton fields. In particular, in the wave fields consisting of solitons with different polarities the freak wave appearance is possible. It is shown numerically in [Shurgalina and Pelinovsky, 2015]. Freak waves in the framework of the modified Korteweg-de Vries equation have been studied previously in the case of narrowband initial conditions [Grimshaw et al, 2005, 2010; Talipova, 2011]. In this case, the mechanism of freak wave generation was modulation instability of modulated quasi-sinusoidal wave packets. At the same time the modulation instability of modulated cnoidal waves was studied in the mathematical work [Driscoll & O'Neil, 1976]. Since a sequence of solitary waves can be a special case of cnoidal wave, the modulation instability can be a possible mechanism of freak wave appearance in a soliton gas. Thus, we expect that rogue wave phenomenon in soliton gas appears in nonlinear integrable models admitting an existence of modulation instability of periodic waves (like cnoidal waves). References: 1. Shurgalina E.G., Pelinovsky E.N. Dynamics of irregular wave ensembles in the coastal zone, Nizhny Novgorod State Technical University n.a. R.E. Alekseev. - Nizhny Novgorod, 2015, 179 pp. 2. Grimshaw R., Pelinovsky E., Talipova T., Sergeeva A. Rogue internal waves in the ocean: long wave model. European Physical Journal Special Topics, 2010, 185, 195 - 208. 3. Grimshaw R., Pelinovsky E., Talipova T., Ruderman M. Erdelyi R. Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg-de Vries equation. Studied Applied Mathematics, 2005, 114 (2), 189. 4. Talipova T.G. Mechanisms of internal freak waves, Fundamental and Applied Hydrophysics, 2011, 4(4), 58-70. 5. Driscoll F., O'Neil T.M. Modulational instability of cnoidal wave solutions of the modified Korteweg-de Vries equation. Journal of Mathematical Physics, 1976, 17 (7), 1196-1200.

Bulk solitary waves in elastic solids

NASA Astrophysics Data System (ADS)

Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.

2015-10-01

A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the duct-like polymer shell and proved, that there is no tensile area behind the wave, the bulk soliton propagates on a distance many times longer than its wave length, while both its shape and amplitude remain unchanged. We demonstrated recently how the strain solitons can be used for non-destructive testing (NDT) of laminated composites, used nowadays for various applications, e.g., in microelectronics, aerospace and automotive industries, and bulk strain solitons are among prospective instruments for NDT. Being aimed to propose the bulk strain solitons as an instrument for NDT in solids, we studied numerically the evolution of them in various wave guides with local defects, and shown that the strain soliton undergoes changes in amplitude, phase shift and the shape, that are distinctive and can be estimated. To sum up, now we are able to propose a new NDT technique, based on bulk strain soliton propagation in structural elements.

Excited-state vibronic wave-packet dynamics in H2 probed by XUV transient four-wave mixing

NASA Astrophysics Data System (ADS)

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

2018-02-01

The complex behavior of a molecular wave packet initiated by an extreme ultraviolet (XUV) pulse is investigated with noncollinear wave mixing spectroscopy. A broadband XUV pulse spanning 12-16 eV launches a wave packet in H2 comprising a coherent superposition of multiple electronic and vibrational levels. The molecular wave packet evolves freely until a delayed few-cycle optical laser pulse arrives to induce nonlinear signals in the XUV via four-wave mixing (FWM). The angularly resolved FWM signals encode rich energy exchange processes between the optical laser field and the XUV-excited molecule. The noncollinear geometry enables spatial separation of ladder and V- or Λ-type transitions induced by the optical field. Ladder transitions, in which the energy exchange with the optical field is around 3 eV, appear off axis from the incident XUV beam. Each vibrationally revolved FWM line probes a different part of the wave packet in energy, serving as a promising tool for energetic tomography of molecular wave packets. V- or Λ-type transitions, in which the energy exchange is well under 1 eV, result in on-axis nonlinear signals. The first-order versus third-order interference of the on-axis signal serves as a mapping tool of the energy flow pathways. Intra- and interelectronic potential energy curve transitions are decisively identified. The current study opens possibilities for accessing complete dynamic information in XUV-excited complex systems.

Vector rogue waves and dark-bright boomeronic solitons in autonomous and nonautonomous settings.

PubMed

Mareeswaran, R Babu; Charalampidis, E G; Kanna, T; Kevrekidis, P G; Frantzeskakis, D J

2014-10-01

In this work we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schrödinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as spatiotemporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark-bright boomeronlike soliton solutions of the latter are converted back into ones of the original nonautonomous model. Using direct numerical simulations we find that, in most cases, the rogue wave formation is rapidly followed by a modulational instability that leads to the emergence of an expanding soliton train. Scenarios different than this generic phenomenology are also reported.

Elliptic-type soliton combs in optical ring microresonators

NASA Astrophysics Data System (ADS)

Dikandé Bitha, Rodrigues D.; Dikandé, Alain M.

2018-03-01

Soliton crystals are periodic patterns of multispot optical fields formed from either time or space entanglements of equally separated identical high-intensity pulses. These specific nonlinear optical structures have gained interest in recent years with the advent and progress in nonlinear optical fibers and fiber lasers, photonic crystals, wave-guided wave systems, and most recently optical ring microresonator devices. In this work an extensive analysis of characteristic features of soliton crystals is carried out, with an emphasis on their one-to-one correspondence with elliptic solitons. With this purpose in mind, we examine their formation, their stability, and their dynamics in ring-shaped nonlinear optical media within the framework of the Lugiato-Lefever equation. The stability analysis deals with internal modes of the system via a 2 ×2 -matrix Lamé-type eigenvalue problem, the spectrum of which is shown to possess a rich set of bound states consisting of stable zero-fequency modes and unstable decaying as well as growing modes. Turning towards the dynamics of elliptic solitons in ring-shaped fiber resonators with Kerr nonlinearity, we first propose a collective-coordinate approach, based on a Lagrangian formalism suitable for elliptic-soliton solutions to the nonlinear Schrödinger equation with an arbitrary perturbation. Next we derive time evolutions of elliptic-soliton parameters in the specific context of ring-shaped optical fiber resonators, where the optical field evolution is thought to be governed by the Lugiato-Lefever equation. By solving numerically the collective-coordinate equations an analysis of the amplitude, the position, the phase of internal oscillations, the phase velocity, the energy, and phase portraits of the amplitude is carried out and reveals a complex dynamics of the elliptic soliton in ring-shaped optical microresonators. Direct numerical simulations of the Lugiato-Lefever equation are also carried out seeking for stationary-wave solutions, and the numerical results are in very good agreement with the collective-coordinate approach.

Analysis of dynamic accumulative damage about the lining structure of high speed railway’s tunnel based on ultrasonic testing technology

NASA Astrophysics Data System (ADS)

Wang, Xiang-qiu; Zhang, Huojun; Xie, Wen-xi

2017-08-01

Based on the similar material model test of full tunnel, the theory of elastic wave propagation and the testing technology of intelligent ultrasonic wave had been used to research the dynamic accumulative damage characteristics of tunnel’s lining structure under the dynamic loads of high speed train. For the more, the dynamic damage variable of lining structure of high speed railway’s tunnel was obtained. The results shown that the dynamic cumulative damage of lining structure increases nonlinearly with the times of cumulative vibration, the weakest part of dynamic cumulative damage is the arch foot of tunnel. Much more attention should be paid to the design and operation management of high speed railway’s tunnel.

Rogue-pair and dark-bright-rogue waves of the coupled nonlinear Schrödinger equations from inhomogeneous femtosecond optical fibers.

PubMed

Yomba, Emmanuel; Zakeri, Gholam-Ali

2016-08-01

The coupled inhomogeneous Schrödinger equations with a wide range of applications describing a field of pluses with the right and the left polarizations that take into account cross-phase modulations, stimulated Ramani scattering, and absorption effects are investigated. A combination of several different approaches is used in a novel way to obtain the explicit expressions for the rogue-pair and dark-bright-rogue waves. We study the dynamics of these structurally stable rogues and analyze the effects of a parameter that controls the region of stability that intrinsically connects the cross-phase modulation and other Kerr nonlinearity factors. The effects of the right and left polarizations on the shape of the rogue-pair and other solitary rogue waves are graphically analyzed. These rogue-pair waves are studied on periodic and non-periodic settings. We observe that rogue-pair wave from the right and left polarizations has a similar structure while the dark-bright-rogue waves have quite different intensity profiles.

Bifurcation analysis for ion acoustic waves in a strongly coupled plasma including trapped electrons

NASA Astrophysics Data System (ADS)

El-Labany, S. K.; El-Taibany, W. F.; Atteya, A.

2018-02-01

The nonlinear ion acoustic wave propagation in a strongly coupled plasma composed of ions and trapped electrons has been investigated. The reductive perturbation method is employed to derive a modified Korteweg-de Vries-Burgers (mKdV-Burgers) equation. To solve this equation in case of dissipative system, the tangent hyperbolic method is used, and a shock wave solution is obtained. Numerical investigations show that, the ion acoustic waves are significantly modified by the effect of polarization force, the trapped electrons and the viscosity coefficients. Applying the bifurcation theory to the dynamical system of the derived mKdV-Burgers equation, the phase portraits of the traveling wave solutions of both of dissipative and non-dissipative systems are analyzed. The present results could be helpful for a better understanding of the waves nonlinear propagation in a strongly coupled plasma, which can be produced by photoionizing laser-cooled and trapped electrons [1], and also in neutron stars or white dwarfs interior.

SPREADING SPEEDS AND TRAVELING WAVES FOR NON-COOPERATIVE INTEGRO-DIFFERENCE SYSTEMS

PubMed Central

Wang, Haiyan; Castillo-Chavez, Carlos

2014-01-01

The study of spatially explicit integro-difference systems when the local population dynamics are given in terms of discrete-time generations models has gained considerable attention over the past two decades. These nonlinear systems arise naturally in the study of the spatial dispersal of organisms. The brunt of the mathematical research on these systems, particularly, when dealing with cooperative systems, has focused on the study of the existence of traveling wave solutions and the characterization of their spreading speed. Here, we characterize the minimum propagation (spreading) speed, via the convergence of initial data to wave solutions, for a large class of non cooperative nonlinear systems of integro-difference equations. The spreading speed turns out to be the slowest speed from a family of non-constant traveling wave solutions. The applicability of these theoretical results is illustrated through the explicit study of an integro-difference system with local population dynamics governed by Hassell and Comins’ non-cooperative competition model (1976). The corresponding integro-difference nonlinear systems that results from the redistribution of individuals via a dispersal kernel is shown to satisfy conditions that guarantee the existence of minimum speeds and traveling waves. This paper is dedicated to Avner Friedman as we celebrate his immense contributions to the fields of partial differential equations, integral equations, mathematical biology, industrial mathematics and applied mathematics in general. His leadership in the mathematical sciences and his mentorship of students and friends over several decades has made a huge difference in the personal and professional lives of many, including both of us. PMID:24899868

Nonlinear Time-Reversal in a Wave Chaotic System

NASA Astrophysics Data System (ADS)

Frazier, Matthew; Taddese, Biniyam; Ott, Edward; Antonsen, Thomas; Anlage, Steven

2012-02-01

Time reversal mirrors are particularly simple to implement in wave chaotic systems and form the basis for a new class of sensors [1-3]. These sensors work by applying the quantum mechanical concepts of Loschmidt echo and fidelity decay to classical waves. The sensors make explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to remotely measure the presence of small perturbations to the system. The underlying ray chaos increases the sensitivity to small perturbations throughout the volume explored by the waves. We extend our time-reversal mirror to include a discrete element with a nonlinear dynamical response. The initially injected pulse interacts with the nonlinear element, generating new frequency components originating at the element. By selectively filtering for and applying the time-reversal mirror to the new frequency components, we focus a pulse only onto the element, without knowledge of its location. Furthermore, we demonstrate transmission of arbitrary patterns of pulses to the element, creating a targeted communication channel to the exclusion of 'eavesdroppers' at other locations in the system. [1] Appl. Phys. Lett. 95, 114103 (2009) [2] J. Appl. Phys. 108, 1 (2010) [3] Acta Physica Polonica A 112, 569 (2007)

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

PubMed Central

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

2015-01-01

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

Super-soliton dust-acoustic waves in four-component dusty plasma using non-extensive electrons and ions distributions

NASA Astrophysics Data System (ADS)

El-Wakil, S. A.; Abulwafa, Essam M.; Elhanbaly, Atalla A.

2017-07-01

Based on Sagdeev pseudo-potential and phase-portrait, the dynamics of four-component dust plasma with non-extensively distributed electrons and ions are investigated. Three distinct types of nonlinear waves, namely, soliton, double layer, and super-soliton, have been found. The basic features of such waves are high sensitivity to Mach number, non-extensive parameter, and dust temperature ratio. It is found that the multi-component plasma is a necessary condition for super-soliton's existence, having a wider amplitude and a larger width than the regular soliton. Super-solitons may also exist when the Sagdeev pseudo-potential curves admit at least four extrema and two roots. In our multi-component plasma system, the super-solitons can be found by increasing the Mach number and the non-extensive parameter beyond those of double-layers. On the contrary, the super-soliton can be produced by decreasing the dust temperature ratio. The conditions of the onset of such nonlinear waves and its merging to regular solitons have been studied. This work shows that the obtained nonlinear waves are found to exist only in the super-sonic Mach number regime. The obtained results may be of wide relevance in the field of space plasma and may also be helpful to better understand the nonlinear fluctuations in the Auroral-zone of the Earth's magnetosphere.

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

A Hamiltonian Model of Dissipative Wave-particle Interactions and the Negative-mass Effect

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

A. Zhmoginov

2011-02-07

The effect of radiation friction is included in the Hamiltonian treatment of wave-particle interactions with autoresonant phase-locking, yielding a generalized canonical approach to the problem of dissipative dynamics near a nonlinear resonance. As an example, the negativemass eff ect exhibited by a charged particle in a pump wave and a static magnetic field is studied in the presence of the friction force due to cyclotron radiation. Particles with negative parallel masses m! are shown to transfer their kinetic energy to the pump wave, thus amplifying it. Counterintuitively, such particles also undergo stable dynamics, decreasing their transverse energy monotonically due tomore » cyclotron cooling, whereas some of those with positive m! undergo cyclotron heating instead, extracting energy from the pump wave.« less

Energy dynamics in a simulation of LAPD turbulence

NASA Astrophysics Data System (ADS)

Friedman, Brett

2012-10-01

It is often assumed that linear instabilities maintain turbulence in plasmas and some fluids, but this is not always the case. It is well known that many fluids display subcritical turbulence at a Reynolds number well below the threashold of linear instability. Certain plasma models such as drift waves in a sheared slab also exhibit subcritical turbulence [1]. In other instances such as drift-ballooning turbulence in tokamak edge plasmas, linear instabilities exist in a system, but they become subdominant to more robust nonlinear mechanisms that sustain a turbulent state [2, 3]. In our simulation of LAPD turbulence, which was previously analyzed in [4], we diagnose the results using an energy dynamics analysis [5]. This allows us to track energy input into turbulent fluctuations and energy dissipation out of them. We also track conservative energy transfer between different energy types (e.g. from potential to kinetic energy) and between different Fourier waves of the system. The result is that a nonlinear instability drives and maintains the turbulence in the steady state saturated phase of the simulation. While a linear restistive drift wave instability resides in the system, the nonlinear drift wave instability dominates when the fluctuation amplitude becomes large enough. The nonlinear instability is identified by its energy growth rate spectrum, which varies significantly from the linear growth rate spectrum. The main differences are the presence of positive growth rates when k|| = 0 and negative growth rates for nonzero k||, which is opposite that of the linear growth rate spectrum.[4pt] [1] B. D. Scott, Phys. Rev. Lett., 65, 3289 (1990).[0pt] [2] A. Zeiler et al, Phys. Plasmas, 3, 2951 (1996).[0pt] [3] B. D. Scott, Phys. Plasmas, 12, 062314 (2005).[0pt] [4] P. Popovich et al, Phys. Plasmas, 17, 122312 (2010).[0pt] [5] [physics.plasm-ph].

Experimental and theoretical modelling of sand-water-object interaction under nonlinear progressive waves

NASA Astrophysics Data System (ADS)

Testik, Firat Yener

An experimental and theoretical study has been conducted to obtain a fundamental understanding of the dynamics of the sand, water and a solid object interaction as progressive gravity waves impinge on a sloping beach. Aside from obvious scientific interest, this exceedingly complex physical problem is important for naval applications, related to the behavior of disk/cylindrical shaped objects (mines) in the coastal waters. To address this problem, it was divided into a set of simpler basic problems. To begin, nonlinear progressive waves were investigated experimentally in a wave tank for the case of a rigid (impermeable) sloping bottom. Parameterizations for wave characteristics were proposed and compared with the experiments. In parallel, a numerical wave tank model (NWT) was calibrated using experimental data from a single run, and wave field in the wave tank was simulated numerically for the selected experiments. Subsequently, a layer of sand was placed on the slope and bottom topography evolution processes (ripple and sandbar dynamics, bottom topography relaxation under variable wave forcing, etc.) were investigated experimentally. Models for those processes were developed and verified by experimental measurements. Flow over a circular cylinder placed horizontally on a plane wall was also studied. The far-flow field of the cylinder placed in the wave tank was investigated experimentally and numerical results from the NWT simulations were compared with the experimental data. In the mean time, the near-flow velocity/vorticity field around a short cylinder under steady and oscillatory flow was studied in a towing tank. Horseshoe vortex formation and periodic shedding were documented and explained. With the understanding gained through the aforementioned studies, dynamics and burial/scour around the bottom objects in the wave tank were studied. Possible scenarios on the behavior of the disk-shaped objects were identified and explained. Scour around 3D cylindrical objects was investigated. Different scour regimes were identified experimentally and explained theoretically. Proper physical parameterizations on the time evolution and equilibrium scour characteristics were proposed and verified experimentally.

Self-accelerating self-trapped nonlinear beams of Maxwell's equations.

PubMed

Kaminer, Ido; Nemirovsky, Jonathan; Segev, Mordechai

2012-08-13

We present shape-preserving self-accelerating beams of Maxwell's equations with optical nonlinearities. Such beams are exact solutions to Maxwell's equations with Kerr or saturable nonlinearity. The nonlinearity contributes to self-trapping and causes backscattering. Those effects, together with diffraction effects, work to maintain shape-preserving acceleration of the beam on a circular trajectory. The backscattered beam is found to be a key issue in the dynamics of such highly non-paraxial nonlinear beams. To study that, we develop two new techniques: projection operator separating the forward and backward waves, and reverse simulation. Finally, we discuss the possibility that such beams would reflect themselves through the nonlinear effect, to complete a 'U' shaped trajectory.

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

Wang, Yunliang; International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Faculty of Physics and Astronomy, Ruhr University Bochum, D-44780 Bochum; Lü, Xiaoxia

A theoretical and numerical study of the modulational instability of large amplitude quantum magnetosonic waves (QMWs) in a relativistically degenerate plasma is presented. A modified nonlinear Schrödinger equation is derived by using the reductive perturbation method. The modulational instability regions of the QMWs and the corresponding growth rates are significantly affected by the relativistic degeneracy parameter, the Pauli spin magnetization effects, and the equilibrium magnetic field. The dynamics and nonlinear saturation of the modulational instability of QMWs are investigated numerically. It is found that the increase of the relativistic degeneracy parameter can increase the growth rate of the instability, andmore » the system is saturated nonlinearly by the formation of envelope solitary waves. The current investigation may have relevance to astrophysical magnetized compact objects, such as white dwarfs and pulsar magnetospheres.« less

Two Studies of Complex Nonlinear Systems: Engineered Granular Crystals and Coarse-Graining Optimization Problems

NASA Astrophysics Data System (ADS)

Pozharskiy, Dmitry

In recent years a nonlinear, acoustic metamaterial, named granular crystals, has gained prominence due to its high accessibility, both experimentally and computationally. The observation of a wide range of dynamical phenomena in the system, due to its inherent nonlinearities, has suggested its importance in many engineering applications related to wave propagation. In the first part of this dissertation, we explore the nonlinear dynamics of damped-driven granular crystals. In one case, we consider a highly nonlinear setting, also known as a sonic vacuum, and derive a nonlinear analogue of a linear spectrum, corresponding to resonant periodic propagation and antiresonances. Experimental studies confirm the computational findings and the assimilation of experimental data into a numerical model is demonstrated. In the second case, global bifurcations in a precompressed granular crystal are examined, and their involvement in the appearance of chaotic dynamics is demonstrated. Both results highlight the importance of exploring the nonlinear dynamics, to gain insight into how a granular crystal responds to different external excitations. In the second part, we borrow established ideas from coarse-graining of dynamical systems, and extend them to optimization problems. We combine manifold learning algorithms, such as Diffusion Maps, with stochastic optimization methods, such as Simulated Annealing, and show that we can retrieve an ensemble, of few, important parameters that should be explored in detail. This framework can lead to acceleration of convergence when dealing with complex, high-dimensional optimization, and could potentially be applied to design engineered granular crystals.

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

NASA Astrophysics Data System (ADS)

Fu, Zhengping

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

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

Spatial Dynamics Methods for Solitary Waves on a Ferrofluid Jet

NASA Astrophysics Data System (ADS)

Groves, M. D.; Nilsson, D. V.

2018-04-01

This paper presents existence theories for several families of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet surrounding a stationary metal rod. The ferrofluid, which is governed by a general (nonlinear) magnetisation law, is subject to an azimuthal magnetic field generated by an electric current flowing along the rod. The ferrohydrodynamic problem for axisymmetric travelling waves is formulated as an infinite-dimensional Hamiltonian system in which the axial direction is the time-like variable. A centre-manifold reduction technique is employed to reduce the system to a locally equivalent Hamiltonian system with a finite number of degrees of freedom, and homoclinic solutions to the reduced system, which correspond to solitary waves, are detected by dynamical-systems methods.

Nonlinear dynamical systems effects of homeopathic remedies on multiscale entropy and correlation dimension of slow wave sleep EEG in young adults with histories of coffee-induced insomnia.

PubMed

Bell, Iris R; Howerter, Amy; Jackson, Nicholas; Aickin, Mikel; Bootzin, Richard R; Brooks, Audrey J

2012-07-01

Investigators of homeopathy have proposed that nonlinear dynamical systems (NDS) and complex systems science offer conceptual and analytic tools for evaluating homeopathic remedy effects. Previous animal studies demonstrate that homeopathic medicines alter delta electroencephalographic (EEG) slow wave sleep. The present study extended findings of remedy-related sleep stage alterations in human subjects by testing the feasibility of using two different NDS analytic approaches to assess remedy effects on human slow wave sleep EEG. Subjects (N=54) were young adult male and female college students with a history of coffee-related insomnia who participated in a larger 4-week study of the polysomnographic effects of homeopathic medicines on home-based all-night sleep recordings. Subjects took one bedtime dose of a homeopathic remedy (Coffea cruda or Nux vomica 30c). We computed multiscale entropy (MSE) and the correlation dimension (Mekler-D2) for stages 3 and 4 slow wave sleep EEG sampled in artifact-free 2-min segments during the first two rapid-eye-movement (REM) cycles for remedy and post-remedy nights, controlling for placebo and post-placebo night effects. MSE results indicate significant, remedy-specific directional effects, especially later in the night (REM cycle 2) (CC: remedy night increases and post-remedy night decreases in MSE at multiple sites for both stages 3 and 4 in both REM cycles; NV: remedy night decreases and post-remedy night increases, mainly in stage 3 REM cycle 2 MSE). D2 analyses yielded more sporadic and inconsistent findings. Homeopathic medicines Coffea cruda and Nux vomica in 30c potencies alter short-term nonlinear dynamic parameters of slow wave sleep EEG in healthy young adults. MSE may provide a more sensitive NDS analytic method than D2 for evaluating homeopathic remedy effects on human sleep EEG patterns. Copyright © 2012 The Faculty of Homeopathy. Published by Elsevier Ltd. All rights reserved.

Nonlinear Dynamical Systems Effects of Homeopathic Remedies on Multiscale Entropy and Correlation Dimension of Slow Wave Sleep EEG in Young Adults with Histories of Coffee-Induced Insomnia

PubMed Central

Bell, Iris R.; Howerter, Amy; Jackson, Nicholas; Aickin, Mikel; Bootzin, Richard R.; Brooks, Audrey J.

2012-01-01

Background Investigators of homeopathy have proposed that nonlinear dynamical systems (NDS) and complex systems science offer conceptual and analytic tools for evaluating homeopathic remedy effects. Previous animal studies demonstrate that homeopathic medicines alter delta electroencephalographic (EEG) slow wave sleep. The present study extended findings of remedy-related sleep stage alterations in human subjects by testing the feasibility of using two different NDS analytic approaches to assess remedy effects on human slow wave sleep EEG. Methods Subjects (N=54) were young adult male and female college students with a history of coffee-related insomnia who participated in a larger 4-week study of the polysomnographic effects of homeopathic medicines on home-based all-night sleep recordings. Subjects took one bedtime dose of a homeopathic remedy (Coffea cruda or Nux vomica 30c). We computed multiscale entropy (MSE) and the correlation dimension (Mekler-D2) for stage 3 and 4 slow wave sleep EEG sampled in artifact-free 2-minute segments during the first two rapid-eye-movement (REM) cycles for remedy and post-remedy nights, controlling for placebo and post-placebo night effects. Results MSE results indicate significant, remedy-specific directional effects, especially later in the night (REM cycle 2) (CC: remedy night increases and post-remedy night decreases in MSE at multiple sites for both stages 3 and 4 in both REM cycles; NV: remedy night decreases and post-remedy night increases, mainly in stage 3 REM cycle 2 MSE). D2 analyses yielded more sporadic and inconsistent findings. Conclusions Homeopathic medicines Coffea cruda and Nux vomica in 30c potencies alter short-term nonlinear dynamic parameters of slow wave sleep EEG in healthy young adults. MSE may provide a more sensitive NDS analytic method than D2 for evaluating homeopathic remedy effects on human sleep EEG patterns. PMID:22818237

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

NASA Astrophysics Data System (ADS)

Wamba, Etienne; Tchakoutio Nguetcho, Aurélien S.

2018-05-01

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

Code Samples Used for Complexity and Control

NASA Astrophysics Data System (ADS)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

The following sections are included: * MathematicaⓇ Code * Generic Chaotic Simulator * Vector Differential Operators * NLS Explorer * 2C++ Code * C++ Lambda Functions for Real Calculus * Accelerometer Data Processor * Simple Predictor-Corrector Integrator * Solving the BVP with the Shooting Method * Linear Hyperbolic PDE Solver * Linear Elliptic PDE Solver * Method of Lines for a Set of the NLS Equations * C# Code * Iterative Equation Solver * Simulated Annealing: A Function Minimum * Simple Nonlinear Dynamics * Nonlinear Pendulum Simulator * Lagrangian Dynamics Simulator * Complex-Valued Crowd Attractor Dynamics * Freeform Fortran Code * Lorenz Attractor Simulator * Complex Lorenz Attractor * Simple SGE Soliton * Complex Signal Presentation * Gaussian Wave Packet * Hermitian Matrices * Euclidean L2-Norm * Vector/Matrix Operations * Plain C-Code: Levenberg-Marquardt Optimizer * Free Basic Code: 2D Crowd Dynamics with 3000 Agents

Nonlinear Recurrent Dynamics and Long-Term Nonstationarities in EEG Alpha Cortical Activity: Implications for Choosing Adequate Segment Length in Nonlinear EEG Analyses.

PubMed

Cerquera, Alexander; Vollebregt, Madelon A; Arns, Martijn

2018-03-01

Nonlinear analysis of EEG recordings allows detection of characteristics that would probably be neglected by linear methods. This study aimed to determine a suitable epoch length for nonlinear analysis of EEG data based on its recurrence rate in EEG alpha activity (electrodes Fz, Oz, and Pz) from 28 healthy and 64 major depressive disorder subjects. Two nonlinear metrics, Lempel-Ziv complexity and scaling index, were applied in sliding windows of 20 seconds shifted every 1 second and in nonoverlapping windows of 1 minute. In addition, linear spectral analysis was carried out for comparison with the nonlinear results. The analysis with sliding windows showed that the cortical dynamics underlying alpha activity had a recurrence period of around 40 seconds in both groups. In the analysis with nonoverlapping windows, long-term nonstationarities entailed changes over time in the nonlinear dynamics that became significantly different between epochs across time, which was not detected with the linear spectral analysis. Findings suggest that epoch lengths shorter than 40 seconds neglect information in EEG nonlinear studies. In turn, linear analysis did not detect characteristics from long-term nonstationarities in EEG alpha waves of control subjects and patients with major depressive disorder patients. We recommend that application of nonlinear metrics in EEG time series, particularly of alpha activity, should be carried out with epochs around 60 seconds. In addition, this study aimed to demonstrate that long-term nonlinearities are inherent to the cortical brain dynamics regardless of the presence or absence of a mental disorder.

Infragravity wave generation and dynamics over a mild slope beach : Experiments and numerical computations

NASA Astrophysics Data System (ADS)

Cienfuegos, R.; Duarte, L.; Hernandez, E.

2008-12-01

Charasteristic frequencies of gravity waves generated by wind and propagating towards the coast are usually comprised between 0.05Hz and 1Hz. Nevertheless, lower frequecy waves, in the range of 0.001Hz and 0.05Hz, have been observed in the nearshore zone. Those long waves, termed as infragravity waves, are generated by complex nonlinear mechanisms affecting the propagation of irregular waves up to the coast. The groupiness of an incident random wave field may be responsible for producing a slow modulation of the mean water surface thus generating bound long waves travelling at the group speed. Similarly, a quasi- periodic oscillation of the break-point location, will be accompained by a slow modulation of set-up/set-down in the surf zone and generation and release of long waves. If the primary structure of the carrying incident gravity waves is destroyed (e.g. by breaking), forced long waves can be freely released and even reflected at the coast. Infragravity waves can affect port operation through resonating conditions, or strongly affect sediment transport and beach morphodynamics. In the present study we investigate infragravity wave generation mechanisms both, from experiments and numerical computations. Measurements were conducted at the 70-meter long wave tank, located at the Instituto Nacional de Hidraulica (Chile), prepared with a beach of very mild slope of 1/80 in order to produce large surf zone extensions. A random JONSWAP type wave field (h0=0.52m, fp=0.25Hz, Hmo=0.17m) was generated by a piston wave-maker and measurements of the free surface displacements were performed all over its length at high spatial resolution (0.2m to 1m). Velocity profiles were also measured at four verticals inside the surf zone using an ADV. Correlation maps of wave group envelopes and infragravity waves are computed in order to identify long wave generation and dynamics in the experimental set-up. It appears that both mechanisms (groupiness and break-point oscillation) are clearly present in this experiment while spectral analysis evidences the reorganization of energy density from the original narrow spectrum into the infragravity band. This experiment provides an opportunity to test numerical models that would in principle be able to reproduce infragravity wave generation and dynamics. We compare numerical results (free surface and velocities) produced by a fully nonlinear Boussinesq model including breaking and runup to the experimental data and show that the complex infragravity wave dynamics is adequately reproduced by the model.

Nonlinear amplitude dynamics in flagellar beating

NASA Astrophysics Data System (ADS)

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

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

Nonlinear amplitude dynamics in flagellar beating.

PubMed

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

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

Nonlinear amplitude dynamics in flagellar beating

PubMed Central

Casademunt, Jaume

2017-01-01

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

Perturbed soliton excitations of Rao-dust Alfvén waves in magnetized dusty plasmas

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

Kavitha, L., E-mail: louiskavitha@yahoo.co.in; The Abdus Salam International Centre for Theoretical Physics, Trieste; Lavanya, C.

We investigate the propagation dynamics of the perturbed soliton excitations in a three component fully ionized dusty magnetoplasma consisting of electrons, ions, and heavy charged dust particulates. We derive the governing equation of motion for the two dimensional Rao-dust magnetohydrodynamic (R-D-MHD) wave by employing the inertialess electron equation of motion, inertial ion equation of motion, the continuity equations in a plasma with immobile charged dust grains, together with the Maxwell's equations, by assuming quasi neutrality and neglecting the displacement current in Ampere's law. Furthermore, we assume the massive dust particles are practically immobile since we are interested in timescales muchmore » shorter than the dusty plasma period, thereby neglecting any damping of the modes due to the grain charge fluctuations. We invoke the reductive perturbation method to represent the governing dynamics by a perturbed cubic nonlinear Schrödinger (pCNLS) equation. We solve the pCNLS, along the lines of Kodama-Ablowitz multiple scale nonlinear perturbation technique and explored the R-D-MHD waves as solitary wave excitations in a magnetized dusty plasma. Since Alfvén waves play an important role in energy transport in driving field-aligned currents, particle acceleration and heating, solar flares, and the solar wind, this representation of R-D-MHD waves as soliton excitations may have extensive applications to study the lower part of the earth's ionosphere.« less

The polarized Debye sheath effect on Kadomtsev-Petviashvili electrostatic structures in strongly coupled dusty plasma

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

Shahmansouri, M.; Alinejad, H.

2015-04-15

We give a theoretical investigation on the dynamics of nonlinear electrostatic waves in a strongly coupled dusty plasma with strong electrostatic interaction between dust grains in the presence of the polarization force (i.e., the force due to the polarized Debye sheath). Adopting a reductive perturbation method, we derived a three-dimensional Kadomtsev-Petviashvili equation that describes the evolution of weakly nonlinear electrostatic localized waves. The energy integral equation is used to study the existence domains of the localized structures. The analysis provides the localized structure existence region, in terms of the effects of strong interaction between the dust particles and polarization force.

Weakly decaying solutions of nonlinear Schrödinger equation in the plane

NASA Astrophysics Data System (ADS)

Villarroel, Javier; Prada, Julia; Estévez, Pilar G.

2017-12-01

We show that the nonlinear Schrödinger equation in 2  +  1 dimensions possesses a class of regular and rationally decaying solutions associated to interacting solitons. The interesting dynamics of the associated pulses is studied in detail and related to homothetic Lagrange configurations of certain N- body problems. These solutions correspond to the discrete spectrum of the Lax pair associated operator. A natural characterization of this spectrum is given. We show that a certain subset of solutions correspond to rogue waves, localized along curves in the plane. Other configurations like grey solitons, cnoidal waves and general N- lumps solutions are also described.

Dynamics of nonautonomous rogue waves in Bose-Einstein condensate

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

Zhao, Li-Chen, E-mail: zhaolichen3@163.com

2013-02-15

We study rogue waves of Bose-Einstein condensate (BEC) analytically in a time-dependent harmonic trap with a complex potential. Properties of the nonautonomous rogue waves are investigated analytically. It is reported that there are possibilities to 'catch' rogue waves through manipulating nonlinear interaction properly. The results provide many possibilities to manipulate rogue waves experimentally in a BEC system. - Highlights: Black-Right-Pointing-Pointer One more generalized rogue wave solutions are presented. Black-Right-Pointing-Pointer Present one possible way to catch a rouge wave. Black-Right-Pointing-Pointer Properties of rogue waves are investigated analytically for the first time. Black-Right-Pointing-Pointer Provide many possibilities to manipulate rogue waves in BEC.

Monitoring localized cracks on under pressure concrete nuclear containment wall using linear and nonlinear ultrasonic coda wave interferometry

NASA Astrophysics Data System (ADS)

Legland, J.-B.; Abraham, O.; Durand, O.; Henault, J.-M.

2018-04-01

Civil engineering is constantly demanding new methods for evaluation and non-destructive testing (NDT), particularly to prevent and monitor serious damage to concrete structures. Tn this work, experimental results are presented on the detection and characterization of cracks using nonlinear modulation of coda waves interferometry (NCWT) [1]. This method consists in mixing high-amplitude low-frequency acoustic waves with multi-scattered probe waves (coda) and analyzing their effects by interferometry. Unlike the classic method of coda analysis (CWT), the NCWT does not require the recording of a coda as a reference before damage to the structure. Tn the framework of the PTA-ENDE project, a 1/3 model of a preconstrained concrete containment (EDF VeRCoRs mock-up) is placed under pressure to study the leakage of the structure. During this evaluation protocol, specific areas are monitored by the NCWT (during 5 days, which correspond to the protocol of nuclear power plant pressurization under maintenance test). The acoustic nonlinear response due to the high amplitude of the acoustic modulation gives pertinent information about the elastic and dissipative nonlinearities of the concrete. Tts effective level is evaluated by two nonlinear observables extracted from the interferometry. The increase of nonlinearities is in agreement with the creation of a crack with a network of microcracks located at its base; however, a change in the dynamics of the evolution of the nonlinearities may indicate the opening of a through crack. Tn addition, as during the experimental campaign, reference codas have been recorded. We used CWT to follow the stress evolution and the gas leaks ratio of the structure. Both CWT and NCWT results are presented in this paper.

Nonequilibrium response of an electron-mediated charge density wave ordered material to a large dc electric field

NASA Astrophysics Data System (ADS)

Matveev, O. P.; Shvaika, A. M.; Devereaux, T. P.; Freericks, J. K.

2016-01-01

Using the Kadanoff-Baym-Keldysh formalism, we employ nonequilibrium dynamical mean-field theory to exactly solve for the nonlinear response of an electron-mediated charge-density-wave-ordered material. We examine both the dc current and the order parameter of the conduction electrons as the ordered system is driven by the electric field. Although the formalism we develop applies to all models, for concreteness, we examine the charge-density-wave phase of the Falicov-Kimball model, which displays a number of anomalous behaviors including the appearance of subgap density of states as the temperature increases. These subgap states should have a significant impact on transport properties, particularly the nonlinear response of the system to a large dc electric field.

Dynamics of nonautonomous discrete rogue wave solutions for an Ablowitz-Musslimani equation with PT-symmetric potential.

PubMed

Yu, Fajun

2017-02-01

Starting from a discrete spectral problem, we derive a hierarchy of nonlinear discrete equations which include the Ablowitz-Ladik (AL) equation. We analytically study the discrete rogue-wave (DRW) solutions of AL equation with three free parameters. The trajectories of peaks and depressions of profiles for the first- and second-order DRWs are produced by means of analytical and numerical methods. In particular, we study the solutions with dispersion in parity-time ( PT) symmetric potential for Ablowitz-Musslimani equation. And we consider the non-autonomous DRW solutions, parameters controlling and their interactions with variable coefficients, and predict the long-living rogue wave solutions. Our results might provide useful information for potential applications of synthetic PT symmetric systems in nonlinear optics and condensed matter physics.

Initial-value problem for the Gardner equation applied to nonlinear internal waves

NASA Astrophysics Data System (ADS)

Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim

2017-04-01

The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of solitons (family with positive polarity, and family with negative polarity bounded below by the amplitude of 2) and two-parametric family of breathers (oscillatory wave packets). In this case varying amplitude and width of bell-shaped initial impulse leads to plenty of different evolutionary scenarios with the generation of solitary waves, breathers, solibores and nonlinear Airy wave in their various combinations. Statistical analysis of the wave field in time shows almost permanent substantial exceedance of the level of the significant wave height in some position in spatial coordinate. Evolution of Fourier spectrum of the wave field is also analyzed, and its behavior after a long time of initial wave evolution demonstrates the power asymptotic for small wave numbers and exponential asymptotic for large wave numbers. The presented results of research are obtained with the support of the grant of the President of the Russian Federation for state support of the young Russian scientists - Candidates of Sciences (MK-5208.2016.5) and Russian Foundation for Basic Research grant 16-05-00049. References: Grimshaw R., Pelinovsky D., Pelinovsky E and Slunyaev A. Generation of large-amplitude solitons in the extended Korteweg-de Vries equation // Chaos, 2002. - V.12. - No 4. - 1070-1076. Grimshaw, R., Slunyaev, A., and Pelinovsky, E. Generation of solitons and breathers in the extended Korteweg-de Vries equation with positive cubic nonlinearity //Chaos, 2010. - vol. 20.-013102. Kurkina O.E., Kurkin A.A., Soomere T., Pelinovsky E.N., Rouvinskaya E.A. Higher-order (2+4) Korteweg-de Vries - like equation for interfacial waves in a symmetric three-layer fluid // Physics of Fluids, 2011. - Volume 23. - Issue 11. - p.116602--1--13. Kurkina O., Rouvinskaya E., Talipova T., Kurkin A., Pelinovsky E. Nonlinear disintegration of sine wave in the framework of the Gardner equation // Physica D: Nonlinear Phenomena, 2015. - doi:10.1016/j.physd.2015.12.007. 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. Rouvinskaya E., Kurkina O., Kurkin A. Dynamics of nonlinear internal gravity waves in layered fluids // NNSTU n.a. R.E. Alekseev Press - Nizhny Novgorod, 2014 - 160 p. [In Russian] Trillo S., Klein M., Clauss G., Onorato M. Observation of dispersive shock waves developing from initial depressions in shallow water // Physica D, 2016. - http://dx.doi.org/10.1016/j.physd.2016.01.007.

Nonlinear physics of electrical wave propagation in the heart: a review

NASA Astrophysics Data System (ADS)

Alonso, Sergio; Bär, Markus; Echebarria, Blas

2016-09-01

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

Lee waves: Benign and malignant

NASA Technical Reports Server (NTRS)

Wurtele, M. G.; Datta, A.; Sharman, R. D.

1993-01-01

The flow of an incompressible fluid over an obstacle will produce an oscillation in which buoyancy is the restoring force, called a gravity wave. For disturbances of this scale, the atmosphere may be treated as dynamically incompressible, even though there exists a mean static upward density gradient. Even in the linear approximation - i.e., for small disturbances - this model explains a great many of the flow phenomena observed in the lee of mountains. However, nonlinearities do arise importantly, in three ways: (1) through amplification due to the decrease of mean density with height; (2) through the large (scaled) size of the obstacle, such as a mountain range; and (3) from dynamically singular levels in the fluid field. These effects produce a complicated array of phenomena - large departure of the streamlines from their equilibrium levels, high winds, generation of small scales, turbulence, etc. - that present hazards to aircraft and to lee surface areas. The nonlinear disturbances also interact with the larger-scale flow in such a manner as to impact global weather forecasts and the climatological momentum balance. If there is no dynamic barrier, these waves can penetrate vertically into the middle atmosphere (30-100 km), where recent observations show them to be of a length scale that must involve the coriolis force in any modeling. At these altitudes, the amplitude of the waves is very large, and the phenomena associated with these wave dynamics are being studied with a view to their potential impact on high performance aircraft, including the projected National Aerospace Plane (NASP). The presentation shows the results of analysis and of state-of-the-art numerical simulations, validated where possible by observational data, and illustrated with photographs from nature.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Solitonlike pulses along a modified Noguchi nonlinear electrical network with second-neighbor interactions: Analytical studies

NASA Astrophysics Data System (ADS)

Kengne, E.; Liu, W. M.

2018-05-01

A modified lossless nonlinear Noguchi transmission network with second-neighbor interactions is considered. In the semidiscrete limit, we apply the reductive perturbation method and show that the dynamics of modulated waves propagating through the network are governed by an NLS equation with linear external potential. Classes of exact solitonic solutions of this network equation are derived, proving possible transmission of both bright and dark solitonlike pulses through the network. The effects of both the coupling second-neighbor parameter L3 and the strength λ of the linear potential on the dynamics of modulated waves through the network are investigated. One of the main results of our work is that with the introduction of the second neighbors in the network, two solitary signals, either two bright solitary signals or one bright and one dark solitary signal, may simultaneously propagate at the same frequency through the network.

Geometric and potential dynamics interpretation of the optic ring resonator bistability

NASA Astrophysics Data System (ADS)

Chiangga, S.; Chittha, T.; Frank, T. D.

2015-07-01

The optical bistability is a fundamental nonlinear feature of the ring resonator. A geometric and potential dynamics interpretation of the bistability is given. Accordingly, the bistability of the nonlinear system is shown to be a consequence of geometric laws of vector calculus describing the resonator ring. In contrast, the so-called transcendental relations that have been obtained in the literature in order to describe the optical wave are interpreted in terms of potential dynamical systems. The proposed novel interpretation provides new insights into the nature of the ring resonator optical bistability. The fundamental work by Rukhlenko, Premaratne and Agrawal (2010) as well as a more recent study by Chiangga, Pitakwongsaporn, Frank and Yupapin (2013) are considered.

Wave Interactions and Fluid Flows

NASA Astrophysics Data System (ADS)

Craik, Alex D. D.

1988-07-01

This up-to-date and comprehensive account of theory and experiment on wave-interaction phenomena covers fluids both at rest and in their shear flows. It includes, on the one hand, water waves, internal waves, and their evolution, interaction, and associated wave-driven means flow and, on the other hand, phenomena on nonlinear hydrodynamic stability, especially those leading to the onset of turbulence. This study provide a particularly valuable bridge between these two similar, yet different, classes of phenomena. It will be of value to oceanographers, meteorologists, and those working in fluid mechanics, atmospheric and planetary physics, plasma physics, aeronautics, and geophysical and astrophysical fluid dynamics.

Metastable modular metastructures for on-demand reconfiguration of band structures and nonreciprocal wave propagation

NASA Astrophysics Data System (ADS)

Wu, Z.; Zheng, Y.; Wang, K. W.

2018-02-01

We present an approach to achieve adaptable band structures and nonreciprocal wave propagation by exploring and exploiting the concept of metastable modular metastructures. Through studying the dynamics of wave propagation in a chain composed of finite metastable modules, we provide experimental and analytical results on nonreciprocal wave propagation and unveil the underlying mechanisms that facilitate such unidirectional energy transmission. In addition, we demonstrate that via transitioning among the numerous metastable states, the proposed metastructure is endowed with a large number of bandgap reconfiguration possibilities. As a result, we illustrate that unprecedented adaptable nonreciprocal wave propagation can be realized using the metastable modular metastructure. Overall, this research elucidates the rich dynamics attainable through the combinations of periodicity, nonlinearity, spatial asymmetry, and metastability and creates a class of adaptive structural and material systems capable of realizing tunable bandgaps and nonreciprocal wave transmissions.

Influence of two-stream relativistic electron beam parameters on the space-charge wave with broad frequency spectrum formation

NASA Astrophysics Data System (ADS)

Alexander, LYSENKO; Iurii, VOLK

2018-03-01

We developed a cubic non-linear theory describing the dynamics of the multiharmonic space-charge wave (SCW), with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam (REB) parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.

Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

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

Cruz, Hans, E-mail: hans@ciencias.unam.mx; Schuch, Dieter; Castaños, Octavio, E-mail: ocasta@nucleares.unam.mx

2015-09-15

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Modulated amplitude waves in collisionally inhomogeneous Bose Einstein condensates

NASA Astrophysics Data System (ADS)

Porter, Mason A.; Kevrekidis, P. G.; Malomed, Boris A.; Frantzeskakis, D. J.

2007-05-01

We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length a subjected to a spatially periodic modulation, a=a(x)=a(x+L). This “collisionally inhomogeneous” BEC is described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of x. We transform this equation into a GP equation with a constant coefficient and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization of the Ince equation. In the small-amplitude limit, we use averaging to construct analytical solutions for modulated amplitude waves (MAWs), whose stability we subsequently examine using both numerical simulations of the original GP equation and fixed-point computations with the MAWs as numerically exact solutions. We show that “on-site” solutions, whose maxima correspond to maxima of a(x), are more robust and likely to be observed than their “off-site” counterparts.

Shapes, spectra and new methods in nonlinear spatial optics

NASA Astrophysics Data System (ADS)

Sun, Can

For a myriad of optical applications, the quality of the light source is poor and the beam is inherently spatially partially-coherent. For this broad class of systems, wave dynamics depends not only on the wave intensity, but also on its distribution of spatial frequencies. Unfortunately, this entire spectrum of problems has often been overlooked - for reasons of theoretical ease or experimental difficulties. Here, we remedy this by demonstrating a novel experimental setup which, for the first time, allows arbitrarily modulation of the spatial spectra of light to obtain any distribution of interest. Using modulation instability as an example, we isolate the effect of different spectral shapes and observe distinct beam dynamics. Next, we turn to a thermodynamic description of the long-term evolution of statistical fields. For quantum systems, a major consequence is Bose-Einstein Condensation. However, recent theoretical studies have suggested that quantum mechanics is not necessary for the condensation process: classical waves with random phases can also self-organize into a coherent state. Starting from a random ensemble, nonlinear interactions can lead to a turbulent energy cascade towards longer spatial scales. In complete analogy with the kinetics of a gas system, there is a statistical dynamics of waves in which particle velocities map to wavepacket k-vectors while collisions are mimicked by four-wave mixing. As with collisions, each wave interaction is formally reversible, yet entropy principles mandate that the ensemble evolves towards an equilibrium state of maximum disorder. The result is an equipartition of energy, in the form of a Rayleigh-Jeans spectrum, with information about the condensation process recorded in small-scale fluctuations. Here, we give the first experimental observation of the condensation of classical waves in any media. Using classical light in a self-defocusing photorefractive, we observe all aspects of the condensation process, including the population of a coherent state, spectral redistribution towards the Rayleigh-Jeans spectrum, and formal reversibility of the interactions. The latter is proved experimentally by introducing a digital "Maxwell's Demon" to reverse (phase-conjugate) the momentum of each wavepacket and recover the original "thermal cloud". The results integrate digital and physical methods of nonlinear processing, confirm fundamental ideas in wave turbulence, and greatly extend the range of Bose-Einstein theory.

Complex activity patterns in arterial wall: results from a model of calcium dynamics.

PubMed

Buchner, Teodor; Pietkun, Jakub; Kuklik, Paweł

2012-03-01

Using a dynamical model of smooth muscle cells in an arterial wall, defined as a system of coupled five-dimensional nonlinear oscillators, on a grid with cylindrical symmetry, we compare the admissible activity patterns with those known from the heart tissue. We postulate on numerical basis the possibility to induce a stable spiral wave in the arterial wall. Such a spiral wave can inhibit the propagation of the axial calcium wave and effectively stop the vasomotion. We also discuss the dynamics of the circumferential calcium wave in comparison to rotors in venous ostia that are a common source of supraventricular ectopy. We show that the velocity and in consequence the frequency range of the circumferential calcium wave is by orders of magnitude too small compared to that of the rotors. The mechanism of the rotor is not likely to involve the calcium-related dynamics of the smooth muscle cells. The calcium-related dynamics which is voltage-independent and hard to be reset seems to actually protect the blood vessels against the electric activity of the atria. We also discuss the microreentry phenomenon, which was found in numerical experiments in the studied model.

Optical turbulence and transverse rogue waves in a cavity with triple-quantum-dot molecules

NASA Astrophysics Data System (ADS)

Eslami, M.; Khanmohammadi, M.; Kheradmand, R.; Oppo, G.-L.

2017-09-01

We show that optical turbulence extreme events can exist in the transverse dynamics of a cavity containing molecules of triple quantum dots under conditions close to tunneling-induced transparency. These nanostructures, when coupled via tunneling, form a four-level configuration with tunable energy-level separations. We show that such a system exhibits multistability and bistability of Turing structures in instability domains with different critical wave vectors. By numerical simulation of the mean-field equation that describes the transverse dynamics of the system, we show that the simultaneous presence of two transverse solutions with opposite nonlinearities gives rise to a series of turbulent structures with the capability of generating two-dimensional rogue waves.

Evolution of rogue waves in dusty plasmas

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

Tolba, R. E., E-mail: tolba-math@yahoo.com; El-Bedwehy, N. A., E-mail: nab-elbedwehy@yahoo.com; Moslem, W. M., E-mail: wmmoslem@hotmail.com

2015-04-15

The evolution of rogue waves associated with the dynamics of positively charged dust grains that interact with streaming electrons and ions is investigated. Using a perturbation method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE). The rational solution of the NLSE is presented, which proposed as an effective tool for studying the rogue waves in Jupiter. It is found that the existence region of rogue waves depends on the dust-acoustic speed and the streaming densities of the ions and electrons. Furthermore, the supersonic rogue waves are much taller than the subsonic rogue waves bymore » ∼25 times.« less

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.

Regular and chaotic dynamics of non-spherical bodies. Zeldovich's pancakes and emission of very long gravitational waves

NASA Astrophysics Data System (ADS)

Bisnovatyi-Kogan, G. S.; Tsupko, O. Yu.

2015-10-01

> In this paper we review a recently developed approximate method for investigation of dynamics of compressible ellipsoidal figures. Collapse and subsequent behaviour are described by a system of ordinary differential equations for time evolution of semi-axes of a uniformly rotating, three-axis, uniform-density ellipsoid. First, we apply this approach to investigate dynamic stability of non-spherical bodies. We solve the equations that describe, in a simplified way, the Newtonian dynamics of a self-gravitating non-rotating spheroidal body. We find that, after loss of stability, a contraction to a singularity occurs only in a pure spherical collapse, and deviations from spherical symmetry prevent the contraction to the singularity through a stabilizing action of nonlinear non-spherical oscillations. The development of instability leads to the formation of a regularly or chaotically oscillating body, in which dynamical motion prevents the formation of the singularity. We find regions of chaotic and regular pulsations by constructing a Poincaré diagram. A real collapse occurs after damping of the oscillations because of energy losses, shock wave formation or viscosity. We use our approach to investigate approximately the first stages of collapse during the large scale structure formation. The theory of this process started from ideas of Ya. B. Zeldovich, concerning the formation of strongly non-spherical structures during nonlinear stages of the development of gravitational instability, known as `Zeldovich's pancakes'. In this paper the collapse of non-collisional dark matter and the formation of pancake structures are investigated approximately. Violent relaxation, mass and angular momentum losses are taken into account phenomenologically. We estimate an emission of very long gravitational waves during the collapse, and discuss the possibility of gravitational lensing and polarization of the cosmic microwave background by these 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.

Postmenopausal estrogen therapy modulates nocturnal nonlinear heart rate dynamics.

PubMed

Virtanen, Irina; Ekholm, Eeva; Polo-Kantola, Päivi; Hiekkanen, Heikki; Huikuri, Heikki

2008-01-01

To study the effects of postmenopausal estrogen therapy (ET) on nocturnal nonlinear heart rate variability (HRV). In this prospective, randomized, double-blind, placebo-controlled study, 71 healthy hysterectomized postmenopausal women received either transdermal estradiol or placebo for 3 months. After a washout period of 1 month, the treatments were reversed. Sleep studies were performed after both treatment periods. One steady-state epoch per night of the awake state, stage 2 (light) non-rapid eye movement (REM) sleep, stage 3-4 (deep) non-REM sleep, also known as slow-wave sleep, and REM sleep was extracted. From the electrocardiogram, nonlinear HRV was analyzed as the fractal scaling exponents alpha1 and alpha2, approximate entropy (ApEn), and the Poincaré plot variability coefficients SD1 and SD2. These were correlated to ET use in both different sleep stages and averaged across all sleep stages. During ET, the nocturnal ApEn decreased from 0.80 +/- 0.01 to 0.74 +/- 0.02 (P < 0.05), the most marked reduction occurring during slow-wave sleep (from 0.77 +/- 0.05 to 0.63 +/- 0.06, P < 0.05). In addition, SD2 decreased in slow-wave sleep and REM sleep during ET (P < 0.05 for both). In light non-REM sleep, alpha1 slightly increased during ET (P < 0.05). ET has a slightly but distinctively attenuating effect on some nocturnal nonlinear measures of HRV, especially on complexity of heart rate dynamics. This implies that ET may have potentially deleterious effects on cardiovascular health during sleep.

Wave effects on ocean-ice interaction in the marginal ice zone

NASA Technical Reports Server (NTRS)

Liu, Antony K.; Hakkinen, Sirpa; Peng, Chih Y.

1993-01-01

The effects of wave train on ice-ocean interaction in the marginal ice zone are studied through numerical modeling. A coupled two-dimensional ice-ocean model has been developed to include wave effects and wind stress for the predictions of ice edge dynamics. The sea ice model is coupled to the reduced-gravity ocean model through interfacial stresses. The main dynamic balance in the ice momentum is between water-ice stress, wind stress, and wave radiation stresses. By considering the exchange of momentum between waves and ice pack through radiation stress for decaying waves, a parametric study of the effects of wave stress and wind stress on ice edge dynamics has been performed. The numerical results show significant effects from wave action. The ice edge is sharper, and ice edge meanders form in the marginal ice zone owing to forcing by wave action and refraction of swell system after a couple of days. Upwelling at the ice edge and eddy formation can be enhanced by the nonlinear effects of wave action; wave action sharpens the ice edge and can produce ice meandering, which enhances local Ekman pumping and pycnocline anomalies. The resulting ice concentration, pycnocline changes, and flow velocity field are shown to be consistent with previous observations.

Nonlinear Dynamics of Cantilever-Sample Interactions in Atomic Force Microscopy

NASA Technical Reports Server (NTRS)

Cantrell, John H.; Cantrell, Sean A.

2010-01-01

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

Mesospheric Non-Migrating Tides Generated With Planetary Waves. 1; Characteristics

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Mengel, J. G.; Talaat, E. L.; Porter, H. S.; Chan, K. L.

2003-01-01

We discuss results from a modeling study with our Numerical Spectral Model (NSM) that specifically deals with the non-migrating tides generated in the mesosphere. The NSM extends from the ground to the thermosphere, incorporates Hines' Doppler Spread Parameterization for small-scale gravity waves (GWs), and it describes the major dynamical features of the atmosphere including the wave driven equatorial oscillations (QBO and SAO), and the seasonal variations of tides and planetary waves. Accounting solely for the excitation sources of the solar migrating tides, the NSM generates through dynamical interactions also non-migrating tides in the mesosphere that are comparable in magnitude to those observed. Large non-migrating tides are produced in the diurnal and semi-diurnal oscillations for the zonal mean (m = 0) and in the semidiurnal oscillation for m = 1. In general, significant eastward and westward propagating tides are generated for all the zonal wave numbers m = 1 to 4. To identify the cause, the NSM is run without the solar heating for the zonal mean (m = 0), and the amplitudes of the resulting non-migrating tides are then negligibly small. In this case, the planetary waves are artificially suppressed, which are generated in the NSM through instabilities. This leads to the conclusion that the non-migrating tides are generated through non-linear interactions between planetary waves and migrating tides, as Forbes et al. and Talaat and Liberman had proposed. In an accompanying paper, we present results from numerical experiments, which indicate that gravity wave filtering contributes significantly to produce the non-linear coupling that is involved.

Liquid Sloshing Dynamics

NASA Astrophysics Data System (ADS)

Ibrahim, Raouf A.

2005-06-01

The problem of liquid sloshing in moving or stationary containers remains of great concern to aerospace, civil, and nuclear engineers; physicists; designers of road tankers and ship tankers; and mathematicians. Beginning with the fundamentals of liquid sloshing theory, this book takes the reader systematically from basic theory to advanced analytical and experimental results in a self-contained and coherent format. The book is divided into four sections. Part I deals with the theory of linear liquid sloshing dynamics; Part II addresses the nonlinear theory of liquid sloshing dynamics, Faraday waves, and sloshing impacts; Part III presents the problem of linear and nonlinear interaction of liquid sloshing dynamics with elastic containers and supported structures; and Part IV considers the fluid dynamics in spinning containers and microgravity sloshing. This book will be invaluable to researchers and graduate students in mechanical and aeronautical engineering, designers of liquid containers, and applied mathematicians.

A hierarchy for modeling high speed propulsion systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Deabreu, Alex

1991-01-01

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery, such as inlets, ramjets, and scramjets. The discussion is separated into four areas: (1) computational fluid dynamics models for the entire nonlinear system or high order nonlinear models; (2) high order linearized models derived from fundamental physics; (3) low order linear models obtained from the other high order models; and (4) low order nonlinear models (order here refers to the number of dynamic states). Included in the discussion are any special considerations based on the relevant control system designs. The methods discussed are for the quasi-one-dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, including moving normal shocks, hammershocks, simple subsonic combustion via heat addition, temperature dependent gases, detonations, and thermal choking. The report also contains a comprehensive list of papers and theses generated by this grant.

Nonlinear vibration and radiation from a panel with transition to chaos

NASA Technical Reports Server (NTRS)

Maestrello, Lucio; Frendi, Abdelkader; Brown, Donald E.

1992-01-01

The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling), and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance bifurcation is diffused and difficult to maintain; thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on an aluminum panel and a graphite epoxy panel having the same size and weight. Good agreement is obtained betwen the experimental and numerical results.

Supratransmission in a metastable modular metastructure for tunable non-reciprocal wave transmission

NASA Astrophysics Data System (ADS)

Wu, Zhen; Wang, K. W.

2018-03-01

In this research, we numerically and analytically investigate the nonlinear energy transmission phenomenon in a metastable modular metastructure. Numerical studies on a 1D metastable chain provide clear evidence that when driving frequency is within the stopband of the periodic structure, there exists a threshold for the driving amplitude, above which sudden increase in the energy transmission can be observed. This onset of transmission is due to nonlinear instability and is known as supratransmission. We discover that due to spatial asymmetry of strategically configured constituents, such transmission thresholds are considerably different when structure is excited from different ends and this discrepancy creates a region of non-reciprocal energy transmission. We demonstrate that when the loss of stability is due to saddlenode bifurcation, the transmission threshold can be predicted analytically using a localized nonlinear-linear system model, and analyzed via combining harmonic balancing and transfer matrix methods. These investigations elucidate the rich and complex dynamics achievable by nonlinearity and metastabilities, and provide synthesize tools for tunable bandgaps and non-reciprocal wave transmissions.

A class of high resolution explicit and implicit shock-capturing methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1989-01-01

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

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

Interactions of solitary waves and compression/expansion waves in core-annular flows

NASA Astrophysics Data System (ADS)

Maiden, Michelle; Anderson, Dalton; El, Gennady; Franco, Nevil; Hoefer, Mark

2017-11-01

The nonlinear hydrodynamics of an initial step leads to the formation of rarefaction waves and dispersive shock waves in dispersive media. Another hallmark of these media is the soliton, a localized traveling wave whose speed is amplitude dependent. Although compression/expansion waves and solitons have been well-studied individually, there has been no mathematical description of their interaction. In this talk, the interaction of solitons and shock/rarefaction waves for interfacial waves in viscous, miscible core-annular flows are modeled mathematically and explored experimentally. If the interior fluid is continuously injected, a deformable conduit forms whose interfacial dynamics are well-described by a scalar, dispersive nonlinear partial differential equation. The main focus is on interactions of solitons with dispersive shock waves and rarefaction waves. Theory predicts that a soliton can either be transmitted through or trapped by the extended hydrodynamic state. The notion of reciprocity is introduced whereby a soliton interacts with a shock wave in a reciprocal or dual fashion as with the rarefaction. Soliton reciprocity, trapping, and transmission are observed experimentally and are found to agree with the modulation theory and numerical simulations. This work was partially supported by NSF CAREER DMS-1255422 (M.A.H.) and NSF GRFP (M.D.M.).

Hurricane genesis: on the breaking African easterly waves and critical layers

NASA Astrophysics Data System (ADS)

Asaadi, Ali; Brunet, Gilbert; Yau, Peter

2015-04-01

This study bring new understanding on the decades-old hurricane genesis problem that starts with westward travelling African easterly waves that can evolve into coherent cyclonic vortices depending on their strength and other nonlinear wave breaking processes. In general, observations indicate that only a small fraction of the African easterly waves that occur in a single hurricane season contribute to tropical cyclogenesis. However, this small fraction includes a large portion of named storms. In addition, a recent study by Dunkerton et al. (2009) has shown that named storms in the Atlantic and eastern Pacific basins are almost all associated with a cyclonic Kelvin "cat's eye" of a tropical easterly wave typical of critical layers, located equatorward of the easterly jet axis. To better understand the dynamics involved in hurricane genesis, the flow characteristics and the physical and dynamical mechanisms by which easterly waves form cat's eyes are investigated with the help of atmospheric reanalyzes and numerical simulations. We perform a climatological study of developing easterly waves covering the 1998-2001 hurricane seasons using ERA-Interim 6-hourly reanalysis data. Composite analyses for all named storms show a monotonic potential vorticity (PV) profile with weak meridional PV gradient and a cyclonic (i.e., south of the easterly jet axis) critical line for time periods of several days preceding the cat's eye formation. In addition, the developing PV anomaly composite shows a statistically significant companion wave-packet of non-developing easterly waves. A barotropic shallow water model is used to study the initial value and forced problems of disturbances on a parabolic jet and realistic profiles associated with weak basic state meridional PV gradients, leading to Kelvin cat's eye formation around the jet axis. The results highlight the synergy of the dynamical mechanisms, including wave breaking and PV redistribution within the nonlinear critical layer characterized by weak PV gradients, and the thermodynamical mechanisms such as convectively generated PV anomalies in the cat's eye formation in tropical cyclogenesis. These findings are consistent with the analytical theory of free and forced disturbances to an easterly parabolic jet (Brunet and Warn, 1990; Brunet and Haynes, 1995; Choboter et al., 2000). 1) Dunkerton, T. J., M. T. Montgomery, and Z. Wang, 2009: Tropical cyclogenesis in a tropical wave critical layer: Easterly waves. Atmos. Chem. Phys., 9, 5587-5646. 2) Brunet, G., and T. Warn, 1990: Rossby Wave Critical Layers on a Jet. J. Atmos. Sci., 47, 1173-1178. 3) Brunet, and P. H. Haynes, 1995: The Nonlinear Evolution of Disturbances to a Parabolic Jet. J. Atmos. Sci., 52, 464-477. 4) Choboter, P. F., G. Brunet, and S. A. Maslowe, 2000: Forced Disturbances in a Zero Absolute Vorticity Gradient Environment. J. Atmos. Sci., 57, 1406-1419.

Relativistic cosmic-ray spectra in the fully nonlinear theory of shock acceleration

NASA Technical Reports Server (NTRS)

Ellison, D. C.; Eichler, D.

1985-01-01

The non-linear theory of shock acceleration was generalized to include wave dynamics. In the limit of rapid wave damping, it is found that a finite wave velocity tempers the acceleration of high Mach number shocks and limits the maximum compression ratio even when energy loss is important. For a given spectrum, the efficiency of relativistic particle production is essentially independent of v sub Ph. For the three families shown, the percentage of kinetic energy flux going into relativistic particles is (1) 72 percent, (2) 44 percent, and (3) 26 percent (this includes the energy loss at the upper energy cutoff). Even small v sub ph, typical of the HISM, produce quasi-universal spectra that depend only weakly on the acoustic Mach number. These spectra should be close enough to e(-2) to satisfy cosmic ray source requirements.

Dynamic of solitary wave solutions in some nonlinear pseudoparabolic models and Dodd-Bullough-Mikhailov equation

NASA Astrophysics Data System (ADS)

Ilhan, O. A.; Bulut, H.; Sulaiman, T. A.; Baskonus, H. M.

2018-02-01

In this study, the modified exp ( - Φ (η )) -expansion function method is used in constructing some solitary wave solutions to the Oskolkov-Benjamin-Bona-Mahony-Burgers, one-dimensional Oskolkov equations and the Dodd-Bullough-Mikhailov equation. We successfully construct some singular solitons and singular periodic waves solutions with the hyperbolic, trigonometric and exponential function structures to these three nonlinear models. Under the choice of some suitable values of the parameters involved, we plot the 2D and 3D graphics to some of the obtained solutions in this study. All the obtained solutions in this study verify their corresponding equation. We perform all the computations in this study with the help of the Wolfram Mathematica software. The obtained solutions in this study may be helpful in explaining some practical physical problems.

A programmable nonlinear acoustic metamaterial

NASA Astrophysics Data System (ADS)

Yang, Tianzhi; Song, Zhi-Guang; Clerkin, Eoin; Zhang, Ye-Wei; Sun, Jia-He; Su, Yi-Shu; Chen, Li-Qun; Hagedorn, Peter

2017-09-01

Acoustic metamaterials with specifically designed lattices can manipulate acoustic/elastic waves in unprecedented ways. Whereas there are many studies that focus on passive linear lattice, with non-reconfigurable structures. In this letter, we present the design, theory and experimental demonstration of an active nonlinear acoustic metamaterial, the dynamic properties of which can be modified instantaneously with reversibility. By incorporating active and nonlinear elements in a single unit cell, a real-time tunability and switchability of the band gap is achieved. In addition, we demonstrate a dynamic "editing" capability for shaping transmission spectra, which can be used to create the desired band gap and resonance. This feature is impossible to achieve in passive metamaterials. These advantages demonstrate the versatility of the proposed device, paving the way toward smart acoustic devices, such as logic elements, diode and transistor.

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.

Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.

2018-05-01

A fully nonlinear model of Choi and Camassa (1999) describing one-dimensional incompressible dynamics of two non-mixing fluids in a horizontal channel, under a shallow water approximation, is considered. An equivalence transformation is presented, leading to a special dimensionless form of the system, involving a single dimensionless constant physical parameter, as opposed to five parameters present in the original model. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of physically meaningful exact closed-form solutions of the two-fluid model are derived, corresponding to periodic, solitary, and kink-type bidirectional traveling waves; specific examples are given, and properties of the exact solutions are analyzed.

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.

Nonlinear dynamic response of a uni-directional model for the tile/pad space shuttle thermal protection system

NASA Technical Reports Server (NTRS)

Housner, J. M.; Edighoffer, H. H.; Park, K. C.

1980-01-01

A unidirectional analysis of the nonlinear dynamic behavior of the space shuttle tile/pad thermal protection system is developed and examined for imposed sinusoidal and random motions of the shuttle skin and/or applied tile pressure. The analysis accounts for the highly nonlinear stiffening hysteresis and viscous behavior of the pad which joins the tile to the shuttle skin. Where available, experimental data are used to confirm the validity of the analysis. Both analytical and experimental studies reveal that the system resonant frequency is very high for low amplitude oscillations but decreases rapidly to a minimum value with increasing amplitude. Analytical studies indicate that with still higher amplitude the resonant frequency increases slowly. The nonlinear pad is also responsible for the analytically and experimentally observed distorted response wave shapes having high sharp peaks when the system is subject to sinusoidal loads. Furthermore, energy dissipation in the pad is studied analytically and it is found that the energy dissipated is sufficiently high to cause rapid decay of dynamic transients. Nevertheless, the sharp peaked nonlinear responses of the system lead to higher magnification factors than would be expected in such a highly damped linear system.

Rogue waves and lump solitons for a ?-dimensional B-type Kadomtsev-Petviashvili equation in fluid dynamics

NASA Astrophysics Data System (ADS)

Sun, Yan; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Yin, Hui-Min

2018-07-01

Under investigation is a ?-dimensional B-type Kadomtsev-Petviashvili equation, which has applications in the propagation of non-linear waves in fluid dynamics. Through the Hirota method and the extended homoclinic test technique, we obtain the breather-type kink soliton solutions and breather rational soliton solutions. Rogue wave solutions are derived, which come from the derivation of breather rational solitons with respect to x. Amplitudes of the breather-type kink solitons and rogue waves decrease with a non-zero parameter in the equation, ?, increasing when ?. In addition, dark rogue waves are derived when ?. Furthermore, with the aid of the Hirota method and symbolic computation, two types of the lump solitons are obtained with the different choices of the parameters. We graphically study the lump solitons related to the parameter ?, and amplitude of the lump soliton is negatively correlated with ? when ?.

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

PubMed

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

2014-12-31

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

Nonlinear dynamics of the 3D FMS and Alfven wave beams propagating in plasma of ionosphere and magnetosphere

NASA Astrophysics Data System (ADS)

Belashov, Vasily

We study the formation, structure, stability and dynamics of the multidimensional soliton-like beam structures forming on the low-frequency branch of oscillation in the ionospheric and magnetospheric plasma for cases when beta=4pinT/B(2) <<1 and beta>1. In first case with the conditions omega>{k_{yz}}(2,) v_{x}$<

A Fluid Dynamic Approach to the Dust-Acoustic Soliton

NASA Astrophysics Data System (ADS)

McKenzie, J. F.; Doyle, T. B.

2002-12-01

The properties of dust-acoustic solitons are derived from a fluid dynamic viewpoint in which conservation of total momentum, combined with the Bernoulli-like energy equations for each species, yields the structure equation for the heavy (or dust) speed in the stationary wave. This fully nonlinear approach reveals the crucial role played by the heavy sonic point in limiting the collective dust-acoustic Mach number, above which solitons cannot exist. An exact solution illustrates that the cold heavy species is compressed and this implies concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave.

Semiconductor Laser Complex Dynamics: From Optical Neurons to Optical Rogue Waves

DTIC Science & Technology

2017-02-11

laser dynamics for innovative applications. The results of the project were published in 5 high- impact journal papers and were presented as invited or...stochastic phenomena and ii) to exploit the laser dynamics for innovative applications. The results of the project were published in 5 high-impact...RESULTS AND DISCUSSION The results of our research were published in 5 articles in high-impact journals in the fields of photonics and nonlinear physics

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation.

PubMed

Liu, Wei; Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation

PubMed Central

Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota’s bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides. PMID:29432495

Single evolution equation in a light-matter pairing system

NASA Astrophysics Data System (ADS)

Bugaychuk, S.; Tobisch, E.

2018-03-01

The coupled system including wave mixing and nonlinear dynamics of a nonlocal optical medium is usually studied (1) numerically, with the medium being regarded as a black box, or (2) experimentally, making use of some empirical assumptions. In this paper we deduce for the first time a single evolution equation describing the dynamics of the pairing system as a holistic complex. For a non-degenerate set of parameters, we obtain the nonlinear Schrödinger equation with coefficients being written out explicitly. Analytical solutions of this equation can be experimentally realized in any photorefractive medium, e.g. in photorefractive, liquid or photonic crystals. For instance, a soliton-like solution can be used in dynamical holography for designing an artificial grating with maximal amplification of an image.

The effect of reflector geometry on the acoustic field and bubble dynamics produced by an electrohydraulic shock wave lithotripter.

PubMed

Zhou, Yufeng; Zhong, Pei

2006-06-01

A theoretical model for the propagation of shock wave from an axisymmetric reflector was developed by modifying the initial conditions for the conventional solution of a nonlinear parabolic wave equation (i.e., the Khokhlov-Zabolotskaya-Kuznestsov equation). The ellipsoidal reflector of an HM-3 lithotripter is modeled equivalently as a self-focusing spherically distributed pressure source. The pressure wave form generated by the spark discharge of the HM-3 electrode was measured by a fiber optic probe hydrophone and used as source conditions in the numerical calculation. The simulated pressure wave forms, accounting for the effects of diffraction, nonlinearity, and thermoviscous absorption in wave propagation and focusing, were compared with the measured results and a reasonably good agreement was found. Furthermore, the primary characteristics in the pressure wave forms produced by different reflector geometries, such as that produced by a reflector insert, can also be predicted by this model. It is interesting to note that when the interpulse delay time calculated by linear geometric model is less than about 1.5 micros, two pulses from the reflector insert and the uncovered bottom of the original HM-3 reflector will merge together. Coupling the simulated pressure wave form with the Gilmore model was carried out to evaluate the effect of reflector geometry on resultant bubble dynamics in a lithotripter field. Altogether, the equivalent reflector model was found to provide a useful tool for the prediction of pressure wave form generated in a lithotripter field. This model may be used to guide the design optimization of reflector geometries for improving the performance and safety of clinical lithotripters.

The effect of reflector geometry on the acoustic field and bubble dynamics produced by an electrohydraulic shock wave lithotripter

PubMed Central

Zhou, Yufeng; Zhong, Pei

2007-01-01

A theoretical model for the propagation of shock wave from an axisymmetric reflector was developed by modifying the initial conditions for the conventional solution of a nonlinear parabolic wave equation (i.e., the Khokhlov–Zabolotskaya–Kuznestsov equation). The ellipsoidal reflector of an HM-3 lithotripter is modeled equivalently as a self-focusing spherically distributed pressure source. The pressure wave form generated by the spark discharge of the HM-3 electrode was measured by a fiber optic probe hydrophone and used as source conditions in the numerical calculation. The simulated pressure wave forms, accounting for the effects of diffraction, nonlinearity, and thermoviscous absorption in wave propagation and focusing, were compared with the measured results and a reasonably good agreement was found. Furthermore, the primary characteristics in the pressure wave forms produced by different reflector geometries, such as that produced by a reflector insert, can also be predicted by this model. It is interesting to note that when the interpulse delay time calculated by linear geometric model is less than about 1.5 μs, two pulses from the reflector insert and the uncovered bottom of the original HM-3 reflector will merge together. Coupling the simulated pressure wave form with the Gilmore model was carried out to evaluate the effect of reflector geometry on resultant bubble dynamics in a lithotripter field. Altogether, the equivalent reflector model was found to provide a useful tool for the prediction of pressure wave form generated in a lithotripter field. This model may be used to guide the design optimization of reflector geometries for improving the performance and safety of clinical lithotripters. PMID:16838506

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.

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

Density waves in granular flow

NASA Astrophysics Data System (ADS)

Herrmann, H. J.; Flekkøy, E.; Nagel, K.; Peng, G.; Ristow, G.

Ample experimental evidence has shown the existence of spontaneous density waves in granular material flowing through pipes or hoppers. Using Molecular Dynamics Simulations we show that several types of waves exist and find that these density fluctuations follow a 1/f spectrum. We compare this behaviour to deterministic one-dimensional traffic models. If positions and velocities are continuous variables the model shows self-organized criticality driven by the slowest car. We also present Lattice Gas and Boltzmann Lattice Models which reproduce the experimentally observed effects. Density waves are spontaneously generated when the viscosity has a nonlinear dependence on density which characterizes granular flow.

A numerical investigation on the influence of engine shape and mixing processes on wave engine performance

NASA Astrophysics Data System (ADS)

Erickson, Robert R.

Wave engines are a class of unsteady, air-breathing propulsion devices that use an intermittent combustion process to generate thrust. The inherently simple mechanical design of the wave engine allows for a relatively low cost per unit propulsion system, yet unsatisfactory overall performance has severely limited the development of commercially successful wave engines. The primary objective of this investigation was to develop a more detailed physical understanding of the influence of gas dynamic nonlinearities, unsteady combustion processes, and engine shape on overall wave engine performance. Within this study, several numerical models were developed and applied to wave engines and related applications. The first portion of this investigation examined the influence of duct shape on driven oscillations in acoustic compression devices, which represent a simplified physical system closely related in several ways to the wave engine. A numerical model based on an application of the Galerkin method was developed to simulate large amplitude, one-dimensional acoustic waves driven in closed ducts. Results from this portion of the investigation showed that gas-dynamic nonlinearities significantly influence the properties of driven oscillations by transferring acoustic energy from the fundamental driven mode into higher harmonic modes. The second portion of this investigation presented and analyzed results from a numerical model of wave engine dynamics based on the quasi one-dimensional conservation equations in addition to separate sub-models for mixing and heat release. This model was then used to perform parametric studies of the characteristics of mixing and engine shape. The objectives of these studies were to determine the influence of mixing characteristics and engine shape on overall wave engine performance and to develop insight into the physical processes controlling overall performance trends. Results from this model showed that wave engine performance was strongly dependent on the coupling between the unsteady heat release that drives oscillations in the engine and the characteristics that determine the acoustic properties of the engine such as engine shape and mean property gradients. Simulation results showed that average thrust generation decreased dramatically when the natural acoustic mode frequencies of the engine and the frequency content of the unsteady heat release were not aligned.

Dynamical Signatures of Living Systems

NASA Technical Reports Server (NTRS)

Zak, M.

1999-01-01

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Dynamics of Ultrasound Contrast Agents and Nonlinear Acoustic Waves: Experiments, Modeling, and Theories

NASA Astrophysics Data System (ADS)

Xia, Lang

Bubbles occur in many natural and biological flows as well as in numerous industrial phenomena, such as pumps, propellers, turbines, and chemical processing plants. They have been widely studied in the past leading to a large body of literature. However, bubbles appearing in different situations differ significantly in their physical characteristics and behaviors. Recently, bubbles of diameter less than 10 micrometers have found applications in diagnostic ultrasound imaging. These microbubble-based ultrasound contrast agents (UCA) are intravenously administered in patients before ultrasound imaging. Due to the compressive gas core, they generate substantial ultrasound echoes leading to significant enhancement of image quality and contrast. Free bubbles of a micrometer diameter experience a large surface tension induced Laplace pressure leading to their quick dissolution in milliseconds. UCAs are stabilized by coating them with a shell of lipids, polymers, proteins, and other surface-active materials and changing the gas content from air to a high molecular weight low solubility gas such as perfluorocarbon. The past literature of bubble dynamics are mostly restricted to free bubbles. The stabilizing shell of UCAs, however, critically affects their dynamics. In this thesis, we performed acoustic characterization of several UCAs coated with polymer and lipids. We experimentally measured their acoustic attenuation and scattering, of which the data were used in mathematical models to determine shell properties and nonlinear dynamics. Several different interfacial rheological models were employed. Experimental acoustic characterization was also extended to a novel type of nanoparticle suspension--polymersomes, vesicles encapsulated by amphiphilic polymers. The later part of the thesis is devoted to modeling the effects of the presence of coated microbubbles to the overall effective bulk properties of bubbly liquids. Introduction of microbubbles in the liquids does not only modify the bulk properties of the medium (bubbly liquids) but also significantly changes the natures of the propagating waves (e.g., the sound velocity in bubble suspension was found to be as low as 20 m/s). We investigate the nonlinear nature of the acoustic wave in bubbly liquids. Specifically, we theoretically show that microbubbles could change the nonlinearity of the medium, characterized by quantity B/A.

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

NASA Technical Reports Server (NTRS)

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

2013-01-01

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

Nonlinear effects in the radiation force generated by amplitude-modulated focused beams

NASA Astrophysics Data System (ADS)

González, Nuria; Jiménez, Noé; Redondo, Javier; Roig, Bernardino; Picó, Rubén; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.; Camarena, Francisco

2012-10-01

Harmonic Motion Imaging (HMI) uses an amplitude-modulated (AM) beam to induce an oscillatory radiation force before, during and after ablation. In this paper, the findings from a numerical analysis of the effects related with the nonlinear propagation of AM focused ultrasonic beams in water on the radiation force and the location of its maxima will be presented. The numerical modeling is performed using the KZK nonlinear parabolic equation. The radiation force is generated by a focused transducer with a gain of 18, a carrier frequency of 1 MHz and a modulation frequency of 25 kHz. The modulated excitation generates a spatially-invariant force proportional to the intensity. Regarding the nonlinear wave propagation, the force is no longer proportional to the intensity, reaching a factor of eight between the nonlinear and linear estimations. Also, a 9 mm shift in the on-axis force peak occurs when the initial pressure increased from 1 to 300 kPa. This spatial shift, due to the nonlinear effects, becomes dynamic in AM focused beams, as the different signal periods have different amplitudes. This study shows that both the value and the spatial position of the force peak are affected by the nonlinear propagation of the ultrasonic waves.

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.

Formation of large-scale structures with sharp density gradient through Rayleigh-Taylor growth in a two-dimensional slab under the two-fluid and finite Larmor radius effects

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

Goto, R.; Hatori, T.; Miura, H., E-mail: miura.hideaki@nifs.ac.jp

Two-fluid and the finite Larmor effects on linear and nonlinear growth of the Rayleigh-Taylor instability in a two-dimensional slab are studied numerically with special attention to high-wave-number dynamics and nonlinear structure formation at a low β-value. The two effects stabilize the unstable high wave number modes for a certain range of the β-value. In nonlinear simulations, the absence of the high wave number modes in the linear stage leads to the formation of the density field structure much larger than that in the single-fluid magnetohydrodynamic simulation, together with a sharp density gradient as well as a large velocity difference. Themore » formation of the sharp velocity difference leads to a subsequent Kelvin-Helmholtz-type instability only when both the two-fluid and finite Larmor radius terms are incorporated, whereas it is not observed otherwise. It is shown that the emergence of the secondary instability can modify the outline of the turbulent structures associated with the primary Rayleigh-Taylor instability.« less

Modelling non-hydrostatic processes in sill regions

NASA Astrophysics Data System (ADS)

Souza, A.; Xing, J.; Davies, A.; Berntsen, J.

2007-12-01

We use a non-hydrostatic model to compute tidally induced flow and mixing in the region of bottom topography representing the sill at the entrance to Loch Etive (Scotland). This site is chosen since detailed measurements were recently made there. With non-hydrostatic dynamics in the model our results showed that the model could reproduce the observed flow characteristics, e.g., hydraulic transition, flow separation and internal waves. However, when calculations were performed using the model in the hydrostatic form, significant artificial convective mixing occurred. This influenced the computed temperature and flow field. We will discuss in detail the effects of non-hydrostatic dynamics on flow over the sill, especially investigate non-linear and non-hydrostatic contributions to modelled internal waves and internal wave energy fluxes.

Large Amplitude Whistler Waves and Electron Acceleration in the Earth's Radiation Belts: A Review of STEREO and Wind Observations

NASA Technical Reports Server (NTRS)

Cattell, Cynthia; Breneman, A.; Goetz, K.; Kellogg, P.; Kersten, K.; Wygant, J.; Wilson, L. B., III; Looper, Mark D.; Blake, J. Bernard; Roth, I.

2012-01-01

One of the critical problems for understanding the dynamics of Earth's radiation belts is determining the physical processes that energize and scatter relativistic electrons. We review measurements from the Wind/Waves and STEREO S/Waves waveform capture instruments of large amplitude whistler-mode waves. These observations have provided strong evidence that large amplitude (100s mV/m) whistler-mode waves are common during magnetically active periods. The large amplitude whistlers have characteristics that are different from typical chorus. They are usually nondispersive and obliquely propagating, with a large longitudinal electric field and significant parallel electric field. We will also review comparisons of STEREO and Wind wave observations with SAMPEX observations of electron microbursts. Simulations show that the waves can result in energization by many MeV and/or scattering by large angles during a single wave packet encounter due to coherent, nonlinear processes including trapping. The experimental observations combined with simulations suggest that quasilinear theoretical models of electron energization and scattering via small-amplitude waves, with timescales of hours to days, may be inadequate for understanding radiation belt dynamics.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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

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

USGS Publications Warehouse

Geist, Eric L.

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Geist, Eric L.

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

Geist, Eric L.

2018-04-01

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

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.

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

NASA Astrophysics Data System (ADS)

Shurgalina, E. G.

2018-02-01

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

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

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

Bierwage, Andreas; Shinohara, Kouji

2016-04-15

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

Dynamic characteristics and simplified numerical methods of an all-vertical-piled wharf in offshore deep water

NASA Astrophysics Data System (ADS)

Zhang, Hua-qing; Sun, Xi-ping; Wang, Yuan-zhan; Yin, Ji-long; Wang, Chao-yang

2015-10-01

There has been a growing trend in the development of offshore deep-water ports in China. For such deep sea projects, all-vertical-piled wharves are suitable structures and generally located in open waters, greatly affected by wave action. Currently, no systematic studies or simplified numerical methods are available for deriving the dynamic characteristics and dynamic responses of all-vertical-piled wharves under wave cyclic loads. In this article, we compare the dynamic characteristics of an all-vertical-piled wharf with those of a traditional inshore high-piled wharf through numerical analysis; our research reveals that the vibration period of an all-vertical-piled wharf under cyclic loading is longer than that of an inshore high-piled wharf and is much closer to the period of the loading wave. Therefore, dynamic calculation and analysis should be conducted when designing and calculating the characteristics of an all-vertical-piled wharf. We establish a dynamic finite element model to examine the dynamic response of an all-vertical-piled wharf under wave cyclic loads and compare the results with those under wave equivalent static load; the comparison indicates that dynamic amplification of the structure is evident when the wave dynamic load effect is taken into account. Furthermore, a simplified dynamic numerical method for calculating the dynamic response of an all-vertical-piled wharf is established based on the P-Y curve. Compared with finite element analysis, the simplified method is more convenient to use and applicable to large structural deformation while considering the soil non-linearity. We confirmed that the simplified method has acceptable accuracy and can be used in engineering applications.

Three-dimensional wave evolution on electrified falling films

NASA Astrophysics Data System (ADS)

Tomlin, Ruben; Papageorgiou, Demetrios; Pavliotis, Greg

2016-11-01

We consider the full three-dimensional model for a thin viscous liquid film completely wetting a flat infinite solid substrate at some non-zero angle to the horizontal, with an electric field normal to the substrate far from the flow. Thin film flows have applications in cooling processes. Many studies have shown that the presence of interfacial waves increases heat transfer by orders of magnitude due to film thinning and convection effects. A long-wave asymptotics procedure yields a Kuramoto-Sivashinsky equation with a non-local term to model the weakly nonlinear evolution of the interface dynamics for overlying film arrangements, with a restriction on the electric field strength. The non-local term is always linearly destabilising and produces growth rates proportional to the cube of the magnitude of the wavenumber vector. A sufficiently strong electric field is able promote non-trivial dynamics for subcritical Reynolds number flows where the flat interface is stable in the absence of an electric field. We present numerical simulations where we observe rich dynamical behavior with competing attractors, including "snaking" travelling waves and other fully three-dimensional wave formations. EPSRC studentship (RJT).

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.

Hidden acoustic information revealed by intentional nonlinearity

NASA Astrophysics Data System (ADS)

Dowling, David R.

2017-11-01

Acoustic waves are omnipresent in modern life and are well described by the linearized equations of fluid dynamics. Once generated, acoustic waves carry and collect information about their source and the environment through which they propagate, respectively, and this information may be retrieved by analyzing recordings of these waves. Because of this, acoustics is the primary means for observation, surveillance, reconnaissance, and remote sensing in otherwise opaque environments, such as the Earth's oceans and crust, and the interior of the human body. For such information-retrieval tasks, acoustic fields are nearly always interrogated within their recorded frequency range or bandwidth. However, this frequency-range restriction is not general; acoustic fields may also carry (hidden) information at frequencies outside their bandwidth. Although such a claim may seem counter intuitive, hidden acoustic-field information can be revealed by re-introducing a marquee trait of fluid dynamics: nonlinearity. In particular, an intentional quadratic nonlinearity - a form of intra-signal heterodyning - can be used to obtain acoustic field information at frequencies outside a recorded acoustic field's bandwidth. This quadratic nonlinearity enables a variety of acoustic remote sensing applications that were long thought to be impossible. In particular, it allows the detrimental effects of sparse recordings and random scattering to be suppressed when the original acoustic field has sufficient bandwidth. In this presentation, the topic is developed heuristically, with a just brief exposition of the relevant mathematics. Hidden acoustic field information is then revealed from simulated and measured acoustic fields in simple and complicated acoustic environments involving frequencies from a few Hertz to more than 100 kHz, and propagation distances from tens of centimeters to hundreds of kilometers. Sponsored by ONR, NAVSEA, and NSF.

The Nonlinear Coupling of Electromagnetic Ion Cyclotron and Lower Hybrid Waves in the Ring Current Region: The Magnetic Storm May 1-7 1998

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Krivorutsky, E.; Gamayunov, K.; Avanov, L.

2003-01-01

The excitation of lower hybrid waves (LHWs) is a widely discussed mechanism of interaction between plasma species in space, and is one of the unresolved questions of magnetospheric multi-ion plasmas. In this paper we present the morphology, dynamics, and level of LHW activity generated by electromagnetic ion cyclotron (EMIC) waves during the May 2-7, 1998 storm period on the global scale. The LHWs were calculated based on our newly developed self-consistent model that couples the system of two kinetic equations: one equation describes the ring current (RC) ion dynamic, and another equation describes the evolution of EMIC waves. It is found that the LHWs are excited by helium ions due to their mass dependent drift in the electric field of EMIC waves. The level of LHW activity is calculated assuming that the induced scattering process is the main saturation mechanism for these waves. The calculated LHWs electric fields are consistent with the observational data.

The Nonlinear Coupling of Electromagnetic Ion Cyclotron and Lower Hybrid Waves in the Ring Current Region

NASA Technical Reports Server (NTRS)

Khazanov, G. V.

2004-01-01

The excitation of lower hybrid waves (LHWs) is a widely discussed mechanism of interaction between plasma species in space, and is one of the unresolved questions of magnetospheric multi-ion plasmas. In this paper we present the morphology, dynamics, and level of LHW activity generated by electromagnetic ion cyclotron (EMIC) waves during the May 2-7, 1998 storm period on the global scale. The LHWs were calculated based on a newly developed self-consistent model (Khazanov et. al., 2002, 2003) that couples the system of two kinetic equations: one equation describes the ring current (RC) ion dynamic, and another equation describes the evolution of EMIC waves. It is found that the LHWs are excited by helium ions due to their mass dependent drift in the electric field of EMIC waves. The level of LHW activity is calculated assuming that the induced scattering process is the main saturation mechanism for these waves. The calculated LHWs electric fields are consistent with the observational data.

Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays.

PubMed

Yunes, Nicolás; Siemens, Xavier

2013-01-01

This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime . Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review ends with a discussion of gravitational-wave tests for compact binary systems.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2000-12-01

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

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

Oblique Propagation of Electrostatic Waves in a Magnetized Electron-Positron-Ion Plasma in the Presence of Heavy Particles

NASA Astrophysics Data System (ADS)

Sarker, M.; Hossen, M. R.; Shah, M. G.; Hosen, B.; Mamun, A. A.

2018-06-01

A theoretical investigation is carried out to understand the basic features of nonlinear propagation of heavy ion-acoustic (HIA) waves subjected to an external magnetic field in an electron-positron-ion plasma that consists of cold magnetized positively charged heavy ion fluids and superthermal distributed electrons and positrons. In the nonlinear regime, the Korteweg-de Vries (K-dV) and modified K-dV (mK-dV) equations describing the propagation of HIA waves are derived. The latter admits a solitary wave solution with both positive and negative potentials (for K-dV equation) and only positive potential (for mK-dV equation) in the weak amplitude limit. It is observed that the effects of external magnetic field (obliqueness), superthermal electrons and positrons, different plasma species concentration, heavy ion dynamics, and temperature ratio significantly modify the basic features of HIA solitary waves. The application of the results in a magnetized EPI plasma, which occurs in many astrophysical objects (e.g. pulsars, cluster explosions, and active galactic nuclei) is briefly discussed.

Upper-hybrid wave-driven Alfvenic turbulence in magnetized dusty plasmas

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

Misra, A. P.; Banerjee, S.

The nonlinear dynamics of coupled electrostatic upper-hybrid (UH) and Alfven waves (AWs) is revisited in a magnetized electron-ion plasma with charged dust impurities. A pair of nonlinear equations that describe the interaction of UH wave envelopes (including the relativistic electron mass increase) and the density as well as the compressional magnetic field perturbations associated with the AWs are solved numerically to show that many coherent solitary patterns can be excited and saturated due to modulational instability of unstable UH waves. The evolution of these solitary patterns is also shown to appear in the states of spatiotemporal coherence, temporal as wellmore » as spatiotemporal chaos, due to collision and fusion among the patterns in stochastic motion. Furthermore, these spatiotemporal features are demonstrated by the analysis of wavelet power spectra. It is found that a redistribution of wave energy takes place to higher harmonic modes with small wavelengths, which, in turn, results in the onset of Alfvenic turbulence in dusty magnetoplasmas. Such a scenario can occur in the vicinity of Saturn's magnetosphere as many electrostatic solitary structures have been observed there by the Cassini spacecraft.« less

Resonance frequency broadening of wave-particle interaction in tokamaks due to Alfvénic eigenmode

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

Meng, Guo; Gorelenkov, Nikolai N.; Duarte, Vinicius N.

We use the guiding center code ORBIT to study the broadening of resonances and the parametric dependence of the resonance frequency broadening widthmore » $$\\Delta\\Omega$$ on the nonlinear particle trapping frequency $$\\omega_b$$ of wave-particle interaction with specific examples using realistic equilibrium DIII-D shot 159243 (Collins et al. 2016 Phys. Rev. Lett. 116 095001). When the mode amplitude is small, the pendulum approximation for energetic particle dynamics near the resonance is found to be applicable and the ratio of the resonance frequency width to the deeply trapped bounce frequency $$\\Delta\\Omega/\\omega_b$$ equals 4, as predicted by theory. Lastly, it is found that as the mode amplitude increases, the coefficient $$a=\\Delta\\Omega/\\omega_b$$ becomes increasingly smaller because of the breaking down of the nonlinear pendulum approximation for the wave-particle interaction.« less

Modulation Instability and Phase-Shifted Fermi-Pasta-Ulam Recurrence

PubMed Central

Kimmoun, O.; Hsu, H. C.; Branger, H.; Li, M. S.; Chen, Y. Y.; Kharif, C.; Onorato, M.; Kelleher, E. J. R.; Kibler, B.; Akhmediev, N.; Chabchoub, A.

2016-01-01

Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected catastrophes and disasters in seemingly normal conditions. One prominent form of instability in a distributed system is its response to a harmonic modulation. Such instability has special names in various branches of physics and is generally known as modulation instability (MI). The MI leads to a growth-decay cycle of unstable waves and is therefore related to Fermi-Pasta-Ulam (FPU) recurrence since breather solutions of the nonlinear Schrödinger equation (NLSE) are known to accurately describe growth and decay of modulationally unstable waves in conservative systems. Here, we report theoretical, numerical and experimental evidence of the effect of dissipation on FPU cycles in a super wave tank, namely their shift in a determined order. In showing that ideal NLSE breather solutions can describe such dissipative nonlinear dynamics, our results may impact the interpretation of a wide range of new physics scenarios. PMID:27436005

Resonance frequency broadening of wave-particle interaction in tokamaks due to Alfvénic eigenmode

DOE PAGES

Meng, Guo; Gorelenkov, Nikolai N.; Duarte, Vinicius N.; ...

2018-01-19

We use the guiding center code ORBIT to study the broadening of resonances and the parametric dependence of the resonance frequency broadening widthmore » $$\\Delta\\Omega$$ on the nonlinear particle trapping frequency $$\\omega_b$$ of wave-particle interaction with specific examples using realistic equilibrium DIII-D shot 159243 (Collins et al. 2016 Phys. Rev. Lett. 116 095001). When the mode amplitude is small, the pendulum approximation for energetic particle dynamics near the resonance is found to be applicable and the ratio of the resonance frequency width to the deeply trapped bounce frequency $$\\Delta\\Omega/\\omega_b$$ equals 4, as predicted by theory. Lastly, it is found that as the mode amplitude increases, the coefficient $$a=\\Delta\\Omega/\\omega_b$$ becomes increasingly smaller because of the breaking down of the nonlinear pendulum approximation for the wave-particle interaction.« less

Early time evolution of a localized nonlinear excitation in the β-FPUT chain

NASA Astrophysics Data System (ADS)

Kashyap, Rahul; Westley, Alexandra; Datta, Amitava; Sen, Surajit

2017-04-01

We present the detailed dynamics of the particles in the β-Fermi-Pasta-Ulam-Tsingou (FPUT) chain after the initiation of a localized nonlinear excitation (LNE) by squeezing a central bond in the monodispersed chain at time t = 0 while all other particles remain in their original relaxed positions. In the absence of phonons in the system, the LNE appears to initiate its relaxation process by symmetrically emitting two very weak solitary waves. The next stage involves the spreading of the LNE and the formation of nonsolitary wave-like objects to broaden the excitation region until a stage is reached when many weak solitary wave-like objects can be emitted as the system begins its journey to quasi-equilibrium and then to equilibrium. In addition to being of fundamental interest, these systems may be realized using cantilever systems and could well hold the key to constructing the next generation of broadband energy harvesting systems.

Magnetic droplet soliton nucleation in oblique fields

NASA Astrophysics Data System (ADS)

Mohseni, Morteza; Hamdi, M.; Yazdi, H. F.; Banuazizi, S. A. H.; Chung, S.; Sani, S. R.; Åkerman, Johan; Mohseni, Majid

2018-05-01

We study the auto-oscillating magnetodynamics in orthogonal spin-torque nano-oscillators (STNOs) as a function of the out-of-plane (OOP) magnetic-field angle. In perpendicular fields and at OOP field angles down to approximately 50°, we observe the nucleation of a droplet. However, for field angles below 50°, experiments indicate that the droplet gives way to propagating spin waves, in agreement with our micromagnetic simulations. Theoretical calculations show that the physical mechanism behind these observations is the sign changing of spin-wave nonlinearity (SWN) by angle. In addition, we show that the presence of a strong perpendicular magnetic anisotropy free layer in the system reverses the angular dependence of the SWN and dynamics in STNOs with respect to the known behavior determined for the in-plane magnetic anisotropy free layer. Our results are of fundamental interest in understanding the rich dynamics of nanoscale solitons and spin-wave dynamics in STNOs.

The laboratory investigation of surface envelope solitons: reflection from a vertical wall and collisions of solitons

NASA Astrophysics Data System (ADS)

Slunyaev, Alexey; Klein, Marco; Clauss, Günther F.

2016-04-01

Envelope soliton solutions are key elements governing the nonlinear wave dynamics within a simplified theory for unidirectional weakly modulated weakly nonlinear wave groups on the water surface. Within integrable models the solitons preserve their structure in collisions with other waves; they do not disperse and can carry energy infinitively long. Steep and short soliton-like wave groups have been shown to exist in laboratory tests [1] and, even earlier, in numerical simulations [2, 3]. Thus, long-living wave groups may play important role in the dynamics of intense sea waves and wave-structure interactions. The solitary wave groups may change the wave statistics and can be taken into account when developing approaches for the deterministic forecasting of dangerous waves, including so-called rogue waves. An experimental campaign has been conducted in the wave basin of the Technical University of Berlin on simulations of intense solitary wave groups. The first successful experimental observation of intense envelope solitons took place in this facility [1]. The new experiments aimed at following main goals: 1) to reproduce intense envelope solitons with different carrier wave lengths; 2) to estimate the rate of envelope soliton dissipation; 3) to consider the reflection of envelope solitons on a vertical wall; 4) to consider head-on collisions of envelope solitons, and 5) to consider overtaking interactions of envelope solitons. Up to 9 wave gauges were used in each experimental run, which enabled registration of the surface movement at different distances from the wavemaker, at different locations across the wave flume and near the wall. Besides surface displacements, the group envelope shapes were directly recorded, with use of phase shifts applied to the modulated waves generated by the wavemaker. [1] A. Slunyaev, G.F. Clauss, M. Klein, M. Onorato, Simulations and experiments of short intense envelope solitons of surface water waves. Phys. Fluids 25, 067105 (2013). [2] A.I. Dyachenko, V.E. Zakharov, On the formation of freak waves on the surface of deep water. JETP Lett. 88, 307 (2008). [3] A.V. Slunyaev, Numerical simulation of "limiting" envelope solitons of gravity waves on deep water. JETP 109, 676 (2009).

Optical supercavitation in soft matter.

PubMed

Conti, C; DelRe, E

2010-09-10

We investigate theoretically, numerically, and experimentally nonlinear optical waves in an absorbing out-of-equilibrium colloidal material at the gelification transition. At a sufficiently high optical intensity, absorption is frustrated and light propagates into the medium. The process is mediated by the formation of a matter-shock wave due to optically induced thermodiffusion and largely resembles the mechanism of hydrodynamical supercavitation, as it is accompanied by a dynamic phase-transition region between the beam and the absorbing material.

Optical Supercavitation in Soft Matter

NASA Astrophysics Data System (ADS)

Conti, C.; Delre, E.

2010-09-01

We investigate theoretically, numerically, and experimentally nonlinear optical waves in an absorbing out-of-equilibrium colloidal material at the gelification transition. At a sufficiently high optical intensity, absorption is frustrated and light propagates into the medium. The process is mediated by the formation of a matter-shock wave due to optically induced thermodiffusion and largely resembles the mechanism of hydrodynamical supercavitation, as it is accompanied by a dynamic phase-transition region between the beam and the absorbing material.

Reduced-order prediction of rogue waves in two-dimensional deep-water waves

NASA Astrophysics Data System (ADS)

Farazmand, Mohammad; Sapsis, Themistoklis P.

2017-07-01

We consider the problem of large wave prediction in two-dimensional water waves. Such waves form due to the synergistic effect of dispersive mixing of smaller wave groups and the action of localized nonlinear wave interactions that leads to focusing. Instead of a direct simulation approach, we rely on the decomposition of the wave field into a discrete set of localized wave groups with optimal length scales and amplitudes. Due to the short-term character of the prediction, these wave groups do not interact and therefore their dynamics can be characterized individually. Using direct numerical simulations of the governing envelope equations we precompute the expected maximum elevation for each of those wave groups. The combination of the wave field decomposition algorithm, which provides information about the statistics of the system, and the precomputed map for the expected wave group elevation, which encodes dynamical information, allows (i) for understanding of how the probability of occurrence of rogue waves changes as the spectrum parameters vary, (ii) the computation of a critical length scale characterizing wave groups with high probability of evolving to rogue waves, and (iii) the formulation of a robust and parsimonious reduced-order prediction scheme for large waves. We assess the validity of this scheme in several cases of ocean wave spectra.

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.

Stochastic Convection Parameterizations

NASA Technical Reports Server (NTRS)

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

2012-01-01

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

WAKES: Wavelet Adaptive Kinetic Evolution Solvers

NASA Astrophysics Data System (ADS)

Mardirian, Marine; Afeyan, Bedros; Larson, David

2016-10-01

We are developing a general capability to adaptively solve phase space evolution equations mixing particle and continuum techniques in an adaptive manner. The multi-scale approach is achieved using wavelet decompositions which allow phase space density estimation to occur with scale dependent increased accuracy and variable time stepping. Possible improvements on the SFK method of Larson are discussed, including the use of multiresolution analysis based Richardson-Lucy Iteration, adaptive step size control in explicit vs implicit approaches. Examples will be shown with KEEN waves and KEEPN (Kinetic Electrostatic Electron Positron Nonlinear) waves, which are the pair plasma generalization of the former, and have a much richer span of dynamical behavior. WAKES techniques are well suited for the study of driven and released nonlinear, non-stationary, self-organized structures in phase space which have no fluid, limit nor a linear limit, and yet remain undamped and coherent well past the drive period. The work reported here is based on the Vlasov-Poisson model of plasma dynamics. Work supported by a Grant from the AFOSR.

A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane.

PubMed

Liu, T Y; Chiu, T L; Clarkson, P A; Chow, K W

2017-09-01

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane

NASA Astrophysics Data System (ADS)

Liu, T. Y.; Chiu, T. L.; Clarkson, P. A.; Chow, K. W.

2017-09-01

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

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

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

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

2015-12-15

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

Numerical Investigation of Three-dimensional Instability of Standing Waves

NASA Astrophysics Data System (ADS)

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

2002-11-01

We study the three-dimensional instability of finite-amplitude standing waves under the influence of gravity using the transition matrix method. For accurate calculation of the transition matrices, we apply an efficient high-order spectral element method for nonlinear wave dynamics in complex domain. We consider two types of standing waves: (a) plane standing waves; and (b) standing waves in a circular tank. For the former, in addition to the confirmation of the side-band-like instability, we find a new three-dimensional instability for arbitrary base standing waves. The dominant component of the unstable disturbance is an oblique standing wave, with an arbitrary angle relative to the base flow, whose frequency is approximately equal to that of the base standing wave. Based on direct simulations, we confirm such a three-dimensional instability and show the occurrence of the Fermi-Pasta-Ulam recurrence phenomenon during nonlinear evolution. For the latter, we find that beyond a threshold wave steepness, the standing wave with frequency Ω becomes unstable to a small three-dimensional disturbance, which contains two dominant standing-wave components with frequencies ω1 and ω_2, provided that 2Ω ω1 + ω_2. The threshold wave steepness is found to decrease/increase as the radial/azimuthal wavenumber of the base standing wave increases. We show that the instability of standing waves in rectangular and circular tanks is caused by third-order quartet resonances between base flow and disturbance.

Numerical modeling of the atmosphere with an isentropic vertical coordinate

NASA Technical Reports Server (NTRS)

Hsu, Yueh-Jiuan G.; Arakawa, Akio

1990-01-01

A theta-coordinate model simulating the nonlinear evolution of a baroclinic wave is presented. In the model, vertical discretization maintains important integral constraints such as conservation of the angular momentum and total energy. A massless-layer approach is used in the treatment of the intersections of coordinate surfaces with the lower boundary. This formally eliminates the intersection problem, but raises other computational problems. Horizontal discretization of the continuity and momentum equations in the model are designed to overcome these problems. Selected results from a 10-day integration with the 25-layer, beta-plane version of the model are presented. It is concluded that the model can simulate the nonlinear evolution of a baroclinic wave and associated dynamical processes without major computational difficulties.

Migrating diurnal tide variability induced by propagating planetary waves

NASA Astrophysics Data System (ADS)

Chang, Loren C.

The migrating diurnal tide is one of the dominant dynamical features in the low latitudes of the Earth's Mesosphere and Lower Thermosphere (MLT) region, representing the atmospheric response to the largest component of solar forcing, propagating upwards from excitation regions in the lower atmosphere. Ground-based observations of the tide have resolved short term variations attributed to nonlinear interactions between the tide and planetary waves also in the region. However, the conditions, effects, and mechanisms of a planetary wave - tidal interaction are still unclear. These questions are addressed using the NCAR Thermosphere Ionosphere Mesosphere Electrodynamics General Circulation Model (TIME-GCM) to examine two types of planetary waves, known to attain significant amplitudes in the low latitude and equatorial region where the migrating diurnal tide is dominant. The quasi-two day wave (QTDW) can rapidly amplify to large amplitudes from the summer hemisphere during post-solstice periods, while ultra fast Kelvin (UFK) waves occur sporadically in the temperature and zonal wind fields of the equatorial lower thermosphere. While child waves resulting from a nonlinear interaction are resolved in both cases, the response of the tidal structure and amplitudes to the two planetary waves differs significantly. In the case of the QTDW, the migrating diurnal tide displays a general amplitude decrease of 20 - 40%, as well as a shortening of vertical wavelength by roughly 4 km. Nonlinear advection is found to result in energy transfer to and from the tide, resulting in latitudinal smoothing of the tidal structure. The QTDW also produces significant changes to the mean zonal winds in the equator and at summer mid to high latitudes that can also account for changes in tidal amplitude and vertical wavelength. Filtering of gravity waves by the altered mean winds can also result in changes to the zonal mean zonal winds in the tropics. However, gravity wave momentum forcing on the tide is smaller than the advective tendencies throughout most of the MLT region, and cannot iv directly account for the changes in the tide during the QTDW model simulation. In the case of the UFK wave, baseline tidal amplitudes are found to show much smaller changes of 10% or less, despite the larger amplitudes of the UFK wave in the lower thermosphere region compared to the QTDW. Analysis of the nonlinear advective tendencies shows smaller magnitudes than those in the the case of the QTDW, with interaction regions limited primarily to a smaller region in latitude and altitude. Increased tidal convergence in the tropical lower thermosphere is attributed to eastward forcing of the background zonal mean winds by the UFK wave. Increasing the UFK wave forcing by an order of magnitude, although unrealistic, results in changes to the tide comparable in magnitude to the case of the QTDW. While child waves generated by nonlinear advection are present with both of the propagating planetary waves examined, the QTDW produces much greater tidal variability through both nonlinear and linear advection due to its broader horizontal and vertical structure, compared to the UFK wave. Planetary wave induced background atmosphere changes can also drive tidal variability, suggesting that changes to the tidal response in the MLT can also result from this indirect coupling mechanism, in addition to nonlinear advection.

Exponential nonlinear electrodynamics and backreaction effects on holographic superconductor in the Lifshitz black hole background

NASA Astrophysics Data System (ADS)

Sherkatghanad, Z.; Mirza, B.; Lalehgani Dezaki, F.

We analytically describe the properties of the s-wave holographic superconductor with the exponential nonlinear electrodynamics in the Lifshitz black hole background in four-dimensions. Employing an assumption the scalar and gauge fields backreact on the background geometry, we calculate the critical temperature as well as the condensation operator. Based on Sturm-Liouville method, we show that the critical temperature decreases with increasing exponential nonlinear electrodynamics and Lifshitz dynamical exponent, z, indicating that condensation becomes difficult. Also we find that the effects of backreaction has a more important role on the critical temperature and condensation operator in small values of Lifshitz dynamical exponent, while z is around one. In addition, the properties of the upper critical magnetic field in Lifshitz black hole background using Sturm-Liouville approach is investigated to describe the phase diagram of the corresponding holographic superconductor in the probe limit. We observe that the critical magnetic field decreases with increasing Lifshitz dynamical exponent, z, and it goes to zero at critical temperature, independent of the Lifshitz dynamical exponent, z.

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.

Thermal responses in a coronal loop maintained by wave heating mechanisms

NASA Astrophysics Data System (ADS)

Matsumoto, Takuma

2018-05-01

A full 3-dimensional compressible magnetohydrodynamic (MHD) simulation is conducted to investigate the thermal responses of a coronal loop to the dynamic dissipation processes of MHD waves. When the foot points of the loop are randomly and continuously forced, the MHD waves become excited and propagate upward. Then, 1-MK temperature corona is produced naturally as the wave energy dissipates. The excited wave packets become non-linear just above the magnetic canopy, and the wave energy cascades into smaller spatial scales. Moreover, collisions between counter-propagating Alfvén wave packets increase the heating rate, resulting in impulsive temperature increases. Our model demonstrates that the heating events in the wave-heated loops can be nanoflare-like in the sense that they are spatially localized and temporally intermittent.

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.).

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.

Breather soliton dynamics in microresonators

NASA Astrophysics Data System (ADS)

Yu, Mengjie; Jang, Jae K.; Okawachi, Yoshitomo; Griffith, Austin G.; Luke, Kevin; Miller, Steven A.; Ji, Xingchen; Lipson, Michal; Gaeta, Alexander L.

2017-02-01

The generation of temporal cavity solitons in microresonators results in coherent low-noise optical frequency combs that are critical for applications in spectroscopy, astronomy, navigation or telecommunications. Breather solitons also form an important part of many different classes of nonlinear wave systems, manifesting themselves as a localized temporal structure that exhibits oscillatory behaviour. To date, the dynamics of breather solitons in microresonators remains largely unexplored, and its experimental characterization is challenging. Here we demonstrate the excitation of breather solitons in two different microresonator platforms based on silicon nitride and on silicon. We investigate the dependence of the breathing frequency on pump detuning and observe the transition from period-1 to period-2 oscillation. Our study constitutes a significant contribution to understanding the soliton dynamics within the larger context of nonlinear science.

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.

On the stability of lumps and wave collapse in water waves.

PubMed

Akylas, T R; Cho, Yeunwoo

2008-08-13

In the classical water-wave problem, fully localized nonlinear waves of permanent form, commonly referred to as lumps, are possible only if both gravity and surface tension are present. While much attention has been paid to shallow-water lumps, which are generalizations of Korteweg-de Vries solitary waves, the present study is concerned with a distinct class of gravity-capillary lumps recently found on water of finite or infinite depth. In the near linear limit, these lumps resemble locally confined wave packets with envelope and wave crests moving at the same speed, and they can be approximated in terms of a particular steady solution (ground state) of an elliptic equation system of the Benney-Roskes-Davey-Stewartson (BRDS) type, which governs the coupled evolution of the envelope along with the induced mean flow. According to the BRDS equations, however, initial conditions above a certain threshold develop a singularity in finite time, known as wave collapse, due to nonlinear focusing; the ground state, in fact, being exactly at the threshold for collapse suggests that the newly discovered lumps are unstable. In an effort to understand the role of this singularity in the dynamics of lumps, here we consider the fifth-order Kadomtsev-Petviashvili equation, a model for weakly nonlinear gravity-capillary waves on water of finite depth when the Bond number is close to one-third, which also admits lumps of the wave packet type. It is found that an exchange of stability occurs at a certain finite wave steepness, lumps being unstable below but stable above this critical value. As a result, a small-amplitude lump, which is linearly unstable and according to the BRDS equations would be prone to wave collapse, depending on the perturbation, either decays into dispersive waves or evolves into an oscillatory state near a finite-amplitude stable lump.

Experimental investigation of change of energy of infragavity waves in dependence on spectral characteristics of an irregular wind waves in coastal zone

NASA Astrophysics Data System (ADS)

Saprykina, Yana; Divinskii, Boris

2013-04-01

An infragravity waves are long waves with periods of 20 - 300 s. Most essential influence of infragarvity waves on dynamic processes is in a coastal zone, where its energy can exceed the energy of wind waves. From practical point of view, the infragravity waves are important, firstly, due to their influence on sand transport processes in a coastal zone. For example, interacting with group structure of wind waves the infragravity waves can define position of underwater bars on sandy coast. Secondly, they are responsible on formation of long waves in harbors. Main source of infragravity waves is wave group structure defined by sub-nonlinear interactions of wind waves (Longuet-Higgins, Stewart, 1962). These infragravity waves are bound with groups of wind waves and propagate with wave group velocity. Another type of infragravity waves are formed in a surf zone as a result of migration a wave breaking point (Symonds, et al., 1982). What from described above mechanisms of formation of infragravity waves prevails, till now it is unknown. It is also unknown how energy of infragravity waves depends on energy of input wind waves and how it changes during nonlinear wave transformation in coastal zone. In our work on the basis of the analysis of data of field experiment and numerical simulation a contribution of infragravity waves in total wave energy in depending on integral characteristics of an irregular wave field in the conditions of a real bathymetry was investigated. For analysis the data of field experiment "Shkorpilovtsy-2007" (Black sea) and data of numerical modeling of Boussinesq type equation with extended dispersion characteristics (Madsen et al., 1997) were used. It was revealed that infragravity waves in a coastal zone are defined mainly by local group structure of waves, which permanently changes due to nonlinearity, shoaling and breaking processes. Free infragravity waves appearing after wave breaking exist together with bound infragravity waves. There are no clear total dependences of energy of infrragravity waves from energy of wind waves and mean period of infragravity waves from mean period of wind waves. But significant wave height of infragravity waves depends on relative water depth (wave height of wind waves divided on water depth). There are different types of this dependence for breaking and non-breaking waves. The influence of peak period, significant wave height and directional spreading of initial wave spectrum on these dependences are discussed. The peculiarities of spectra of infragravity waves for non-breaking, breaking and multibreaking wind waves are shown. This work is supported by the RFBR, project 12-05-00965. References: Longuet-Higgins, M. S., R. W. Stewart, 1962. Radiation stress and mass transport in gravity waves, with an application to surf beats. J. Fluid Mech., 13, pp. 481-504. Symonds G., D.A. Huntley, A.J. Bowen, 1982. Two dimensional surf beat: long wave generation by a time-varying breakpoint. J. of Geoph. Res., 87(C), pp.492-498. Madsen P.A., Sorensen O.R., Shaffer H.A. 1997. Surf zone dynamics simulated by a Boussinesq type model. Coastal Engineering, 32, p. 255-287.

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

NASA Astrophysics Data System (ADS)

Wang, Rui; Balachandran, Balakumar

2018-07-01

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

A Landau fluid model for dispersive magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Passot, T.; Sulem, P. L.

2004-11-01

A monofluid model with Landau damping is presented for strongly magnetized electron-proton collisionless plasmas whose distribution functions are close to bi-Maxwellians. This description that includes dynamical equations for the gyrotropic components of the pressure and heat flux tensors, extends the Landau-fluid model of Snyder, Hammett, and Dorland [Phys. Plasmas 4, 3974 (1997)] by retaining Hall effect and finite Larmor radius corrections. It accurately reproduces the weakly nonlinear dynamics of dispersive Alfvén waves whose wavelengths are large compared to the ion inertial length, whatever their direction of propagation, and also the rapid Landau dissipation of long magnetosonic waves in a warm plasma.

Alfvén wave dynamics at the neighborhood of a 2.5D magnetic null-point

NASA Astrophysics Data System (ADS)

Sabri, S.; Vasheghani Farahani, S.; Ebadi, H.; Hosseinpour, M.; Fazel, Z.

2018-05-01

The aim of the present study is to highlight the energy transfer via the interaction of magnetohydrodynamic waves with a 2.5D magnetic null-point in a finite plasma-β regime of the solar corona. An initially symmetric Alfvén pulse at a specific distance from a magnetic null-point is kicked towards the isothermal null-point. A shock-capturing Godunov-type PLUTO code is used to solve the ideal magnetohydrodynamic set equations in the context of wave-plasma energy transfer. As the Alfvén wave propagates towards the magnetic null-point it experiences speed lowering which ends up in releasing energy along the separatrices. In this line owing to the Alfvén wave, a series of events take place that contribute towards coronal heating. Nonlinear induced waves are by products of the torsional Alfvén interaction with magnetic null-points. The energy of these induced waves which are fast magnetoacoustic (transverse) and slow magnetoacoustic (longitudinal) waves are supplied by the Alfvén wave. The nonlinearly induced density perturbations are proportional to the Alfvén wave energy loss. This supplies energy for the propagation of fast and slow magnetoacoustic waves, where in contrast to the fast wave the slow wave experiences a continuous energy increase. As such, the slow wave may transfer its energy to the medium at later times, maintaining a continuous heating mechanism at the neighborhood of a magnetic null-point.

Detonation shock dynamics with an acceleration relation for nitromethane and TATB

NASA Astrophysics Data System (ADS)

Swift, Damian; Kraus, Richard; Mulford, Roberta; White, Stephen

2015-06-01

The propagation of curved detonation waves has been treated phenomenologically through models of the speed D of a detonation wave as a function of its curvature K, in the Whitham-Bdzil-Lambourn model, also known as detonation shock dynamics. D(K) relations, and the edge angle with adjacent material, have been deduced from the steady shape of detonation waves in long rods and slabs of explosive. Nonlinear D(K) relations have proven necessary to interpret data from charges of different diameter, and even then the D(K) relation may not transfer between diameters. This is an indication that the D(K) relation oversimplifies the kinematics. It is also possible to interpret wave-shape data in terms of an acceleration relation, as used in Brun's Jouguet relaxe model. One form of acceleration behavior is to couple an asymptotic D(K) relation with a time-dependent relaxation toward it from the instantaneous, local speed. This approach is also capable of modeling overdriving of a detonation by a booster. Using archival data for the TATB-based explosive EDC35 and for nitromethane, we found that a simple linear asymptotic D(K) relation with a constant relaxation rate was able to reproduce the experimental wave-shapes better, with fewer parameters, than a nonlinear instantaneous D(K) relation. This work was performed in part under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

The fluid-dynamic paradigm of the dust-acoustic soliton

NASA Astrophysics Data System (ADS)

McKenzie, J. F.

2002-06-01

In most studies, the properties of dust-acoustic solitons are derived from the first integral of the Poisson equation, in which the shape of the pseudopotential determines both the conditions in which a soliton may exist and its amplitude. Here this first integral is interpreted as conservation of total momentum, which, along with the Bernoulli-like energy equations for each species, may be cast as the structure equation for the dust (or heavy-ion) speed in the wave. In this fluid-dynamic picture, the significance of the sonic points of each species becomes apparent. In the wave, the heavy-ion (or dust) flow speed is supersonic (relative to its sound speed), whereas the protons and electrons are subsonic (relative to their sound speeds), and the dust flow is driven towards its sonic point. It is this last feature that limits the strength (amplitude) of the wave, since the equilibrium point (the centre of the wave) must be reached before the dust speed becomes sonic. The wave is characterized by a compression in the heavies and a compression (rarefaction) in the electrons and a rarefaction (compression) in the protons if the heavies have positive (negative) charge, and the corresponding potential is a hump (dip). These features are elucidated by an exact analytical soliton, in a special case, which provides the fully nonlinear counterpoint to the weakly nonlinear sech2-type solitons associated with the Korteweg de Vries equation, and indicates the parameter regimes in which solitons may exist.

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations.

PubMed

Schüler, D; Alonso, S; Torcini, A; Bär, M

2014-12-01

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.

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.

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.

Controlling soliton excitations in Heisenberg spin chains through the magic angle.

PubMed

Lu, Jing; Zhou, Lan; Kuang, Le-Man; Sun, C P

2009-01-01

We study the nonlinear dynamics of collective excitation in an N -site XXZ quantum spin chain, which is manipulated by an oblique magnetic field. We show that, when the tilted field is applied along the magic angle, theta_{0}=+/-arccossqrt[13] , the anisotropic Heisenberg spin chain becomes isotropic and thus an freely propagating spin wave is stimulated. Also, in the regime of tilted angles larger and smaller than the magic angle, two types of nonlinear excitations appear: bright and dark solitons.

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.

Collective pulsatile expansion and swirls in proliferating tumor tissue

NASA Astrophysics Data System (ADS)

Yang, Taeseok Daniel; Kim, Hyun; Yoon, Changhyeong; Baek, Seung-Kuk; Lee, Kyoung J.

2016-10-01

Understanding the dynamics of expanding biological tissues is essential to a wide range of phenomena in morphogenesis, wound healing and tumor proliferation. Increasing evidence suggests that many of the relevant phenomena originate from complex collective dynamics, inherently nonlinear, of constituent cells that are physically active. Here, we investigate thin disk layers of proliferating, cohesive, monoclonal tumor cells and report the discovery of macroscopic, periodic, soliton-like mechanical waves with which cells are collectively ratcheting, as in the traveling-wave chemotaxis of dictyostelium discodium amoeba cells. The relevant length-scale of the waves is remarkably large (∼1 mm), compared to the thickness of a mono-layer tissue (∼ 10 μ {{m}}). During the tissue expansion, the waves are found to repeat several times with a quite well defined period of approximately 4 h. Our analyses suggest that the waves are initiated by the leading edge that actively pulls the tissue in the outward direction, while the cells within the bulk tissue do not seem to generate a strong self-propulsion. Subsequently, we demonstrate that a simple mathematical model chain of nonlinear springs that are constantly pulled in the outward direction at the leading edge recapitulates the observed phenomena well. As the areal cell density becomes too high, the tissue expansion stalls and the periodic traveling waves yield to multiple swirling vortices. Cancer cells are known to possess a broad spectrum of migration mechanisms. Yet, our finding has established a new unusual mode of tumor tissue expansion, and it may be equally applicable for many different expanding thin layers of cell tissues.

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.

A study of the mechanism of internal gravity wave generation by quasigeostrophic meteorological motions

NASA Technical Reports Server (NTRS)

Medvedev, A. S.

1987-01-01

Numerous experiments on the detection of atmospheric waves in the frequency range from acoustic to planetary at meteor heights have revealed that important wave sources are meteorological processes in the troposphere (cyclones, atmospheric fronts, jet streams, etc.). A dynamical theory based on the others work include describing the adaptation of meteorological fields to the geostropic equilibrium state. According to this theory, wave motions appear as a result of constant competition between the maladjustment of the wind and pressure fields due to nonlinear effects and the tendency of the atmosphere to establish a quasi-geostrophic equilibrium of these fields. These meteorological fields are discussed.

A study of the mechanism of internal gravity wave generation by quasigeostrophic meteorological motions

NASA Astrophysics Data System (ADS)

Medvedev, A. S.

1987-08-01

Numerous experiments on the detection of atmospheric waves in the frequency range from acoustic to planetary at meteor heights have revealed that important wave sources are meteorological processes in the troposphere (cyclones, atmospheric fronts, jet streams, etc.). A dynamical theory based on the others work include describing the adaptation of meteorological fields to the geostropic equilibrium state. According to this theory, wave motions appear as a result of constant competition between the maladjustment of the wind and pressure fields due to nonlinear effects and the tendency of the atmosphere to establish a quasi-geostrophic equilibrium of these fields. These meteorological fields are discussed.

Turbulence regeneration in pipe flow at moderate Reynolds numbers.

PubMed

Hof, Björn; van Doorne, Casimir W H; Westerweel, Jerry; Nieuwstadt, Frans T M

2005-11-18

We present the results of an experimental investigation into the nature and structure of turbulent pipe flow at moderate Reynolds numbers. A turbulence regeneration mechanism is identified which sustains a symmetric traveling wave within the flow. The periodicity of the mechanism allows comparison to the wavelength of numerically observed exact traveling wave solutions and close agreement is found. The advection speed of the upstream turbulence laminar interface in the experimental flow is observed to form a lower bound on the phase velocities of the exact traveling wave solutions. Overall our observations suggest that the dynamics of the turbulent flow at moderate Reynolds numbers are governed by unstable nonlinear traveling waves.