Nonlinear Drift-Kinetic Equation in the Presence of a Circularly Polarized Wave

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Krivorutsky, E. N.; Six, N. Frank (Technical Monitor)

2002-01-01

Equations of the single particle motion and nonlinear kinetic equation for plasma in the presence of a circularly polarized wave of arbitrary frequency in the drift approximation are presented. The nonstationarity and inhomogeneity of the plasma-wave system are taken into account. The time dependent part of the ponderomotive force is discussed.

Modeling Elastic Wave Propagation from an Underground Chemical Explosion Using Higher Order Finite Difference Approximation: Theory, Validation and Application to SPE

NASA Astrophysics Data System (ADS)

Hirakawa, E. T.; Ezzedine, S. M.; Petersson, A.; Sjogreen, B.; Vorobiev, O.; Pitarka, A.; Antoun, T.; Walter, W. R.

2016-12-01

Motions from underground explosions are governed by non-linear hydrodynamic response of material. However, the numerical calculation of this non-linear constitutive behavior is computationally intensive in contrast to the elastic and acoustic linear wave propagation solvers. Here, we develop a hybrid modeling approach with one-way hydrodynamic-to-elastic coupling in three dimensions in order to propagate explosion generated ground motions from the non-linear near-source region to the far-field. Near source motions are computed using GEODYN-L, a Lagrangian hydrodynamics code for high-energy loading of earth materials. Motions on a dense grid of points sampled on two nested shells located beyond the non-linear damaged zone are saved, and then passed to SW4, an anelastic anisotropic fourth order finite difference code for seismic wave modeling. Our coupling strategy is based on the decomposition and uniqueness theorems where motions are introduced into SW4 as a boundary source and continue to propagate as elastic waves at a much lower computational cost than by using GEODYN-L to cover the entire near- and the far-field domain. The accuracy of the numerical calculations and the coupling strategy is demonstrated in cases with a purely elastic medium as well as non-linear medium. Our hybrid modeling approach is applied to SPE-4' and SPE-5 which are the most recent underground chemical explosions conducted at the Nevada National Security Site (NNSS) where the Source Physics Experiments (SPE) are performed. Our strategy by design is capable of incorporating complex non-linear effects near the source as well as volumetric and topographic material heterogeneity along the propagation path to receiver, and provides new prospects for modeling and understanding explosion generated seismic waveforms. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-698608.

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

PubMed

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

2015-01-28

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

Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion.

PubMed

Leszczynski, Henryk; Wrzosek, Monika

2017-02-01

We consider nonlinear stochastic wave equations driven by one-dimensional white noise with respect to time. The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.

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

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1988-01-01

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

Nonlinear longitudinal resonance interaction of energetic charged particles and VLF waves in the magnetosphere

NASA Technical Reports Server (NTRS)

Tkalcevic, S.

1982-01-01

The longitudinal resonance of waves and energetic electrons in the Earth's magnetosphere, and the possible role this resonance may play in generating various magnetospheric phenomena are studied. The derivation of time-averaged nonlinear equations of motion for energetic particles longitudinally resonant with a whistler mode wave propagating with nonzero wave normal is considered. It is shown that the wave magnetic forces can be neglected at lower particle pitch angles, while they become equal to or larger than the wave electric forces for alpha 20 deg. The time-averaged equations of motion were used in test particle simulation which were done for a wide range of wave amplitudes, wave normals, particle pitch angles, particle parallel velocities, and in an inhomogeneous medium such as the magnetosphere. It was found that there are two classes of particles, trapped and untrapped, and that the scattering and energy exchange for those two groups exhibit significantly different behavior.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

A novel control algorithm for interaction between surface waves and a permeable floating structure

NASA Astrophysics Data System (ADS)

Tsai, Pei-Wei; Alsaedi, A.; Hayat, T.; Chen, Cheng-Wu

2016-04-01

An analytical solution is undertaken to describe the wave-induced flow field and the surge motion of a permeable platform structure with fuzzy controllers in an oceanic environment. In the design procedure of the controller, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller by blending all local state feedback controllers. A stability analysis is carried out for a real structure system by using Lyapunov method. The corresponding boundary value problems are then incorporated into scattering and radiation problems. They are analytically solved, based on separation of variables, to obtain series solutions in terms of the harmonic incident wave motion and surge motion. The dependence of the wave-induced flow field and its resonant frequency on wave characteristics and structure properties including platform width, thickness and mass has been thus drawn with a parametric approach. From which mathematical models are applied for the wave-induced displacement of the surge motion. A nonlinearly inverted pendulum system is employed to demonstrate that the controller tuned by swarm intelligence method can not only stabilize the nonlinear system, but has the robustness against external disturbance.

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

NASA Astrophysics Data System (ADS)

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

2012-09-01

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

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.

Derivation of Nonlinear Wave Equation for Flexural Motions of AN Elastic Beam Travelling in AN Air-Filled Tube

NASA Astrophysics Data System (ADS)

Sugimoto, N.; Kugo, K.; Watanabe, Y.

2002-07-01

Asymptotic analysis is carried out to derive a nonlinear wave equation for flexural motions of an elastic beam of circular cross-section travelling along the centre-axis of an air-filled, circular tube placed coaxially. Both the beam and tube are assumed to be long enough for end-effects to be ignored and the aerodynamic loading on the lateral surface of the beam is considered. Assuming a compressible inviscid fluid, the velocity potential of the air is sought systematically in the form of power series in terms of the ratios of the tube radius to a wavelength and of a typical deflection to the radius. Evaluating the pressure force acting on the lateral surface of the beam, the aerodynamic loading including the effects of finite deflection as well as of air's compressibility and axial curvature of the beam are obtained. Although the nonlinearity arises from the kinematical condition on the beam surface, it may be attributed to the presence of the tube wall. With the aerodynamic loading thus obtained, a nonlinear wave equation is derived, whereas linear theory is assumed for the flexural motions of the beam. Some discussions are given on the results.

Time-Reversal Generation of Rogue Waves

NASA Astrophysics Data System (ADS)

Chabchoub, Amin; Fink, Mathias

2014-03-01

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.

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

NASA Astrophysics Data System (ADS)

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

2008-05-01

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

Nonlinear coseismic infrasound waves in the upper atmosphere and ionosphere

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Mechanics of the acoustic radiation force in tissue-like solids

NASA Astrophysics Data System (ADS)

Dontsov, Egor V.

The acoustic radiation force (ARF) is a phenomenon affiliated with the nonlinear effects of high-intensity wave propagation. It represents the mean momentum transfer from the sound wave to the medium, and allows for an effective computation of the mean motion (e.g. acoustic streaming in fluids) induced by a high-intensity sound wave. Nowadays, the high-intensity focused ultrasound is frequently used in medical diagnosis applications due to its ability to "push" inside the tissue with the radiation body force and facilitate the local quantification of tissue's viscoelastic properties. The main objectives of this study include: i) the theoretical investigation of the ARF in fluids and tissue-like solids generated respectively by the amplitude modulated plane wave and focused ultrasound; ii) computation of the nonlinear acoustic wave propagation when the amplitude of the focused ultrasound field is modulated by a low-frequency signal, and iii) modeling of the ARF-induced motion in tissue-like solids for the purpose of quantifying their nonlinear elasticity via the magnitude of the ARF. Regarding the first part, a comparison with the existing theory of the ARF reveals a number of key features that are brought to light by the new formulation, including the contributions to the ARF of ultrasound modulation and thermal expansion, as well as the precise role of constitutive nonlinearities in generating the sustained body force in tissue-like solids by a focused ultrasound beam. In the second part, the hybrid time-frequency domain algorithm for the numerical analysis of the nonlinear wave equation is proposed. The approach is validated by comparing the results to the finite-difference modeling in time domain. Regarding the third objective, the Fourier transform approach is used to compute the ARF-induced shear wave motion in tissue-mimicking phantoms. A comparison between the experiment (tests performed at the Mayo Clinic) and model permitted the estimation of a particular coefficient of nonlinear tissue elasticity from the amplitude of the ARF-generated shear waves. For completeness, the ARF estimates of this coefficient are verified via an established technique known as acoustoelasticity.

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.

Nonlinear energy transport in one-dimensional lattices

NASA Astrophysics Data System (ADS)

Vuppuluri, P.; Hamilton, M.; de Alcantara Bonfim, O. F.

2007-03-01

We present a simple lattice model consisting of a one-dimensional chain, where the masses are interconnected by linear springs and allowed to move in the horizontal direction only, as in a monorail. In the transverse direction each mass is also attached to two other 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. In the transverse directions the springs are either in the extended or compressed state depending on the position of the mass. Under these conditions we show that solitary waves are present in the system. In the long wavelength limit an analytical solution for these nonlinear waves is found. Numeric 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. Nonlinear supratransmission is examined and shown to exist in the model and an explanation of its mechanism is presented.

Nonlinear wave interaction in a plasma column

NASA Technical Reports Server (NTRS)

Larsen, J.

1972-01-01

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

The interaction between a propagating coastal vortex and topographic waves

NASA Astrophysics Data System (ADS)

Parry, Simon Wyn

This thesis investigates the motion of a point vortex near coastal topography in a rotating frame of reference at constant latitude (f-plane) in the linear and weakly nonlinear limits. Topography is considered in the form of an infinitely long escarpment running parallel to a wall. The vortex motion and topographic waves are governed by the conservation of quasi-geostrophic potential vorticity in shallow water, from which a nonlinear system of equations is derived. First the linear limit is studied for three cases; a weak vortex on- and off-shelf and a weak vortex close to the wall. For the first two cases it is shown that to leading order the vortex motion is stationary and a solution for the topographic waves at the escarpment can be found in terms of Fourier integrals. For a weak vortex close to a wall, the leading order solution is a steadily propagating vortex with a topographic wavetrain at the step. Numerical results for the higher order interactions are also presented and explained in terms of conservation of momentum in the along-shore direction. For the second case a resonant interaction between the vortex and the waves occurs when the vortex speed is equal to the maximum group velocity of the waves and the linear response becomes unbounded at large times. Thus it becomes necessary to examine the weakly nonlinear near-resonant case. Using a long wave approximation a nonlinear evolution equation for the interface separating the two regions of differing relative potential vorticity is derived and has similar form to the BDA (Benjamin, Davies, Acrivos 1967) equation. Results for the leading order steadily propagating vortex and for the vortex-wave feedback problem are calculated numerically using spectral multi-step Adams methods.

The Alfvénic nature of energy transfer mediation in localized, strongly nonlinear Alfvén wavepacket collisions

NASA Astrophysics Data System (ADS)

Verniero, J. L.; Howes, G. G.

2018-02-01

In space and astrophysical plasmas, violent events or instabilities inject energy into turbulent motions at large scales. Nonlinear interactions among the turbulent fluctuations drive a cascade of energy to small perpendicular scales at which the energy is ultimately converted into plasma heat. Previous work with the incompressible magnetohydrodynamic (MHD) equations has shown that this turbulent energy cascade is driven by the nonlinear interaction between counterpropagating Alfvén waves - also known as Alfvén wave collisions. Direct numerical simulations of weakly collisional plasma turbulence enables deeper insight into the nature of the nonlinear interactions underlying the turbulent cascade of energy. In this paper, we directly compare four cases: both periodic and localized Alfvén wave collisions in the weakly and strongly nonlinear limits. Our results reveal that in the more realistic case of localized Alfvén wave collisions (rather than the periodic case), all nonlinearly generated fluctuations are Alfvén waves, which mediates nonlinear energy transfer to smaller perpendicular scales.

Analysis of Three-Dimensional, Nonlinear Development of Wave-Like Structure in a Compressible Round Jet

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Mankbadi, Reda R.

2002-01-01

An analysis of the nonlinear development of the large-scale structures or instability waves in compressible round jets was conducted using the integral energy method. The equations of motion were decomposed into two sets of equations; one set governing the mean flow motion and the other set governing the large-scale structure motion. The equations in each set were then combined to derive kinetic energy equations that were integrated in the radial direction across the jet after the boundary-layer approximations were applied. Following the application of further assumptions regarding the radial shape of the mean flow and the large structures, equations were derived that govern the nonlinear, streamwise development of the large structures. Using numerically generated mean flows, calculations show the energy exchanges and the effects of the initial amplitude on the coherent structure development in the jet.

Water waves generated by impulsively moving obstacle

NASA Astrophysics Data System (ADS)

Makarenko, Nikolay; Kostikov, Vasily

2017-04-01

There are several mechanisms of tsunami-type wave formation such as piston displacement of the ocean floor due to a submarine earthquake, landslides, etc. We consider simplified mathematical formulation which involves non-stationary Euler equations of infinitely deep ideal fluid with submerged compact wave-maker. We apply semi-analytical method [1] based on the reduction of fully nonlinear water wave problem to the integral-differential system for the wave elevation together with normal and tangential fluid velocities at the free surface. Recently, small-time asymptotic solutions were constructed by this method for submerged piston modeled by thin elliptic cylinder which starts with constant acceleration from rest [2,3]. By that, the leading-order solution terms describe several regimes of non-stationary free surface flow such as formation of inertial fluid layer, splash jets and diverging waves over the obstacle. Now we construct asymptotic solution taking into account higher-order nonlinear terms in the case of submerged circular cylinder. The role of non-linearity in the formation mechanism of surface waves is clarified in comparison with linear approximations. This work was supported by RFBR (grant No 15-01-03942). References [1] Makarenko N.I. Nonlinear interaction of submerged cylinder with free surface, JOMAE Trans. ASME, 2003, 125(1), 75-78. [2] Makarenko N.I., Kostikov V.K. Unsteady motion of an elliptic cylinder under a free surface, J. Appl. Mech. Techn. Phys., 2013, 54(3), 367-376. [3] Makarenko N.I., Kostikov V.K. Non-linear water waves generated by impulsive motion of submerged obstacle, NHESS, 2014, 14(4), 751-756.

Effects of Second-Order Sum- and Difference-Frequency Wave Forces on the Motion Response of a Tension-Leg Platform Considering the Set-down Motion

NASA Astrophysics Data System (ADS)

Wang, Bin; Tang, Yougang; Li, Yan; Cai, Runbo

2018-04-01

This paper presents a study on the motion response of a tension-leg platform (TLP) under first- and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function (QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.

Nonlinear equations of motion for Landau resonance interactions with a whistler mode wave

NASA Technical Reports Server (NTRS)

Inan, U. S.; Tkalcevic, S.

1982-01-01

A simple set of equations is presented for the description of the cyclotron averaged motion of Landau resonant particles in a whistler mode wave propagating at an angle to the static magnetic field. A comparison is conducted of the wave magnetic field and electric field effects for the parameters of the magnetosphere, and the parameter ranges for which the wave magnetic field effects would be negligible are determined. It is shown that the effect of the wave magnetic field can be neglected for low pitch angles, high normal wave angles, and/or high normalized wave frequencies.

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

PubMed

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

2018-05-12

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

Preliminary Analysis of a Submerged Wave Energy Device

NASA Astrophysics Data System (ADS)

Wagner, J. R.; Wagner, J. J.; Hayatdavoodi, M.; Ertekin, R. C.

2016-02-01

Preliminary analysis of a submerged wave energy harvesting device is presented. The device is composed of a thin, horizontally submerged plate that is restricted to heave oscillations under the influence of surface waves. The submerged plate is oscillating, and it can be attached to a fixed rotor, or a piston, to harvest the wave energy. A fully submerged wave energy converter is preferred over a surface energy convertor due to its durability and less visual and physical distractions it presents. In this study, the device is subject to nonlinear shallow-water waves. Wave loads on the submerged oscillating plate are obtained via the Level I Green-Naghdi equations. The unsteady motion of the plate is obtained by solving the nonlinear equations of motion. The results are obtained for a range of waves with varying heights and periods. The amplitude and period of plate oscillations are analyzed as functions of the wave parameters and plate width. Particular attention is given to the selection of the site of desired wave field. Initial estimation on the amount of energy extraction from the device, located near shore at a given site, is provided.

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

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.

Nonlinear stability of Halley comethosheath with transverse plasma motion

NASA Technical Reports Server (NTRS)

Srivastava, Krishna M.; Tsurutani, Bruce T.

1994-01-01

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

Nonclassical acoustics

NASA Technical Reports Server (NTRS)

Kentzer, C. P.

1976-01-01

A statistical approach to sound propagation is considered in situations where, due to the presence of large gradients of properties of the medium, the classical (deterministic) treatment of wave motion is inadequate. Mathematical methods for wave motions not restricted to small wavelengths (analogous to known methods of quantum mechanics) are used to formulate a wave theory of sound in nonuniform flows. Nonlinear transport equations for field probabilities are derived for the limiting case of noninteracting sound waves and it is postulated that such transport equations, appropriately generalized, may be used to predict the statistical behavior of sound in arbitrary flows.

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.

Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves

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

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

2017-05-10

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

Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Nonlinear dust-lattice waves: a modified Toda lattice

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

Cramer, N. F.

Charged dust grains in a plasma interact with a Coulomb potential, but also with an exponential component to the potential, due to Debye shielding in the background plasma. Here we investigate large-amplitude oscillations and waves in dust-lattices, employing techniques used in Toda lattice analysis. The lattice consists of a linear chain of particles, or a periodic ring as occurs in experimentally observed dust particle clusters. The particle motion has a triangular waveform, and chaotic motion for large amplitude motion of a grain.

A Fully Nonlinear, Dynamically Consistent Numerical Model for Solid-Body Ship Motion. I. Ship Motion with Fixed Heading

NASA Technical Reports Server (NTRS)

Lin, Ray-Quing; Kuang, Weijia

2011-01-01

In this paper, we describe the details of our numerical model for simulating ship solidbody motion in a given environment. In this model, the fully nonlinear dynamical equations governing the time-varying solid-body ship motion under the forces arising from ship wave interactions are solved with given initial conditions. The net force and moment (torque) on the ship body are directly calculated via integration of the hydrodynamic pressure over the wetted surface and the buoyancy effect from the underwater volume of the actual ship hull with a hybrid finite-difference/finite-element method. Neither empirical nor free parametrization is introduced in this model, i.e. no a priori experimental data are needed for modelling. This model is benchmarked with many experiments of various ship hulls for heave, roll and pitch motion. In addition to the benchmark cases, numerical experiments are also carried out for strongly nonlinear ship motion with a fixed heading. These new cases demonstrate clearly the importance of nonlinearities in ship motion modelling.

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.

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

PubMed

Zubarev, Nikolay M; Zubareva, Olga V

2010-10-01

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

Nonlinear Longitudinal Mode Instability in Liquid Propellant Rocket Engine Preburners

NASA Technical Reports Server (NTRS)

Sims, J. D. (Technical Monitor); Flandro, Gary A.; Majdalani, Joseph; Sims, Joseph D.

2004-01-01

Nonlinear pressure oscillations have been observed in liquid propellant rocket instability preburner devices. Unlike the familiar transverse mode instabilities that characterize primary combustion chambers, these oscillations appear as longitudinal gas motions with frequencies that are typical of the chamber axial acoustic modes. In several respects, the phenomenon is similar to longitudinal mode combustion instability appearing in low-smoke solid propellant motors. An important feature is evidence of steep-fronted wave motions with very high amplitude. Clearly, gas motions of this type threaten the mechanical integrity of associated engine components and create unacceptably high vibration levels. This paper focuses on development of the analytical tools needed to predict, diagnose, and correct instabilities of this type. For this purpose, mechanisms that lead to steep-fronted, high-amplitude pressure waves are described in detail. It is shown that such gas motions are the outcome of the natural steepening process in which initially low amplitude standing acoustic waves grow into shock-like disturbances. The energy source that promotes this behavior is a combination of unsteady combustion energy release and interactions with the quasi-steady mean chamber flow. Since shock waves characterize the gas motions, detonation-like mechanisms may well control the unsteady combustion processes. When the energy gains exceed the losses (represented mainly by nozzle and viscous damping), the waves can rapidly grow to a finite amplitude limit cycle. Analytical tools are described that allow the prediction of the limit cycle amplitude and show the dependence of this wave amplitude on the system geometry and other design parameters. This information can be used to guide corrective procedures that mitigate or eliminate the oscillations.

Comparison of formulas for resonant interactions between energetic electrons and oblique whistler-mode waves

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

Li, Jinxing, E-mail: lijx@pku.edu.cn; Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California 90095; Bortnik, Jacob

2015-05-15

Test particle simulation is a useful method for studying both linear and nonlinear wave-particle interactions in the magnetosphere. The gyro-averaged equations of particle motion for first-order and other cyclotron harmonic resonances with oblique whistler-mode waves were first derived by Bell [J. Geophys. Res. 89, 905 (1984)] and the most recent relativistic form was given by Ginet and Albert [Phys. Fluids B 3, 2994 (1991)], and Bortnik [Ph.D. thesis (Stanford University, 2004), p. 40]. However, recently we found there was a (−1){sup l−1} term difference between their formulas of perpendicular motion for the lth-order resonance. This article presents the detailed derivationmore » process of the generalized resonance formulas, and suggests a check of the signs for self-consistency, which is independent of the choice of conventions, that is, the energy variation equation resulting from the momentum equations should not contain any wave magnetic components, simply because the magnetic field does not contribute to changes of particle energy. In addition, we show that the wave centripetal force, which was considered small and was neglect in previous studies of nonlinear interactions, has a profound time derivative and can significantly enhance electron phase trapping especially in high frequency waves. This force can also bounce the low pitch angle particles out of the loss cone. We justify both the sign problem and the missing wave centripetal force by demonstrating wave-particle interaction examples, and comparing the gyro-averaged particle motion to the full particle motion under the Lorentz force.« less

Comparison of formulas for resonant interactions between energetic electrons and oblique whistler-mode waves

NASA Astrophysics Data System (ADS)

Li, Jinxing; Bortnik, Jacob; Xie, Lun; Pu, Zuyin; Chen, Lunjin; Ni, Binbin; Tao, Xin; Thorne, Richard M.; Fu, Suiyan; Yao, Zhonghua; Guo, Ruilong

2015-05-01

Test particle simulation is a useful method for studying both linear and nonlinear wave-particle interactions in the magnetosphere. The gyro-averaged equations of particle motion for first-order and other cyclotron harmonic resonances with oblique whistler-mode waves were first derived by Bell [J. Geophys. Res. 89, 905 (1984)] and the most recent relativistic form was given by Ginet and Albert [Phys. Fluids B 3, 2994 (1991)], and Bortnik [Ph.D. thesis (Stanford University, 2004), p. 40]. However, recently we found there was a ( - 1 ) l - 1 term difference between their formulas of perpendicular motion for the lth-order resonance. This article presents the detailed derivation process of the generalized resonance formulas, and suggests a check of the signs for self-consistency, which is independent of the choice of conventions, that is, the energy variation equation resulting from the momentum equations should not contain any wave magnetic components, simply because the magnetic field does not contribute to changes of particle energy. In addition, we show that the wave centripetal force, which was considered small and was neglect in previous studies of nonlinear interactions, has a profound time derivative and can significantly enhance electron phase trapping especially in high frequency waves. This force can also bounce the low pitch angle particles out of the loss cone. We justify both the sign problem and the missing wave centripetal force by demonstrating wave-particle interaction examples, and comparing the gyro-averaged particle motion to the full particle motion under the Lorentz force.

Verification of nonlinear particle simulation of radio frequency waves in fusion plasmas

NASA Astrophysics Data System (ADS)

Kuley, Animesh; Bao, Jian; Lin, Zhihong

2015-11-01

Nonlinear global particle simulation model has been developed in GTC to study the nonlinear interactions of radio frequency (RF) waves with plasmas in tokamak. In this model, ions are considered as fully kinetic particles using the Vlasov equation and electrons are treated as guiding centers using the drift kinetic. Boris push scheme for the ion motion has been implemented in the toroidal geometry using magnetic coordinates and successfully verified for the ion cyclotron, ion Bernstein and lower hybrid waves. The nonlinear GTC simulation of the lower hybrid wave shows that the amplitude of the electrostatic potential is oscillatory due to the trapping of resonant electrons by the electric field of the lower hybrid wave. The nonresonant parametric decay is observed an IBW sideband and an ion cyclotron quasimode (ICQM). The ICQM induces an ion perpendicular heating with a heating rate proportional to the pump wave intensity. This work is supported by PPPL subcontract number S013849-F and US Department of Energy (DOE) SciDAC GSEP Program.

Analytical and Numerical Modeling of Tsunami Wave Propagation for double layer state in Bore

NASA Astrophysics Data System (ADS)

Yuvaraj, V.; Rajasekaran, S.; Nagarajan, D.

2018-04-01

Tsunami wave enters into the river bore in the landslide. Tsunami wave propagation are described in two-layer states. The velocity and amplitude of the tsunami wave propagation are calculated using the double layer. The numerical and analytical solutions are given for the nonlinear equation of motion of the wave propagation in a bore.

Nonlinear water waves generated by impulsive motion of submerged obstacle

NASA Astrophysics Data System (ADS)

Makarenko, N.; Kostikov, V.

2012-04-01

The fully nonlinear problem on generation of unsteady water waves by impulsively moving obstacle is studied analytically. The method involves the reduction of basic Euler equations to the integral-differential system for the wave elevation together with normal and tangential fluid velocities at the free surface. Exact model equations are derived in explicit form when the isolated obstacle is presented by totally submerged circular- or elliptic cylinder. Small-time asymptotic solution is constructed for the cylinder which starts moving with constant acceleration from rest. It is demonstrated that the leading-order solution terms describe several wave regimes such as the formation of non-stationary splash jets by vertical rising or vertical submersion of the obstacle, as well as the generation of diverging waves by horizontal- and combined motion of the obstacle under free surface. This work was supported by RFBR (grant No 10-01-00447) and by Research Program of the Russian Government (grant No 11.G34.31.0035).

A novel nonlinear damage resonance intermodulation effect for structural health monitoring

NASA Astrophysics Data System (ADS)

Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele

2017-04-01

This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

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.

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.

Nonlinear transient waves in coupled phase oscillators with inertia.

PubMed

Jörg, David J

2015-05-01

Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.

Nonlinear Wave propagation at sediment layers

NASA Astrophysics Data System (ADS)

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

2002-12-01

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

Simple estimation of linear 1+1 D tsunami run-up

NASA Astrophysics Data System (ADS)

Fuentes, M.; Campos, J. A.; Riquelme, S.

2016-12-01

An analytical expression is derived concerning the linear run-up for any given initial wave generated over a sloping bathymetry. Due to the simplicity of the linear formulation, complex transformations are unnecessay, because the shoreline motion is directly obtained in terms of the initial wave. This analytical result not only supports maximum run-up invariance between linear and non-linear theories, but also the time evolution of shoreline motion and velocity. The results exhibit good agreement with the non-linear theory. The present formulation also allows computing the shoreline motion numerically from a customised initial waveform, including non-smooth functions. This is useful for numerical tests, laboratory experiments or realistic cases in which the initial disturbance might be retrieved from seismic data rather than using a theoretical model. It is also shown that the real case studied is consistent with the field observations.

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.

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

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

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1989-01-01

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

Study of nonlinear MHD equations governing the wave propagation in twisted coronal loops

NASA Technical Reports Server (NTRS)

Parhi, S.; DeBruyne, P.; Goossens, M.; Zhelyazkov, I.

1995-01-01

The solar corona, modelled by a low beta, resistive plasma slab, sustains MHD wave propagations due to shearing footpoint motions in the photosphere. By using a numerical algorithm the excitation and nonlinear development of MHD waves in twisted coronal loops are studied. The plasma responds to the footpoint motion by sausage waves if there is no twist. The twist in the magnetic field of the loop destroys initially developed sausage-like wave modes and they become kinks. The transition from sausage to kink modes is analyzed. The twist brings about mode degradation producing high harmonics and this generates more complex fine structures. This can be attributed to several local extrema in the perturbed velocity profiles. The Alfven wave produces remnants of the ideal 1/x singularity both for zero and non-zero twist and this pseudo-singularity becomes less pronounced for larger twist. The effect of nonlinearity is clearly observed by changing the amplitude of the driver by one order of magnitude. The magnetosonic waves also exhibit smoothed remnants of ideal logarithmic singularities when the frequency of the driver is correctly chosen. This pseudo-singularity for fast waves is absent when the coronal loop does not undergo any twist but becomes pronounced when twist is included. On the contrary, it is observed for slow waves even if there is no twist. Increasing the twist leads to a higher heating rate of the loop. The larger twist shifts somewhat uniformly distributed heating to layers inside the slab corresponding to peaks in the magnetic field strength.

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.

Complexiton and solitary wave solutions of the coupled nonlinear Maccari’s system using two integration schemes

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Nuray, Elif

2018-01-01

In this paper, we consider a coupled nonlinear Maccari’s system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the solitary wave solutions. They are the modified F-Expansion and the generalized projective Riccati equation methods. Topological, non-topological, complexiton, singular and trigonometric function solutions are derived. A comparison between the results in this paper and the well-known results in the literature is also given. The derived structures of the obtained solutions offer a rich platform to study the nonlinear CNMS. Numerical simulation of the obtained solutions are presented with interesting figures showing the physical meaning of the solutions.

Nonlocal Sediment Transport on Steep Lateral Moraines, Eastern Sierra Nevada, California, USA

NASA Astrophysics Data System (ADS)

Doane, Tyler H.; Furbish, David Jon; Roering, Joshua J.; Schumer, Rina; Morgan, Daniel J.

2018-01-01

Recent work has highlighted the significance of long-distance particle motions in hillslope sediment transport. Such motions imply that the flux at a given hillslope position is appropriately described as a weighted function of surrounding conditions that influence motions reaching the given position. Although the idea of nonlocal sediment transport is well grounded in theory, limited field evidence has been provided. We test local and nonlocal formulations of the flux and compare their ability to reproduce land surface profiles of steep moraines in California. We show that nonlocal and nonlinear models better reproduce evolved land surface profiles, notably the amount of lowering and concavity near the moraine crest and the lengthening and straightening of the depositional apron. The analysis provides the first estimates of key parameters that set sediment entrainment rates and travel distances in nonlocal formulations and highlights the importance of correctly specifying the entrainment rate when modeling land surface evolution. Moraine evolution associated with nonlocal and nonlinear transport formulations, when described in terms of the evolution of the Fourier transform of the moraine surface, displays a distinct behavior involving growth of certain wave numbers, in contrast to the decay of all wave numbers associated with linear transport. Nonlinear and nonlocal formulations share key mathematical elements yielding a nonlinear relation between the flux and the land surface slope.

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.

Effect of magnetic quantization on ion acoustic waves ultra-relativistic dense plasma

NASA Astrophysics Data System (ADS)

Javed, Asif; Rasheed, A.; Jamil, M.; Siddique, M.; Tsintsadze, N. L.

2017-11-01

In this paper, we have studied the influence of magnetic quantization of orbital motion of the electrons on the profile of linear and nonlinear ion-acoustic waves, which are propagating in the ultra-relativistic dense magneto quantum plasmas. We have employed both Thomas Fermi and Quantum Magneto Hydrodynamic models (along with the Poisson equation) of quantum plasmas. To investigate the large amplitude nonlinear structure of the acoustic wave, Sagdeev-Pseudo-Potential approach has been adopted. The numerical analysis of the linear dispersion relation and the nonlinear acoustic waves has been presented by drawing their graphs that highlight the effects of plasma parameters on these waves in both the linear and the nonlinear regimes. It has been noticed that only supersonic ion acoustic solitary waves can be excited in the above mentioned quantum plasma even when the value of the critical Mach number is less than unity. Both width and depth of Sagdeev potential reduces on increasing the magnetic quantization parameter η. Whereas the amplitude of the ion acoustic soliton reduces on increasing η, its width appears to be directly proportional to η. The present work would be helpful to understand the excitation of nonlinear ion-acoustic waves in the dense astrophysical environments such as magnetars and in intense-laser plasma interactions.

Second-harmonic generation in shear wave beams with different polarizations

NASA Astrophysics Data System (ADS)

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

2015-10-01

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1988-01-01

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

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

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

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

2011-01-04

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

Nonlinear and linear bottom interaction effects in shallow water

NASA Technical Reports Server (NTRS)

Shemdin, O.; Hsiao, S. V.; Hasselmann, K.; Herterich, K.

1978-01-01

The paper examines wave-energy dissipation rates in shallow water calculated from measured wave spectra at different distances from the shore. Different linear and nonlinear transfer and dissipation mechanisms are discussed. The various data sets are interpreted in terms of prevailing mechanisms at the respective sites. The incorporation of different processes in a predictive shallow-water model is outlined. The analysis suggests that bottom motion is primarily responsible for wave-energy dissipation in the Delta Region of the Gulf of Mexico, that friction is mainly responsible for wave-energy dissipation in Marineland, Panama City and Melkbosstrand, and that percolation is probably the dominant mechanism in the JONSWAP area of the North Sea.

Modeling nonlinearities in MEMS oscillators.

PubMed

Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A

2013-08-01

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

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.

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.

Linear stability and nonlinear analyses of traffic waves for the general nonlinear car-following model with multi-time delays

NASA Astrophysics Data System (ADS)

Sun, Dihua; Chen, Dong; Zhao, Min; Liu, Weining; Zheng, Linjiang

2018-07-01

In this paper, the general nonlinear car-following model with multi-time delays is investigated in order to describe the reactions of vehicle to driving behavior. Platoon stability and string stability criteria are obtained for the general nonlinear car-following model. Burgers equation and Korteweg de Vries (KdV) equation and their solitary wave solutions are derived adopting the reductive perturbation method. We investigate the properties of typical optimal velocity model using both analytic and numerical methods, which estimates the impact of delays about the evolution of traffic congestion. The numerical results show that time delays in sensing relative movement is more sensitive to the stability of traffic flow than time delays in sensing host motion.

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

NASA Astrophysics Data System (ADS)

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

2007-09-01

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

Introduction to Plasma Physics

NASA Astrophysics Data System (ADS)

Gurnett, Donald A.; Bhattacharjee, Amitava

2017-03-01

Preface; 1. Introduction; 2. Characteristic parameters of a plasma; 3. Single particle motions; 4. Waves in a cold plasma; 5. Kinetic theory and the moment equations; 6. Magnetohydrodynamics; 7. MHD equilibria and stability; 8. Discontinuities and shock waves; 9. Electrostatic waves in a hot unmagnetized plasma; 10. Waves in a hot magnetized plasma; 11. Nonlinear effects; 12. Collisional processes; Appendix A. Symbols; Appendix B. Useful trigonometric identities; Appendix C. Vector differential operators; Appendix D. Vector calculus identities; Index.

Acoustic-radiation stress in solids. I - Theory

NASA Technical Reports Server (NTRS)

Cantrell, J. H., Jr.

1984-01-01

The general case of acoustic-radiation stress associated with quasi-compressional and quasi-shear waves propagating in infinite and semiinfinite lossless solids of arbitrary crystalline symmetry is studied. The Boussinesq radiation stress is defined and found to depend directly on an acoustic nonlinearity parameter which characterizes the radiation-induced static strain, a stress-generalized nonlinearity parameter which characterizes the stress nonlinearity, and the energy density of the propagating wave. Application of the Boltzmann-Ehrenfest principle of adiabatic invariance to a self-constrained system described by the nonlinear equations of motion allows the acoustic-radiation-induced static strain to be identified with a self-constrained variation in the time-averaged product of the internal energy density and displacement gradient. The time-averaged product is scaled by the acoustic nonlinearity parameter and represents the first-order nonlinearity in the virial theorem. Finally, the relationship between the Boussinesq and the Cauchy radiation stress is obtained in a closed three-dimensional form.

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

NASA Astrophysics Data System (ADS)

Wang, Zhiqiang; Zhai, Hao; Gao, Zhuxiu

2017-12-01

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

Time and space analysis of turbulence of gravity surface waves

NASA Astrophysics Data System (ADS)

Mordant, Nicolas; Aubourg, Quentin; Viboud, Samuel; Sommeria, Joel

2016-11-01

Wave turbulence is a statistical state made of a very large number of nonlinearly interacting waves. The Weak Turbulence Theory was developed to describe such a situation in the weakly nonlinear regime. Although, oceanic data tend to be compatible with the theory, laboratory data fail to fulfill the theoretical predictions. A space-time resolved measurement of the waves have proven to be especially fruitful to identify the mechanism at play in turbulence of gravity-capillary waves. We developed an image processing algorithm to measure the motion of the surface of water with both space and time resolution. We first seed the surface with slightly buoyant polystyrene particles and use 3 cameras to reconstruct the surface. Our stereoscopic algorithm is coupled to PIV so that to obtain both the surface deformation and the velocity of the water surface. Such a coupling is shown to improve the sensitivity of the measurement by one order of magnitude. We use this technique to probe the existence of weakly nonlinear turbulence excited by two small wedge wavemakers in a 13-m diameter wave flume. We observe a truly weakly nonlinear regime of isotropic wave turbulence. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No 647018-WATU).

Transmission and reflection of strongly nonlinear solitary waves at granular interfaces.

PubMed

Tichler, A M; Gómez, L R; Upadhyaya, N; Campman, X; Nesterenko, V F; Vitelli, V

2013-07-26

The interaction of a solitary wave with an interface formed by two strongly nonlinear noncohesive granular lattices displays rich behavior, characterized by the breakdown of continuum equations of motion in the vicinity of the interface. By treating the solitary wave as a quasiparticle with an effective mass, we construct an intuitive (energy- and linear-momentum-conserving) discrete model to predict the amplitudes of the transmitted solitary waves generated when an incident solitary-wave front, parallel to the interface, moves from a denser to a lighter granular hexagonal lattice. Our findings are corroborated with simulations. We then successfully extend this model to oblique interfaces, where we find that the angle of refraction and reflection of a solitary wave follows, below a critical value, an analogue of Snell's law in which the solitary-wave speed replaces the speed of sound, which is zero in the sonic vacuum.

Transmission and Reflection of Strongly Nonlinear Solitary Waves at Granular Interfaces

NASA Astrophysics Data System (ADS)

Tichler, A. M.; Gómez, L. R.; Upadhyaya, N.; Campman, X.; Nesterenko, V. F.; Vitelli, V.

2013-07-01

The interaction of a solitary wave with an interface formed by two strongly nonlinear noncohesive granular lattices displays rich behavior, characterized by the breakdown of continuum equations of motion in the vicinity of the interface. By treating the solitary wave as a quasiparticle with an effective mass, we construct an intuitive (energy- and linear-momentum-conserving) discrete model to predict the amplitudes of the transmitted solitary waves generated when an incident solitary-wave front, parallel to the interface, moves from a denser to a lighter granular hexagonal lattice. Our findings are corroborated with simulations. We then successfully extend this model to oblique interfaces, where we find that the angle of refraction and reflection of a solitary wave follows, below a critical value, an analogue of Snell’s law in which the solitary-wave speed replaces the speed of sound, which is zero in the sonic vacuum.

Particle motions beneath irrotational water waves

NASA Astrophysics Data System (ADS)

Bakhoday-Paskyabi, Mostafa

2015-08-01

Neutral and buoyant particle motions in an irrotational flow are investigated under the passage of linear, nonlinear gravity, and weakly nonlinear solitary waves at a constant water depth. The developed numerical models for the particle trajectories in a non-turbulent flow incorporate particle momentum, size, and mass (i.e., inertial particles) under the influence of various surface waves such as Korteweg-de Vries waves which admit a three parameter family of periodic cnoidal wave solutions. We then formulate expressions of mass-transport velocities for the neutral and buoyant particles. A series of test cases suggests that the inertial particles possess a combined horizontal and vertical drifts from the locations of their release, with a fall velocity as a function of particle material properties, ambient flow, and wave parameters. The estimated solutions exhibit good agreement with previously explained particle behavior beneath progressive surface gravity waves. We further investigate the response of a neutrally buoyant water parcel trajectories in a rotating fluid when subjected to a series of wind and wave events. The results confirm the importance of the wave-induced Coriolis-Stokes force effect in both amplifying (destroying) the pre-existing inertial oscillations and in modulating the direction of the flow particles. Although this work has mainly focused on wave-current-particle interaction in the absence of turbulence stochastic forcing effects, the exercise of the suggested numerical models provides additional insights into the mechanisms of wave effects on the passive trajectories for both living and nonliving particles such as swimming trajectories of plankton in non-turbulent flows.

Strong Langmuir Turbulence and Four-Wave Mixing

NASA Astrophysics Data System (ADS)

Glanz, James

1991-02-01

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

Mechanics of the Mammalian Cochlea

PubMed Central

Robles, Luis; Ruggero, Mario A.

2013-01-01

In mammals, environmental sounds stimulate the auditory receptor, the cochlea, via vibrations of the stapes, the innermost of the middle ear ossicles. These vibrations produce displacement waves that travel on the elongated and spirally wound basilar membrane (BM). As they travel, waves grow in amplitude, reaching a maximum and then dying out. The location of maximum BM motion is a function of stimulus frequency, with high-frequency waves being localized to the “base” of the cochlea (near the stapes) and low-frequency waves approaching the “apex” of the cochlea. Thus each cochlear site has a characteristic frequency (CF), to which it responds maximally. BM vibrations produce motion of hair cell stereocilia, which gates stereociliar transduction channels leading to the generation of hair cell receptor potentials and the excitation of afferent auditory nerve fibers. At the base of the cochlea, BM motion exhibits a CF-specific and level-dependent compressive nonlinearity such that responses to low-level, near-CF stimuli are sensitive and sharply frequency-tuned and responses to intense stimuli are insensitive and poorly tuned. The high sensitivity and sharp-frequency tuning, as well as compression and other nonlinearities (two-tone suppression and intermodulation distortion), are highly labile, indicating the presence in normal cochleae of a positive feedback from the organ of Corti, the “cochlear amplifier.” This mechanism involves forces generated by the outer hair cells and controlled, directly or indirectly, by their transduction currents. At the apex of the cochlea, nonlinearities appear to be less prominent than at the base, perhaps implying that the cochlear amplifier plays a lesser role in determining apical mechanical responses to sound. Whether at the base or the apex, the properties of BM vibration adequately account for most frequency-specific properties of the responses to sound of auditory nerve fibers. PMID:11427697

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

Benisti, Didier; Morice, Olivier; Gremillet, Laurent

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

Nonlinear damping based semi-active building isolation system

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks

NASA Astrophysics Data System (ADS)

Santucci, F.; Santini, P. M.

2016-10-01

We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

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

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation formore » the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.« less

Solitonic Dispersive Hydrodynamics: Theory and Observation

NASA Astrophysics Data System (ADS)

Maiden, Michelle D.; Anderson, Dalton V.; Franco, Nevil A.; El, Gennady A.; Hoefer, Mark A.

2018-04-01

Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental investigations of each separately, experiments and a unified theory of solitons and dispersive hydrodynamics are lacking. Here, a general soliton-mean field theory is introduced and used to describe the propagation of solitons in macroscopic hydrodynamic flows. Two universal adiabatic invariants of motion are identified that predict trapping or transmission of solitons by hydrodynamic states. The result of solitons incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves is the same, an effect termed hydrodynamic reciprocity. Experiments on viscous fluid conduits quantitatively confirm the soliton-mean field theory with broader implications for nonlinear optics, superfluids, geophysical fluids, and other dispersive hydrodynamic media.

Numerical simulation of solitary waves on deep water with constant vorticity

NASA Astrophysics Data System (ADS)

Dosaev, A. S.; Shishina, M. I.; Troitskaya, Yu I.

2018-01-01

Characteristics of solitary deep water waves on a flow with constant vorticity are investigated by numerical simulation within the framework of fully nonlinear equations of motion (Euler equations) using the method of surface-tracking conformal coordinates. To ensure that solutions observed are stable, soliton formation as a result of disintegration of an initial pulse-like disturbance is modeled. Evidence is obtained that solitary waves with height above a certain threshold are unstable.

Modulation theory, dispersive shock waves and Gerald Beresford Whitham

NASA Astrophysics Data System (ADS)

Minzoni, A. A.; Smyth, Noel F.

2016-10-01

Gerald Beresford (GB) Whitham, FRS, (13th December, 1927-26th January, 2014) was one of the leading applied mathematicians of the twentieth century whose work over forty years had a profound, formative impact on research on wave motion across a broad range of areas. Many of the ideas and techniques he developed have now become the standard tools used to analyse and understand wave motion, as the papers of this special issue of Physica D testify. Many of the techniques pioneered by GB Whitham have spread beyond wave propagation into other applied mathematics areas, such as reaction-diffusion, and even into theoretical physics and pure mathematics, in which Whitham modulation theory is an active area of research. GB Whitham's classic textbook Linear and Nonlinear Waves, published in 1974, is still the standard reference for the applied mathematics of wave motion. In honour of his scientific achievements, GB Whitham was elected a Fellow of the American Academy of Arts and Sciences in 1959 and a Fellow of the Royal Society in 1965. He was awarded the Norbert Wiener Prize for Applied Mathematics in 1980.

Nonautonomous characteristics of the breathers and rogue waves for a amplifier nonlinear Schrödinger Maxwell-Bloch system

NASA Astrophysics Data System (ADS)

Wang, Lei; Li, Xiao; Zhang, Lu Lu; Li, Min; Qi, Feng-Hua

2015-09-01

Under investigation in this paper is a amplifier nonlinear Schrödinger Maxwell-Bloch (NLS-MB) system which describes the propagation of optical pulses in an inhomogeneous erbium doped fiber. Nonautonomous breather and rogue wave (RW) solutions of the amplifier NLS-MB system are constructed via the modified Darboux transformation with the inhomogeneous parameters. By suitably choosing the dispersion coefficient function, several types of inhomogeneous nonlinear waves are obtained in: (1) periodically fluctuating dispersion profile; (2) exponentially increasing (or decreasing) dispersion profile; and (3) linearly decreasing (increasing) dispersion profile. The nonautonomous characteristics of the breathers and RWs are graphically investigated, including the breather accelerating and decelerating motions, boomerang breather, breather compression, breather evolution, periodic RW, boomerang RW and stationary RW. Such novel patterns as the periodic breathers and rogue-wave fission of the amplifier NLS-MB system are exhibited by properly adjusting the group velocity dispersion function and interaction parameter between silica and doped atoms.

Modeling stick-slip-separation dynamics in a bimodal standing wave ultrasonic motor

NASA Astrophysics Data System (ADS)

Li, Xiang; Yao, Zhiyuan; Lv, Qibao; Liu, Zhen

2016-11-01

Ultrasonic motor (USM) is an electromechanical coupling system with ultrasonic vibration, which is driven by the frictional contact force between the stator (vibrating body) and the rotor/slider (driven body). Stick-slip motion can occur at the contact interface when USM is operating, which may affect the performance of the motor. This paper develops a physically-based model to investigate the complex stick-slip-separation dynamics in a bimodal standing wave ultrasonic motor. The model includes both friction nonlinearity and intermittent separation nonlinearity of the system. Utilizing Hamilton's principle and assumed mode method, the dynamic equations of the stator are deduced. Based on the dynamics of the stator and the slider, sticking force during the stick phase is derived, which is used to examine the stick-to-slip transition. Furthermore, the stick-slip-separation kinematics is analyzed by establishing analytical criteria that predict the transition between stick, slip and separation of the interface. Stick-slip-separation motion is observed in the resulting model, and numerical simulations are performed to study the influence of parameters on the range of possible motions. Results show that stick-slip motion can occur with greater preload and smaller voltage amplitude. Furthermore, a dimensionless parameter is proposed to predict the occurrence of stick-slip versus slip-separation motions, and its role in designing ultrasonic motors is discussed. It is shown that slip-separation motion is favorable for the slider velocity.

Turbulence and wave particle interactions in solar-terrestrial plasmas

NASA Technical Reports Server (NTRS)

Dulk, G. A.

1982-01-01

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

On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

NASA Astrophysics Data System (ADS)

Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

2015-04-01

The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.

Nonlinear Propagation of Alfven Waves Driven by Observed Photospheric Motions: Application to the Coronal Heating and Spicule Formation

NASA Astrophysics Data System (ADS)

Matsumoto, Takuma; Shibata, Kazunari

We have performed MHD simulations of Alfven wave propagation along an open ux tube in the solar atmosphere. In our numerical model, Alfven waves are generated by the photospheric granular motion. As the wave generator, we used a derived temporal spectrum of the photo-spheric granular motion from G-band movies of Hinode/SOT. It is shown that the total energy ux at the corona becomes larger and the transition region height becomes higher in the case when we use the observed spectrum rather than white/pink noise spectrum as the wave gener-ator. This difference can be explained by the Alfven wave resonance between the photosphere and the transition region. After performing Fourier analysis on our numerical results, we have found that the region between the photosphere and the transition region becomes an Alfven wave resonant cavity. We have conrmed that there are at least three resonant frequencies, 1, 3 and 5 mHz, in our numerical model. Alfven wave resonance is one of the most effective mechanisms to explain the dynamics of the spicules and the sufficient energy ux to heat the corona.

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.

Modeling Boulder Transport by Smooth Particle Hydrodynamics

NASA Astrophysics Data System (ADS)

Karpytchev, M.

2017-12-01

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

Analysis of Ground Motion from An Underground Chemical Explosion

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

Pitarka, Arben; Mellors, Robert J.; Walter, William R.

Here in this paper we investigate the excitation and propagation of far-field seismic waves from the 905 kg trinitrotoluene equivalent underground chemical explosion SPE-3 recorded during the Source Physics Experiment (SPE) at the Nevada National Security Site. The recorded far-field ground motion at short and long distances is characterized by substantial shear-wave energy, and large azimuthal variations in P-and S-wave amplitudes. The shear waves observed on the transverse component of sensors at epicentral distances <50 m suggests they were generated at or very near the source. The relative amplitude of the shear waves grows as the waves propagate away frommore » the source. We analyze and model the shear-wave excitation during the explosion in the 0.01–10 Hz frequency range, at epicentral distances of up to 1 km. We used two simulation techniques. One is based on the empirical isotropic Mueller–Murphy (MM) (Mueller and Murphy, 1971) nuclear explosion source model, and 3D anelastic wave propagation modeling. The second uses a physics-based approach that couples hydrodynamic modeling of the chemical explosion source with anelastic wave propagation modeling. Comparisons with recorded data show the MM source model overestimates the SPE-3 far-field ground motion by an average factor of 4. The observations show that shear waves with substantial high-frequency energy were generated at the source. However, to match the observations additional shear waves from scattering, including surface topography, and heterogeneous shallow structure contributed to the amplification of far-field shear motion. Comparisons between empirically based isotropic and physics-based anisotropic source models suggest that both wave-scattering effects and near-field nonlinear effects are needed to explain the amplitude and irregular radiation pattern of shear motion observed during the SPE-3 explosion.« less

Analysis of Ground Motion from An Underground Chemical Explosion

DOE PAGES

Pitarka, Arben; Mellors, Robert J.; Walter, William R.; ...

2015-09-08

Here in this paper we investigate the excitation and propagation of far-field seismic waves from the 905 kg trinitrotoluene equivalent underground chemical explosion SPE-3 recorded during the Source Physics Experiment (SPE) at the Nevada National Security Site. The recorded far-field ground motion at short and long distances is characterized by substantial shear-wave energy, and large azimuthal variations in P-and S-wave amplitudes. The shear waves observed on the transverse component of sensors at epicentral distances <50 m suggests they were generated at or very near the source. The relative amplitude of the shear waves grows as the waves propagate away frommore » the source. We analyze and model the shear-wave excitation during the explosion in the 0.01–10 Hz frequency range, at epicentral distances of up to 1 km. We used two simulation techniques. One is based on the empirical isotropic Mueller–Murphy (MM) (Mueller and Murphy, 1971) nuclear explosion source model, and 3D anelastic wave propagation modeling. The second uses a physics-based approach that couples hydrodynamic modeling of the chemical explosion source with anelastic wave propagation modeling. Comparisons with recorded data show the MM source model overestimates the SPE-3 far-field ground motion by an average factor of 4. The observations show that shear waves with substantial high-frequency energy were generated at the source. However, to match the observations additional shear waves from scattering, including surface topography, and heterogeneous shallow structure contributed to the amplification of far-field shear motion. Comparisons between empirically based isotropic and physics-based anisotropic source models suggest that both wave-scattering effects and near-field nonlinear effects are needed to explain the amplitude and irregular radiation pattern of shear motion observed during the SPE-3 explosion.« less

Simulation of broadband ground motion including nonlinear soil effects for a magnitude 6.5 earthquake on the Seattle fault, Seattle, Washington

USGS Publications Warehouse

Hartzell, S.; Leeds, A.; Frankel, A.; Williams, R.A.; Odum, J.; Stephenson, W.; Silva, W.

2002-01-01

The Seattle fault poses a significant seismic hazard to the city of Seattle, Washington. A hybrid, low-frequency, high-frequency method is used to calculate broadband (0-20 Hz) ground-motion time histories for a M 6.5 earthquake on the Seattle fault. Low frequencies (1 Hz) are calculated by a stochastic method that uses a fractal subevent size distribution to give an ω-2 displacement spectrum. Time histories are calculated for a grid of stations and then corrected for the local site response using a classification scheme based on the surficial geology. Average shear-wave velocity profiles are developed for six surficial geologic units: artificial fill, modified land, Esperance sand, Lawton clay, till, and Tertiary sandstone. These profiles together with other soil parameters are used to compare linear, equivalent-linear, and nonlinear predictions of ground motion in the frequency band 0-15 Hz. Linear site-response corrections are found to yield unreasonably large ground motions. Equivalent-linear and nonlinear calculations give peak values similar to the 1994 Northridge, California, earthquake and those predicted by regression relationships. Ground-motion variance is estimated for (1) randomization of the velocity profiles, (2) variation in source parameters, and (3) choice of nonlinear model. Within the limits of the models tested, the results are found to be most sensitive to the nonlinear model and soil parameters, notably the over consolidation ratio.

Modeling of fatigue crack induced nonlinear ultrasonics using a highly parallelized explicit local interaction simulation approach

NASA Astrophysics Data System (ADS)

Shen, Yanfeng; Cesnik, Carlos E. S.

2016-04-01

This paper presents a parallelized modeling technique for the efficient simulation of nonlinear ultrasonics introduced by the wave interaction with fatigue cracks. The elastodynamic wave equations with contact effects are formulated using an explicit Local Interaction Simulation Approach (LISA). The LISA formulation is extended to capture the contact-impact phenomena during the wave damage interaction based on the penalty method. A Coulomb friction model is integrated into the computation procedure to capture the stick-slip contact shear motion. The LISA procedure is coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized supercomputing on powerful graphic cards. Both the explicit contact formulation and the parallel feature facilitates LISA's superb computational efficiency over the conventional finite element method (FEM). The theoretical formulations based on the penalty method is introduced and a guideline for the proper choice of the contact stiffness is given. The convergence behavior of the solution under various contact stiffness values is examined. A numerical benchmark problem is used to investigate the new LISA formulation and results are compared with a conventional contact finite element solution. Various nonlinear ultrasonic phenomena are successfully captured using this contact LISA formulation, including the generation of nonlinear higher harmonic responses. Nonlinear mode conversion of guided waves at fatigue cracks is also studied.

Solar coronal loop heating by cross-field wave transport

NASA Technical Reports Server (NTRS)

Amendt, Peter; Benford, Gregory

1989-01-01

Solar coronal arches heated by turbulent ion-cyclotron waves may suffer significant cross-field transport by these waves. Nonlinear processes fix the wave-propagation speed at about a tenth of the ion thermal velocity, which seems sufficient to spread heat from a central core into a large cool surrounding cocoon. Waves heat cocoon ions both through classical ion-electron collisions and by turbulent stochastic ion motions. Plausible cocoon sizes set by wave damping are in roughly kilometers, although the wave-emitting core may be only 100 m wide. Detailed study of nonlinear stabilization and energy-deposition rates predicts that nearby regions can heat to values intermediate between the roughly electron volt foot-point temperatures and the about 100 eV core, which is heated by anomalous Ohmic losses. A volume of 100 times the core volume may be affected. This qualitative result may solve a persistent problem with current-driven coronal heating; that it affects only small volumes and provides no way to produce the extended warm structures perceptible to existing instruments.

Nonintegrable Schrodinger discrete breathers.

PubMed

Gómez-Gardeñes, J; Floría, L M; Peyrard, M; Bishop, A R

2004-12-01

In an extensive numerical investigation of nonintegrable translational motion of discrete breathers in nonlinear Schrödinger lattices, we have used a regularized Newton algorithm to continue these solutions from the limit of the integrable Ablowitz-Ladik lattice. These solutions are shown to be a superposition of a localized moving core and an excited extended state (background) to which the localized moving pulse is spatially asymptotic. The background is a linear combination of small amplitude nonlinear resonant plane waves and it plays an essential role in the energy balance governing the translational motion of the localized core. Perturbative collective variable theory predictions are critically analyzed in the light of the numerical results.

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

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

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

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

Euler flow predictions for an oscillating cascade using a high resolution wave-split scheme

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Swafford, Timothy W.; Reddy, T. S. R.

1991-01-01

A compressible flow code that can predict the nonlinear unsteady aerodynamics associated with transonic flows over oscillating cascades is developed and validated. The code solves the two dimensional, unsteady Euler equations using a time-marching, flux-difference splitting scheme. The unsteady pressures and forces can be determined for arbitrary input motions, although only harmonic pitching and plunging motions are addressed. The code solves the flow equations on a H-grid which is allowed to deform with the airfoil motion. Predictions are presented for both flat plate cascades and loaded airfoil cascades. Results are compared to flat plate theory and experimental data. Predictions are also presented for several oscillating cascades with strong normal shocks where the pitching amplitudes, cascade geometry and interblade phase angles are varied to investigate nonlinear behavior.

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

Ro, Stephen; Matzner, Christopher D., E-mail: ro@astro.utoronto.ca

Wave-driven outflows and non-disruptive explosions have been implicated in pre-supernova outbursts, supernova impostors, luminous blue variable eruptions, and some narrow-line and superluminous supernovae. To model these events, we investigate the dynamics of stars set in motion by strong acoustic pulses and wave trains, focusing on nonlinear wave propagation, shock formation, and an early phase of the development of a weak shock. We identify the shock formation radius, showing that a heuristic estimate based on crossing characteristics matches an exact expansion around the wave front and verifying both with numerical experiments. Our general analytical condition for shock formation applies to one-dimensionalmore » motions within any static environment, including both eruptions and implosions. We also consider the early phase of shock energy dissipation. We find that waves of super-Eddington acoustic luminosity always create shocks, rather than damping by radiative diffusion. Therefore, shock formation is integral to super-Eddington outbursts.« less

Generation of realistic tsunami waves using a bottom-tilting wave maker

NASA Astrophysics Data System (ADS)

Park, Yong Sung; Hwang, Jin Hwan

2016-11-01

Tsunamis have caused more than 260,000 human losses and 250 billion in damage worldwide in the last ten years. Observations made during 2011 Japan Tohoku Tsunami revealed that the commonly used waves (solitary waves) to model tsunamis are at least an order-of-magnitude shorter than the real tsunamis, which calls for re-evaluation of the current understanding of tsunamis. To prompt the required paradigm shift, a new wave generator, namely the bottom-tilting wave generator, has been developed at the University of Dundee. The wave tank is fitted with an adjustable slope and a bottom flap hinged at the beginning of the slope. By moving the bottom flap up and down, we can generate very long waves. Here we will report characteristics of waves generated by simple bottom motions, either moving it upward or downward from an initial displacement ending it being horizontal. Two parameters, namely the initial displacement of the bottom and the speed of the motion, determine characteristics of the generated waves. Wave amplitudes scale well with the volume flux of the displaced water. On the other hand, due to combined effects of nonlinearity and dispersion, wavelengths show more complicated relationship with the two bottom motion parameters. We will also demonstrate that by combining simple up and down motions, it is possible to generate waves resembling the one measured during 2011 tsunami. YSP acknowledges financial support from the Royal Society of Edinburgh through the Royal Society of Edinburgh and Scottish Government Personal Research Fellowship Co-Funded by the Marie-Curie Actions.

Response functions for dimers and square-symmetric molecules in four-wave-mixing experiments with polarized light

NASA Astrophysics Data System (ADS)

Smith, Eric Ryan; Farrow, Darcie A.; Jonas, David M.

2005-07-01

Four-wave-mixing nonlinear-response functions are given for intermolecular and intramolecular vibrations of a perpendicular dimer and intramolecular vibrations of a square-symmetric molecule containing a doubly degenerate state. A two-dimensional particle-in-a-box model is used to approximate the electronic wave functions and obtain harmonic potentials for nuclear motion. Vibronic interactions due to symmetry-lowering distortions along Jahn-Teller active normal modes are discussed. Electronic dephasing due to nuclear motion along both symmetric and asymmetric normal modes is included in these response functions, but population transfer between states is not. As an illustration, these response functions are used to predict the pump-probe polarization anisotropy in the limit of impulsive excitation.

Collision of Identical Solitary Waves in Hertzian Chains

NASA Astrophysics Data System (ADS)

Sen, Surajit; Manciu, Marian; Hurd, Alan J.

2000-03-01

We consider a chain of elastic beads, which repel upon contact according to the non-linear Hertz potential. We further assume that the chain is under zero loading, i.e., the grains have zero initial overlap. We show via careful numerical solution of the equations of motion that an impulse propagates as a solitary wave and that the collision of identical solitary waves propagating in opposite directions along the chain spawns a hierarchy of multiple weak solitary waves [1]. [1] M. Manciu, S. Sen and A.J. Hurd, Phys Lett A (submitted).

Parametric Study of Flow Patterns behind the Standing Accretion Shock Wave for Core-Collapse Supernovae

NASA Astrophysics Data System (ADS)

Iwakami, Wakana; Nagakura, Hiroki; Yamada, Shoichi

2014-05-01

In this study, we conduct three-dimensional hydrodynamic simulations systematically to investigate the flow patterns behind the accretion shock waves that are commonly formed in the post-bounce phase of core-collapse supernovae. Adding small perturbations to spherically symmetric, steady, shocked accretion flows, we compute the subsequent evolutions to find what flow pattern emerges as a consequence of hydrodynamical instabilities such as convection and standing accretion shock instability for different neutrino luminosities and mass accretion rates. Depending on these two controlling parameters, various flow patterns are indeed realized. We classify them into three basic patterns and two intermediate ones; the former includes sloshing motion (SL), spiral motion (SP), and multiple buoyant bubble formation (BB); the latter consists of spiral motion with buoyant-bubble formation (SPB) and spiral motion with pulsationally changing rotational velocities (SPP). Although the post-shock flow is highly chaotic, there is a clear trend in the pattern realization. The sloshing and spiral motions tend to be dominant for high accretion rates and low neutrino luminosities, and multiple buoyant bubbles prevail for low accretion rates and high neutrino luminosities. It is interesting that the dominant pattern is not always identical between the semi-nonlinear and nonlinear phases near the critical luminosity; the intermediate cases are realized in the latter case. Running several simulations with different random perturbations, we confirm that the realization of flow pattern is robust in most cases.

Interactions between gravity waves and cold air outflows in a stably stratified uniform flow

NASA Technical Reports Server (NTRS)

Lin, Yuh-Lang; Wang, Ting-An; Weglarz, Ronald P.

1993-01-01

Interactions between gravity waves and cold air outflows in a stably stratified uniform flow forced by various combinations of prescribed heat sinks and sources are studied using a hydrostatic two-dimensional nonlinear numerical model. The formation time for the development of a stagnation point or reversed flow at the surface is not always directly proportional to the Froude number when wave reflections exist from upper levels. A density current is able to form by the wave-otuflow interaction, even though the Froude number is greater than a critical value. This is the result of the wave-outflow interaction shifting the flow response to a different location in the characteristic parameter space. A density current is able to form or be destroyed due to the wave-outflow interaction between a traveling gravity wave and cold air outflow. This is proved by performing experiments with a steady-state heat sink and an additional transient heat source. In a quiescent fluid, a region of cold air, convergence, and upward motion is formed after the collision between two outflows produced by two prescribed heat sinks. After the collision, the individual cold air outflows lose their own identity and merge into a single, stationary, cold air outflow region. Gravity waves tend to suppress this new stationary cold air outflow after the collision. The region of upward motion associated with the collision is confined to a very shallow layer. In a moving airstream, a density current produced by a heat sink may be suppressed or enhanced nonlinearly by an adjacent heat sink due to the wave-outflow interaction.

Evolution of nonlinear waves in a blood-filled artery with an aneurysm

NASA Astrophysics Data System (ADS)

Nikolova, E. V.; Jordanov, I. P.; Dimitrova, Z. I.; Vitanov, N. K.

2017-10-01

We discuss propagation of traveling waves in a blood-filled hyper-elastic artery with a local dilatation (an aneurysm). The processes in the injured artery are modeled by an equation of the motion of the arterial wall and by equations of the motion of the fluid (the blood). Taking into account the specific arterial geometry and applying the reductive perturbation method in long-wave approximation we reduce the model equations to a version of the perturbed Korteweg-de Vries kind equation with variable coefficients. Exact traveling-wave solutions of this equation are obtained by the modified method of simplest equation where the differential equation of Abel is used as a simplest equation. A particular case of the obtained exact solution is numerically simulated and discussed from the point of view of arterial disease mechanics.

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.

Nonlinear ball chain waveguides for acoustic emission and ultrasound sensing of ablation

NASA Astrophysics Data System (ADS)

Pearson, Stephen H.

Harsh environment acoustic emission and ultrasonic wave sensing applications often benefit from placing the sensor in a remote and more benign physical location by using waveguides to transmit elastic waves between the structural location under test and the transducer. Waveguides are normally designed to have high fidelity over broad frequency ranges to minimize distortion -- often difficult to achieve in practice. This thesis reports on an examination of using nonlinear ball chain waveguides for the transmission of acoustic emission and ultrasonic waves for the monitoring of thermal protection systems undergoing severe heat loading, leading to ablation and similar processes. Experiments test the nonlinear propagation of solitary, harmonic and mixed harmonic elastic waves through a copper tube filled with steel and elastomer balls and various other waveguides. Triangulation of pencil lead breaks occurs on a steel plate. Data are collected concerning the usage of linear waveguides and a water-cooled linear waveguide. Data are collected from a second water-cooled waveguide monitoring Atmospheric Reentry Materials in UVM's Inductively-Coupled Plasma Torch Facility. The motion of the particles in the dimer waveguides is linearly modeled with a three ball and spring chain model and the results are compared per particle. A theoretical nonlinear model is presented which is capable of exactly modeling the motion of the dimer chains. The shape of the waveform propagating through the dimer chain is modeled in a sonic vacuum. Mechanical pulses of varying time widths and amplitudes are launched into one end of the ball chain waveguide and observed at the other end in both time and frequency domains. Similarly, harmonic and mixed harmonic mechanical loads are applied to one end of the waveguide. Balls of different materials are analyzed and discriminated into categories. A copper tube packed with six steel particles, nine steel or marble particles and a longer copper tube packed with 17 steel particles are studied with a frequency sweep. The deformation experienced by a single steel particle in the dimer chain is approximated. Steel ball waveguides and steel rods are fitted with piezoelectric sensors to monitor the force at different points inside the waveguide during testing. The corresponding frequency responses, including intermodulation products, are compared based on amplitude and preloads. A nonlinear mechanical model describes the motion of the dimer chains in a vacuum. Based on the results of these studies it is anticipated that a nonlinear waveguide will be designed, built, and tested as a possible replacement for the high-fidelity waveguides presently being used in an Inductively Coupled Plasma Torch facility for high heat flux thermal protection system testing. The design is intended to accentuate acoustic emission signals of interest, while suppressing other forms of elastic wave noise.

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

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

Periodic nonlinear waves resulting from the contact interaction of a crack

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Poincaré analysis of wave motion in ultrarelativistic electron-ion plasmas.

PubMed

Lehmann, G; Spatschek, K H

2011-03-01

Based on a relativistic Maxwell-fluid description, the existence of ultrarelativistic laser-induced periodic waves in an electron-ion plasma is investigated. Within a one-dimensional propagation geometry nonlinear coupling of the electromagnetic and electrostatic components occurs that makes the fourth-order problem nonintegrable. A Hamiltonian description is derived, and the manifolds of periodic solutions are studied by Poincaré section plots. The influence of ion motion is investigated in different intensity regimes. For ultrarelativistic laser intensities the phase-space structures change significantly compared to the weakly relativistic case. Ion motion becomes very important such that finally electron-ion plasmas in the far-ultrarelativistic regime behave similarly to electron-positron plasmas. The characteristic new types of periodic solutions of the system are identified and discussed.

Nonlinear mechanisms of two-dimensional wave-wave transformations in the initially coupled acoustic structure

NASA Astrophysics Data System (ADS)

Vorotnikov, K.; Starosvetsky, Y.

2018-01-01

The present study concerns two-dimensional nonlinear mechanisms of bidirectional and unidirectional channeling of longitudinal and shear waves emerging in the locally resonant acoustic structure. The system under consideration comprises an oscillatory chain of the axially coupled masses. Each mass of the chain is subject to the local linear potential along the lateral direction and incorporates the lightweight internal rotator. In the present work, we demonstrate the emergence of special resonant regimes of complete bi- and unidirectional transitions between the longitudinal and the shear waves of the locally resonant chain. These regimes are manifested by the two-dimensional energy channeling between the longitudinal and the shear traveling waves in the recurrent as well as the irreversible fashion. We show that the spatial control of the two dimensional energy flow between the longitudinal and the shear waves is solely governed by the motion of the internal rotators. Nonlinear analysis of the regimes of a bidirectional wave channeling unveils their global bifurcation structure and predicts the zones of their spontaneous transitions from a complete bi-directional wave channeling to the one-directional entrapment. An additional regime of a complete irreversible resonant transformation of the longitudinal wave into a shear wave is analyzed in the study. The intrinsic mechanism governing the unidirectional wave reorientation is described analytically. The results of the analysis of both mechanisms are substantiated by the numerical simulations of the full model and are found to be in a good agreement.

Generation of High Frequency Response in a Dynamically Loaded, Nonlinear Soil Column

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

Spears, Robert Edward; Coleman, Justin Leigh

2015-08-01

Detailed guidance on linear seismic analysis of soil columns is provided in “Seismic Analysis of Safety-Related Nuclear Structures and Commentary (ASCE 4, 1998),” which is currently under revision. A new Appendix in ASCE 4-2014 (draft) is being added to provide guidance for nonlinear time domain analysis which includes evaluation of soil columns. When performing linear analysis, a given soil column is typically evaluated with a linear, viscous damped constitutive model. When submitted to a sine wave motion, this constitutive model produces a smooth hysteresis loop. For nonlinear analysis, the soil column can be modelled with an appropriate nonlinear hysteretic soilmore » model. For the model in this paper, the stiffness and energy absorption result from a defined post yielding shear stress versus shear strain curve. This curve is input with tabular data points. When submitted to a sine wave motion, this constitutive model produces a hysteresis loop that looks similar in shape to the input tabular data points on the sides with discontinuous, pointed ends. This paper compares linear and nonlinear soil column results. The results show that the nonlinear analysis produces additional high frequency response. The paper provides additional study to establish what portion of the high frequency response is due to numerical noise associated with the tabular input curve and what portion is accurately caused by the pointed ends of the hysteresis loop. Finally, the paper shows how the results are changed when a significant structural mass is added to the top of the soil column.« less

Oscillations and waves in a spatially distributed system with a 1/f spectrum

NASA Astrophysics Data System (ADS)

Koverda, V. P.; Skokov, V. N.

2018-02-01

A spatially distributed system with a 1/f power spectrum is described by two nonlinear stochastic equations. Conditions for the formation of auto-oscillations have been found using numerical methods. The formation of a 1/f and 1/k spectrum simultaneously with the formation and motion of waves under the action of white noise has been demonstrated. The large extreme fluctuations with 1/f and 1/k spectra correspond to the maximum entropy, which points to the stability of such processes. It is shown that on the background of formation and motion of waves at an external periodic action there appears spatio-temporal stochastic resonance, at which one can observe the expansion of the region of periodic pulsations under the action of white noise.

Five parameters for the evaluation of the soil nonlinearity during the Ms8.0 Wenchuan Earthquake using the HVSR method

NASA Astrophysics Data System (ADS)

Ren, Yefei; Wen, Ruizhi; Yao, Xinxin; Ji, Kun

2017-08-01

The consideration of soil nonlinearity is important for the accurate estimation of the site response. To evaluate the soil nonlinearity during the 2008 Ms8.0 Wenchuan Earthquake, 33 strong-motion records obtained from the main shock and 890 records from 157 aftershocks were collected for this study. The horizontal-to-vertical spectral ratio (HVSR) method was used to calculate five parameters: the ratio of predominant frequency (RFp), degree of nonlinearity (DNL), absolute degree of nonlinearity (ADNL), frequency of nonlinearity (fNL), and percentage of nonlinearity (PNL). The purpose of this study was to evaluate the soil nonlinearity level of 33 strong-motion stations and to investigate the characteristics, performance, and effective usage of these five parameters. Their correlations with the peak ground acceleration (PGA), peak ground velocity (PGV), average uppermost 30-m shear-wave velocity ( V S30), and maximum amplitude of HVSR ( A max) were investigated. The results showed that all five parameters correlate well with PGA and PGV. The DNL, ADNL, and PNL also show a good correlation with A max, which means that the degree of soil nonlinearity not only depends on the ground-motion amplitude (e.g., PGA and PGV) but also on the site condition. The fNL correlates with PGA and PGV but shows no correlation with either A max or V S30, implying that the frequency width affected by the soil nonlinearity predominantly depends on the ground-motion amplitude rather than the site condition. At 16 of the 33 stations analyzed in this study, the site response showed evident (i.e., strong and medium) nonlinearity during the main shock of the Wenchuan Earthquake, where the ground-motion level was almost beyond the threshold of PGA > 200 cm/s2 or PGV > 15 cm/s. The site response showed weak and no nonlinearity at the other 14 and 3 stations. These results also confirm that RFp, DNL, ADNL, and PNL are effective in identifying the soil nonlinearity behavior. The identification results vary for different parameters because each parameter has individual features. The performance of the PNL was better than that of DNL and ADNL in this case study. The thresholds of ADNL and PNL are proposed to be 2.0 and 7%, respectively.[Figure not available: see fulltext.

A nonlinear cochlear model with the outer hair cell piezoelectric activity

NASA Astrophysics Data System (ADS)

Jiang, Xiaoai; Grosh, Karl

2003-10-01

In this paper we present a simple cochlear model which captures the most important aspect of nonlinearity in the cochlea-the nonlinearity caused by the piezoelectric-like activity of outer hair cells and the variable conductance of the outer hair cell stereocilia. A one-dimensional long-wave model is built to simulate the dynamic response of the fluid-loaded basilar membrane. The basilar membrane is simulated as isolated linear oscillators along the cochlear length, and its motion is coupled with the fluid pressure and the nonlinear force produced by the outer hair cells. As the basilar membrane moves, the fluid shears stereocilia, and the resulting ion flow changes the transmembrane potential of the outer hair cells and subsequently their length, leading to further movement of the basilar membrane. The piezoelectric-like activity of the outer hair cell is simulated by a current source, and stereocilia motion is modeled as a varying conductance that changes as the basilar membrane moves. A solution in the time domain will be presented. [Work supported by NIH.

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

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Traveling-wave solutions in continuous chains of unidirectionally coupled oscillators

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Kolesov, A. Yu; Rozov, N. Kh

2017-12-01

Proposed is a mathematical model of a continuous annular chain of unidirectionally coupled generators given by certain nonlinear advection-type hyperbolic boundary value problem. Such problems are constructed by a limit transition from annular chains of unidirectionally coupled ordinary differential equations with an unbounded increase in the number of links. It is shown that any preassigned finite number of stable periodic motions of the traveling-wave type can coexist in the model.

Parametric study of flow patterns behind the standing accretion shock wave for core-collapse supernovae

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

Iwakami, Wakana; Nagakura, Hiroki; Yamada, Shoichi, E-mail: wakana@heap.phys.waseda.ac.jp

2014-05-10

In this study, we conduct three-dimensional hydrodynamic simulations systematically to investigate the flow patterns behind the accretion shock waves that are commonly formed in the post-bounce phase of core-collapse supernovae. Adding small perturbations to spherically symmetric, steady, shocked accretion flows, we compute the subsequent evolutions to find what flow pattern emerges as a consequence of hydrodynamical instabilities such as convection and standing accretion shock instability for different neutrino luminosities and mass accretion rates. Depending on these two controlling parameters, various flow patterns are indeed realized. We classify them into three basic patterns and two intermediate ones; the former includes sloshingmore » motion (SL), spiral motion (SP), and multiple buoyant bubble formation (BB); the latter consists of spiral motion with buoyant-bubble formation (SPB) and spiral motion with pulsationally changing rotational velocities (SPP). Although the post-shock flow is highly chaotic, there is a clear trend in the pattern realization. The sloshing and spiral motions tend to be dominant for high accretion rates and low neutrino luminosities, and multiple buoyant bubbles prevail for low accretion rates and high neutrino luminosities. It is interesting that the dominant pattern is not always identical between the semi-nonlinear and nonlinear phases near the critical luminosity; the intermediate cases are realized in the latter case. Running several simulations with different random perturbations, we confirm that the realization of flow pattern is robust in most cases.« less

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

Generation of Magnetohydrodynamic Waves in Low Solar Atmospheric Flux Tubes by Photospheric Motions

NASA Astrophysics Data System (ADS)

Mumford, S. J.; Fedun, V.; Erdélyi, R.

2015-01-01

Recent ground- and space-based observations reveal the presence of small-scale motions between convection cells in the solar photosphere. In these regions, small-scale magnetic flux tubes are generated via the interaction of granulation motion and the background magnetic field. This paper studies the effects of these motions on magnetohydrodynamic (MHD) wave excitation from broadband photospheric drivers. Numerical experiments of linear MHD wave propagation in a magnetic flux tube embedded in a realistic gravitationally stratified solar atmosphere between the photosphere and the low choromosphere (above β = 1) are performed. Horizontal and vertical velocity field drivers mimic granular buffeting and solar global oscillations. A uniform torsional driver as well as Archimedean and logarithmic spiral drivers mimic observed torsional motions in the solar photosphere. The results are analyzed using a novel method for extracting the parallel, perpendicular, and azimuthal components of the perturbations, which caters to both the linear and non-linear cases. Employing this method yields the identification of the wave modes excited in the numerical simulations and enables a comparison of excited modes via velocity perturbations and wave energy flux. The wave energy flux distribution is calculated to enable the quantification of the relative strengths of excited modes. The torsional drivers primarily excite Alfvén modes (≈60% of the total flux) with small contributions from the slow kink mode, and, for the logarithmic spiral driver, small amounts of slow sausage mode. The horizontal and vertical drivers primarily excite slow kink or fast sausage modes, respectively, with small variations dependent upon flux surface radius.

Simulations of Magnetohydrodynamic Waves Driven by Photospheric Motions

NASA Astrophysics Data System (ADS)

Mumford, Stuart

2016-04-01

This thesis investigates the properties of various modelled photospheric motions as generation mechanisms for magnetohydrodynamic (MHD) waves in the low solar atmosphere. The solar atmosphere is heated to million-degree temperatures, yet there is no fully understood heating mechanism which can provide the ≈ 300 W/m^2) required to keep the quiet corona at its observed temperatures. MHD waves are one mechanism by which this energy could be provided to the upper solar atmosphere, however, these waves need to be excited. The excitation of these waves, in or below the photosphere is a complex interaction between the plasma and the magnetic field embedded within it. This thesis studies a model of a small-scale magnetic flux tube based upon a magnetic bright point (MBP). These features are very common in the photosphere and have been observed to be affected by the plasma motions. The modelled flux tube has a foot point magnetic field strength of 120 mT and a FWHM of 90 km, and is embedded in a realistic, stratified solar atmosphere based upon the VALIIIc model. To better understand the excitation of MHD waves in this type of magnetic structures, a selection of velocity profiles are implemented to excite waves. Initially a study of five different driving profiles was performed. A uniform torsional driver as well as Archimedean and logarithmic spiral drivers which mimic observed torsional motions in the solar photosphere, along with vertical and horizontal drivers to mimic different motions caused by convection in the photosphere. The results are then analysed using a novel method for extracting the parallel, perpendicular and azimuthal components of the perturbations, which caters to both the linear and non-linear cases. Employing this method yields the identification of the wave modes excited in the numerical simulations and enables a comparison of excited modes via velocity perturbations and wave energy flux. The wave energy flux distribution is calculated, to enable the quantification of the relative strengths of excited modes. The torsional drivers primarily excite Alfvén modes (≈ 60 %) of the total flux) with contributions from the slow mode. The horizontal and vertical drivers primarily excite slow and fast modes respectively, with small variations dependent upon flux surface radius. This analysis is then applied to more in depth studies of the logarithmic spiral driver. Firstly, five different values for the (B_L) spiral expansion factor are chosen which control how rapidly the spiral expands. Larger values of (B_L) make the driving profile more radial. The results of this analysis show that the Alfvén wave is the dominant wave for lower values of the expansion factor, whereas, for the higher values the parallel component is dominant. This transition occurs within the range of the observational constraints, demonstrating that under realistic conditions spiral drivers may not excite most of their wave flux in the Alfvén mode. Finally, the logarithmic spiral is further studied, but with a variety of different periods. Ten periods from 30 to 300 seconds are chosen, and the simulations are again analysed using the flux surface method employed previously. The results of this study are minimal variation in the percentage wave flux in each mode, with no more than 20 % variation in any mode for any flux surface studied. Within this small variation, some non-linear changes in the wave flux were observed, especially around the more important small periods. Due to the short life time of the MBPs it is thought the short period waves would have more effect and therefore this non-linear variation in wave flux could have some impact on the modes present in the solar atmosphere.

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.

Electromagnetic-continuum-induced nonlinearity

NASA Astrophysics Data System (ADS)

Matsko, Andrey B.; Vyatchanin, Sergey P.

2018-05-01

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

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

The motions of hinged-barge systems in regular seas

NASA Astrophysics Data System (ADS)

Kraemer, David Robert Burke

Harnessing the oceans' vast, clean, and renewable energy to do useful work is a tempting prospect. For over a century, wave-energy conversion devices have been proposed, but none has emerged as a clearly practical and economical solution. One promising system is the McCabe Wave Pump (MWP), an articulated-barge system consisting of three barges hinged together with a large horizontal plate attached below the central barge. Water pumps are driven by the relative pitching motions of the barges excited by ocean waves. This high-pressure water can be used to produce potable water or electricity. A simulation of the motions of a generic hinged-barge system is developed. The equations of motion are developed so that the nonlinear interactions between the barges are included. The simulation is general so that it can be used to study other hinged-barge systems, such as causeway ferry systems or floating airports. The simulation is used to predict the motions of a scale model that was studied in wave-tank experiments. In the experimental study, it was observed that the plate attached to the central barge acted as a pendulum. It was also observed that the phases of the pitching motions of the barges was such that the motions were enhanced by the pendulum effect at all of the wave periods studied. Hence, the increased angular displacements produced greater relative pitching motions which would lead to higher volume rates of pumped water in the operational system. The numerical simulations are found to predict the pendulum effect. In addition, the theory predicted that the after barge motions were significantly less than those of the forward barge, as was observed in the experimental study. The good agreement between the two data sets gives confidence in the ability of the theory to predict the performance of the MWP prototype. The motions of the MWP prototype in regular ocean waves are predicted by the simulation, and its performance is calculated. By modifying the length of the system to be compatible with the wavelength for maximum pitching excitation, the power output of the system is shown to increase by more than 150%.

Modulational instability of beat waves in a transversely magnetized plasma: Ion effects

NASA Astrophysics Data System (ADS)

Ferdous, T.; Amin, M. R.; Salimullah, M.

1996-05-01

The effect of ion dynamics on the modulational instability of the electrostatic beat wave at the difference frequency of two incident laser beams in a hot, collisionless, and transversely magnetized plasma has been studied theoretically. The full Vlasov equation in terms of gyrokinetic variables is employed to obtain the nonlinear response of ions and electrons. It is found that the growth rate of modulational instability is about two orders higher when ion motions are included.

Seeing blur: 'motion sharpening' without motion.

PubMed Central

Georgeson, Mark A; Hammett, Stephen T

2002-01-01

It is widely supposed that things tend to look blurred when they are moving fast. Previous work has shown that this is true for sharp edges but, paradoxically, blurred edges look sharper when they are moving than when stationary. This is 'motion sharpening'. We show that blurred edges also look up to 50% sharper when they are presented briefly (8-24 ms) than at longer durations (100-500 ms) without motion. This argues strongly against high-level models of sharpening based specifically on compensation for motion blur. It also argues against a recent, low-level, linear filter model that requires motion to produce sharpening. No linear filter model can explain our finding that sharpening was similar for sinusoidal and non-sinusoidal gratings, since linear filters can never distort sine waves. We also conclude that the idea of a 'default' assumption of sharpness is not supported by experimental evidence. A possible source of sharpening is a nonlinearity in the contrast response of early visual mechanisms to fast or transient temporal changes, perhaps based on the magnocellular (M-cell) pathway. Our finding that sharpening is not diminished at low contrast sets strong constraints on the nature of the nonlinearity. PMID:12137571

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.

New formulations for tsunami runup estimation

NASA Astrophysics Data System (ADS)

Kanoglu, U.; Aydin, B.; Ceylan, N.

2017-12-01

We evaluate shoreline motion and maximum runup in two folds: One, we use linear shallow water-wave equations over a sloping beach and solve as initial-boundary value problem similar to the nonlinear solution of Aydın and Kanoglu (2017, Pure Appl. Geophys., https://doi.org/10.1007/s00024-017-1508-z). Methodology we present here is simple; it involves eigenfunction expansion and, hence, avoids integral transform techniques. We then use several different types of initial wave profiles with and without initial velocity, estimate shoreline properties and confirm classical runup invariance between linear and nonlinear theories. Two, we use the nonlinear shallow water-wave solution of Kanoglu (2004, J. Fluid Mech. 513, 363-372) to estimate maximum runup. Kanoglu (2004) presented a simple integral solution for the nonlinear shallow water-wave equations using the classical Carrier and Greenspan transformation, and further extended shoreline position and velocity to a simpler integral formulation. In addition, Tinti and Tonini (2005, J. Fluid Mech. 535, 33-64) defined initial condition in a very convenient form for near-shore events. We use Tinti and Tonini (2005) type initial condition in Kanoglu's (2004) shoreline integral solution, which leads further simplified estimates for shoreline position and velocity, i.e. algebraic relation. We then use this algebraic runup estimate to investigate effect of earthquake source parameters on maximum runup and present results similar to Sepulveda and Liu (2016, Coast. Eng. 112, 57-68).

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.

Aeroelastic impact of above-rated wave-induced structural motions on the near-wake stability of a floating offshore wind turbine rotor

NASA Astrophysics Data System (ADS)

Rodriguez, Steven; Jaworski, Justin

2017-11-01

The impact of above-rated wave-induced motions on the stability of floating offshore wind turbine near-wakes is studied numerically. The rotor near-wake is generated using a lifting-line free vortex wake method, which is strongly coupled to a finite element solver for kinematically nonlinear blade deformations. A synthetic time series of relatively high-amplitude/high-frequency representative of above-rated conditions of the NREL 5MW referece wind turbine is imposed on the rotor structure. To evaluate the impact of these above-rated conditions, a linear stability analysis is first performed on the near wake generated by a fixed-tower wind turbine configuration at above-rated inflow conditions. The platform motion is then introduced via synthetic time series, and a stability analysis is performed on the wake generated by the floating offshore wind turbine at the same above-rated inflow conditions. The stability trends (disturbance modes versus the divergence rate of vortex structures) of the two analyses are compared to identify the impact that above-rated wave-induced structural motions have on the stability of the floating offshore wind turbine wake.

Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics

DTIC Science & Technology

2007-09-30

sub-processor must be added as shown in the blue box of Fig. 1. We first consider the Kadomtsev - Petviashvili (KP) equation ηt + coηx +αηηx + βη ...analytic integration of the so-called “soliton equations ,” I have discovered how the GFT can be used to solved higher order equations for which study...analytical study and extremely fast numerical integration of the extended nonlinear Schroedinger equation for fully three dimensional wave motion

Numerical and Analytical Study of Nonlinear Effects of Transonic Flow Past a Wing Airfoil in Oscillation of its Surface Element

NASA Astrophysics Data System (ADS)

Aul'chenko, S. M.; Zamuraev, V. P.; Kalinina, A. P.

2014-05-01

The present work is devoted to a criterial analysis and mathematical modeling of the influence of forced oscillations of surface elements of a wing airfoil on the shock-wave structure of transonic flow past it. Parameters that govern the regimes of interaction of the oscillatory motion of airfoil sections with the breakdown compression shock have been established. The qualitative and quantitative influence of these parameters on the wave resistance of the airfoil has been investigated.

Convective cell generation by kinetic Alfven wave turbulence in the auroral ionosphere

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

Zhao, J. S.; Wu, D. J.; Yu, M. Y.

2012-06-15

Modulation of convective cells by kinetic Alfven wave (KAW) turbulence is investigated. The interaction is governed by a nonlinear dispersion relation for the convective cells. It is shown that KAW turbulence is disrupted by excitation of the large-scale convective motion through a resonant instability. Application of the results to the auroral ionosphere shows that cross-scale coupling of the KAW turbulence and convective cells plays an important role in the evolution of ionospheric plasma turbulence.

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.

Using the HHT to Search for Gravitational Waves

NASA Technical Reports Server (NTRS)

Camp, Jordan

2008-01-01

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

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

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.

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.

Copepod Behavior Response in an Internal Wave Apparatus

NASA Astrophysics Data System (ADS)

Webster, D. R.; Jung, S.; Haas, K. A.

2017-11-01

This study is motivated to understand the bio-physical forcing in zooplankton transport in and near internal waves, where high levels of zooplankton densities have been observed in situ. A laboratory-scale internal wave apparatus was designed to create a standing internal wave for various physical arrangements that mimic conditions observed in the field. A theoretical analysis of a standing internal wave inside a two-layer stratification system including non-linear wave effects was conducted to derive the expressions for the independent variables controlling the wave motion. Focusing on a case with a density jump of 1.0 σt, a standing internal wave was generated with a clean interface and minimal mixing across the pycnocline. Spatial and frequency domain measurements of the internal wave were evaluated in the context of the theoretical analysis. Behavioral assays with a mixed population of three marine copepods were conducted in control (stagnant homogeneous fluid), stagnant density jump interface, and internal wave flow configurations. In the internal wave treatment, the copepods showed an acrobatic, orbital-like motion in and around the internal wave region (bounded by the crests and the troughs of the waves). Trajectories of passive, neutrally-buoyant particles in the internal wave flow reveal that they generally oscillate back-and-forth along fixed paths. Thus, we conclude that the looping, orbital trajectories of copepods in the region near the internal wave interface are due to animal behavior rather than passive transport.

Full-field drift Hamiltonian particle orbits in 3D geometry

NASA Astrophysics Data System (ADS)

Cooper, W. A.; Graves, J. P.; Brunner, S.; Isaev, M. Yu

2011-02-01

A Hamiltonian/Lagrangian theory to describe guiding centre orbit drift motion which is canonical in the Boozer coordinate frame has been extended to include full electromagnetic perturbed fields in anisotropic pressure 3D equilibria with nested magnetic flux surfaces. A redefinition of the guiding centre velocity to eliminate the motion due to finite equilibrium radial magnetic fields and the choice of a gauge condition that sets the radial component of the electromagnetic vector potential to zero are invoked to guarantee that the Boozer angular coordinates retain the canonical structure. The canonical momenta are identified and the guiding centre particle radial drift motion and parallel gyroradius evolution are derived. The particle coordinate position is linearly modified by wave-particle interactions. All the nonlinear wave-wave interactions appear explicitly only in the evolution of the parallel gyroradius. The radial variation of the electrostatic potential is related to the binormal component of the displacement vector for MHD-type perturbations. The electromagnetic vector potential projections can then be determined from the electrostatic potential and the radial component of the MHD displacement vector.

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.

2007-01-01

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

Magnetic Shocks and Substructures Excited by Torsional Alfvén Wave Interactions in Merging Expanding Flux Tubes

NASA Astrophysics Data System (ADS)

Snow, B.; Fedun, V.; Gent, F. A.; Verth, G.; Erdélyi, R.

2018-04-01

Vortex motions are frequently observed on the solar photosphere. These motions may play a key role in the transport of energy and momentum from the lower atmosphere into the upper solar atmosphere, contributing to coronal heating. The lower solar atmosphere also consists of complex networks of flux tubes that expand and merge throughout the chromosphere and upper atmosphere. We perform numerical simulations to investigate the behavior of vortex-driven waves propagating in a pair of such flux tubes in a non-force-free equilibrium with a realistically modeled solar atmosphere. The two flux tubes are independently perturbed at their footpoints by counter-rotating vortex motions. When the flux tubes merge, the vortex motions interact both linearly and nonlinearly. The linear interactions generate many small-scale transient magnetic substructures due to the magnetic stress imposed by the vortex motions. Thus, an initially monolithic tube is separated into a complex multithreaded tube due to the photospheric vortex motions. The wave interactions also drive a superposition that increases in amplitude until it exceeds the local Mach number and produces shocks that propagate upward with speeds of approximately 50 km s‑1. The shocks act as conduits transporting momentum and energy upward, and heating the local plasma by more than an order of magnitude, with a peak temperature of approximately 60,000 K. Therefore, we present a new mechanism for the generation of magnetic waveguides from the lower solar atmosphere to the solar corona. This wave guide appears as the result of interacting perturbations in neighboring flux tubes. Thus, the interactions of photospheric vortex motions is a potentially significant mechanism for energy transfer from the lower to upper solar atmosphere.

Nonlinear soil response in the vicinity of the Van Norman Complex following the 1994 Northridge, California, earthquake

USGS Publications Warehouse

Cultrera, G.; Boore, D.M.; Joyner, W.B.; Dietel, C.M.

1999-01-01

Ground-motion recordings obtained at the Van Norman Complex from the 1994 Northridge, California, mainshock and its aftershocks constitute an excellent data set for the analysis of soil response as a function of ground-motion amplitude. We searched for nonlinear response by comparing the Fourier spectral ratios of two pairs of sites for ground motions of different levels, using data from permanent strong-motion recorders and from specially deployed portable instruments. We also compared the amplitude dependence of the observed ratios with the amplitude dependence of the theoretical ratios obtained from 1-D linear and 1-D equivalent-linear transfer functions, using recently published borehole velocity profiles at the sites to provide the low-strain material properties. One pair of sites was at the Jensen Filtration Plant (JFP); the other pair was the Rinaldi Receiving Station (RIN) and the Los Angeles Dam (LAD). Most of the analysis was concentrated on the motions at the Jensen sites. Portable seismometers were installed at the JFP to see if the motions inside the structures housing the strong-motion recorders differed from nearby free-field motions. We recorded seven small earthquakes and found that the high-frequency, low-amplitude motions in the administration building were about 0.3 of those outside the building. This means that the lack of high frequencies on the strong-motion recordings in the administration building relative to the generator building is not due solely to nonlinear soil effects. After taking into account the effects of the buildings, however, analysis of the suite of strong- and weak-motion recordings indicates that nonlinearity occurred at the JFP. As predicted by equivalent-linear analysis, the largest events (the mainshock and the 20 March 1994 aftershock) show a significant deamplification of the high-frequency motion relative to the weak motions from aftershocks occurring many months after the mainshock. The weak-motion aftershocks recorded within 12 hours of the mainshock, however, show a relative deamplification similar to that in the mainshock. The soil behavior may be a consequence of a pore pressure buildup during large-amplitude motion that was not dissipated until sometime later. The motions at (RIN) and (LAD) are from free-field sites. The comparison among spectral ratios of the mainshock, weak-motion coda waves of the mainshock, and an aftershock within ten minutes of the mainshock indicate that some nonlinearity occurred, presumably at (RIN) because it is the softer site. The spectral ratio for the mainshock is between that calculated for pure linear response and that calculated from the equivalent-linear method, using commonly used modulus reduction and damping ratio curves. In contrast to the Jensen sites, the ratio of motions soon after the high-amplitude portion of the mainshock differs from the ratio of the mainshock motions, indicating the mechanical properties of the soil returned to the low-strain values as the high-amplitude motion ended. This may indicate a type of nonlinear soil response different from that affecting motion at the Jensen administration building.

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)

A study of the extended-range forecasting problem blocking

NASA Technical Reports Server (NTRS)

Chen, T. C.; Marshall, H. G.; Shukla, J.

1981-01-01

Wavenumber frequency spectral analysis of a 90 day winter (Jan. 15 - April 14) wind field simulated by a climate experiment of the GLAS atmospheric circulation model is made using the space time Fourier analysis which is modified with Tukey's numerical spectral analysis. Computations are also made to examine how the model wave disturbances in the wavenumber frequency domain are maintained by nonlinear interactions. Results are compared with observation. It is found that equatorial easterlies do not show up in this climate experiment at 200 mb. The zonal kinetic energy and momentum transport of stationary waves are too small in the model's Northern Hemisphere. The wavenumber and frequency spectra of the model are generally in good agreement with observation. However, some distinct features of the model's spectra are revealed. The wavenumber spectra of kinetic energy show that the eastward moving waves of low wavenumbers have stronger zonal motion while the eastward moving waves of intermediate wavenumbers have larger meridional motion compared with observation. Furthermore, the eastward moving waves show a band of large spectral value in the medium frequency regime.

Boundary mediated position control of traveling waves

NASA Astrophysics Data System (ADS)

Martens, Steffen; Ziepke, Alexander; Engel, Harald

Reaction control is an essential task in biological systems and chemical process industry. Often, the excitable medium supporting wave propagation exhibits an irregular shape and/or is limited in size. In particular, the analytic treatment of wave phenomena is notoriously difficult due to the spatial modulation of the domain's. Recently, we have provided a first systematic treatment by applying asymptotic perturbation analysis leading to an approximate description that involves a reduction of dimensionality; the 3D RD equation with spatially dependent NFBCs on the reactants reduces to a 1D reaction-diffusion-advection equation. Here, we present a novel method to control the position ϕ (t) of traveling waves in modulated domains according to a prespecified protocol of motion. Given this protocol, the ``optimal'' geometry of reactive domains Q (x) is found as the solution of the perturbatively derived equation of motion. Noteworthy, such a boundary control can be expressed in terms of the uncontrolled wave profile and its propagation velocity, rendering detailed knowledge of the reaction kinetics unnecessary. German Science Foundation DFG through the SFB 910 ''Control of Self-Organizing Nonlinear Systems''.

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

Non-classical light generated by quantum-noise-driven cavity optomechanics.

PubMed

Brooks, Daniel W C; Botter, Thierry; Schreppler, Sydney; Purdy, Thomas P; Brahms, Nathan; Stamper-Kurn, Dan M

2012-08-23

Optomechanical systems, in which light drives and is affected by the motion of a massive object, will comprise a new framework for nonlinear quantum optics, with applications ranging from the storage and transduction of quantum information to enhanced detection sensitivity in gravitational wave detectors. However, quantum optical effects in optomechanical systems have remained obscure, because their detection requires the object’s motion to be dominated by vacuum fluctuations in the optical radiation pressure; so far, direct observations have been stymied by technical and thermal noise. Here we report an implementation of cavity optomechanics using ultracold atoms in which the collective atomic motion is dominantly driven by quantum fluctuations in radiation pressure. The back-action of this motion onto the cavity light field produces ponderomotive squeezing. We detect this quantum phenomenon by measuring sub-shot-noise optical squeezing. Furthermore, the system acts as a low-power, high-gain, nonlinear parametric amplifier for optical fluctuations, demonstrating a gain of 20 dB with a pump corresponding to an average of only seven intracavity photons. These findings may pave the way for low-power quantum optical devices, surpassing quantum limits on position and force sensing, and the control and measurement of motion in quantum gases.

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

NASA Astrophysics Data System (ADS)

Cannon, Patrick; Honary, Farideh; Borisov, Nikolay

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

Arbitrary amplitude nucleus-acoustic solitons in multi-ion quantum plasmas with relativistically degenerate electrons

NASA Astrophysics Data System (ADS)

Sultana, S.; Schlickeiser, R.

2018-02-01

A three component degenerate relativistic quantum plasma (consisting of relativistically degenerate electrons, nondegenerate inertial light nuclei, and stationary heavy nuclei) is considered to model the linear wave and also the electrostatic solitary waves in the light nuclei-scale length. A well-known normal mode analysis is employed to investigate the linear wave properties. A mechanical-motion analog (Sagdeev-type) pseudo-potential approach, which reveals the existence of large amplitude solitary excitations, is adopted to study the nonlinear wave properties. Only the positive potential solitary excitations are found to exist in the plasma medium under consideration. The basic properties of the arbitrary amplitude electrostatic acoustic modes in the light nuclei-scale length and their existence domain in terms of soliton speed (Mach number) are examined. The modifications of solitary wave characteristics and their existence domain with the variation of different key plasma configuration parameters (e.g., electrons degeneracy parameter, inertial light nuclei number density, and degenerate electron number density) are also analyzed. Our results, which may be helpful to explain the basic features of the nonlinear wave propagation in multi-component degenerate quantum plasmas, in connection with astrophysical compact objects (e.g., white dwarfs) are briefly discussed.

On some nonlinear effects in ultrasonic fields

PubMed

Tjotta

2000-03-01

Nonlinear effects associated with intense sound fields in fluids are considered theoretically. Special attention is directed to the study of higher effects that cannot be described within the standard propagation models of nonlinear acoustics (the KZK and Burgers equations). The analysis is based on the fundamental equations of motion for a thermoviscous fluid, for which thermal equations of state exist. Model equations are derived and used to analyze nonlinear sources for generation of flow and heat, and other changes in the ambient state of the fluid. Fluctuations in the coefficients of viscosity and thermal conductivity caused by the sound field, are accounted for. Also considered are nonlinear effects induced in the fluid by flexural vibrations. The intensity and absorption of finite amplitude sound waves are calculated, and related to the sources for generation of higher order effects.

Theoretical analysis of rotating two phase detonation in a rocket motor

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

6-C polarization analysis using point measurements of translational and rotational ground-motion: theory and applications

NASA Astrophysics Data System (ADS)

Sollberger, David; Greenhalgh, Stewart A.; Schmelzbach, Cedric; Van Renterghem, Cédéric; Robertsson, Johan O. A.

2018-04-01

We provide a six-component (6-C) polarization model for P-, SV-, SH-, Rayleigh-, and Love-waves both inside an elastic medium as well as at the free surface. It is shown that single-station 6-C data comprised of three components of rotational motion and three components of translational motion provide the opportunity to unambiguously identify the wave type, propagation direction, and local P- and S-wave velocities at the receiver location by use of polarization analysis. To extract such information by conventional processing of three-component (3-C) translational data would require large and dense receiver arrays. The additional rotational components allow the extension of the rank of the coherency matrix used for polarization analysis. This enables us to accurately determine the wave type and wave parameters (propagation direction and velocity) of seismic phases, even if more than one wave is present in the analysis time window. This is not possible with standard, pure-translational 3-C recordings. In order to identify modes of vibration and to extract the accompanying wave parameters, we adapt the multiple signal classification algorithm (MUSIC). Due to the strong nonlinearity of the MUSIC estimator function, it can be used to detect the presence of specific wave types within the analysis time window at very high resolution. We show how the extracted wavefield properties can be used, in a fully automated way, to separate the wavefield into its different wave modes using only a single 6-C recording station. As an example, we apply the method to remove surface wave energy while preserving the underlying reflection signal and to suppress energy originating from undesired directions, such as side-scattered waves.

On the coupled evolution of oceanic internal waves and quasi-geostrophic flow

NASA Astrophysics Data System (ADS)

Wagner, Gregory LeClaire

Oceanic motion outside thin boundary layers is primarily a mixture of quasi-geostrophic flow and internal waves with either near-inertial frequencies or the frequency of the semidiurnal lunar tide. This dissertation seeks a deeper understanding of waves and flow through reduced models that isolate their nonlinear and coupled evolution from the Boussinesq equations. Three physical-space models are developed: an equation that describes quasi-geostrophic evolution in an arbitrary and prescribed field of hydrostatic internal waves; a three-component model that couples quasi-geostrophic flow to both near-inertial waves and the near-inertial second harmonic; and a model for the slow evolution of hydrostatic internal tides in quasi-geostrophic flow of near-arbitrary scale. This slow internal tide equation opens the path to a coupled model for the energetic interaction of quasi-geostrophic flow and oceanic internal tides. Four results emerge. First, the wave-averaged quasi-geostrophic equation reveals that finite-amplitude waves give rise to a mean flow that advects quasi-geostrophic potential vorticity. Second is the definition of a new material invariant: Available Potential Vorticity, or APV. APV isolates the part of Ertel potential vorticity available for balanced-flow evolution in Eulerian frames and proves necessary in the separating waves and quasi-geostrophic flow. The third result, hashed out for near-inertial waves and quasi-geostrophic flow, is that wave-flow interaction leads to energy exchange even under conditions of weak nonlinearity. For storm-forced oceanic near-inertial waves the interaction often energizes waves at the expense of flow. We call this extraction of balanced quasi-geostrophic energy 'stimulated generation' since it requires externally-forced rather than spontaneously-generated waves. The fourth result is that quasi-geostrophic flow can encourage or 'catalyze' a nonlinear interaction between a near-inertial wave field and its second harmonic that transfers energy to the small near-inertial vertical scales of wave breaking and mixing.

Exhaustive Classification of the Invariant Solutions for a Specific Nonlinear Model Describing Near Planar and Marginally Long-Wave Unstable Interfaces for Phase Transition

NASA Astrophysics Data System (ADS)

Ahangari, Fatemeh

2018-05-01

Problems of thermodynamic phase transition originate inherently in solidification, combustion and various other significant fields. If the transition region among two locally stable phases is adequately narrow, the dynamics can be modeled by an interface motion. This paper is devoted to exhaustive analysis of the invariant solutions for a modified Kuramoto-Sivashinsky equation in two spatial and one temporal dimensions is presented. This nonlinear partial differential equation asymptotically characterizes near planar interfaces, which are marginally long-wave unstable. For this purpose, by applying the classical symmetry method for this model the classical symmetry operators are attained. Moreover, the structure of the Lie algebra of symmetries is discussed and the optimal system of subalgebras, which yields the preliminary classification of group invariant solutions is constructed. Mainly, the Lie invariants corresponding to the infinitesimal symmetry generators as well as associated similarity reduced equations are also pointed out. Furthermore, the nonclassical symmetries of this nonlinear PDE are also comprehensively investigated.

Low-Power Photothermal Self-Oscillation of Bimetallic Nanowires.

PubMed

De Alba, Roberto; Abhilash, T S; Rand, Richard H; Craighead, Harold G; Parpia, Jeevak M

2017-07-12

We investigate the nonlinear mechanics of a bimetallic, optically absorbing SiN-Nb nanowire in the presence of incident laser light and a reflecting Si mirror. Situated in a standing wave of optical intensity and subject to photothermal forces, the nanowire undergoes self-induced oscillations at low incident light thresholds of <1 μW due to engineered strong temperature-position (T-z) coupling. Along with inducing self-oscillation, laser light causes large changes to the mechanical resonant frequency ω 0 and equilibrium position z 0 that cannot be neglected. We present experimental results and a theoretical model for the motion under laser illumination. In the model, we solve the governing nonlinear differential equations by perturbative means to show that self-oscillation amplitude is set by the competing effects of direct T-z coupling and 2ω 0 parametric excitation due to T-ω 0 coupling. We then study the linearized equations of motion to show that the optimal thermal time constant τ for photothermal feedback is τ → ∞ rather than the previously reported ω 0 τ = 1. Lastly, we demonstrate photothermal quality factor (Q) enhancement of driven motion as a means to counteract air damping. Understanding photothermal effects on nano- and micromechanical devices, as well as nonlinear aspects of optics-based motion detection, can enable new device applications as oscillators or other electronic elements with smaller device footprints and less stringent ambient vacuum requirements.

Observation of redshifting and harmonic radiation in inverse Compton scattering

DOE PAGES

Sakai, Y.; Pogorelsky, I.; Williams, O.; ...

2015-06-17

Inverse Compton scattering of laser photons by ultrarelativistic electron beam provides polarized x- to γ-ray pulses due to the Doppler blueshifting. Nonlinear electrodynamics in the relativistically intense linearly polarized laser field changes the radiation kinetics established during the Compton interaction. These are due to the induced figure-8 motion, which introduces an overall redshift in the radiation spectrum, with the concomitant emission of higher order harmonics. To experimentally analyze the strong field physics associated with the nonlinear electron-laser interaction, clear modifications to the angular and wavelength distributions of x rays are observed. The relativistic photon wave field is provided by themore » ps CO 2 laser of peak normalized vector potential of 0.5L<0.7, which due to the quadratic dependence of the strength of nonlinear phenomena on aL permits sufficient effects not observed in past 2 nd harmonic study with a L ≈ 0.3 laser [M. Babzien et al., Phys. Rev. Lett. 96, 054802 (2006)]. The angular spectral characteristics are revealed using K-, L-edge, and high energy attenuation filters. The observation indicates existence of the electrons’ longitudinal motion through frequency redshifting understood as the mass shift effect. The 3 rd harmonic radiation has been observed containing on-axis x-ray component that is directly associated with the induced figure-8 motion. These are further supported by an initial evidence of off-axis 2 nd harmonic radiation produced in a circularly polarized laser wave field. Total x-ray photon number per pulse, scattered by 65 MeV electron beam of 0.3 nC, at the interaction point is measured to be approximately 10 9.« less

Infrasonic induced ground motions

NASA Astrophysics Data System (ADS)

Lin, Ting-Li

On January 28, 2004, the CERI seismic network recorded seismic signals generated by an unknown source. Our conclusion is that the acoustic waves were initiated by an explosive source near the ground surface. The meteorological temperature and effective sound speed profiles suggested existence of an efficient near-surface waveguide that allowed the acoustic disturbance to propagate to large distances. An explosion occurring in an area of forest and farms would have limited the number of eyewitnesses. Resolution of the source might be possible by experiment or by detailed analysis of the ground motion data. A seismo-acoustic array was built to investigate thunder-induced ground motions. Two thunder events with similar N-wave waveforms but different horizontal slownesses are chosen to evaluate the credibility of using thunder as a seismic source. These impulsive acoustic waves excited P and S reverberations in the near surface that depend on both the incident wave horizontal slowness and the velocity structure in the upper 30 meters. Nineteen thunder events were chosen to further investigate the seismo-acoustic coupling. The consistent incident slowness differences between acoustic pressure and ground motions suggest that ground reverberations were first initiated somewhat away from the array. Acoustic and seismic signals were used to generate the time-domain transfer function through the deconvolution technique. Possible non-linear interaction for acoustic propagation into the soil at the surface was observed. The reverse radial initial motions suggest a low Poisson's ratio for the near-surface layer. The acoustic-to-seismic transfer functions show a consistent reverberation series of the Rayleigh wave type, which has a systematic dispersion relation to incident slownesses inferred from the seismic ground velocity. Air-coupled Rayleigh wave dispersion was used to quantitatively constrain the near-surface site structure with constraints afforded by near-surface body wave refraction and Rayleigh wave dispersion data. Theoretical standard high-frequency and air-coupled Rayleigh wave dispersion calculated by the inferred site structure match the observed dispersion curves. Our study suggests that natural or controlled air-borne pressure sources can be used to investigate the near-surface site structures for earthquake shaking hazard studies.

Nonlinear collisionless electron cyclotron interaction in the pre-ionisation stage

NASA Astrophysics Data System (ADS)

Farina, D.

2018-06-01

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

Inducing in situ, nonlinear soil response applying an active source

USGS Publications Warehouse

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

2009-01-01

[1] It is well known that soil sites have a profound effect on ground motion during large earthquakes. The complex structure of soil deposits and the highly nonlinear constitutive behavior of soils largely control nonlinear site response at soil sites. Measurements of nonlinear soil response under natural conditions are critical to advancing our understanding of soil behavior during earthquakes. Many factors limit the use of earthquake observations to estimate nonlinear site response such that quantitative characterization of nonlinear behavior relies almost exclusively on laboratory experiments and modeling of wave propagation. Here we introduce a new method for in situ characterization of the nonlinear behavior of a natural soil formation using measurements obtained immediately adjacent to a large vibrator source. To our knowledge, we are the first group to propose and test such an approach. Employing a large, surface vibrator as a source, we measure the nonlinear behavior of the soil by incrementally increasing the source amplitude over a range of frequencies and monitoring changes in the output spectra. We apply a homodyne algorithm for measuring spectral amplitudes, which provides robust signal-to-noise ratios at the frequencies of interest. Spectral ratios are computed between the receivers and the source as well as receiver pairs located in an array adjacent to the source, providing the means to separate source and near-source nonlinearity from pervasive nonlinearity in the soil column. We find clear evidence of nonlinearity in significant decreases in the frequency of peak spectral ratios, corresponding to material softening with amplitude, observed across the array as the source amplitude is increased. The observed peak shifts are consistent with laboratory measurements of soil nonlinearity. Our results provide constraints for future numerical modeling studies of strong ground motion during earthquakes.

Theoretical and lidar studies of the density response of the mesospheric sodium layer to gravity wave perturbations

NASA Technical Reports Server (NTRS)

Shelton, J. D.; Gardner, C. S.

1981-01-01

The density response of atmospheric layers to gravity waves is developed in two forms, an exact solution and a perturbation series solution. The degree of nonlinearity in the layer density response is described by the series solution whereas the exact solution gives insight into the nature of the responses. Density perturbation in an atmospheric layer are shown to be substantially greater than the atmospheric density perturbation associated with the propagation of a gravity wave. Because of the density gradients present in atmospheric layers, interesting effects were observed such as a phase reversal in the linear layer response which occurs near the layer peak. Once the layer response is understood, the sodium layer can be used as a tracer of atmospheric wave motions. A two dimensional digital signal processing technique was developed. Both spatial and temporal filtering are utilized to enhance the resolution by decreasing shot noise by more han 10 dB. Many of the features associated with a layer density response to gravity waves were observed in high resolution density profiles of the mesospheric sodium layer. These include nonlinearities as well as the phase reversal in the linear layer response.

A single-degree-of-freedom model for non-linear soil amplification

USGS Publications Warehouse

Erdik, Mustafa Ozder

1979-01-01

For proper understanding of soil behavior during earthquakes and assessment of a realistic surface motion, studies of the large-strain dynamic response of non-linear hysteretic soil systems are indispensable. Most of the presently available studies are based on the assumption that the response of a soil deposit is mainly due to the upward propagation of horizontally polarized shear waves from the underlying bedrock. Equivalent-linear procedures, currently in common use in non-linear soil response analysis, provide a simple approach and have been favorably compared with the actual recorded motions in some particular cases. Strain compatibility in these equivalent-linear approaches is maintained by selecting values of shear moduli and damping ratios in accordance with the average soil strains, in an iterative manner. Truly non-linear constitutive models with complete strain compatibility have also been employed. The equivalent-linear approaches often raise some doubt as to the reliability of their results concerning the system response in high frequency regions. In these frequency regions the equivalent-linear methods may underestimate the surface motion by as much as a factor of two or more. Although studies are complete in their methods of analysis, they inevitably provide applications pertaining only to a few specific soil systems, and do not lead to general conclusions about soil behavior. This report attempts to provide a general picture of the soil response through the use of a single-degree-of-freedom non-linear-hysteretic model. Although the investigation is based on a specific type of nonlinearity and a set of dynamic soil properties, the method described does not limit itself to these assumptions and is equally applicable to other types of nonlinearity and soil parameters.

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

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.

Wave friction factor rediscovered

NASA Astrophysics Data System (ADS)

Le Roux, J. P.

2012-02-01

The wave friction factor is commonly expressed as a function of the horizontal water particle semi-excursion ( A wb) at the top of the boundary layer. A wb, in turn, is normally derived from linear wave theory by {{U_{{wb}}/T_{{w}}}}{{2π }} , where U wb is the maximum water particle velocity measured at the top of the boundary layer and T w is the wave period. However, it is shown here that A wb determined in this way deviates drastically from its real value under both linear and non-linear waves. Three equations for smooth, transitional and rough boundary conditions, respectively, are proposed to solve this problem, all three being a function of U wb, T w, and δ, the thickness of the boundary layer. Because these variables can be determined theoretically for any bottom slope and water depth using the deepwater wave conditions, there is no need to physically measure them. Although differing substantially from many modern attempts to define the wave friction factor, the results coincide with equations proposed in the 1960s for either smooth or rough boundary conditions. The findings also confirm that the long-held notion of circular water particle motion down to the bottom in deepwater conditions is erroneous, the motion in fact being circular at the surface and elliptical at depth in both deep and shallow water conditions, with only horizontal motion at the top of the boundary layer. The new equations are incorporated in an updated version (WAVECALC II) of the Excel program published earlier in this journal by Le Roux et al. Geo-Mar Lett 30(5): 549-560, (2010).

Modeling of matter-wave solitons in a nonlinear inductor-capacitor network through a Gross-Pitaevskii equation with time-dependent linear potential

NASA Astrophysics Data System (ADS)

Kengne, E.; Lakhssassi, A.; Liu, W. M.

2017-08-01

A lossless nonlinear L C transmission network is considered. With the use of the reductive perturbation method in the semidiscrete limit, we show that the dynamics of matter-wave solitons in the network can be modeled by a one-dimensional Gross-Pitaevskii (GP) equation with a time-dependent linear potential in the presence of a chemical potential. An explicit expression for the growth rate of a purely growing modulational instability (MI) is presented and analyzed. We find that the potential parameter of the GP equation of the system does not affect the different regions of the MI. Neglecting the chemical potential in the GP equation, we derive exact analytical solutions which describe the propagation of both bright and dark solitary waves on continuous-wave (cw) backgrounds. Using the found exact analytical solutions of the GP equation, we investigate numerically the transmission of both bright and dark solitary voltage signals in the network. Our numerical studies show that the amplitude of a bright solitary voltage signal and the depth of a dark solitary voltage signal as well as their width, their motion, and their behavior depend on (i) the propagation frequencies, (ii) the potential parameter, and (iii) the amplitude of the cw background. The GP equation derived in this paper with a time-dependent linear potential opens up different ideas that may be of considerable theoretical interest for the management of matter-wave solitons in nonlinear L C transmission networks.

On guided circumferential waves in soft electroactive tubes under radially inhomogeneous biasing fields

NASA Astrophysics Data System (ADS)

Wu, Bin; Su, Yipin; Chen, Weiqiu; Zhang, Chuanzeng

2017-02-01

Soft electroactive (EA) tube actuators and many other cylindrical devices have been proposed recently in literature, which show great advantages over those made from conventional hard solid materials. However, their practical applications may be limited because these soft EA devices are prone to various failure modes. In this paper, we present an analysis of the guided circumferential elastic waves in soft EA tube actuators, which has potential applications in the in-situ nondestructive evaluation (NDE) or online structural health monitoring (SHM) to detect structural defects or fatigue cracks in soft EA tube actuators and in the self-sensing of soft EA tube actuators based on the concept of guided circumferential elastic waves. Both circumferential SH and Lamb-type waves in an incompressible soft EA cylindrical tube under inhomogeneous biasing fields are considered. The biasing fields, induced by the application of an electric voltage difference to the electrodes on the inner and outer cylindrical surfaces of the EA tube in addition to an axial pre-stretch, are inhomogeneous in the radial direction. Dorfmann and Ogden's theory of nonlinear electroelasticity and the associated linear theory for small incremental motion constitute the basis of our analysis. By means of the state-space formalism for the incremental wave motion along with the approximate laminate technique, dispersion relations are derived in a particularly efficient way. For a neo-Hookean ideal dielectric model, the proposed approach is first validated numerically. Numerical examples are then given to show that the guided circumferential wave propagation characteristics are significantly affected by the inhomogeneous biasing fields and the geometrical parameters. Some particular phenomena such as the frequency veering and the nonlinear dependence of the phase velocity on the radial electric voltage are discussed. Our numerical findings demonstrate that it is feasible to use guided circumferential elastic waves for the ultrasonic non-destructive online SHM to detect interior structural defects or fatigue cracks and for the self-sensing of the actual state of the soft EA tube actuator.

A general introduction to aeroacoustics and atmospheric sound

NASA Technical Reports Server (NTRS)

Lighthill, James

1992-01-01

A single unifying principle (based upon the nonlinear 'momentum-flux' effects produced when different components of a motion transport different components of its momentum) is used to give a broad scientific background to several aspects of the interaction between airflows and atmospheric sound. First, it treats the generation of sound by airflows of many different types. These include, for example, jet-like flows involving convected turbulent motions (with the resulting aeroacoustic radiation sensitively dependent on the Mach number of convection) and they include, as an extreme case, the supersonic 'boom' (shock waves generated by a supersonically convected flow pattern). Next, an analysis is given of sound propagation through nonuniformly moving airflows, and the exchange is quantified of energy between flow and sound; while, finally, problems are examined of how sound waves 'on their own' may generate the airflows known as acoustic streaming.

Non-linear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure

NASA Astrophysics Data System (ADS)

Wienkers, A. F.; Ogilvie, G. I.

2018-07-01

Non-linear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce exponentially growing eccentricities at certain mean-motion resonances. However, the details of an efficient saturation mechanism balancing this growth still are not fully understood. This paper develops a local numerical model for an eccentric quasi-axisymmetric shearing box which generalizes the often-used Cartesian shearing box model. The numerical method is an overall second-order well-balanced finite volume method which maintains the stratified and oscillatory steady-state solution by construction. This implementation is employed to study the non-linear outcome of the parametric instability in eccentric discs with vertical structure. Stratification is found to constrain the perturbation energy near the mid-plane and localize the effective region of inertial wave breaking that sources turbulence. A saturated marginally sonic turbulent state results from the non-linear breaking of inertial waves and is subsequently unstable to large-scale axisymmetric zonal flow structures. This resulting limit-cycle behaviour reduces access to the eccentric energy source and prevents substantial transport of angular momentum radially through the disc. Still, the saturation of this parametric instability of inertial waves is shown to damp eccentricity on a time-scale of a thousand orbital periods. It may thus be a promising mechanism for intermittently regaining balance with the exponential growth of eccentricity from the eccentric Lindblad resonances and may also help explain the occurrence of 'bursty' dynamics such as the superhump phenomenon.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

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.

Nonlinear distortion of thin liquid sheets

NASA Astrophysics Data System (ADS)

Mehring, Carsten Ralf

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

Spectral evolution and extreme value analysis of non-linear numerical simulations of narrow band random surface gravity waves.

NASA Astrophysics Data System (ADS)

Socquet-Juglard, H.; Dysthe, K. B.; Trulsen, K.; Liu, J.; Krogstad, H. E.

2003-04-01

Numerical simulations of a narrow band gaussian spectrum of random surface gravity waves have been carried out in two and three spatial dimensions [7]. Different types of non-linear Schr&{uml;o}dinger equations, [1] and [4], have been used in these simulations. Simulations have now been carried with a JONSWAP spectrum associated with a spreading function of the type cosine-squared [5]. The evolution of the spectrum, skewness, kurtosis, ... will be presented. In addition, some results about stochastic properties of the surface will be shown. Based on the approach found in [2], [3] and [6], the results are presented in terms of deviations from linear Gaussian theory and the standard second order small slope perturbation theory. begin{thebibliography}{9} bibitem{kk96} Trulsen, K. &Dysthe, K. B. (1996). A modified nonlinear Schr&{uml;o}dinger equation for broader bandwidth gravity waves on deep water. Wave Motion, 24, pp. 281-289. bibitem{BK2000} Krogstad, H.E. and S.F. Barstow (2000). A uniform approach to extreme value analysis of ocean waves, Proc. ISOPE'2000, Seattle, USA, 3, pp. 103-108. bibitem{PRK} Prevosto, M., H. E. Krogstad and A. Robin (2000). Probability distributions for maximum wave and crest heights, Coast. Eng., 40, 329-360. bibitem{ketal} Trulsen, K., Kliakhandler, I., Dysthe, K. B. &Velarde, M. G. (2000) On weakly nonlinear modulation of waves on deep water, Phys. Fluids, 12, pp. L25-L28. bibitem{onorato} Onorato, M., Osborne, A.R. and Serio, M. (2002) Extreme wave events in directional, random oceanic sea states, Phys. Fluids, 14, pp. 2432-2437. bibitem{BK2002} Krogstad, H.E. and S.F. Barstow (2002). Analysis and Applications of Second Order Models for the Maximum Crest height, % Proc. 21nd Int. Conf. Offshore Mechanics and Arctic Engineering, Oslo. Paper no. OMAE2002-28479. bibitem{JFMP} Dysthe, K. B., Trulsen, K., Krogstad, H. E. and Socquet-Juglard, H. (2002, in press) Evolution of a narrow band spectrum of random surface gravity waves, J. Fluid Mech.

Dynamics of a spherical particle in an acoustic field: A multiscale approach

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

Xie, Jin-Han, E-mail: J.H.Xie@ed.ac.uk; Vanneste, Jacques

2014-10-15

A rigid spherical particle in an acoustic wave field oscillates at the wave period but has also a mean motion on a longer time scale. The dynamics of this mean motion is crucial for numerous applications of acoustic microfluidics, including particle manipulation and flow visualisation. It is controlled by four physical effects: acoustic (radiation) pressure, streaming, inertia, and viscous drag. In this paper, we carry out a systematic multiscale analysis of the problem in order to assess the relative importance of these effects depending on the parameters of the system that include wave amplitude, wavelength, sound speed, sphere radius, andmore » viscosity. We identify two distinguished regimes characterised by a balance among three of the four effects, and we derive the equations that govern the mean particle motion in each regime. This recovers and organises classical results by King [“On the acoustic radiation pressure on spheres,” Proc. R. Soc. A 147, 212–240 (1934)], Gor'kov [“On the forces acting on a small particle in an acoustical field in an ideal fluid,” Sov. Phys. 6, 773–775 (1962)], and Doinikov [“Acoustic radiation pressure on a rigid sphere in a viscous fluid,” Proc. R. Soc. London A 447, 447–466 (1994)], clarifies the range of validity of these results, and reveals a new nonlinear dynamical regime. In this regime, the mean motion of the particle remains intimately coupled to that of the surrounding fluid, and while viscosity affects the fluid motion, it plays no part in the acoustic pressure. Simplified equations, valid when only two physical effects control the particle motion, are also derived. They are used to obtain sufficient conditions for the particle to behave as a passive tracer of the Lagrangian-mean fluid motion.« less

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Doppler-shifted self-reflected wave from a semiconductor

NASA Astrophysics Data System (ADS)

Schuelzgen, Alex; Hughes, S.; Peyghambarian, Nasser

1997-06-01

We report the first experimental observation of a self- reflected wave inside a very dense saturable absorber. An intense femtosecond pulse saturates the absorption and causes a density front moving into the semiconductor sample. Due to the motion of the boundary between saturated and unsaturated areas of the sample the light reflected at this boundary is red-shifted by the Doppler effect. The spectrally shifted reflection makes it possible to distinguish between surface reflection and self-reflection and is used to proof the concept of the dynamic nonlinear skin effect experimentally. Quite well agreement with model calculations is found.

Double-Diffusive Convection at Low Prandtl Number

NASA Astrophysics Data System (ADS)

Garaud, Pascale

2018-01-01

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

Nonlinear waves in electron-positron-ion plasmas including charge separation

NASA Astrophysics Data System (ADS)

Mugemana, A.; Moolla, S.; Lazarus, I. J.

2017-02-01

Nonlinear low-frequency electrostatic waves in a magnetized, three-component plasma consisting of hot electrons, hot positrons and warm ions have been investigated. The electrons and positrons are assumed to have Boltzmann density distributions while the motion of the ions are governed by fluid equations. The system is closed with the Poisson equation. This set of equations is numerically solved for the electric field. The effects of the driving electric field, ion temperature, positron density, ion drift, Mach number and propagation angle are investigated. It is shown that depending on the driving electric field, ion temperature, positron density, ion drift, Mach number and propagation angle, the numerical solutions exhibit waveforms that are sinusoidal, sawtooth and spiky. The introduction of the Poisson equation increased the Mach number required to generate the waveforms but the driving electric field E 0 was reduced. The results are compared with satellite observations.

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.

Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold.

PubMed

Yamada, H; Nakagaki, T; Baker, R E; Maini, P K

2007-06-01

In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication.

Pressure and tension waves from bubble collapse near a solid boundary: A numerical approach.

PubMed

Lechner, Christiane; Koch, Max; Lauterborn, Werner; Mettin, Robert

2017-12-01

The acoustic waves being generated during the motion of a bubble in water near a solid boundary are calculated numerically. The open source package OpenFOAM is used for solving the Navier-Stokes equation and extended to include nonlinear acoustic wave effects via the Tait equation for water. A bubble model with a small amount of gas is chosen, the gas obeying an adiabatic law. A bubble starting from a small size with high internal pressure near a flat, solid boundary is studied. The sequence of events from bubble growth via axial microjet formation, jet impact, annular nanojet formation, torus-bubble collapse, and bubble rebound to second collapse is described. The different pressure and tension waves with their propagation properties are demonstrated.

Punchets: nonlinear transport in Hamiltonian pump-ratchet hybrids

NASA Astrophysics Data System (ADS)

Dittrich, Thomas; Medina Sánchez, Nicolás

2018-02-01

‘Punchets’ are hybrids between ratchets and pumps, combining a spatially periodic static potential, typically asymmetric under space inversion, with a local driving that breaks time-reversal invariance, and are intended to model metal or semiconductor surfaces irradiated by a collimated laser beam. Their crucial feature is irregular driven scattering between asymptotic regions supporting periodic (as opposed to free) motion. With all binary spatio-temporal symmetries broken, scattering in punchets typically generates directed currents. We here study the underlying nonlinear transport mechanisms, from chaotic scattering to the parameter dependence of the currents, in three types of Hamiltonian models, (i) with spatially periodic potentials where only in the driven scattering region, spatial and temporal symmetries are broken, and (ii), spatially asymmetric (ratchet) potentials with a driving that only breaks time-reversal invariance. As more realistic models of laser-irradiated surfaces, we consider (iii), a driving in the form of a running wave confined to a compact region by a static envelope. In this case, the induced current can even run against the direction of wave propagation, drastically evidencing its nonlinear nature. Quantizing punchets is indicated as a viable research perspective.

V S30, slope, H 800 and f 0: performance of various site-condition proxies in reducing ground-motion aleatory variability and predicting nonlinear site response

NASA Astrophysics Data System (ADS)

Derras, Boumédiène; Bard, Pierre-Yves; Cotton, Fabrice

2017-09-01

The aim of this paper is to investigate the ability of various site-condition proxies (SCPs) to reduce ground-motion aleatory variability and evaluate how SCPs capture nonlinearity site effects. The SCPs used here are time-averaged shear-wave velocity in the top 30 m ( V S30), the topographical slope (slope), the fundamental resonance frequency ( f 0) and the depth beyond which V s exceeds 800 m/s ( H 800). We considered first the performance of each SCP taken alone and then the combined performance of the 6 SCP pairs [ V S30- f 0], [ V S30- H 800], [ f 0-slope], [ H 800-slope], [ V S30-slope] and [ f 0- H 800]. This analysis is performed using a neural network approach including a random effect applied on a KiK-net subset for derivation of ground-motion prediction equations setting the relationship between various ground-motion parameters such as peak ground acceleration, peak ground velocity and pseudo-spectral acceleration PSA ( T), and M w, R JB, focal depth and SCPs. While the choice of SCP is found to have almost no impact on the median ground-motion prediction, it does impact the level of aleatory uncertainty. V S30 is found to perform the best of single proxies at short periods ( T < 0.6 s), while f 0 and H 800 perform better at longer periods; considering SCP pairs leads to significant improvements, with particular emphasis on [ V S30- H 800] and [ f 0-slope] pairs. The results also indicate significant nonlinearity on the site terms for soft sites and that the most relevant loading parameter for characterising nonlinear site response is the "stiff" spectral ordinate at the considered period.[Figure not available: see fulltext.

The production of phantom partials due to nonlinearities in the structural components of the piano.

PubMed

Rokni, Eric; Neldner, Lauren M; Adkison, Camille; Moore, Thomas R

2017-10-01

Phantom partials are anomalous overtones in the spectrum of the piano sound that occur at sum and difference frequencies of the natural overtones of the string. Although they are commonly assumed to be produced by forced longitudinal waves in the string, analysis of the sound of a piano produced by mechanically vibrating the soundboard while all the strings are damped indicates that phantom partials can occur in the absence of string motion. The magnitude of the effect leads to the conclusion that nonlinearity in the non-string components may be responsible for some of the power in the phantom partials.

Interaction of a weak shock wave with a discontinuous heavy-gas cylinder

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

Wang, Xiansheng; Yang, Dangguo; Wu, Junqiang

2015-06-15

The interaction between a cylindrical inhomogeneity and a weak planar shock wave is investigated experimentally and numerically, and special attention is given to the wave patterns and vortex dynamics in this scenario. A soap-film technique is realized to generate a well-controlled discontinuous cylinder (SF{sub 6} surrounded by air) with no supports or wires in the shock-tube experiment. The symmetric evolving interfaces and few disturbance waves are observed in a high-speed schlieren photography. Numerical simulations are also carried out for a detailed analysis. The refracted shock wave inside the cylinder is perturbed by the diffracted shock waves and divided into threemore » branches. When these shock branches collide, the shock focusing occurs. A nonlinear model is then proposed to elucidate effects of the wave patterns on the evolution of the cylinder. A distinct vortex pair is gradually developing during the shock-cylinder interaction. The numerical results show that a low pressure region appears at the vortex core. Subsequently, the ambient fluid is entrained into the vortices which are expanding at the same time. Based on the relation between the vortex motion and the circulation, several theoretical models of circulation in the literature are then checked by the experimental and numerical results. Most of these theoretical circulation models provide a reasonably good prediction of the vortex motion in the present configuration.« less

Development of a nearshore oscillating surge wave energy converter with variable geometry

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

Tom, N. M.; Lawson, M. J.; Yu, Y. H.

This paper presents an analysis of a novel wave energy converter concept that combines an oscillating surge wave energy converter (OSWEC) with control surfaces. The control surfaces allow for a variable device geometry that enables the hydrodynamic properties to be adapted with respect to structural loading, absorption range and power-take-off capability. The device geometry is adjusted on a sea state-to-sea state time scale and combined with wave-to-wave manipulation of the power take-off (PTO) to provide greater control over the capture efficiency, capacity factor, and design loads. This work begins with a sensitivity study of the hydrodynamic coefficients with respect tomore » device width, support structure thickness, and geometry. A linear frequency domain analysis is used to evaluate device performance in terms of absorbed power, foundation loads, and PTO torque. Previous OSWEC studies included nonlinear hydrodynamics, in response a nonlinear model that includes a quadratic viscous damping torque that was linearized via the Lorentz linearization. Inclusion of the quadratic viscous torque led to construction of an optimization problem that incorporated motion and PTO constraints. Results from this study found that, when transitioning from moderate-to-large sea states the novel OSWEC was capable of reducing structural loads while providing a near constant power output.« less

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.

Systematic analysis of nonlinear ground motion and temporal changes of material properties produced by small and medium earthquakes

NASA Astrophysics Data System (ADS)

Wu, C.; Peng, Z.; Ben-Zion, Y.

2009-12-01

Recent studies based on spectral ratio analysis have found clear temporal changes of material properties in the shallow crust and around active fault zones during large earthquakes with peak ground acceleration (PGA) larger than 100-200 gals (e.g., Sawazaki et al., GRL, 2006; Rubenstein et al., JGR, 2007; Wu et al., GJI, 2009). The temporal evolution of properties is generally characterized by a clear drop of resonant frequency and increased damping, followed by logarithmic recoveries with time. The shift in resonant frequency and damping are considered two hallmarks of nonlinear response associated with increasing material damage. However, an existing damage can produce similar changes in resonance curves with increasing wave amplitude, even in cases when the material damage does not increase (Lyakhovsky et al., GJI, 2009). In such cases the recovery of resonance properties with reduced source amplitude should be essentially instantaneous. It is important to distinguish with in situ seismic data nonlinear wave propagation effects that reflect fixed vs. evolving material damage. Here we systematically analyze temporal changes of material properties and nonlinear response associated with small and medium earthquakes, using seismic data recorded by the Japanese Strong Motion Network KIK-Net, a temporary 10-station PASSCAL seismic network along the North Anatolian Fault in Turkey, and the borehole and surface stations around the Parkfield section of the San Andreas fault. We compute the spectral ratios of windowed records from a pair of target and reference stations, and apply the sliding-window to the entire seismic records including the pre-event noise, P and S waves, and the early and late S-coda waves. We choose small and medium events to reduce the effects from additional material damage and use small sliding-window size to capture the subtle changes in the spectral ratios. The spectral ratio traces from windows within certain PGA ranges are then stacked to enhance the stability of the results. The preliminary results from the KIK-Net data suggest that the resonant frequency starts to decrease for PGA levels of several tens of gals, followed by near instantaneous recovery. Updated results from analysis of all the datasets will be presented in the meeting.

Nonlinear and linear site response and basin effects in Seattle for the M 6.8 Nisqually, Washington, earthquake

USGS Publications Warehouse

Frankel, A.D.; Carver, D.L.; Williams, R.A.

2002-01-01

We used recordings of the M 6.8 Nisqually earthquake and its ML 3.4 aftershock to study site response and basin effects for 35 locations in Seattle, Washington. We determined site amplification from Fourier spectral ratios of the recorded horizontal ground motions, referenced to a soft-rock site. Soft-soil sites (generally National Earthquake Hazard Reduction Program [NEHRP] class E) on artificial fill and young alluvium have the largest 1-Hz amplifications (factors of 3-7) for both the mainshock and aftershock. These amplifications are correlated with areas of higher damage from the mainshock to major buildings and liquefaction. There are several indications of nonlinear response at the soft-soil sites for the mainshock ground motions, despite relatively modest peak accelerations in the S waves of 15%-22%g. First, the mainshock spectral ratios do not show amplification at 2-8 Hz as do the aftershock spectral ratios. Spectral peaks at frequencies below 2 Hz generally occur at lower frequencies for the mainshock spectral ratios than for the aftershock ratios. At one soft-soil site, there is a clear shift of the resonant frequency to a lower frequency for the mainshock compared with the aftershock. The frequency of this resonance increases in the coda of the mainshock record, indicating that the site response during the weaker motions of the coda is more linear than that of the initial S wave. Three of the soft-soil sites display cusped, one-sided mainshock accelerograms after the S wave. These soft-soil sites also show amplification at 10-20 Hz in the S wave, relative to the rock site, that is not observed for the aftershock. The cusped waveforms and 10-20-Hz amplification are symptomatic of nonlinear response at the soft-soil sites. These sites had nearby liquefaction. The largest amplifications for 0.5 Hz occur at soft-soil sites on the southern portion of the Seattle Basin. Stiff-soil sites (NEHRP classes D and C) on Pleistocene-age glacial deposits display similar spectral amplification for the mainshock and aftershock, indicating approximately linear response. The stiff-soil sites generally have moderate amplification (factors of 1.1-2.4) at 0.5 and 1 Hz. Amplifications at 1 and 5 Hz for all sites generally increase with decreasing shear-wave velocity measured in the top 30 m (Vs 30). However, larger amplifications at 0.5 and 1 Hz for sites with similar Vs 30 values are observed for sites in the Seattle Basin, illustrating the amplification from the deeper (>30 m) sediments and the contribution from basin surface waves. Record sections for the mainshock and aftershock show that basin surface waves produce the peak velocities for many of the sites in the Seattle Basin and often dominate the amplitude at 1 Hz and lower frequencies.

FORTRAN programs for calculating nonlinear seismic ground response in two dimensions

USGS Publications Warehouse

Joyner, W.B.

1978-01-01

The programs described here were designed for calculating the nonlinear seismic response of a two-dimensional configuration of soil underlain by a semi-infinite elastic medium representing bedrock. There are two programs. One is for plane strain motions, that is, motions in the plane perpendicular to the long axis of the structure, and the other is for antiplane strain motions, that is motions parallel to the axis. The seismic input is provided by specifying what the motion of the rock-soil boundary would be if the soil were absent and the boundary were a free surface. This may be done by supplying a magnetic tape containing the values of particle velocity for every boundary point at every instant of time. Alternatively, a punch card deck may be supplied giving acceleration values at every instant of time. In the plane strain program it is assumed that the acceleration values apply simultaneously to every point on the boundary; in the antiplane strain program it is assumed that the acceleration values characterize a plane shear wave propagating upward in the underlying elastic medium at a specified angle with the vertical. The nonlinear hysteretic behavior of the soil is represented by a three-dimensional rheological model. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. Computations are done in terms of stress departures from an unspecified initial state. Source listings are provided here along with instructions for preparing the input. A more detailed discussion of the method is presented elsewhere.

A mathematical model of the structure and evolution of small scale discrete auroral arcs

NASA Technical Reports Server (NTRS)

Seyler, C. E.

1990-01-01

A three dimensional fluid model which includes the dispersive effect of electron inertia is used to study the nonlinear macroscopic plasma dynamics of small scale discrete auroral arcs within the auroral acceleration zone and ionosphere. The motion of the Alfven wave source relative to the magnetospheric and ionospheric plasma forms an oblique Alfven wave which is reflected from the topside ionosphere by the negative density gradient. The superposition of the incident and reflected wave can be described by a steady state analytical solution of the model equations with the appropriate boundary conditions. This two dimensional discrete auroral arc equilibrium provides a simple explanation of auroral acceleration associated with the parallel electric field. Three dimensional fully nonlinear numerical simulations indicate that the equilibrium arc configuration evolves three dimensionally through collisionless tearing and reconnection of the current layer. The interaction of the perturbed flow and the transverse magnetic field produces complex transverse structure that may be the origin of the folds and curls observed to be associated with small scale discrete arcs.

Near-surface energy transfers from internal tide beams to smaller vertical scale motions

NASA Astrophysics Data System (ADS)

Chou, S.; Staquet, C.; Carter, G. S.; Luther, D. S.

2016-02-01

Mechanical energy capable of causing diapycnal mixing in the ocean is transferred to the internal wave field when barotropic tides pass over underwater topography and generate internal tides. The resulting internal tide energy is confined in vertically limited structures, or beams. As internal tide beams (ITBs) propagate through regions of non-uniform stratification in the upper ocean, wave energy can be scattered through multiple reflections and refractions, be vertically trapped, or transferred to non-tidal frequencies through different nonlinear processes. Various observations have shown that ITBs are no longer detectable in horizontal kinetic energy beyond the first surface reflection. Importantly, this implies that some of the internal tide energy no longer propagates in to the abyssal ocean and consequently will not be available to maintain the density stratification. Using the NHM, a nonlinear and nonhydrostatic model based on the MITgcm, simulations of an ITB propagating up to the sea surface are examined in order to quantify the transformation of ITB energy to other motions. We compare and contrast the transformations enabled by idealized, smoothly-varying stratification with transformations enabled by realistic stratification containing a broad-band vertical wavenumber spectrum of variations. Preliminary two-dimensional results show that scattering due to small-scale structure in realistic stratification profiles from Hawaii can lead to energy being vertically trapped near the surface. Idealized simulations of "locally" generated internal solitary waves are analyzed in terms of energy flux transfers from the ITB to solitary waves, higher harmonics, and mean flow. The amount of internal tide energy which propagates back down after near-surface reflection of the ITB in different environments is quantified.

Rigid rotators. [deriving the time-independent energy states associated with rotational motions of the molecule

NASA Technical Reports Server (NTRS)

1976-01-01

The two-particle, steady-state Schroedinger equation is transformed to center of mass and internuclear distance vector coordinates, leading to the free particle wave equation for the kinetic energy motion of the molecule and a decoupled wave equation for a single particle of reduced mass moving in a spherical potential field. The latter describes the vibrational and rotational energy modes of the diatomic molecule. For fixed internuclear distance, this becomes the equation of rigid rotator motion. The classical partition function for the rotator is derived and compared with the quantum expression. Molecular symmetry effects are developed from the generalized Pauli principle that the steady-state wave function of any system of fundamental particles must be antisymmetric. Nuclear spin and spin quantum functions are introduced and ortho- and para-states of rotators, along with their degeneracies, are defined. Effects of nuclear spin on entropy are deduced. Next, rigid polyatomic rotators are considered and the partition function for this case is derived. The patterns of rotational energy levels for nonlinear molecules are discussed for the spherical symmetric top, for the prolate symmetric top, for the oblate symmetric top, and for the asymmetric top. Finally, the equilibrium energy and specific heat of rigid rotators are derived.

The Vajont disaster: a 3D numerical simulation for the slide and the waves

NASA Astrophysics Data System (ADS)

Rubino, Angelo; Androsov, Alexey; Vacondio, Renato; Zanchettin, Davide; Voltzinger, Naum

2016-04-01

A very high resolution O(5 m), 3D hydrostatic nonlinear numerical model was used to simulate the dynamics of both the slide and the surface waves produced during the Vajont disaster (north Italy, 1963), one of the major landslide-induced tsunamis ever documented. Different simulated wave phenomena like, e.g., maximum run-up on the opposite shore, maximum height, and water velocity were analyzed and compared with data available in literature, including the results of a fully 3D simulation obtained with a Smoothed Particle Hydrodynamic code. The difference between measured and simulated after-slide bathymetries was calculated and used in an attempt to quantify the relative magnitude and extension of rigid and fluid motion components during the event.

Modeling Seismoacoustic Propagation from the Nonlinear to Linear Regimes

NASA Astrophysics Data System (ADS)

Chael, E. P.; Preston, L. A.

2015-12-01

Explosions at shallow depth-of-burial can cause nonlinear material response, such as fracturing and spalling, up to the ground surface above the shot point. These motions at the surface affect the generation of acoustic waves into the atmosphere, as well as the surface-reflected compressional and shear waves. Standard source scaling models for explosions do not account for such nonlinear interactions above the shot, while some recent studies introduce a non-isotropic addition to the moment tensor to represent them (e.g., Patton and Taylor, 2011). We are using Sandia's CTH shock physics code to model the material response in the vicinity of underground explosions, up to the overlying ground surface. Across a boundary where the motions have decayed to nearly linear behavior, we couple the signals from CTH into a linear finite-difference (FD) seismoacoustic code to efficiently propagate the wavefields to greater distances. If we assume only one-way transmission of energy through the boundary, then the particle velocities there suffice as inputs for the FD code, simplifying the specification of the boundary condition. The FD algorithm we use applies the wave equations for velocity in an elastic medium and pressure in an acoustic one, and matches the normal traction and displacement across the interface. Initially we are developing and testing a 2D, axisymmetric seismoacoustic routine; CTH can use this geometry in the source region as well. The Source Physics Experiment (SPE) in Nevada has collected seismic and acoustic data on numerous explosions at different scaled depths, providing an excellent testbed for investigating explosion phenomena (Snelson et al., 2013). We present simulations for shots SPE-4' and SPE-5, illustrating the importance of nonlinear behavior up to the ground surface. Our goal is to develop the capability for accurately predicting the relative signal strengths in the air and ground for a given combination of source yield and depth. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Vorticity equation for MHD fast waves in geospace environment

NASA Technical Reports Server (NTRS)

Yamauchi, M.; Lundin, R.; Lui, A. T. Y.

1993-01-01

The MHD vorticity equation is modified in order to apply it to nonlinear MHD fast waves or shocks when their extent along the magnetic field is limited. Field-aligned current (FAC) generation is also discussed on the basis of this modified vorticity equation. When the wave normal is not aligned to the finite velocity convection and the source region is spatially limited, a longitudinal polarization causes a pair of plus and minus charges inside the compressional plane waves or shocks, generating a pair of FACs. This polarization is not related to the separation between the electrons and ions caused by their difference in mass, a separation which is inherent to compressional waves. The resultant double field-aligned current structure exists both with and without the contributions from curvature drift, which is questionable in terms of its contribution to vorticity change from the viewpoint of single-particle motion.

Time-domain hybrid method for simulating large amplitude motions of ships advancing in waves

NASA Astrophysics Data System (ADS)

Liu, Shukui; Papanikolaou, Apostolos D.

2011-03-01

Typical results obtained by a newly developed, nonlinear time domain hybrid method for simulating large amplitude motions of ships advancing with constant forward speed in waves are presented. The method is hybrid in the way of combining a time-domain transient Green function method and a Rankine source method. The present approach employs a simple double integration algorithm with respect to time to simulate the free-surface boundary condition. During the simulation, the diffraction and radiation forces are computed by pressure integration over the mean wetted surface, whereas the incident wave and hydrostatic restoring forces/moments are calculated on the instantaneously wetted surface of the hull. Typical numerical results of application of the method to the seakeeping performance of a standard containership, namely the ITTC S175, are herein presented. Comparisons have been made between the results from the present method, the frequency domain 3D panel method (NEWDRIFT) of NTUA-SDL and available experimental data and good agreement has been observed for all studied cases between the results of the present method and comparable other data.

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

Vortex formation through inertial wave focusing

NASA Astrophysics Data System (ADS)

Duran-Matute, Matias; Flor, Jan-Bert; Godeferd, Fabien

2011-11-01

We present a novel experimental and numerical study on the formation of columnar vortical structures by inertial waves in a rotating fluid. Two inertial-wave cones are generated by a vertically oscillating torus in a fluid in solid body rotation At the tip of the cones, there is a singular point towards which the energy of the waves gets focused. The particularity of this configuration, as compared to those of previous experiments (e.g. oscillating sphere or disc), is that the singular point's position within the fluid leads to complex non-linear wave interaction, which may lead to the formation of a localized vortex that expands in the vertical in the form of a Taylor column. Using detailed PIV measurements we consider the flow evolution from the localized wave overturning motion to the Taylor column formation as well as the inertial wave dynamics during this process, The results are discussed in the context of turbulence in rotating fluids. We acknowledge financial support from projects ANR ANISO and CIBLE.

Effects of discrete-electrode arrangement on traveling-wave electroosmotic pumping

NASA Astrophysics Data System (ADS)

Liu, Weiyu; Shao, Jinyou; Ren, Yukun; Wu, Yupan; Wang, Chunhui; Ding, Haitao; Jiang, Hongyuan; Ding, Yucheng

2016-09-01

Traveling-wave electroosmotic (TWEO) pumping arises from the action of an imposed traveling-wave (TW) electric field on its own induced charge in the diffuse double layer, which is formed on top of an electrode array immersed in electrolyte solutions. Such a traveling field can be merely realized in practice by a discrete electrode array upon which the corresponding voltages of correct phase are imposed. By employing the theory of linear and weakly nonlinear double-layer charging dynamics, a physical model incorporating both the nonlinear surface capacitance of diffuse layer and Faradaic current injection is developed herein in order to quantify the changes in TWEO pumping performance from a single-mode TW to discrete electrode configuration. Benefiting from the linear analysis, we investigate the influence of using discrete electrode array to create the TW signal on the resulting fluid motion, and several approaches are suggested to improve the pumping performance. In the nonlinear regime, our full numerical analysis considering the intervening isolation spacing indicates that a practical four-phase discrete electrode configuration of equal electrode and gap width exhibits stronger nonlinearity than expected from the idealized pump applied with a single-mode TW in terms of voltage-dependence of the ideal pumping frequency and peak flow rate, though it has a much lower pumping performance. For model validation, pumping of electrolytes by TWEO is achieved over a confocal spiral four-phase electrode array covered by an insulating microchannel; measurement of flow velocity indicates the modified nonlinear theory considering moderate Faradaic conductance is indeed a more accurate physical description of TWEO. These results offer useful guidelines for designing high-performance TWEO microfluidic pumps with discrete electrode array.

Three-Dimensional Numerical Analyses of Earth Penetration Dynamics

DTIC Science & Technology

1979-01-31

Lagrangian formulation based on the HEMP method and has been adapted and validated for treatment of normal-incidence (axisymmetric) impact and...code, is a detailed analysis of the structural response of the EPW. This analysis is generated using a nonlinear dynamic, elastic- plastic finite element...based on the HEMP scheme. Thus, the code has the same material modeling capabilities and abilities to track large scale motion found in the WAVE-L code

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

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

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

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

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

NASA Astrophysics Data System (ADS)

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

2003-10-01

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

Path planning on cellular nonlinear network using active wave computing technique

NASA Astrophysics Data System (ADS)

Yeniçeri, Ramazan; Yalçın, Müstak E.

2009-05-01

This paper introduces a simple algorithm to solve robot path finding problem using active wave computing techniques. A two-dimensional Cellular Neural/Nonlinear Network (CNN), consist of relaxation oscillators, has been used to generate active waves and to process the visual information. The network, which has been implemented on a Field Programmable Gate Array (FPGA) chip, has the feature of being programmed, controlled and observed by a host computer. The arena of the robot is modelled as the medium of the active waves on the network. Active waves are employed to cover the whole medium with their own dynamics, by starting from an initial point. The proposed algorithm is achieved by observing the motion of the wave-front of the active waves. Host program first loads the arena model onto the active wave generator network and command to start the generation. Then periodically pulls the network image from the generator hardware to analyze evolution of the active waves. When the algorithm is completed, vectorial data image is generated. The path from any of the pixel on this image to the active wave generating pixel is drawn by the vectors on this image. The robot arena may be a complicated labyrinth or may have a simple geometry. But, the arena surface always must be flat. Our Autowave Generator CNN implementation which is settled on the Xilinx University Program Virtex-II Pro Development System is operated by a MATLAB program running on the host computer. As the active wave generator hardware has 16, 384 neurons, an arena with 128 × 128 pixels can be modeled and solved by the algorithm. The system also has a monitor and network image is depicted on the monitor simultaneously.

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

The Gravity Wave Response Above Deep Convection in a Squall Line Simulation

NASA Technical Reports Server (NTRS)

Alexander, M. J.; Holton, J. R.; Durran, D. R.

1995-01-01

High-frequency gravity waves generated by convective storms likely play an important role in the general circulation of the middle atmosphere. Yet little is known about waves from this source. This work utilizes a fully compressible, nonlinear, numerical, two-dimensional simulation of a midlatitude squall line to study vertically propagating waves generated by deep convection. The model includes a deep stratosphere layer with high enough resolution to characterize the wave motions at these altitudes. A spectral analysis of the stratospheric waves provides an understanding of the necessary characteristics of the spectrum for future studies of their effects on the middle atmosphere in realistic mean wind scenarios. The wave spectrum also displays specific characteristics that point to the physical mechanisms within the storm responsible for their forcing. Understanding these forcing mechanisms and the properties of the storm and atmosphere that control them are crucial first steps toward developing a parameterization of waves from this source. The simulation also provides a description of some observable signatures of convectively generated waves, which may promote observational verification of these results and help tie any such observations to their convective source.

Vorticity Transport and Wave Emission In A Protoplanetary Disk

NASA Technical Reports Server (NTRS)

Davis, S. S.; Davis, Sanford (Technical Monitor)

2002-01-01

Higher order numerical algorithms (4th order in time, 3rd order in space) are applied to the Euler equations and are used to examine vorticity transport and wave motion in a non-self gravitating, initially isentropic Keplerian disk. In this talk we will examine the response of the disk to an isolated vortex with a circulation about equal to the rotation rate of Jupiter. The vortex is located on the 4 AU circle and the nebula is simulated from 1 to 24 AU. We show that the vortex emits pressure-supported density and Rossby-type wave packets before it decays within a few orbits. The acoustic density waves evolve into weak (non entropy preserving) shock waves that propagate over the entire disk. The Rossby waves remain in the vicinity of the initial vortex disturbance, but are rapidly damped. Temporal frequencies and spatial wavenumbers are derived from the nonlinear simulation data and correlated with analytical dispersion relations from the linearized Euler and energy equations.

Oscillating two-stream instability of beat waves in a hot magnetized plasma

NASA Astrophysics Data System (ADS)

Ferdous, T.; Amin, M. R.; Salimullah, M.

1997-02-01

It is shown that an electrostatic electron plasma beat wave is efficiently unstable for a low-frequency and short-wave-length purely growing perturbation (ω, k), i.e. an oscillating two-stream instability in a transversely magnetized hot plasma. The nonlinear response of electrons and ions with strong finite Larmor radius effects has been obtained by solving the Vlasov equation expressed in the guiding-center coordinates. The effect of ion dynamics has been found to play a vital role around ω ∼ ωci, where ωci is the ion-cyclotron frequency. For typical plasma parameters, it is found that the maximum growth rate of the instability is about two orders higher when ion motion is taken into account in addition to the electron dynamics.

Lorentz-Abraham-Dirac versus Landau-Lifshitz radiation friction force in the ultrarelativistic electron interaction with electromagnetic wave (exact solutions).

PubMed

Bulanov, Sergei V; Esirkepov, Timur Zh; Kando, Masaki; Koga, James K; Bulanov, Stepan S

2011-11-01

When the parameters of electron-extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crucially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possesses unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency. For this, a class of the exact solutions to the nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.

Lorentz-Abraham-Dirac versus Landau-Lifshitz radiation friction force in the ultrarelativistic electron interaction with electromagnetic wave (exact solutions)

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

Bulanov, Sergei V.; Esirkepov, Timur Zh.; Kando, Masaki

2011-11-15

When the parameters of electron-extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crucially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possesses unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency. For this, a class of the exact solutions to themore » nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.« less

Effect of higher order nonlinearity, directionality and finite water depth on wave statistics: Comparison of field data and numerical simulations

NASA Astrophysics Data System (ADS)

Fernández, Leandro; Monbaliu, Jaak; Onorato, Miguel; Toffoli, Alessandro

2014-05-01

This research is focused on the study of nonlinear evolution of irregular wave fields in water of arbitrary depth by comparing field measurements and numerical simulations.It is now well accepted that modulational instability, known as one of the main mechanisms for the formation of rogue waves, induces strong departures from Gaussian statistics. However, whereas non-Gaussian properties are remarkable when wave fields follow one direction of propagation over an infinite water depth, wave statistics only weakly deviate from Gaussianity when waves spread over a range of different directions. Over finite water depth, furthermore, wave instability attenuates overall and eventually vanishes for relative water depths as low as kh=1.36 (where k is the wavenumber of the dominant waves and h the water depth). Recent experimental results, nonetheless, seem to indicate that oblique perturbations are capable of triggering and sustaining modulational instability even if kh<1.36. In this regard, the aim of this research is to understand whether the combined effect of directionality and finite water depth has a significant effect on wave statistics and particularly on the occurrence of extremes. For this purpose, numerical experiments have been performed solving the Euler equation of motion with the Higher Order Spectral Method (HOSM) and compared with data of short crested wave fields for different sea states observed at the Lake George (Australia). A comparative analysis of the statistical properties (i.e. density function of the surface elevation and its statistical moments skewness and kurtosis) between simulations and in-situ data provides a confrontation between the numerical developments and real observations in field conditions.

Inviscid dynamics of a wet foam drop with monodisperse bubble size distribution

NASA Astrophysics Data System (ADS)

McDaniel, J. Gregory; Akhatov, Iskander; Holt, R. Glynn

2002-06-01

Motivated by recent experiments involving the acoustic levitation of foam drops, we develop a model for nonlinear oscillations of a spherical drop composed of monodisperse aqueous foam with void fraction below 0.1. The model conceptually divides a foam drop into many cells, each cell consisting of a spherical volume of liquid with a bubble at its center. By treating the liquid as incompressible and inviscid, a nonlinear equation is obtained for bubble motion due to a pressure applied at the outer radius of the liquid sphere. Upon linearizing this equation and connecting the cells at their outer radii, a wave equation is obtained with a dispersion relation for the sound waves in a bubbly liquid. For the spherical drop, this equation is solved by a normal mode expansion that yields the natural frequencies as functions of standard foam parameters. Numerical examples illustrate how the analysis may be used to extract foam parameters, such as void fraction and bubble radius, from the experimentally measured natural frequencies of a foam drop.

Robust output tracking control of a laboratory helicopter for automatic landing

NASA Astrophysics Data System (ADS)

Liu, Hao; Lu, Geng; Zhong, Yisheng

2014-11-01

In this paper, robust output tracking control problem of a laboratory helicopter for automatic landing in high seas is investigated. The motion of the helicopter is required to synchronise with that of an oscillating platform, e.g. the deck of a vessel subject to wave-induced motions. A robust linear time-invariant output feedback controller consisting of a nominal controller and a robust compensator is designed. The robust compensator is introduced to restrain the influences of parametric uncertainties, nonlinearities and external disturbances. It is shown that robust stability and robust tracking property can be achieved simultaneously. Experimental results on the laboratory helicopter for automatic landing demonstrate the effectiveness of the designed control approach.

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

Quantum Optomechanics with Silicon Nanostructures

NASA Astrophysics Data System (ADS)

Safavi-Naeini, Amir H.

Mechanical resonators are the most basic and ubiquitous physical systems known. In on-chip form, they are used to process high frequency signals in every cell phone, television, and laptop. They have also been in the last few decades in different shapes and forms, a critical part of progress in quantum information sciences with kilogram scale mirrors for gravitational wave detection measuring motion at its quantum limits, and the motion of single ions being used to link qubits for quantum computation. Optomechanics is a field primarily concerned with coupling light to the motion of mechanical structures. This thesis contains descriptions of recent work with mechanical systems in the megahertz to gigahertz frequency range, formed by nanofabricating novel photonic/phononic structures on a silicon chip. These structures are designed to have both optical and mechanical resonances, and laser light is used to address and manipulate their motional degrees of freedom through radiation pressure forces. We laser cool these mechanical resonators to their ground states, and observe for the first time the quantum zero-point motion of a nanomechanical resonator. Conversely, we show that engineered mechanical resonances drastically modify the optical response of our structures, creating large effective optical nonlinearities not present in bulk silicon. We experimentally demonstrate aspects of these nonlinearities by proposing and observing ``electromagnetically induced transparency'' and light slowed down to 6 m/s, as well as wavelength conversion, and generation of nonclassical optical radiation. Finally, the application of optomechanics to longstanding problems in quantum and classical communications are proposed and investigated.

Near-Inertial Internal Gravity Waves in the Ocean.

PubMed

Alford, Matthew H; MacKinnon, Jennifer A; Simmons, Harper L; Nash, Jonathan D

2016-01-01

We review the physics of near-inertial waves (NIWs) in the ocean and the observations, theory, and models that have provided our present knowledge. NIWs appear nearly everywhere in the ocean as a spectral peak at and just above the local inertial period f, and the longest vertical wavelengths can propagate at least hundreds of kilometers toward the equator from their source regions; shorter vertical wavelengths do not travel as far and do not contain as much energy, but lead to turbulent mixing owing to their high shear. NIWs are generated by a variety of mechanisms, including the wind, nonlinear interactions with waves of other frequencies, lee waves over bottom topography, and geostrophic adjustment; the partition among these is not known, although the wind is likely the most important. NIWs likely interact strongly with mesoscale and submesoscale motions, in ways that are just beginning to be understood.

Eddy, drift wave and zonal flow dynamics in a linear magnetized plasma

PubMed Central

Arakawa, H.; Inagaki, S.; Sasaki, M.; Kosuga, Y.; Kobayashi, T.; Kasuya, N.; Nagashima, Y.; Yamada, T.; Lesur, M.; Fujisawa, A.; Itoh, K.; Itoh, S.-I.

2016-01-01

Turbulence and its structure formation are universal in neutral fluids and in plasmas. Turbulence annihilates global structures but can organize flows and eddies. The mutual-interactions between flow and the eddy give basic insights into the understanding of non-equilibrium and nonlinear interaction by turbulence. In fusion plasma, clarifying structure formation by Drift-wave turbulence, driven by density gradients in magnetized plasma, is an important issue. Here, a new mutual-interaction among eddy, drift wave and flow in magnetized plasma is discovered. A two-dimensional solitary eddy, which is a perturbation with circumnavigating motion localized radially and azimuthally, is transiently organized in a drift wave – zonal flow (azimuthally symmetric band-like shear flows) system. The excitation of the eddy is synchronized with zonal perturbation. The organization of the eddy has substantial impact on the acceleration of zonal flow. PMID:27628894

Nonlinear-drifted Brownian motion with multiple hidden states for remaining useful life prediction of rechargeable batteries

NASA Astrophysics Data System (ADS)

Wang, Dong; Zhao, Yang; Yang, Fangfang; Tsui, Kwok-Leung

2017-09-01

Brownian motion with adaptive drift has attracted much attention in prognostics because its first hitting time is highly relevant to remaining useful life prediction and it follows the inverse Gaussian distribution. Besides linear degradation modeling, nonlinear-drifted Brownian motion has been developed to model nonlinear degradation. Moreover, the first hitting time distribution of the nonlinear-drifted Brownian motion has been approximated by time-space transformation. In the previous studies, the drift coefficient is the only hidden state used in state space modeling of the nonlinear-drifted Brownian motion. Besides the drift coefficient, parameters of a nonlinear function used in the nonlinear-drifted Brownian motion should be treated as additional hidden states of state space modeling to make the nonlinear-drifted Brownian motion more flexible. In this paper, a prognostic method based on nonlinear-drifted Brownian motion with multiple hidden states is proposed and then it is applied to predict remaining useful life of rechargeable batteries. 26 sets of rechargeable battery degradation samples are analyzed to validate the effectiveness of the proposed prognostic method. Moreover, some comparisons with a standard particle filter based prognostic method, a spherical cubature particle filter based prognostic method and two classic Bayesian prognostic methods are conducted to highlight the superiority of the proposed prognostic method. Results show that the proposed prognostic method has lower average prediction errors than the particle filter based prognostic methods and the classic Bayesian prognostic methods for battery remaining useful life prediction.

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 dynamics of steep surface waves as derived from a Lagrangian

NASA Astrophysics Data System (ADS)

Longuet-Higgins, Michael

1999-11-01

A simple and natural method for calculating the deformation of surface gravity waves on deep water was recently formulated by A.M. Balk (1996). The equations of motion are derived from a Lagrangian (T-V) where T and V are the kinetic and potential energies, expressed in terms of the Fourier coefficients a_n(t) of the motion in an auxiliary half-space. The method has certain advantages over the more usual Hamiltonian equations: (1) The expressions for T and V are of finite order N <= 4 in the Fourier coefficients a_n(t) and their rates of change dota(t); (2) the constants in these expressions are low integers, mainly ± 1 or 0; (3) breaking or overturning waves are described by single-valued functions of a parameter. The analysis leads to dynamical equations for än of the form sumj P_ij äj = Qi (a, ; dota) (P_ij and Qi being polynomials of low degree in the coefficients a_n) which can in general be solved to allow time-stepping to proceed. Conveniently, the determinant Δ of P_ij is found to factorise. Some examples will be discussed, particularly the case of standing waves, when the coefficients a_n(t) are all real. The phenomena of ``flip through'' and jet formation are of special interest.

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.

Dynamics from a mathematical model of a two-state gas laser

NASA Astrophysics Data System (ADS)

Kleanthous, Antigoni; Hua, Tianshu; Manai, Alexandre; Yawar, Kamran; Van Gorder, Robert A.

2018-05-01

Motivated by recent work in the area, we consider the behavior of solutions to a nonlinear PDE model of a two-state gas laser. We first review the derivation of the two-state gas laser model, before deriving a non-dimensional model given in terms of coupled nonlinear partial differential equations. We then classify the steady states of this system, in order to determine the possible long-time asymptotic solutions to this model, as well as corresponding stability results, showing that the only uniform steady state (the zero motion state) is unstable, while a linear profile in space is stable. We then provide numerical simulations for the full unsteady model. We show for a wide variety of initial conditions that the solutions tend toward the stable linear steady state profiles. We also consider traveling wave solutions, and determine the unique wave speed (in terms of the other model parameters) which allows wave-like solutions to exist. Despite some similarities between the model and the inviscid Burger's equation, the solutions we obtain are much more regular than the solutions to the inviscid Burger's equation, with no evidence of shock formation or loss of regularity.

Validation and Performance Comparison of Numerical Codes for Tsunami Inundation

NASA Astrophysics Data System (ADS)

Velioglu, D.; Kian, R.; Yalciner, A. C.; Zaytsev, A.

2015-12-01

In inundation zones, tsunami motion turns from wave motion to flow of water. Modelling of this phenomenon is a complex problem since there are many parameters affecting the tsunami flow. In this respect, the performance of numerical codes that analyze tsunami inundation patterns becomes important. The computation of water surface elevation is not sufficient for proper analysis of tsunami behaviour in shallow water zones and on land and hence for the development of mitigation strategies. Velocity and velocity patterns are also crucial parameters and have to be computed at the highest accuracy. There are numerous numerical codes to be used for simulating tsunami inundation. In this study, FLOW 3D and NAMI DANCE codes are selected for validation and performance comparison. Flow 3D simulates linear and nonlinear propagating surface waves as well as long waves by solving three-dimensional Navier-Stokes (3D-NS) equations. FLOW 3D is used specificaly for flood problems. NAMI DANCE uses finite difference computational method to solve linear and nonlinear forms of shallow water equations (NSWE) in long wave problems, specifically tsunamis. In this study, these codes are validated and their performances are compared using two benchmark problems which are discussed in 2015 National Tsunami Hazard Mitigation Program (NTHMP) Annual meeting in Portland, USA. One of the problems is an experiment of a single long-period wave propagating up a piecewise linear slope and onto a small-scale model of the town of Seaside, Oregon. Other benchmark problem is an experiment of a single solitary wave propagating up a triangular shaped shelf with an island feature located at the offshore point of the shelf. The computed water surface elevation and velocity data are compared with the measured data. The comparisons showed that both codes are in fairly good agreement with each other and benchmark data. All results are presented with discussions and comparisons. The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement No 603839 (Project ASTARTE - Assessment, Strategy and Risk Reduction for Tsunamis in Europe)

Effects of eddy initial conditions on nonlinear forcing of planetary scale waves by amplifying baroclinic eddies

NASA Technical Reports Server (NTRS)

Young, Richard E.

1986-01-01

The previous study of Young and Villere concerning growth of planetary scale waves forced by wave-wave interactions of amplifying intermediate scale baroclinic eddies is extended to investigate effects of different eddy initial conditions. A global, spectral, primitive equation model is used for the calculations. For every set of eddy initial conditions considered, growth rates of planetary modes are considerably greater than growth rates computed from linear instability theory for a fixed zonally independent basic state. However, values of growth rates ranged over a factor of 3 depending on the particular set of eddy initial conditions used. Nonlinear forcing of planetary modes via wave-wave coupling becomes more important than baroclinic growth on the basic state at small values of the intermediate-scale modal amplitudes. The relative importance of direct transfer of kinetic energy from intermediate scales of motion to a planetary mode, compared to baroclinic conversion of available potential energy to kinetic energy within that planetary mode, depends on the individual case. In all cases, however, the transfer of either kinetic or available potential energy to the planetary modes was accomplished principally by wave-wave transfer from intermediate scale eddies, rather than from the zonally averaged state. The zonal wavenumber 2 planetary mode was prominent in all solutions, even in those for which eddy initial conditions were such that a different planetary mode was selectively forced at the start. General characteristics of the structural evolution of the planetary wave components of total heat and momentum flux, and modal structures themselves, were relatively insensitive to variations in eddy initial conditions, even though quantitative details varied from case to case.

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.

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

PubMed

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

2018-06-01

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

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Nonlinear relativistic plasma resonance: Renormalization group approach

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

Metelskii, I. I., E-mail: metelski@lebedev.ru; Kovalev, V. F., E-mail: vfkvvfkv@gmail.com; Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru

An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy ofmore » the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.« less

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

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

3D numerical simulation of the long range propagation of acoustical shock waves through a heterogeneous and moving medium

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

Luquet, David; Marchiano, Régis; Coulouvrat, François, E-mail: francois.coulouvrat@upmc.fr

2015-10-28

Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength,more » the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D aspect, the code was massively parallelized using the single program, multiple data paradigm with the Message Passing Interfaces (MPI) for distributed memory architectures. This allows us to handle problems in the order of a thousand billion mesh points in the four dimensions (3 dimensions of space plus time). The validity of the method has been thoroughly evaluated on many cases with known solutions: linear piston, scattering of plane wave by a heterogeneous sphere, propagation in a waveguide with a shear flow, scattering by a finite amplitude vortex and nonlinear propagation in a thermoviscous medium. This validation process allows for a detailed assessment of the advantages and limitations of the method. Finally, applications to atmospheric propagation of shock waves will be presented.« less

3D numerical simulation of the long range propagation of acoustical shock waves through a heterogeneous and moving medium

NASA Astrophysics Data System (ADS)

Luquet, David; Marchiano, Régis; Coulouvrat, François

2015-10-01

Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D aspect, the code was massively parallelized using the single program, multiple data paradigm with the Message Passing Interfaces (MPI) for distributed memory architectures. This allows us to handle problems in the order of a thousand billion mesh points in the four dimensions (3 dimensions of space plus time). The validity of the method has been thoroughly evaluated on many cases with known solutions: linear piston, scattering of plane wave by a heterogeneous sphere, propagation in a waveguide with a shear flow, scattering by a finite amplitude vortex and nonlinear propagation in a thermoviscous medium. This validation process allows for a detailed assessment of the advantages and limitations of the method. Finally, applications to atmospheric propagation of shock waves will be presented.

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.

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.

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.

Development of a Tomography Technique for Assessment of the Material Condition of Concrete Using Optimized Elastic Wave Parameters.

PubMed

Chai, Hwa Kian; Liu, Kit Fook; Behnia, Arash; Yoshikazu, Kobayashi; Shiotani, Tomoki

2016-04-16

Concrete is the most ubiquitous construction material. Apart from the fresh and early age properties of concrete material, its condition during the structure life span affects the overall structural performance. Therefore, development of techniques such as non-destructive testing which enable the investigation of the material condition, are in great demand. Tomography technique has become an increasingly popular non-destructive evaluation technique for civil engineers to assess the condition of concrete structures. In the present study, this technique is investigated by developing reconstruction procedures utilizing different parameters of elastic waves, namely the travel time, wave amplitude, wave frequency, and Q-value. In the development of algorithms, a ray tracing feature was adopted to take into account the actual non-linear propagation of elastic waves in concrete containing defects. Numerical simulation accompanied by experimental verifications of wave motion were conducted to obtain wave propagation profiles in concrete containing honeycomb as a defect and in assessing the tendon duct filling of pre-stressed concrete (PC) elements. The detection of defects by the developed tomography reconstruction procedures was evaluated and discussed.

Nonlinear gyrotropic motion of skyrmion in a magnetic nanodisk

NASA Astrophysics Data System (ADS)

Chen, Yi-fu; Li, Zhi-xiong; Zhou, Zhen-wei; Xia, Qing-lin; Nie, Yao-zhuang; Guo, Guang-hua

2018-07-01

We study the nonlinear gyrotropic motion of a magnetic skyrmion in a nanodisk by means of micromagnetic simulations. The skyrmion is driven by a linearly polarized harmonic field with the frequency of counterclockwise gyrotropic mode. It is found that the motion of the skyrmion displays different patterns with increasing field amplitude. In the linear regime of weak driving field, the skyrmion performs a single counterclockwise gyrotropic motion. The guiding center of the skyrmion moves along a helical line from the centre of the nanodisk to a stable circular orbit. The stable orbital radius increases linearly with the field amplitude. When the driving field is larger than a critical value, the skyrmion exhibits complex nonlinear motion. With the advance of time, the motion trajectory of the skyrmion goes through a series of evolution process, from a single circular motion to a bird nest-like and a flower-like trajectory and finally, to a gear-like steady-state motion. The frequency spectra show that except the counterclockwise gyrotropic mode, the clockwise gyrotropic mode is also nonlinearly excited and its amplitude increases with time. The complex motion trajectory of the skyrmion is the result of superposition of the two gyrotropic motions with changing amplitude. Both the linear and nonlinear gyrotropic motions of the skyrmion can be well described by a generalized Thiele's equation of motion.

Research in Nonlinear Motion.

DTIC Science & Technology

1984-06-30

solved one version of the Kadomtsev - Petviashvili equation , (ut + 6uux + U )x - 3uyy, (KP) on the plane (- * < x, y < -). Nanakov’s results were formal...dimensions. 3. Periodic Waves In Shallow Water The other version of the Kadomtsev - Petviashvili equation is (ut + 6uux U )x 3Uy 0. (KP2) Both equations have...A. I. P. Conf. Proc. #88, ed. by M. Tabor & Y. M. Treve, 1982, with T. Bountis. 14. "Comments on Inverse Scattering for the Kadomtsev - Petviashvili

Buffering effect in continuous chains of unidirectionally coupled generators

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Kolesov, A. Yu.; Rozov, N. Kh.

2014-11-01

We propose a mathematical model of a continuous annular chain of unidirectionally coupled generators given by some nonlinear advection-type hyperbolic boundary value problem. Such problems are constructed by a limit transition from annular chains of unidirectionally coupled ordinary differential equations with an unbounded increase in the number of links. We find that a certain buffering phenomenon is realized in our boundary value problem. Namely, we show that any preassigned finite number of stable periodic motions of the traveling-wave type can coexist in the model.

Complex Rayleigh Waves Produced by Shallow Sedimentary Basins and their Potential Effects on Mid-Rise Buildings

NASA Astrophysics Data System (ADS)

Kohler, M. D.; Castillo, J.; Massari, A.; Clayton, R. W.

2017-12-01

Earthquake-induced motions recorded by spatially dense seismic arrays in buildings located in the northern Los Angeles basin suggest the presence of complex, amplified surface wave effects on the seismic demand of mid-rise buildings. Several moderate earthquakes produced large-amplitude, seismic energy with slow shear-wave velocities that cannot be explained or accurately modeled by any published 3D seismic velocity models or by Vs30 values. Numerical experiments are conducted to determine if sedimentary basin features are responsible for these rarely modeled and poorly documented contributions to seismic demand computations. This is accomplished through a physics-based wave propagation examination of the effects of different sedimentary basin geometries on the nonlinear response of a mid-rise structural model based on an existing, instrumented building. Using two-dimensional finite-difference predictive modeling, we show that when an earthquake focal depth is near the vertical edge of an elongated and relatively shallow sedimentary basin, dramatically amplified and complex surface waves are generated as a result of the waveguide effect introduced by this velocity structure. In addition, for certain source-receiver distances and basin geometries, body waves convert to secondary Rayleigh waves that propagate both at the free-surface interface and along the depth interface of the basin that show up as multiple large-amplitude arrivals. This study is motivated by observations from the spatially dense, high-sample-rate acceleration data recorded by the Community Seismic Network, a community-hosted strong-motion network, currently consisting of hundreds of sensors located in the southern California area. The results provide quantitative insight into the causative relationship between a sedimentary basin shape and the generation of Rayleigh waves at depth, surface waves at the free surface, scattered seismic energy, and the sensitivity of building responses to each of these.

Nonlinear vs. linear biasing in Trp-cage folding simulations

NASA Astrophysics Data System (ADS)

Spiwok, Vojtěch; Oborský, Pavel; Pazúriková, Jana; Křenek, Aleš; Králová, Blanka

2015-03-01

Biased simulations have great potential for the study of slow processes, including protein folding. Atomic motions in molecules are nonlinear, which suggests that simulations with enhanced sampling of collective motions traced by nonlinear dimensionality reduction methods may perform better than linear ones. In this study, we compare an unbiased folding simulation of the Trp-cage miniprotein with metadynamics simulations using both linear (principle component analysis) and nonlinear (Isomap) low dimensional embeddings as collective variables. Folding of the mini-protein was successfully simulated in 200 ns simulation with linear biasing and non-linear motion biasing. The folded state was correctly predicted as the free energy minimum in both simulations. We found that the advantage of linear motion biasing is that it can sample a larger conformational space, whereas the advantage of nonlinear motion biasing lies in slightly better resolution of the resulting free energy surface. In terms of sampling efficiency, both methods are comparable.

Nonlinear vs. linear biasing in Trp-cage folding simulations.

PubMed

Spiwok, Vojtěch; Oborský, Pavel; Pazúriková, Jana; Křenek, Aleš; Králová, Blanka

2015-03-21

Biased simulations have great potential for the study of slow processes, including protein folding. Atomic motions in molecules are nonlinear, which suggests that simulations with enhanced sampling of collective motions traced by nonlinear dimensionality reduction methods may perform better than linear ones. In this study, we compare an unbiased folding simulation of the Trp-cage miniprotein with metadynamics simulations using both linear (principle component analysis) and nonlinear (Isomap) low dimensional embeddings as collective variables. Folding of the mini-protein was successfully simulated in 200 ns simulation with linear biasing and non-linear motion biasing. The folded state was correctly predicted as the free energy minimum in both simulations. We found that the advantage of linear motion biasing is that it can sample a larger conformational space, whereas the advantage of nonlinear motion biasing lies in slightly better resolution of the resulting free energy surface. In terms of sampling efficiency, both methods are comparable.

Decay instability of an electron plasma wave in a dusty plasma

NASA Astrophysics Data System (ADS)

Amin, M. R.; Ferdous, T.; Salimullah, M.

1996-03-01

The parametric decay instability of an electron plasma wave in a homogeneous, unmagnetized, hot and collisionless dusty plasma has been investigated analytically. The Vlasov equation has been solved perturbatively to find the nonlinear response of the plasma particles. The presence of the charged dust grains introduces a background inhomogeneous electric field that significantly influences the dispersive properties of the plasma and the decay process. The growth rate of the decay instability through the usual ion-acoustic mode is modified, and depends upon the dust perturbation parameter μi, dust correlation length q0, and the related ion motion. However, the decay process of the electron plasma wave through the ultralow frequency dust mode, excited due to the presence of the dust particles, is more efficient than the decay through the usual ion-acoustic mode in the dusty plasma.

Comment on "Dynamics and properties of waves in a modified Noguchi electrical transmission line"

NASA Astrophysics Data System (ADS)

Kenmogne, Fabien; Yemélé, David; Marquié, Patrick

2016-09-01

A recent paper [Phys. Rev. E 91, 022925 (2015), 10.1103/PhysRevE.91.022925] presents the derivation of the nonlinear equation modeling envelope waves in a specific case of band passed filter discrete nonlinear electrical transmission line (NLTL), called "A modified Noguchi electrical transmission line" according to the authors. Using the reductive perturbation approach in the semidiscrete approximation, they showed that the modulated waves propagating in this NLTL are described by the ordinary nonlinear Schrödinger (NLS) equation. On the basis of their results, the authors claimed that all previous works on the band passed filter NLTL, which considered the vanishing of the dc component of the signal voltage, are incorrect, and this dc term is nonzero. As a consequence, the dispersion and nonlinearity coefficients of the NLS equation are strongly different from those usually obtained, and they found, according to the sign of the product P Q , the existence of one more region (compared to the work of Marquié et al. [Phys. Rev. E 49, 828 (1994)], 10.1103/PhysRevE.49.828) in the dispersion curve that allows the motion of envelope solitons of higher frequency in the system. In this Comment we provide sufficient theoretical and numerical evidence showing that the evidence obtained by the authors otherwise is due to certain terms missed in their mathematical developments when they derived the NLS equation. Our results also suggest that the previous work of Marquié and co-workers correctly predict the fact that the dc term of the signal voltage does not exist and there exist only two regions in the dispersion curve according to the sign of the product P Q .

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.

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.

Nonlinear Motion Cueing Algorithm: Filtering at Pilot Station and Development of the Nonlinear Optimal Filters for Pitch and Roll

NASA Technical Reports Server (NTRS)

Zaychik, Kirill B.; Cardullo, Frank M.

2012-01-01

Telban and Cardullo have developed and successfully implemented the non-linear optimal motion cueing algorithm at the Visual Motion Simulator (VMS) at the NASA Langley Research Center in 2005. The latest version of the non-linear algorithm performed filtering of motion cues in all degrees-of-freedom except for pitch and roll. This manuscript describes the development and implementation of the non-linear optimal motion cueing algorithm for the pitch and roll degrees of freedom. Presented results indicate improved cues in the specified channels as compared to the original design. To further advance motion cueing in general, this manuscript describes modifications to the existing algorithm, which allow for filtering at the location of the pilot's head as opposed to the centroid of the motion platform. The rational for such modification to the cueing algorithms is that the location of the pilot's vestibular system must be taken into account as opposed to the off-set of the centroid of the cockpit relative to the center of rotation alone. Results provided in this report suggest improved performance of the motion cueing algorithm.

Controllable optical rogue waves via nonlinearity management.

PubMed

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

2018-03-19

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

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

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

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

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

Nonlinear wavenumber shift of large amplitude Langmuir waves

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

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

2016-07-15

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

Formulation of the relativistic moment implicit particle-in-cell method

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

Noguchi, Koichi; Tronci, Cesare; Zuccaro, Gianluca

2007-04-15

A new formulation is presented for the implicit moment method applied to the time-dependent relativistic Vlasov-Maxwell system. The new approach is based on a specific formulation of the implicit moment method that allows us to retain the same formalism that is valid in the classical case despite the formidable complication introduced by the nonlinear nature of the relativistic equations of motion. To demonstrate the validity of the new formulation, an implicit finite difference algorithm is developed to solve the Maxwell's equations and equations of motion. A number of benchmark problems are run: two stream instability, ion acoustic wave damping, Weibelmore » instability, and Poynting flux acceleration. The numerical results are all in agreement with analytical solutions.« less

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

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

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

2014-01-15

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

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

Full-wave and half-wave rectification in second-order motion perception

NASA Technical Reports Server (NTRS)

Solomon, J. A.; Sperling, G.

1994-01-01

Microbalanced stimuli are dynamic displays which do not stimulate motion mechanisms that apply standard (Fourier-energy or autocorrelational) motion analysis directly to the visual signal. In order to extract motion information from microbalanced stimuli, Chubb and Sperling [(1988) Journal of the Optical Society of America, 5, 1986-2006] proposed that the human visual system performs a rectifying transformation on the visual signal prior to standard motion analysis. The current research employs two novel types of microbalanced stimuli: half-wave stimuli preserve motion information following half-wave rectification (with a threshold) but lose motion information following full-wave rectification; full-wave stimuli preserve motion information following full-wave rectification but lose motion information following half-wave rectification. Additionally, Fourier stimuli, ordinary square-wave gratings, were used to stimulate standard motion mechanisms. Psychometric functions (direction discrimination vs stimulus contrast) were obtained for each type of stimulus when presented alone, and when masked by each of the other stimuli (presented as moving masks and also as nonmoving, counterphase-flickering masks). RESULTS: given sufficient contrast, all three types of stimulus convey motion. However, only one-third of the population can perceive the motion of the half-wave stimulus. Observers are able to process the motion information contained in the Fourier stimulus slightly more efficiently than the information in the full-wave stimulus but are much less efficient in processing half-wave motion information. Moving masks are more effective than counterphase masks at hampering direction discrimination, indicating that some of the masking effect is interference between motion mechanisms, and some occurs at earlier stages. When either full-wave and Fourier or half-wave and Fourier gratings are presented simultaneously, there is a wide range of relative contrasts within which the motion directions of both gratings are easily determinable. Conversely, when half-wave and full-wave gratings are combined, the direction of only one of these gratings can be determined with high accuracy. CONCLUSIONS: the results indicate that three motion computations are carried out, any two in parallel: one standard ("first order") and two non-Fourier ("second-order") computations that employ full-wave and half-wave rectification.

Nonlinear VLF Wave Physics in the Radiation Belts

NASA Astrophysics Data System (ADS)

Crabtree, C. E.; Tejero, E. M.; Ganguli, G.; Mithaiwala, M.; Rudakov, L.; Hospodarsky, G. B.; Kletzing, C.

2014-12-01

Electromagnetic VLF waves, such as whistler mode waves, both control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering and are responsible for the energization of electrons during storms. Traditional approaches to understanding the influence of waves on trapped electrons have assumed that the wave characteristics (frequency spectrum, wave-normal angle distribution, etc.) were both stationary in time and amplitude independent from event to event. In situ data from modern satellite missions, such as the Van Allen probes, are showing that this assumption may not be justified. In addition, recent theoretical results [Crabtree et al. 2012] show that the threshold for nonlinear wave 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 wave scattering (Nonlinear Landau Damping) is an amplitude dependent mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation. 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]. Nonlinear scattering can 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]. Such nonlinear wave effects can dramatically reduce electron lifetimes. Nonlinear wave dynamics such as these occur when there are more than one wave present, such a condition necessarily violates the assumption of traditional wave-normal analysis [Santolik et al., 2003] which rely on the plane wave assumption. To investigate nonlinear wave dynamics using modern in situ data we apply the maximum entropy method [Skilling and Bryan, 1984] to solve for the wave distribution function [Storey and Lefeuvre, 1979] to yield the power distribution as a function of wave-normal angle and local azimuthal angle. We have validated this technique in the NRL space chamber and applied this methodology to Van Allen probe data to demonstrate that traditional wave-normal analaysis can give misleading results when multiple waves are present.

Nonlinear automatic landing control of unmanned aerial vehicles on moving platforms via a 3D laser radar

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

Hervas, Jaime Rubio; Tang, Hui; Reyhanoglu, Mahmut

2014-12-10

This paper presents a motion tracking and control system for automatically landing Unmanned Aerial Vehicles (UAVs) on an oscillating platform using Laser Radar (LADAR) observations. The system itself is assumed to be mounted on a ship deck. A full nonlinear mathematical model is first introduced for the UAV. The ship motion is characterized by a Fourier transform based method which includes a realistic characterization of the sea waves. LADAR observation models are introduced and an algorithm to process those observations for yielding the relative state between the vessel and the UAV is presented, from which the UAV's state relative tomore » an inertial frame can be obtained and used for feedback purposes. A sliding mode control algorithm is derived for tracking a landing trajectory defined by a set of desired waypoints. An extended Kalman filter (EKF) is proposed to account for process and observation noises in the design of a state estimator. The effectiveness of the control algorithm is illustrated through a simulation example.« less

GEOPHYSICS, ASTRONOMY AND ASTROPHYSICS: Numerical method of studying nonlinear interactions between long waves and multiple short waves

NASA Astrophysics Data System (ADS)

Xie, Tao; Kuang, Hai-Lan; William, Perrie; Zou, Guang-Hui; Nan, Cheng-Feng; He, Chao; Shen, Tao; Chen, Wei

2009-07-01

Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water. Specifically, this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves. Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train. From simulation results, we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train (expressed as wave train 2) leads to the energy focusing of the other short wave train (expressed as wave train 3). This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3.

Rogue Wave Modes for the Long Wave-Short Wave Resonance and the Derivative Nonlinear Schrödinger Models

NASA Astrophysics Data System (ADS)

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

2014-11-01

Rogue waves are unexpectedly large displacements of the water surface and will obviously pose threat to maritime activities. Recently, the formation of rogue waves is correlated with the onset of modulation instabilities of plane waves of the system. The long wave-short wave resonance and the derivative nonlinear Schrödinger models are considered. They are relevant in a two-layer fluid and a fourth order perturbation expansion of free surface waves respectively. Analytical solutions of rogue wave modes for the two models are derived by the Hirota bilinear method. Properties and amplitudes of these rogue wave modes are investigated. Conditions for modulation instability of the plane waves are shown to be precisely the requirements for the occurrence of rogue waves. In contrast with the nonlinear Schrödinger equation, rogue wave modes for the derivative nonlinear Schrödinger model exist even if the dispersion and cubic nonlinearity are of the opposite signs, provided that a sufficiently strong self-steepening nonlinearity is present. Extensions to the coupled case (multiple waveguides) will be discussed. This work is partially supported by the Research Grants Council General Research Fund Contract HKU 711713E.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Source characterization of underground explosions from hydrodynamic-to-elastic coupling simulations

NASA Astrophysics Data System (ADS)

Chiang, A.; Pitarka, A.; Ford, S. R.; Ezzedine, S. M.; Vorobiev, O.

2017-12-01

A major improvement in ground motion simulation capabilities for underground explosion monitoring during the first phase of the Source Physics Experiment (SPE) is the development of a wave propagation solver that can propagate explosion generated non-linear near field ground motions to the far-field. The calculation is done using a hybrid modeling approach with a one-way hydrodynamic-to-elastic coupling in three dimensions where near-field motions are computed using GEODYN-L, a Lagrangian hydrodynamics code, and then passed to WPP, an elastic finite-difference code for seismic waveform modeling. The advancement in ground motion simulation capabilities gives us the opportunity to assess moment tensor inversion of a realistic volumetric source with near-field effects in a controlled setting, where we can evaluate the recovered source properties as a function of modeling parameters (i.e. velocity model) and can provide insights into previous source studies on SPE Phase I chemical shots and other historical nuclear explosions. For example the moment tensor inversion of far-field SPE seismic data demonstrated while vertical motions are well-modeled using existing velocity models large misfits still persist in predicting tangential shear wave motions from explosions. One possible explanation we can explore is errors and uncertainties from the underlying Earth model. Here we investigate the recovered moment tensor solution, particularly on the non-volumetric component, by inverting far-field ground motions simulated from physics-based explosion source models in fractured material, where the physics-based source models are based on the modeling of SPE-4P, SPE-5 and SPE-6 near-field data. The hybrid modeling approach provides new prospects in modeling explosion source and understanding the uncertainties associated with it.

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

NASA Astrophysics Data System (ADS)

Wang, Yingguang

2018-03-01

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

High-frequency ground motion amplification during the 2011 Tohoku earthquake explained by soil dilatancy

NASA Astrophysics Data System (ADS)

Roten, D.; Fäh, D.; Bonilla, L. F.

2013-05-01

Ground motions of the 2011 Tohoku earthquake recorded at Onahama port (Iwaki, Fukushima prefecture) rank among the highest accelerations ever observed, with the peak amplitude of the 3-D acceleration vector approaching 2g. The response of the site was distinctively non-linear, as indicated by the presence of horizontal acceleration spikes which have been linked to cyclic mobility during similar observations. Compared to records of weak ground motions, the response of the site during the Mw 9.1 earthquake was characterized by increased amplification at frequencies above 10 Hz and in peak ground acceleration. This behaviour contrasts with the more common non-linear response encountered at non-liquefiable sites, which results in deamplification at higher frequencies. We simulate propagation of SH waves through the dense sand deposit using a non-linear finite difference code that is capable of modelling the development of excess pore water pressure. Dynamic soil parameters are calibrated using a direct search method that minimizes the difference between observed and simulated acceleration envelopes and response spectra. The finite difference simulations yield surface acceleration time-series that are consistent with the observations in shape and amplitude, pointing towards soil dilatancy as a likely explanation for the high-frequency pulses recorded at Onahama port. The simulations also suggest that the occurrence of high-frequency spikes coincided with a rapid increase in pore water pressure in the upper part of the sand deposit between 145 and 170 s. This sudden increase is possibly linked to a burst of high-frequency energy from a large slip patch below the Iwaki region.

Numerical Simulation of Floating Bodies in Extreme Free Surface Waves

NASA Astrophysics Data System (ADS)

Hu, Zheng Zheng; Causon, Derek; Mingham, Clive; Qiang, Ling

2010-05-01

A task of the EPSRC funded research project 'Extreme Wave loading on Offshore Wave Energy Devices: a Hierarchical Team Approach' is to investigate the survivability of two wave energy converter (WEC) devices Pelamis and the Manchester Bobber using different CFD approaches. Both devices float on the water surface, generating the electricity from the motion of the waves. In this paper, we describe developments of the AMAZON-SC 3D numerical wave tank (NWT) to study extreme wave loading of a fixed or floating (in Heave motion) structure. The extreme wave formulation as an inlet condition is due to Dalzell (1999) and Ning et. al. (2009) in which a first or second-order Stokes focused wave can be prescribed. The AMAZON-SC 3D code (see e.g. Hu et al. (2009)) uses a cell centred finite volume method of the Godunov-type for the space discretization of the Euler and Navier Stokes equations. The computational domain includes both air and water regions with the air/water boundary captured as a discontinuity in the density field thereby admitting the break up and recombination of the free surface. Temporal discretisation uses the artificial compressibility method and a dual time stepping strategy to maintain a divergence free velocity field. Cartesian cut cells are used to provide a fully boundary-fitted gridding capability on an regular background Cartesian grid. Solid objects are cut out of the background mesh leaving a set of irregularly shaped cells fitted to the boundary. The advantages of the cut cell approach have been outlined previously by Causon et al. (2000, 2001) including its flexibility for dealing with complex geometries whether stationary or in relative motion. The field grid does not need to be recomputed globally or even locally for moving body cases; all that is necessary is to update the local cut cell data at the body contour for as long as the motion continues. The handing of numerical wave paddles and device motion in a NWT is therefore straightforward and efficient. Firstly, extreme design wave conditions are generated in an empty NWT and compared with physical experiments as a precursor to calculations to investigate the survivability of the Bobber device operating in a challenging wave climate. Secondly, we consider a bench-mark test case involving in a first order regular wave maker acting on a fixed cylinder and Pelamis. Finally, a floating Bobber has been simulated under extreme wave conditions. These results will be reported at the meeting. Causon D.M., Ingram D.M., Mingham C.G., Yang G. Pearson R.V. (2000). Calculation of shallow water flows using a Cartesian cut cell approach. Advances in Water resources, 23: 545-562. Causon D.M., Ingram D.M., Mingham C.G. (2000). A Cartesian cut cell method for shallow water flows with moving boundaries. Advances in Water resources, 24: 899-911. Dalzell J.F. 1999 A note on finite depth second-order wave-wave interactions. Appl. Ocean Res. 21, 105-111. Ning D.Z., Zang J., Liu S.X. Eatock Taylor R. Teng B. & Taylor P.H. 2009 Free surface and wave kinematics for nonlinear focused wave groups. J. Ocean Engineering. Accepted. Hu Z.Z., Causon D.M., Mingham C.M. and Qian L.(2009). Numerical wave tank study of a wave energy converter in heave. Proceedlings 19th ISOPE conference, Osaka, Japan Qian L., Causon D.M. & Mingham C.G., Ingram D.M. 2006 A free-surface capturing method for two fluid flows with moving bodies. Proc. Roy. Soc. London, Vol. A 462 21-42.

Detecting chaos in particle accelerators through the frequency map analysis method.

PubMed

Papaphilippou, Yannis

2014-06-01

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects, which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.

Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium

PubMed Central

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

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

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

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

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

Nonlinear vs. linear biasing in Trp-cage folding simulations

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

Spiwok, Vojtěch, E-mail: spiwokv@vscht.cz; Oborský, Pavel; Králová, Blanka

2015-03-21

Biased simulations have great potential for the study of slow processes, including protein folding. Atomic motions in molecules are nonlinear, which suggests that simulations with enhanced sampling of collective motions traced by nonlinear dimensionality reduction methods may perform better than linear ones. In this study, we compare an unbiased folding simulation of the Trp-cage miniprotein with metadynamics simulations using both linear (principle component analysis) and nonlinear (Isomap) low dimensional embeddings as collective variables. Folding of the mini-protein was successfully simulated in 200 ns simulation with linear biasing and non-linear motion biasing. The folded state was correctly predicted as the free energymore » minimum in both simulations. We found that the advantage of linear motion biasing is that it can sample a larger conformational space, whereas the advantage of nonlinear motion biasing lies in slightly better resolution of the resulting free energy surface. In terms of sampling efficiency, both methods are comparable.« less

Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation.

PubMed

Wen, Xiao-Yong; Yan, Zhenya

2015-12-01

We study higher-order rogue wave (RW) solutions of the coupled integrable dispersive AB system (also called Pedlosky system), which describes the evolution of wave-packets in a marginally stable or unstable baroclinic shear flow in geophysical fluids. We propose its continuous-wave (CW) solutions and existent conditions for their modulation instability to form the rogue waves. A new generalized N-fold Darboux transformation (DT) is proposed in terms of the Taylor series expansion for the spectral parameter in the Darboux matrix and its limit procedure and applied to the CW solutions to generate multi-rogue wave solutions of the coupled AB system, which satisfy the general compatibility condition. The dynamical behaviors of these higher-order rogue wave solutions demonstrate both strong and weak interactions by modulating parameters, in which some weak interactions can generate the abundant triangle, pentagon structures, etc. Particularly, the trajectories of motion of peaks and depressions of profiles of the first-order RWs are explicitly analyzed. The generalized DT method used in this paper can be extended to other nonlinear integrable systems. These results may be useful for understanding the corresponding rogue-wave phenomena in fluid mechanics and related fields.

Trapping of high-energy electrons into regime of surfatron acceleration by electromagnetic waves in space plasma

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

Erokhin, A. N.; Erokhin, N. S.; Milant'ev, V. P.

2012-05-15

The phenomenon of trapping of weakly relativistic charged particles (with kinetic energies on the order of mc{sup 2}) into a regime of surfatron acceleration by an electromagnetic wave that propagates in plasma across a weak external magnetic field has been studied using nonlinear numerical calculations based on a solution of the relativistic equations of motion. Analysis showed that, for the wave amplitude above a certain threshold value and the initial wave phase outside the interval favorable for the surfing regime, the trajectory of a charged particle initially corresponds to its cyclotron rotation in the external magnetic field. For the initialmore » particle energies studied, the period of this rotation is relatively short. After a certain number (from several dozen to several thousand and above) of periods of rotation, the wave phase takes a value that is favorable for trapping of the charged particle on its trajectory by the electromagnetic wave, provided the Cherenkov resonance conditions are satisfied. As a result, the wave traps the charged particle and imparts it an ultrarelativistic acceleration. In momentum space, the region of trapping into the regime of surfing on an electromagnetic wave turns out to be rather large.« less

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

DTIC Science & Technology

2015-09-30

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

Negative stiffness honeycombs as tunable elastic metamaterials

NASA Astrophysics Data System (ADS)

Goldsberry, Benjamin M.; Haberman, Michael R.

2018-03-01

Acoustic and elastic metamaterials are media with a subwavelength structure that behave as effective materials displaying atypical effective dynamic properties. These material systems are of interest because the design of their sub-wavelength structure allows for direct control of macroscopic wave dispersion. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify wave propagation in the metamaterial with an external stimulus is highly desirable for numerous applications and therefore remains a significant challenge in elastic metamaterials research. In this work, a honeycomb structure composed of a doubly periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable elastic metamaterial. The nonlinear static elastic response that results from large deformations of the NSH unit cell leads to a large variation in linear elastic wave dispersion associated with infinitesimal motion superposed on the externally imposed pre-strain. A finite element model is utilized to model the static deformation and subsequent linear wave motion at the pre-strained state. Analysis of the slowness surface and group velocity demonstrates that the NSH exhibits significant tunability and a high degree of anisotropy which can be used to guide wave energy depending on static pre-strain levels. In addition, it is shown that partial band gaps exist where only longitudinal waves propagate. The NSH therefore behaves as a meta-fluid, or pentamode metamaterial, which may be of use for applications of transformation elastodynamics such as cloaking and gradient index lens devices.

Asymmetric nonlinear system is not sufficient for a nonreciprocal wave diode

NASA Astrophysics Data System (ADS)

Wu, Gaomin; Long, Yang; Ren, Jie

2018-05-01

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

Book review: Nonlinear ocean waves and the inverse scattering transform

USGS Publications Warehouse

Geist, Eric L.

2011-01-01

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

Simulation and modeling of whistler mode wave growth through cyclotron resonance with energetic electrons in the magnetosphere

NASA Astrophysics Data System (ADS)

Carlson, Curtis Ray

New models and simulations of wave growth experienced by electromagnetic waves propagating through the magnetosphere in the whistler mode are presented. The main emphasis is to simulate single frequency wave pulses, in the 2 to 6 kHz range, that have been injected into the magnetosphere, near L approximately 4. Simulations using a new transient model reproduce exponential wave growth and saturation coincident with a linearly increasing frequency versus time (up to 60 Hz/s). Unique methods for calculating the phased bunched currents, stimulated radiation, and radiation propagation are based upon test particle trajectories calculated by integrating nonlinear equations of motion generalized to allow the evolution of the frequency and wave number at each point in space. Results show the importance of the transient aspects in the wave growth process. The wave growth established as the wave propagates toward the equator is given a spatially advancing wave phase structure by the geomagnetic inhomogeneity. Through the feedback of this radiation upon other electrons, the conditions are set up which result in the linearly increasing output frequency with time. The transient simulations also show that features like growth rate and total growth are simply related to the various parameters, such as applied wave intensity, energetic electron flux, and energetic electron distribution.

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

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

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

Foundations of radiation hydrodynamics

NASA Astrophysics Data System (ADS)

Mihalas, D.; Mihalas, B. W.

This book is the result of an attempt, over the past few years, to gather the basic tools required to do research on radiating flows in astrophysics. The microphysics of gases is discussed, taking into account the equation of state of a perfect gas, the first and second law of thermodynamics, the thermal properties of a perfect gas, the distribution function and Boltzmann's equation, the collision integral, the Maxwellian velocity distribution, Boltzmann's H-theorem, the time of relaxation, and aspects of classical statistical mechanics. Other subjects explored are related to the dynamics of ideal fluids, the dynamics of viscous and heat-conducting fluids, relativistic fluid flow, waves, shocks, winds, radiation and radiative transfer, the equations of radiation hydrodynamics, and radiating flows. Attention is given to small-amplitude disturbances, nonlinear flows, the interaction of radiation and matter, the solution of the transfer equation, acoustic waves, acoustic-gravity waves, basic concepts of special relativity, and equations of motion and energy.

Fokker-Planck electron diffusion caused by an obliquely propagating electromagnetic wave packet of narrow bandwidth

NASA Technical Reports Server (NTRS)

Hizanidis, Kyriakos

1989-01-01

The relativistic motion of electrons in an intense electromagnetic wave packet propagating obliquely to a uniform magnetic field is analytically studied on the basis of the Fokker-Planck-Kolmogorov (FPK) approach. The wavepacket consists of circularly polarized electron-cyclotron waves. The dynamical system in question is shown to be reducible to one with three degrees of freedom. Within the framework of the Hamiltonian analysis the nonlinear diffusion tensor is derived, and it is shown that this tensor can be separated into zeroth-, first-, and second-order parts with respect to the relative bandwidth. The zeroth-order part describes diffusive acceleration along lines of constant unperturbed Hamiltonian. The second-order part, which corresponds to the longest time scale, describes diffusion across those lines. A possible transport theory is outlined on the basis of this separation of the time scales.

Experimental and numerical investigations of temporally and spatially periodic modulated wave trains

NASA Astrophysics Data System (ADS)

Houtani, H.; Waseda, T.; Tanizawa, K.

2018-03-01

A number of studies on steep nonlinear waves were conducted experimentally with the temporally periodic and spatially evolving (TPSE) wave trains and numerically with the spatially periodic and temporally evolving (SPTE) ones. The present study revealed that, in the vicinity of their maximum crest height, the wave profiles of TPSE and SPTE modulated wave trains resemble each other. From the investigation of the Akhmediev-breather solution of the nonlinear Schrödinger equation (NLSE), it is revealed that the dispersion relation deviated from the quadratic dependence of frequency on wavenumber and became linearly dependent instead. Accordingly, the wave profiles of TPSE and SPTE breathers agree. The range of this agreement is within the order of one wave group of the maximum crest height and persists during the long-term evolution. The findings extend well beyond the NLSE regime and can be applied to modulated wave trains that are highly nonlinear and broad-banded. This was demonstrated from the numerical wave tank simulations with a fully nonlinear potential flow solver based on the boundary element method, in combination with the nonlinear wave generation method based on the prior simulation with the higher-order spectral model. The numerical wave tank results were confirmed experimentally in a physical wave tank. The findings of this study unravel the fundamental nature of the nonlinear wave evolution. The deviation of the dispersion relation of the modulated wave trains occurs because of the nonlinear phase variation due to quasi-resonant interaction, and consequently, the wave geometry of temporally and spatially periodic modulated wave trains coincides.

The effects of variable dust size and charge on dust acoustic waves propagating in a hybrid Cairns–Tsallis complex plasma

NASA Astrophysics Data System (ADS)

El-Taibany, W. F.; El-Siragy, N. M.; Behery, E. E.; Elbendary, A. A.; Taha, R. M.

2018-05-01

The propagation characteristics of dust acoustic waves (DAWs) in a dusty plasma consisting of variable size dust grains, hybrid Cairns-Tsallis-distributed electrons, and nonthermal ions are studied. The charging of the dust grains is described by the orbital-motion-limited theory and the size of the dust grains obeys the power law dust size distribution. To describe the nonlinear propagation of the DAWs, a Zakharov-Kuznetsov equation is derived using a reductive perturbation method. It is found that the nonthermal and nonextensive parameters influence the main properties of DAWs. Moreover, our results reveal that the rarefactive waves can propagate mainly in the proposed plasma model while compressive waves can be detected for a very small range of the distribution parameters of plasma species, and the DAWs are faster and wider for smaller size dust grains. Applications of the present results to dusty plasma observations are briefly discussed.

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

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

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

2011-01-15

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

Manipulating acoustic wave reflection by a nonlinear elastic metasurface

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Test of a flexible spacecraft dynamics simulator

NASA Technical Reports Server (NTRS)

Dichmann, Donald; Sedlak, Joseph

1998-01-01

There are a number of approaches one can take to modeling the dynamics of a flexible body. While one can attempt to capture the full dynamical behavior subject to disturbances from actuators and environmental torques, such a detailed description often is unnecessary. Simplification is possible either by limiting the amplitude of motion to permit linearization of the dynamics equations or by restricting the types of allowed motion. In this work, we study the nonlinear dynamics of bending deformations of wire booms on spinning spacecraft. The theory allows for large amplitude excursions from equilibrium while enforcing constraints on the dynamics to prohibit those modes that are physically less relevant or are expected to damp out fast. These constraints explicitly remove the acoustic modes (i.e., longitudinal sound waves and shear waves) while allowing for arbitrary bending and twisting, motions which typically are of lower frequency. As a test case, a spin axis reorientation maneuver by the Polar Plasma Laboratory (POLAR) spacecraft has been simulated. POLAR was chosen as a representative spacecraft because it has flexible wire antennas that extend to a length of 65 meters. Bending deformations in these antennas could be quite large and have a significant effect on the attitude dynamics of the spacecraft body. Summary results from the simulation are presented along, with a comparison with POLAR flight data.

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.

Wave induced density modification in RF sheaths and close to wave launchers

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

Van Eester, D., E-mail: d.van.eester@fz-juelich.de; Crombé, K.; Department of Applied Physics, Ghent University, Ghent

2015-12-10

With the return to full metal walls - a necessary step towards viable fusion machines - and due to the high power densities of current-day ICRH (Ion Cyclotron Resonance Heating) or RF (radio frequency) antennas, there is ample renewed interest in exploring the reasons for wave-induced sputtering and formation of hot spots. Moreover, there is experimental evidence on various machines that RF waves influence the density profile close to the wave launchers so that waves indirectly influence their own coupling efficiency. The present study presents a return to first principles and describes the wave-particle interaction using a 2-time scale modelmore » involving the equation of motion, the continuity equation and the wave equation on each of the time scales. Through the changing density pattern, the fast time scale dynamics is affected by the slow time scale events. In turn, the slow time scale density and flows are modified by the presence of the RF waves through quasilinear terms. Although finite zero order flows are identified, the usual cold plasma dielectric tensor - ignoring such flows - is adopted as a first approximation to describe the wave response to the RF driver. The resulting set of equations is composed of linear and nonlinear equations and is tackled in 1D in the present paper. Whereas the former can be solved using standard numerical techniques, the latter require special handling. At the price of multiple iterations, a simple ’derivative switch-on’ procedure allows to reformulate the nonlinear problem as a sequence of linear problems. Analytical expressions allow a first crude assessment - revealing that the ponderomotive potential plays a role similar to that of the electrostatic potential arising from charge separation - but numerical implementation is required to get a feeling of the full dynamics. A few tentative examples are provided to illustrate the phenomena involved.« less

Study of a Novel Oscillating Surge Wave Energy Converter: Preprint

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

Tom, Nathan M; Choiniere, Michael; Thiagarajan, Krish P.

This study investigates the performance of an oscillating surge wave energy converter (OSWEC) that utilizes adjustable geometry as a means of controlling the hydrodynamic coefficients, a concept originally proposed by [1]. The body of the device consists of a bottom-hinged solid rectangular frame with five horizontal flaps spanning the interior of the frame. The flaps can rotate independently about their center of rotation within the frame like a large window shutter. Changing the orientation of the flaps alters the hydrodynamic coefficients and natural frequency of the device as well as the ability to shed or absorb structural loads accordingly. Thismore » ability may allow the device to operate in a wider range of sea states than other current wave energy converter designs. This paper presents and compares the results of numerical simulations and experimental testing of the OSWEC's response to regular waves with all five of the horizontal fin configurations sharing the same orientation of 0 degrees (fully closed interior) and 90 degrees (fully open). The numerical simulations were performed using WAMIT, which calculates hydrodynamic coefficients using a boundary element method code to solve the linear potential flow problem, and WEC-Sim, a MATLAB-based tool that simulates multibody devices in the time domain by solving the governing equations of motion. A 1:14 scale model of the device was built for experimental evaluation in an 8-m-long, 1-m wide wave tank, which supports a water depth of 0.7 m. The OSWEC motion in different wave conditions was measured with displacement sensors while nonlinear wave-structure interaction effects like slamming and overtopping were captured using a high-speed camera and used to understand differences between the simulation and experiments.« less

Rotor vibration caused by external excitation and rub

NASA Technical Reports Server (NTRS)

Matsushita, O.; Takagi, M.; Kikuchi, K.; Kaga, M.

1982-01-01

For turbomachinery with low natural frequencies, considerations have been recently required for rotor vibrations caused by external forces except unbalance one, such as foundation motion, seismic wave, rub and so forth. Such a forced vibration is investigated analytically and experimentally in the present paper. Vibrations in a rotor-bearing system under a harmonic excitation are analyzed by the modal technique in the case of a linear system including gyroscopic effect. For a nonlinear system a new and powerful quasi-modal technique is developed and applied to the vibration caused by rub.

Stochastic wave-function unravelling of the generalized Lindblad equation

NASA Astrophysics Data System (ADS)

Semin, V.; Semina, I.; Petruccione, F.

2017-12-01

We investigate generalized non-Markovian stochastic Schrödinger equations (SSEs), driven by a multidimensional counting process and multidimensional Brownian motion introduced by A. Barchielli and C. Pellegrini [J. Math. Phys. 51, 112104 (2010), 10.1063/1.3514539]. We show that these SSEs can be translated in a nonlinear form, which can be efficiently simulated. The simulation is illustrated by the model of a two-level system in a structured bath, and the results of the simulations are compared with the exact solution of the generalized master equation.

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.

Ion Streaming Instabilities in Pair Ion Plasma and Localized Structure with Non-Thermal Electrons

NASA Astrophysics Data System (ADS)

Nasir Khattak, M.; Mushtaq, A.; Qamar, A.

2015-12-01

Pair ion plasma with a fraction of non-thermal electrons is considered. We investigate the effects of the streaming motion of ions on linear and nonlinear properties of unmagnetized, collisionless plasma by using the fluid model. A dispersion relation is derived, and the growth rate of streaming instabilities with effect of streaming motion of ions and non-thermal electrons is calculated. A qausi-potential approach is adopted to study the characteristics of ion acoustic solitons. An energy integral equation involving Sagdeev potential is derived during this process. The presence of the streaming term in the energy integral equation affects the structure of the solitary waves significantly along with non-thermal electrons. Possible application of the work to the space and laboratory plasmas are highlighted.

Influence of the Enteric Nervous System on Gut Motility Patterns in Zebrafish

NASA Astrophysics Data System (ADS)

Baker, Ryan; Ganz, Julia; Melancon, Ellie; Eisen, Judith; Parthasarathy, Raghuveer

The enteric nervous system (ENS), composed of diverse neuronal subtypes and glia, regulates essential gut functions including motility, secretion, and homeostasis. In humans and animals, decreased numbers of enteric neurons lead to a variety of types of gut dysfunction. However, surprisingly little is known about how the number, position, or subtype of enteric neurons affect the regulation of gut peristalsis, due to the lack of good model systems and the lack of tools for the quantitative characterization of gut motion. We have therefore developed a method of quantitative spatiotemporal mapping using differential interference contrast microscopy and particle image velocimetry, and have applied this to investigate intestinal dynamics in normal and mutant larval zebrafish. From movies of gut motility, we obtain a velocity vector field representative of gut motion, from which we can quantify parameters relating to gut peristalsis such as frequency, wave speed, deformation amplitudes, wave duration, and non-linearity of waves. We show that mutants with reduced neuron number have contractions that are more regular in time and reduced in amplitude compared to wild-type (normal) fish. We also show that feeding fish before their yolk is consumed leads to stronger motility patterns. We acknowledge support from NIH awards P50 GM098911 and P01 HD022486.

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.

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

PubMed

Merkel, A; Tournat, V; Gusev, V

2014-08-01

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

Fatigue crack detection by nonlinear spectral correlation with a wideband input

NASA Astrophysics Data System (ADS)

Liu, Peipei; Sohn, Hoon

2017-04-01

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

Observing (non)linear lattice dynamics in graphite by ultrafast Kikuchi diffraction

PubMed Central

Liang, Wenxi; Vanacore, Giovanni M.; Zewail, Ahmed H.

2014-01-01

In materials, the nature of the strain–stress relationship, which is fundamental to their properties, is determined by both the linear and nonlinear elastic responses. Whereas the linear response can be measured by various techniques, the nonlinear behavior is nontrivial to probe and to reveal its nature. Here, we report the methodology of time-resolved Kikuchi diffraction for mapping the (non)linear elastic response of nanoscale graphite following an ultrafast, impulsive strain excitation. It is found that the longitudinal wave propagating along the c-axis exhibits echoes with a frequency of 9.1 GHz, which indicates the reflections of strain between the two surfaces of the material with a speed of ∼4 km/s. Because Kikuchi diffraction enables the probing of strain in the transverse direction, we also observed a higher-frequency mode at 75.5 GHz, which has a relatively long lifetime, on the order of milliseconds. The fluence dependence and the polarization properties of this nonlinear mode are entirely different from those of the linear, longitudinal mode, and here we suggest a localized breather motion in the a-b plane as the origin of the nonlinear shear dynamics. The approach presented in this contribution has the potential for a wide range of applications because most crystalline materials exhibit Kikuchi diffraction. PMID:24706785

Nonlinear coherent structures of Alfvén wave in a collisional plasma

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

Jana, Sayanee; Chakrabarti, Nikhil; Ghosh, Samiran

2016-07-15

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

Toward a new paradigm for boulder dislodgement during storms

NASA Astrophysics Data System (ADS)

Weiss, Robert; Sheremet, Alex

2017-07-01

Boulders are an important coastal hazard event deposit because they can only be moved by tsunamis and energetic storms effects of storms. Storms and tsunami are competing processes for coastal change along many shorelines. Therefore, distinguishing the boulders that were moved during a storm from those moved by a tsunami is important. In this contribution, we present the results of a parameter study based on the TRIADS model for wave shoaling on mildly sloping beaches, coupled with a boulder-dislodgement model that is based on Newton's Second Law of Motion. The results show how smaller slopes expose the waves longer to the nonlinear processes, thus increasing the energy in the infragravity wave band. More energy in the infragravity wave band means that there are more energy wave lengths that can dislodge larger boulders. At the same time, a steeper slope lowers the threshold for boulder dislodgement (critical angle of dislodgement), making it more likely for larger boulders to be dislodged on a steeper slope. The competition between these two processes govern boulder dislodgement during storms and is investigated inhere.

Motion Cueing Algorithm Development: New Motion Cueing Program Implementation and Tuning

NASA Technical Reports Server (NTRS)

Houck, Jacob A. (Technical Monitor); Telban, Robert J.; Cardullo, Frank M.; Kelly, Lon C.

2005-01-01

A computer program has been developed for the purpose of driving the NASA Langley Research Center Visual Motion Simulator (VMS). This program includes two new motion cueing algorithms, the optimal algorithm and the nonlinear algorithm. A general description of the program is given along with a description and flowcharts for each cueing algorithm, and also descriptions and flowcharts for subroutines used with the algorithms. Common block variable listings and a program listing are also provided. The new cueing algorithms have a nonlinear gain algorithm implemented that scales each aircraft degree-of-freedom input with a third-order polynomial. A description of the nonlinear gain algorithm is given along with past tuning experience and procedures for tuning the gain coefficient sets for each degree-of-freedom to produce the desired piloted performance. This algorithm tuning will be needed when the nonlinear motion cueing algorithm is implemented on a new motion system in the Cockpit Motion Facility (CMF) at the NASA Langley Research Center.

Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation

NASA Astrophysics Data System (ADS)

Gao, Hui; Cheng, Wenguang; Xu, Tianzhou; Wang, Gangwei

2018-03-01

The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.

Seagrass blade motion under waves and its impact on wave decay

NASA Astrophysics Data System (ADS)

Luhar, M.; Infantes, E.; Nepf, H.

2017-05-01

The hydrodynamic drag generated by seagrass meadows can dissipate wave-energy, causing wave decay. It is well known that this drag depends on the relative motion between the water and the seagrass blades, yet the impact of blade motion on drag and wave-energy dissipation remains to be fully characterized. In this experimental study, we examined the impact of blade motion on wave decay by concurrently recording blade posture during a wave cycle and measuring wave decay over a model seagrass meadow. We also identified a scaling law that predicts wave decay over the model meadow for a range of seagrass blade density, wave period, wave height, and water depth scaled from typical field conditions. Blade flexibility led to significantly lower drag and wave decay relative to theoretical predictions for rigid, upright blades. To quantify the impact of blade motion on wave decay, we employed an effective blade length, le, defined as the rigid blade length that leads to equivalent wave-energy dissipation. We estimated le directly from images of blade motion. Consistent with previous studies, these estimates showed that the effective blade length depends on the dimensionless Cauchy number, which describes the relative magnitude of the wave hydrodynamic drag and the restoring force due to blade rigidity. As the hydrodynamic forcing increases, the blades exhibit greater motion. Greater blade motion leads to smaller relative velocities, reducing drag, and wave-energy dissipation (i.e., smaller le).

Self-modulational formation of pulsar microstructures

NASA Technical Reports Server (NTRS)

Kennel, C. F.; Chian, A. C.-L.

1987-01-01

A nonlinear plasma theory for self modulation of pulsar radio pulses is discussed. A nonlinear Schroedinger equation is derived for strong electromagnetic waves propagating in an electron positron plasma. The nonlinearities arising from wave intensity induced particle mass variation may excite the modulational instability of circularly and linearly polarized pulsar radiation. The resulting wave envelopes can take the form of periodic wave trains or solitons. These nonlinear stationary waveforms may account for the formation of pulsar microstructures.

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

PubMed

Li, Li; Yu, Fajun

2017-09-06

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

Method to improve optical parametric oscillator beam quality

DOEpatents

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

2003-11-11

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

Optical parametric osicllators with improved beam quality

DOEpatents

Smith, Arlee V.; Alford, William J.

2003-11-11

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

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).

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.

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

USGS Publications Warehouse

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

2010-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2004-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Generation of Caustics and Rogue Waves from Nonlinear Instability.

PubMed

Safari, Akbar; Fickler, Robert; Padgett, Miles J; Boyd, Robert W

2017-11-17

Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.

Generation of Caustics and Rogue Waves from Nonlinear Instability

NASA Astrophysics Data System (ADS)

Safari, Akbar; Fickler, Robert; Padgett, Miles J.; Boyd, Robert W.

2017-11-01

Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.

Evolution of basic equations for nearshore wave field

PubMed Central

ISOBE, Masahiko

2013-01-01

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

Analysis of strong ground motions and site effects at Kantipath, Kathmandu, from 2015 Mw 7.8 Gorkha, Nepal, earthquake and its aftershocks

NASA Astrophysics Data System (ADS)

Dhakal, Yadab P.; Kubo, Hisahiko; Suzuki, Wataru; Kunugi, Takashi; Aoi, Shin; Fujiwara, Hiroyuki

2016-04-01

Strong ground motions from the 2015 Mw 7.8 Gorkha, Nepal, earthquake and its eight aftershocks recorded by a strong-motion seismograph at Kantipath (KATNP), Kathmandu, were analyzed to assess the ground-motion characteristics and site effects at this location. Remarkably large elastic pseudo-velocity responses exceeding 300 cm/s at 5 % critical damping were calculated for the horizontal components of the mainshock recordings at peak periods of 4-5 s. Conversely, the short-period ground motions of the mainshock were relatively weak despite the proximity of the site to the source fault. The horizontal components of all large-magnitude (Mw ≥ 6.3) aftershock recordings showed peak pseudo-velocity responses at periods of 3-4 s. Ground-motion prediction equations (GMPEs) describing the Nepal Himalaya region have not yet been developed. A comparison of the observational data with GMPEs for Japan showed that with the exception of the peak ground acceleration (PGA) of the mainshock, the observed PGAs and peak ground velocities at the KATNP site are generally well described by the GMPEs for crustal and plate interface events. A comparison of the horizontal-to-vertical ( H/ V) spectral ratios for the S-waves of the mainshock and aftershock recordings suggested that the KATNP site experienced a considerable nonlinear site response, which resulted in the reduced amplitudes of short-period ground motions. The GMPEs were found to underestimate the response values at the peak periods (approximately 4-5 s) of the large-magnitude events. The deep subsurface velocity model of the Kathmandu basin has not been well investigated. Therefore, a one-dimensional velocity model was constructed for the deep sediments beneath the recording station based on an analysis of the H/ V spectral ratios for S-wave coda from aftershock recordings, and it was revealed that the basin sediments strongly amplified the long-period components of the ground motions of the mainshock and large-magnitude aftershocks.

A Nonlinear, Human-Centered Approach to Motion Cueing with a Neurocomputing Solver

NASA Technical Reports Server (NTRS)

Telban, Robert J.; Cardullo, Frank M.; Houck, Jacob A.

2002-01-01

This paper discusses the continuation of research into the development of new motion cueing algorithms first reported in 1999. In this earlier work, two viable approaches to motion cueing were identified: the coordinated adaptive washout algorithm or 'adaptive algorithm', and the 'optimal algorithm'. In this study, a novel approach to motion cueing is discussed that would combine features of both algorithms. The new algorithm is formulated as a linear optimal control problem, incorporating improved vestibular models and an integrated visual-vestibular motion perception model previously reported. A control law is generated from the motion platform states, resulting in a set of nonlinear cueing filters. The time-varying control law requires the matrix Riccati equation to be solved in real time. Therefore, in order to meet the real time requirement, a neurocomputing approach is used to solve this computationally challenging problem. Single degree-of-freedom responses for the nonlinear algorithm were generated and compared to the adaptive and optimal algorithms. Results for the heave mode show the nonlinear algorithm producing a motion cue with a time-varying washout, sustaining small cues for a longer duration and washing out larger cues more quickly. The addition of the optokinetic influence from the integrated perception model was shown to improve the response to a surge input, producing a specific force response with no steady-state washout. Improved cues are also observed for responses to a sway input. Yaw mode responses reveal that the nonlinear algorithm improves the motion cues by reducing the magnitude of negative cues. The effectiveness of the nonlinear algorithm as compared to the adaptive and linear optimal algorithms will be evaluated on a motion platform, the NASA Langley Research Center Visual Motion Simulator (VMS), and ultimately the Cockpit Motion Facility (CMF) with a series of pilot controlled maneuvers. A proposed experimental procedure is discussed. The results of this evaluation will be used to assess motion cueing performance.

Interactions of large amplitude solitary waves in viscous fluid conduits

NASA Astrophysics Data System (ADS)

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

2014-07-01

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

Nonlinear Landau damping in the ionosphere

NASA Technical Reports Server (NTRS)

Kiwamoto, Y.; Benson, R. F.

1978-01-01

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

Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

NASA Astrophysics Data System (ADS)

LeMesurier, Brenton

2012-01-01

A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

Nonlinear electrostatic solitary waves in electron-positron plasmas

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

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

NASA Astrophysics Data System (ADS)

Hasanian, Mostafa; Lissenden, Cliff J.

2017-08-01

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

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

PubMed

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

2017-03-01

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

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

Influence of unbalance on the nonlinear dynamical response and stability of flexible rotor-bearing systems

NASA Technical Reports Server (NTRS)

Gunter, E. J.; Humphris, R. R.; Springer, H.

1983-01-01

In this paper, some of the effects of unbalance on the nonlinear response and stability of flexible rotor-bearing systems is presented from both a theoretical and experimental standpoint. In a linear system, operating above its stability threshold, the amplitude of motion grows exponentially with time and the orbits become unbounded. In an actual system, this is not necessarily the case. The actual amplitudes of motion may be bounded due to various nonlinear effects in the system. These nonlinear effects cause limit cycles of motion. Nonlinear effects are inherent in fluid film bearings and seals. Other contributors to nonlinear effects are shafts, couplings and foundations. In addition to affecting the threshold of stability, the nonlinear effects can cause jump phenomena to occur at not only the critical speeds, but also at stability onset or restabilization speeds.

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

PubMed

Li, Nianbei; Ren, Jie

2014-08-29

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

Nonlinear gas oscillations in pipes. I - Theory.

NASA Technical Reports Server (NTRS)

Jimenez, J.

1973-01-01

The problem of forced acoustic oscillations in a pipe is studied theoretically. The oscillations are produced by a moving piston in one end of the pipe, while a variety of boundary conditions ranging from a completely closed to a completely open mouth at the other end are considered. The linear theory predicts large amplitudes near resonance and that nonlinear effects become crucially important. By expanding the equations of motion in a series in the Mach number, both the amplitude and waveform of the oscillation are predicted there. In both the open- and closed-end cases the need for shock waves in some range of parameters is found. The amplitude of the oscillation is different for the two cases, however, being proportional to the square root of the piston amplitude in the closed-end case and to the cube root for the open end.

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

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

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

2016-04-15

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

Roles Played by Electrostatic Waves in Producing Radio Emissions

NASA Technical Reports Server (NTRS)

Cairns, Iver H.

2000-01-01

Processes in which electromagnetic radiation is produced directly or indirectly via intermediate waves are reviewed. It is shown that strict theoretical constraints exist for electrons to produce nonthermal levels of radiation directly by the Cerenkov or cyclotron resonances. In contrast, indirect emission processes in which intermediary plasma waves are converted into radiation are often favored on general and specific grounds. Four classes of mechanisms involving the conversion of electrostatic waves into radiation are linear mode conversion, hybrid linear/nonlinear mechanisms, nonlinear wave-wave and wave-particle processes, and radiation from localized wave packets. These processes are reviewed theoretically and observational evidence summarized for their occurrence. Strong evidence exists that specific nonlinear wave processes and mode conversion can explain quantitatively phenomena involving type III solar radio bursts and ionospheric emissions. On the other hand, no convincing evidence exists that magnetospheric continuum radiation is produced by mode conversion instead of nonlinear wave processes. Further research on these processes is needed.

Features in the Behavior of the Solar Wind behind the Bow Shock Front near the Boundary of the Earth's Magnetosphere

NASA Astrophysics Data System (ADS)

Grib, S. A.; Leora, S. N.

2017-12-01

Macroscopic discontinuous structures observed in the solar wind are considered in the framework of magnetic hydrodynamics. The interaction of strong discontinuities is studied based on the solution of the generalized Riemann-Kochin problem. The appearance of discontinuities inside the magnetosheath after the collision of the solar wind shock wave with the bow shock front is taken into account. The propagation of secondary waves appearing in the magnetosheath is considered in the approximation of one-dimensional ideal magnetohydrodynamics. The appearance of a compression wave reflected from the magnetopause is indicated. The wave can nonlinearly break with the formation of a backward shock wave and cause the motion of the bow shock towards the Sun. The interaction between shock waves is considered with the well-known trial calculation method. It is assumed that the velocity of discontinuities in the magnetosheath in the first approximation is constant on the average. All reasonings and calculations correspond to consideration of a flow region with a velocity less than the magnetosonic speed near the Earth-Sun line. It is indicated that the results agree with the data from observations carried out on the WIND and Cluster spacecrafts.

Quantum Statistical Properties of the Codirectional Kerr Nonlinear Coupler in Terms of su (2 ) Lie Group in Interaction with a Two-level Atom

NASA Astrophysics Data System (ADS)

Abdalla, M. Sebawe; Khalil, E. M.; Obada, A. S.-F.

2017-08-01

The problem of the codirectional Kerr coupler has been considered several times from different point of view. In the present paper we introduce the interaction between a two-level atom and the codirectional Kerr nonlinear coupler in terms of su (2 ) Lie algebra. Under certain conditions we have adjusted the Kerr coupler and consequently we have managed to handle the problem. The wave function is obtained by using the evolution operator where the Heisnberg equation of motion is invoked to get the constants of the motion. We note that the Kerr parameter χ as well as the quantum number j plays the role of controlling the atomic inversion behavior. Also the maximum entanglement occurs after a short period of time when χ = 0. On the other hand for the entropy and the variance squeezing we observe that there is exchange between the quadrature variances. Furthermore, the variation in the quantum number j as well as in the parameter χ leads to increase or decrease in the number of fluctuations. Finally we examined the second order correlation function where classical and nonclassical phenomena are observed.

Thermal motion of a nonlinear localized pattern in a quasi-one-dimensional system.

PubMed

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

2016-07-01

We study the dynamics of localized nonlinear patterns in a quasi-one-dimensional many-particle system near a subcritical pitchfork bifurcation. The normal form at the bifurcation is given and we show that these patterns can be described as solitary-wave envelopes. They are stable in a large temperature range and can diffuse along the chain of interacting particles. During their displacements the particles are continually redistributed on the envelope. This change of particle location induces a small modulation of the potential energy of the system, with an amplitude that depends on the transverse confinement. At high temperature, this modulation is irrelevant and the thermal motion of the localized patterns displays all the characteristics of a free quasiparticle diffusion with a diffusion coefficient that may be deduced from the normal form. At low temperature, significant physical effects are induced by the modulated potential. In particular, the localized pattern may be trapped at very low temperature. We also exhibit a series of confinement values for which the modulation amplitudes vanishes. For these peculiar confinements, the mean-square displacement of the localized patterns also evidences free-diffusion behavior at low temperature.

Rogue waves generation in a left-handed nonlinear transmission line with series varactor diodes

NASA Astrophysics Data System (ADS)

Onana Essama, B. G.; Atangana, J.; Biya Motto, F.; Mokhtari, B.; Cherkaoui Eddeqaqi, N.; Kofane, Timoleon C.

2014-07-01

We investigate the electromagnetic wave behavior and its characterization using collective variables technique. Second-order dispersion, first- and second-order nonlinearities, which strongly act in a left-handed nonlinear transmission line with series varactor diodes, are taken into account. Four frequency ranges have been found. The first one gives the so-called energetic soliton due to a perfect combination of second-order dispersion and first-order nonlinearity. The second frequency range presents a dispersive soliton leading to the collapse of the electromagnetic wave at the third frequency range. But the fourth one shows physical conditions which are able to provoke the appearance of wave trains generation with some particular waves, the rogue waves. Moreover, we demonstrate that the number of rogue waves increases with frequency. The soliton, thereafter, gains a relative stability when second-order nonlinearity comes into play with some specific values in the fourth frequency range. Furthermore, the stability conditions of the electromagnetic wave at high frequencies have been also discussed.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Nonlinear fractional waves at elastic interfaces

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

Wang, Heng; Zheng, Shuhua

2017-06-01

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

Rayleigh lidar observations of enhanced stratopause temperature over Gadanki (13.5° N, 79.2° E) during major stratospheric warming in 2006

NASA Astrophysics Data System (ADS)

Sridharan, S.; Sathishkumar, S.; Raghunath, K.

2009-01-01

Rayleigh lidar observations of temperature structure and gravity wave activity were carried out at Gadanki (13.5° N, 79.2° E) during January-February 2006. A major stratospheric warming event occurred at high latitude during the end of January and early February. There was a sudden enhancement in the stratopause temperature over Gadanki coinciding with the date of onset of the major stratospheric warming event which occurred at high latitudes. The temperature enhancement persisted even after the end of the high latitude major warming event. During the same time, the UKMO (United Kingdom Meteorological Office) zonal mean temperature showed a similar warming episode at 10° N and cooling episode at 60° N around the region of stratopause. This could be due to ascending (descending) motions at high (low) latitudes above the critical level of planetary waves, where there was no planetary wave flux. The time variation of the gravity wave potential energy computed from the temperature perturbations over Gadanki shows variabilities at planetary wave periods, suggesting a non-linear interaction between gravity waves and planetary waves. The space-time analysis of UKMO temperature data at high and low latitudes shows the presence of similar periodicities of planetary wave of zonal wavenumber 1.

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

Liu, Rumeng; Wang, Lifeng, E-mail: walfe@nuaa.edu.cn

The nonlinear thermal vibration behavior of a single-walled carbon nanotube (SWCNT) is investigated by molecular dynamics simulation and a nonlinear, nonplanar beam model. Whirling motion with energy transfer between flexural motions is found in the free vibration of the SWCNT excited by the thermal motion of atoms where the geometric nonlinearity is significant. A nonlinear, nonplanar beam model considering the coupling in two vertical vibrational directions is presented to explain the whirling motion of the SWCNT. Energy in different vibrational modes is not equal even over a time scale of tens of nanoseconds, which is much larger than the periodmore » of fundamental natural vibration of the SWCNT at equilibrium state. The energy of different modes becomes equal when the time scale increases to the microsecond range.« less

Prediction of nonlinear soil effects

USGS Publications Warehouse

Hartzell, S.; Bonilla, L.F.; Williams, R.A.

2004-01-01

Mathematical models of soil nonlinearity in common use and recently developed nonlinear codes compared to investigate the range of their predictions. We consider equivalent linear formulations with and without frequency-dependent moduli and damping ratios and nonlinear formulations for total and effective stress. Average velocity profiles to 150 m depth with midrange National Earthquake Hazards Reduction Program site classifications (B, BC, C, D, and E) in the top 30 m are used to compare the response of a wide range of site conditions from rock to soft soil. Nonlinear soil models are compared using the amplification spectrum, calculated as the ratio of surface ground motion to the input motion at the base of the velocity profile. Peak input motions from 0.1g to 0.9g are considered. For site class B, no significant differences exist between the models considered in this article. For site classes BC and C, differences are small at low input motions (0.1g to 0.2g), but become significant at higher input levels. For site classes D and E the overdamping of frequencies above about 4 Hz by the equivalent linear solution with frequency-independent parameters is apparent for the entire range of input motions considered. The equivalent linear formulation with frequency-dependent moduli and damping ratios under damps relative to the nonlinear models considered for site class C with larger input motions and most input levels for site classes D and E. At larger input motions the underdamping for site classes D and E is not as severe as the overdamping with the frequency-independent formulation, but there are still significant differences in the time domain. A nonlinear formulation is recommended for site classes D and E and for site classes BC and C with input motions greater than a few tenths of the acceleration of gravity. The type of nonlinear formulation to use is driven by considerations of the importance of water content and the availability of laboratory soils data. Our average amplification curves from a nonlinear effective stress formulation compare favorably with observed spectral amplification at class D and E sites in the Seattle area for the 2001 Nisqually earthquake.

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

NASA Technical Reports Server (NTRS)

Tsurutani, Bruce T.

1991-01-01

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

Numerical Modeling of Footpoint-driven Magneto-acoustic Wave Propagation in a Localized Solar Flux Tube

NASA Astrophysics Data System (ADS)

Fedun, V.; Shelyag, S.; Erdélyi, R.

2011-01-01

In this paper, we present and discuss results of two-dimensional simulations of linear and nonlinear magneto-acoustic wave propagation through an open magnetic flux tube embedded in the solar atmosphere expanding from the photosphere through to the transition region and into the low corona. Our aim is to model and analyze the response of such a magnetic structure to vertical and horizontal periodic motions originating in the photosphere. To carry out the simulations, we employed our MHD code SAC (Sheffield Advanced Code). A combination of the VALIIIC and McWhirter solar atmospheres and coronal density profiles were used as the background equilibrium model in the simulations. Vertical and horizontal harmonic sources, located at the footpoint region of the open magnetic flux tube, are incorporated in the calculations, to excite oscillations in the domain of interest. To perform the analysis we have constructed a series of time-distance diagrams of the vertical and perpendicular components of the velocity with respect to the magnetic field lines at each height of the computational domain. These time-distance diagrams are subject to spatio-temporal Fourier transforms allowing us to build ω-k dispersion diagrams for all of the simulated regions in the solar atmosphere. This approach makes it possible to compute the phase speeds of waves propagating throughout the various regions of the solar atmosphere model. We demonstrate the transformation of linear slow and fast magneto-acoustic wave modes into nonlinear ones, i.e., shock waves, and also show that magneto-acoustic waves with a range of frequencies efficiently leak through the transition region into the solar corona. It is found that the waves interact with the transition region and excite horizontally propagating surface waves along the transition region for both types of drivers. Finally, we estimate the phase speed of the oscillations in the solar corona and compare it with the phase speed derived from observations.

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

PubMed

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

2018-07-01

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

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

PubMed

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

2014-01-01

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

The dissipation of electromagnetic waves in plasmas

NASA Astrophysics Data System (ADS)

Basov, N. G.

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

The coupled nonlinear dynamics of a lift system

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

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

2014-12-10

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

Observations and modeling of the effects of waves and rotors on submeso and turbulence variability within the stable boundary layer over central Pennsylvania

NASA Astrophysics Data System (ADS)

Suarez Mullins, Astrid

Terrain-induced gravity waves and rotor circulations have been hypothesized to enhance the generation of submeso motions (i.e., nonstationary shear events with spatial and temporal scales greater than the turbulence scale and smaller than the meso-gamma scale) and to modulate low-level intermittency in the stable boundary layer (SBL). Intermittent turbulence, generated by submeso motions and/or the waves, can affect the atmospheric transport and dispersion of pollutants and hazardous materials. Thus, the study of these motions and the mechanisms through which they impact the weakly to very stable SBL is crucial for improving air quality modeling and hazard predictions. In this thesis, the effects of waves and rotor circulations on submeso and turbulence variability within the SBL is investigated over the moderate terrain of central Pennsylvania using special observations from a network deployed at Rock Springs, PA and high-resolution Weather Research and Forecasting (WRF) model forecasts. The investigation of waves and rotors over central PA is important because 1) the moderate topography of this region is common to most of the eastern US and thus the knowledge acquired from this study can be of significance to a large population, 2) there have been little evidence of complex wave structures and rotors reported for this region, and 3) little is known about the waves and rotors generated by smaller and more moderate topographies. Six case studies exhibiting an array of wave and rotor structures are analyzed. Observational evidence of the presence of complex wave structures, resembling nonstationary trapped gravity waves and downslope windstorms, and complex rotor circulations, resembling trapped and jump-type rotors, is presented. These motions and the mechanisms through which they modulate the SBL are further investigated using high-resolution WRF forecasts. First, the efficacy of the 0.444-km horizontal grid spacing WRF model to reproduce submeso and meso-gamma motions, generated by waves and rotors and hypothesized to impact the SBL, is investigated using a new wavelet-based verification methodology for assessing non-deterministic model skill in the submeso and meso-gamma range to complement standard deterministic measures. This technique allows the verification and/or intercomparison of any two nonstationary stochastic systems without many of the limitations of typical wavelet-based verification approaches (e.g., selection of noise models, testing for significance, etc.). Through this analysis, it is shown that the WRF model largely underestimates the number of small amplitude fluctuations in the small submeso range, as expected; and it overestimates the number of small amplitude fluctuations in the meso-gamma range, generally resulting in forecasts that are too smooth. Investigation of the variability for different initialization strategies shows that deterministic wind speed predictions are less sensitive to the choice of initialization strategy than temperature forecasts. Similarly, investigation of the variability for various planetary boundary layer (PBL) parameterizations reveals that turbulent kinetic energy (TKE)-based schemes have an advantage over the non-local schemes for non-deterministic motions. The larger spread in the verification scores for various PBL parameterizations than initialization strategies indicates that PBL parameterization may play a larger role modulating the variability of non-deterministic motions in the SBL for these cases. These results confirm previous findings that have shown WRF to have limited skill forecasting submeso variability for periods greater than ~20 min. The limited skill of the WRF at these scales in these cases is related to the systematic underestimation of the amplitude of observed fluctuations. These results are implemented in the model design and configuration for the investigation of nonstationary waves and rotor structures modulating submeso and mesogamma motions and the SBL. Observations and WRF forecasts of two wave cases characterized by nonstationary waves and rotors are investigated to show the WRF model to have reasonable accuracy forecasting low-level temperature and wind speed in the SBL and to qualitatively produce rotors, similar to those observed, as well as some of the mechanisms modulating their development and evolution. Finally, observations and high-resolution WRF forecasts under different environmental conditions using various initialization strategies are used to investigate the impact of nonlinear gravity waves and rotor structures on the generation of intermittent turbulence and valley transport in the SBL. Evidence of the presence of elevated regions of TKE generated by the complex waves and rotors is presented and investigated using an additional four case studies, exhibiting two synoptic flow regimes and different wave and rotor structures. Throughout this thesis, terrain-induced gravity waves and rotors in the SBL are shown to synergistically interact with the surface cold pool and to enhance low-level turbulence intermittency through the development of submeso and meso-gamma motions. These motions are shown to be an important source of uncertainty for the atmospheric transport and dispersion of pollutants and hazardous materials under very stable conditions. (Abstract shortened by ProQuest.).

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

NASA Astrophysics Data System (ADS)

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

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

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

PubMed

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

2014-01-01

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

Transient Tsunamis in Lakes

NASA Astrophysics Data System (ADS)

Couston, L.; Mei, C.; Alam, M.

2013-12-01

A large number of lakes are surrounded by steep and unstable mountains with slopes prone to failure. As a result, landslides are likely to occur and impact water sitting in closed reservoirs. These rare geological phenomena pose serious threats to dam reservoirs and nearshore facilities because they can generate unexpectedly large tsunami waves. In fact, the tallest wave experienced by contemporary humans occurred because of a landslide in the narrow bay of Lituya in 1958, and five years later, a deadly landslide tsunami overtopped Lake Vajont's dam, flooding and damaging villages along the lakefront and in the Piave valley. If unstable slopes and potential slides are detected ahead of time, inundation maps can be drawn to help people know the risks, and mitigate the destructive power of the ensuing waves. These maps give the maximum wave runup height along the lake's vertical and sloping boundaries, and can be obtained by numerical simulations. Keeping track of the moving shorelines along beaches is challenging in classical Eulerian formulations because the horizontal extent of the fluid domain can change over time. As a result, assuming a solid slide and nonbreaking waves, here we develop a nonlinear shallow-water model equation in the Lagrangian framework to address the problem of transient landslide-tsunamis. In this manner, the shorelines' three-dimensional motion is part of the solution. The model equation is hyperbolic and can be solved numerically by finite differences. Here, a 4th order Runge-Kutta method and a compact finite-difference scheme are implemented to integrate in time and spatially discretize the forced shallow-water equation in Lagrangian coordinates. The formulation is applied to different lake and slide geometries to better understand the effects of the lake's finite lengths and slide's forcing mechanism on the generated wavefield. Specifically, for a slide moving down a plane beach, we show that edge-waves trapped by the shoreline and free-waves moving away from it coexist. On an open coast, these two types of waves would never interact, but because of the lake's finite dimensions, here we show that local inundation height maxima are due to wave superposition on the shoreline. These interactions can be dramatic near the lake's corners. For instance, in a rectangular lake delimited by two opposite and plane beaches and two vertical walls, we find that a landslide tsunami results in an inundation height at a corner 50% larger than anywhere else. The nonlinear and linear models produce different inundation maps, and here we show that maximum wave runups can be increased by up to 56% when nonlinear terms are included.

Identification and classification of very low frequency waves on a coral reef flat

USGS Publications Warehouse

Gawehn, Matthijs; van Dongeran, Ap; van Rooijen, Arnold; Storlazzi, Curt; Cheriton, Olivia; Reniers, Ad

2016-01-01

Very low frequency (VLF, 0.001–0.005 Hz) waves are important drivers of flooding of low-lying coral reef-islands. In particular, VLF wave resonance is known to drive large wave runup and subsequent overwash. Using a 5 month data set of water levels and waves collected along a cross-reef transect on Roi-Namur Island in the Republic of the Marshall Islands, the observed VLF motions were categorized into four different classes: (1) resonant, (2) (nonresonant) standing, (3) progressive-growing, and (4) progressive-dissipative waves. Each VLF class is set by the reef flat water depth and, in the case of resonance, the incident-band offshore wave period. Using an improved method to identify VLF wave resonance, we find that VLF wave resonance caused prolonged (∼0.5–6.0 h), large-amplitude water surface oscillations at the inner reef flat ranging in wave height from 0.14 to 0.83 m. It was induced by relatively long-period, grouped, incident-band waves, and occurred under both storm and nonstorm conditions. Moreover, observed resonant VLF waves had nonlinear, bore-like wave shapes, which likely have a larger impact on the shoreline than regular, sinusoidal waveforms. As an alternative technique to the commonly used Fast Fourier Transformation, we propose the Hilbert-Huang Transformation that is more computationally expensive but can capture the wave shape more accurately. This research demonstrates that understanding VLF waves on reef flats is important for evaluating coastal flooding hazards.

Identification and classification of very low frequency waves on a coral reef flat

NASA Astrophysics Data System (ADS)

Gawehn, Matthijs; van Dongeren, Ap; van Rooijen, Arnold; Storlazzi, Curt D.; Cheriton, Olivia M.; Reniers, Ad

2016-10-01

Very low frequency (VLF, 0.001-0.005 Hz) waves are important drivers of flooding of low-lying coral reef-islands. In particular, VLF wave resonance is known to drive large wave runup and subsequent overwash. Using a 5 month data set of water levels and waves collected along a cross-reef transect on Roi-Namur Island in the Republic of the Marshall Islands, the observed VLF motions were categorized into four different classes: (1) resonant, (2) (nonresonant) standing, (3) progressive-growing, and (4) progressive-dissipative waves. Each VLF class is set by the reef flat water depth and, in the case of resonance, the incident-band offshore wave period. Using an improved method to identify VLF wave resonance, we find that VLF wave resonance caused prolonged (˜0.5-6.0 h), large-amplitude water surface oscillations at the inner reef flat ranging in wave height from 0.14 to 0.83 m. It was induced by relatively long-period, grouped, incident-band waves, and occurred under both storm and nonstorm conditions. Moreover, observed resonant VLF waves had nonlinear, bore-like wave shapes, which likely have a larger impact on the shoreline than regular, sinusoidal waveforms. As an alternative technique to the commonly used Fast Fourier Transformation, we propose the Hilbert-Huang Transformation that is more computationally expensive but can capture the wave shape more accurately. This research demonstrates that understanding VLF waves on reef flats is important for evaluating coastal flooding hazards.

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

PubMed Central

Li, Nianbei; Ren, Jie

2014-01-01

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

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

PubMed

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

2009-04-13

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

Analytical and numerical construction of vertical periodic orbits about triangular libration points based on polynomial expansion relations among directions

NASA Astrophysics Data System (ADS)

Qian, Ying-Jing; Yang, Xiao-Dong; Zhai, Guan-Qiao; Zhang, Wei

2017-08-01

Innovated by the nonlinear modes concept in the vibrational dynamics, the vertical periodic orbits around the triangular libration points are revisited for the Circular Restricted Three-body Problem. The ζ -component motion is treated as the dominant motion and the ξ and η -component motions are treated as the slave motions. The slave motions are in nature related to the dominant motion through the approximate nonlinear polynomial expansions with respect to the ζ -position and ζ -velocity during the one of the periodic orbital motions. By employing the relations among the three directions, the three-dimensional system can be transferred into one-dimensional problem. Then the approximate three-dimensional vertical periodic solution can be analytically obtained by solving the dominant motion only on ζ -direction. To demonstrate the effectiveness of the proposed method, an accuracy study was carried out to validate the polynomial expansion (PE) method. As one of the applications, the invariant nonlinear relations in polynomial expansion form are used as constraints to obtain numerical solutions by differential correction. The nonlinear relations among the directions provide an alternative point of view to explore the overall dynamics of periodic orbits around libration points with general rules.

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

PubMed

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

2013-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

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

NASA Astrophysics Data System (ADS)

Hasanian, Mostafa; Lissenden, Cliff J.

2018-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Generation mechanisms of fundamental rogue wave spatial-temporal structure.

PubMed

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

2017-08-01

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

Signatures of Nonlinear Waves in Coronal Plumes and Holes

NASA Technical Reports Server (NTRS)

Ofman, Leon

1999-01-01

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

Nonlinear modes of snap-through motions of a shallow arch

NASA Astrophysics Data System (ADS)

Breslavsky, I.; Avramov, K. V.; Mikhlin, Yu.; Kochurov, R.

2008-03-01

Nonlinear modes of snap-through motions of a shallow arch are analyzed. Dynamics of shallow arch is modeled by a two-degree-of-freedom system. Two nonlinear modes of this discrete system are treated. The methods of Ince algebraization and Hill determinants are used to study stability of nonlinear modes. The analytical results are compared with the data of the numerical simulations.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Biomimetic propulsion under random heaving conditions, using active pitch control

NASA Astrophysics Data System (ADS)

Politis, Gerasimos; Politis, Konstantinos

2014-05-01

Marine mammals travel long distances by utilizing and transforming wave energy to thrust through proper control of their caudal fin. On the other hand, manmade ships traveling in a wavy sea store large amounts of wave energy in the form of kinetic energy for heaving, pitching, rolling and other ship motions. A natural way to extract this energy and transform it to useful propulsive thrust is by using a biomimetic wing. The aim of this paper is to show how an actively pitched biomimetic wing could achieve this goal when it performs a random heaving motion. More specifically, we consider a biomimetic wing traveling with a given translational velocity in an infinitely extended fluid and performing a random heaving motion with a given energy spectrum which corresponds to a given sea state. A formula is invented by which the instantaneous pitch angle of the wing is determined using the heaving data of the current and past time steps. Simulations are then performed for a biomimetic wing at different heave energy spectra, using an indirect Source-Doublet 3-D-BEM, together with a time stepping algorithm capable to track the random motion of the wing. A nonlinear pressure type Kutta condition is applied at the trailing edge of the wing. With a mollifier-based filtering technique, the 3-D unsteady rollup pattern created by the random motion of the wing is calculated without any simplifying assumptions regarding its geometry. Calculated unsteady forces, moments and useful power, show that the proposed active pitch control always results in thrust producing motions, with significant propulsive power production and considerable beneficial stabilizing action to ship motions. Calculation of the power required to set the pitch angle prove it to be a very small percentage of the useful power and thus making the practical application of the device very tractable.

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

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

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

2015-05-15

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Wave excitation by nonlinear coupling among shear Alfvén waves in a mirror-confined plasma

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

Ikezoe, R., E-mail: ikezoe@prc.tsukuba.ac.jp; Ichimura, M.; Okada, T.

2015-09-15

A shear Alfvén wave at slightly below the ion-cyclotron frequency overcomes the ion-cyclotron damping and grows because of the strong anisotropy of the ion temperature in the magnetic mirror configuration, and is called the Alfvén ion-cyclotron (AIC) wave. Density fluctuations caused by the AIC waves and the ion-cyclotron range of frequencies (ICRF) waves used for ion heating have been detected using a reflectometer in a wide radial region of the GAMMA 10 tandem mirror plasma. Various wave-wave couplings are clearly observed in the density fluctuations in the interior of the plasma, but these couplings are not so clear in themore » magnetic fluctuations at the plasma edge when measured using a pick-up coil. A radial dependence of the nonlinearity is found, particularly in waves with the difference frequencies of the AIC waves; bispectral analysis shows that such wave-wave coupling is significant near the core, but is not so evident at the periphery. In contrast, nonlinear coupling with the low-frequency background turbulence is quite distinct at the periphery. Nonlinear coupling associated with the AIC waves may play a significant role in the beta- and anisotropy-limits of a mirror-confined plasma through decay of the ICRF heating power and degradation of the plasma confinement by nonlinearly generated waves.« less

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

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

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

Coupled matter-wave solitons in optical lattices

NASA Astrophysics Data System (ADS)

Golam Ali, Sk; Talukdar, B.

2009-06-01

We make use of a potential model to study the dynamics of two coupled matter-wave or Bose-Einstein condensate (BEC) solitons loaded in optical lattices. With separate attention to linear and nonlinear lattices we find some remarkable differences for response of the system to effects of these lattices. As opposed to the case of linear optical lattice (LOL), the nonlinear lattice (NOL) can be used to control the mutual interaction between the two solitons. For a given lattice wave number k, the effective potentials in which the two solitons move are such that the well (Veff(NOL)), resulting from the juxtaposition of soliton interaction and nonlinear lattice potential, is deeper than the corresponding well Veff(LOL). But these effective potentials have opposite k dependence in the sense that the depth of Veff(LOL) increases as k increases and that of Veff(NOL) decreases for higher k values. We verify that the effectiveness of optical lattices to regulate the motion of the coupled solitons depends sensitively on the initial locations of the motionless solitons as well as values of the lattice wave number. For both LOL and NOL the two solitons meet each other due to mutual interaction if their initial locations are taken within the potential wells with the difference that the solitons in the NOL approach each other rather rapidly and take roughly half the time to meet as compared with the time needed for such coalescence in the LOL. In the NOL, the soliton profiles can move freely and respond to the lattice periodicity when the separation between their initial locations are as twice as that needed for a similar free movement in the LOL. We observe that, in both cases, slow tuning of the optical lattices by varying k with respect to a time parameter τ drags the oscillatory solitons apart to take them to different locations. In our potential model the oscillatory solitons appear to propagate undistorted. But a fully numerical calculation indicates that during evolution they exhibit decay and revival.

Investigating the generation of Love waves in secondary microseisms using 3D numerical simulations

NASA Astrophysics Data System (ADS)

Wenk, Stefan; Hadziioannou, Celine; Pelties, Christian; Igel, Heiner

2014-05-01

Longuet-Higgins (1950) proposed that secondary microseismic noise can be attributed to oceanic disturbances by surface gravity wave interference causing non-linear, second-order pressure perturbations at the ocean bottom. As a first approximation, this source mechanism can be considered as a force acting normal to the ocean bottom. In an isotropic, layered, elastic Earth model with plain interfaces, vertical forces generate P-SV motions in the vertical plane of source and receiver. In turn, only Rayleigh waves are excited at the free surface. However, several authors report on significant Love wave contributions in the secondary microseismic frequency band of real data measurements. The reason is still insufficiently analysed and several hypothesis are under debate: - The source mechanism has strongest influence on the excitation of shear motions, whereas the source direction dominates the effect of Love wave generation in case of point force sources. Darbyshire and Okeke (1969) proposed the topographic coupling effect of pressure loads acting on a sloping sea-floor to generate the shear tractions required for Love wave excitation. - Rayleigh waves can be converted into Love waves by scattering. Therefore, geometric scattering at topographic features or internal scattering by heterogeneous material distributions can cause Love wave generation. - Oceanic disturbances act on large regions of the ocean bottom, and extended sources have to be considered. In combination with topographic coupling and internal scattering, the extent of the source region and the timing of an extended source should effect Love wave excitation. We try to elaborate the contribution of different source mechanisms and scattering effects on Love to Rayleigh wave energy ratios by 3D numerical simulations. In particular, we estimate the amount of Love wave energy generated by point and extended sources acting on the free surface. Simulated point forces are modified in their incident angle, whereas extended sources are adapted in their spatial extent, magnitude and timing. Further, the effect of variations in the correlation length and perturbation magnitude of a random free surface topography as well as an internal random material distribution are studied.

Learning physics in a water park

NASA Astrophysics Data System (ADS)

Cabeza, Cecilia; Rubido, Nicolás; Martí, Arturo C.

2014-03-01

Entertaining and educational experiments that can be conducted in a water park, illustrating physics concepts, principles and fundamental laws, are described. These experiments are suitable for students ranging from senior secondary school to junior university level. Newton’s laws of motion, Bernoulli’s equation, based on the conservation of energy, buoyancy, linear and non-linear wave propagation, turbulence, thermodynamics, optics and cosmology are among the topics that can be discussed. Commonly available devices like smartphones, digital cameras, laptop computers and tablets, can be used conveniently to enable accurate calculation and a greater degree of engagement on the part of students.

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

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

NASA Astrophysics Data System (ADS)

Aver'yanov, M. V.; Khokhlova, V. A.; Sapozhnikov, O. A.; Blanc-Benon, Ph.; Cleveland, R. O.

2006-12-01

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption.

Investigation of scaling characteristics for defining design environments due to transient ground winds and near-field, nonlinear acoustic fields

NASA Technical Reports Server (NTRS)

Shih, C. C.

1973-01-01

In order to establish a foundation of scaling laws for the highly nonlinear waves associated with the launch vehicle, the basic knowledge of the relationships among the paramaters pertinent to the energy dissipation process associated with the propagation of nonlinear pressure waves in thermoviscous media is required. The problem of interest is to experimentally investigate the temporal and spacial velocity profiles of fluid flow in a 3-inch open-end pipe of various lengths, produced by the propagation of nonlinear pressure waves for various diaphragm burst pressures of a pressure wave generator. As a result, temporal and spacial characteristics of wave propagation for a parametric set of nonlinear pressure waves in the pipe containing air under atmospheric conditions were determined. Velocity measurements at five sections along the pipes of up to 210 ft. in length were made with hot-film anemometers for five pressure waves produced by a piston. The piston was derived with diaphragm burst pressures at 20, 40, 60, 80 and 100 psi in the driver chamber of the pressure wave generator.

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).

Altimeter Observations of Baroclinic Oceanic Inertia-Gravity Wave Turbulence

NASA Technical Reports Server (NTRS)

Glazman, R. E.; Cheng, B.

1996-01-01

For a wide range of nonlinear wave processes - from capillary to planetary waves - theory predicts the existence of Kolmogorov-type spectral cascades of energy and other conserved quantities occuring via nonlinear resonant wave-wave interactions. So far, observations of wave turbulence (WT) have been limited to small-scale processes such as surface gravity and capillary-gravity waves.

Transition from geostrophic turbulence to inertia-gravity waves in the atmospheric energy spectrum.

PubMed

Callies, Jörn; Ferrari, Raffaele; Bühler, Oliver

2014-12-02

Midlatitude fluctuations of the atmospheric winds on scales of thousands of kilometers, the most energetic of such fluctuations, are strongly constrained by the Earth's rotation and the atmosphere's stratification. As a result of these constraints, the flow is quasi-2D and energy is trapped at large scales—nonlinear turbulent interactions transfer energy to larger scales, but not to smaller scales. Aircraft observations of wind and temperature near the tropopause indicate that fluctuations at horizontal scales smaller than about 500 km are more energetic than expected from these quasi-2D dynamics. We present an analysis of the observations that indicates that these smaller-scale motions are due to approximately linear inertia-gravity waves, contrary to recent claims that these scales are strongly turbulent. Specifically, the aircraft velocity and temperature measurements are separated into two components: one due to the quasi-2D dynamics and one due to linear inertia-gravity waves. Quasi-2D dynamics dominate at scales larger than 500 km; inertia-gravity waves dominate at scales smaller than 500 km.

Transition from geostrophic turbulence to inertia–gravity waves in the atmospheric energy spectrum

PubMed Central

Callies, Jörn; Ferrari, Raffaele; Bühler, Oliver

2014-01-01

Midlatitude fluctuations of the atmospheric winds on scales of thousands of kilometers, the most energetic of such fluctuations, are strongly constrained by the Earth’s rotation and the atmosphere’s stratification. As a result of these constraints, the flow is quasi-2D and energy is trapped at large scales—nonlinear turbulent interactions transfer energy to larger scales, but not to smaller scales. Aircraft observations of wind and temperature near the tropopause indicate that fluctuations at horizontal scales smaller than about 500 km are more energetic than expected from these quasi-2D dynamics. We present an analysis of the observations that indicates that these smaller-scale motions are due to approximately linear inertia–gravity waves, contrary to recent claims that these scales are strongly turbulent. Specifically, the aircraft velocity and temperature measurements are separated into two components: one due to the quasi-2D dynamics and one due to linear inertia–gravity waves. Quasi-2D dynamics dominate at scales larger than 500 km; inertia–gravity waves dominate at scales smaller than 500 km. PMID:25404349

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

PubMed

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

2017-04-01

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

Rogue wave solutions for the infinite integrable nonlinear Schrödinger equation hierarchy.

PubMed

Ankiewicz, A; Akhmediev, N

2017-07-01

We present rogue wave solutions of the integrable nonlinear Schrödinger equation hierarchy with an infinite number of higher-order terms. The latter include higher-order dispersion and higher-order nonlinear terms. In particular, we derive the fundamental rogue wave solutions for all orders of the hierarchy, with exact expressions for velocities, phase, and "stretching factors" in the solutions. We also present several examples of exact solutions of second-order rogue waves, including rogue wave triplets.

Optical rogue waves for the inhomogeneous generalized nonlinear Schrödinger equation.

PubMed

Loomba, Shally; Kaur, Harleen

2013-12-01

We present optical rogue wave solutions for a generalized nonlinear Schrodinger equation by using similarity transformation. We have predicted the propagation of rogue waves through a nonlinear optical fiber for three cases: (i) dispersion increasing (decreasing) fiber, (ii) periodic dispersion parameter, and (iii) hyperbolic dispersion parameter. We found that the rogue waves and their interactions can be tuned by properly choosing the parameters. We expect that our results can be used to realize improved signal transmission through optical rogue waves.

Empirical Site Amplification Factors Incorporating Soil Nonlinearity in Taiwan

NASA Astrophysics Data System (ADS)

Kuo, C. H.; Chung, C. H.; Che-Min, L.; Huang, J. Y.; Wen, K. L.

2017-12-01

Characteristics of site amplifications caused by both crustal and subduction earthquakes are important in Taiwan. For example, seismic waves were amplified and led to significant building damages in the Taipei Basin by the 1986 Hualien offshore (subduction interface) and the 1999 Chi-Chi earthquakes (crustal), for which the epicentral distances were about 100 km. To understand local site amplifications in Taiwan, empirical site amplification factors for horizontal ground motions are studied using recently constructed strong motion and site databases for the free-field TSMIP stations in Taiwan. Records of large magnitude earthquakes of ML larger than six from 1994 to 2014 were selected for this study. Site amplification factors at site conditions with Vs30 of 120 m/s to 1500 m/s and base accelerations up to 0.7g were inferred from intensity ratios of station pairs within specific distances. The reference site condition is assumed as Vs30 of 760 m/s (B/C boundary). Preliminary results indicate: 1. Soil nonlinearity is more obviously at short periods (PGA, Sa0.3) than long periods (PGV, Sa1.0). 2. Soil nonlinearity is significant for stations belong to site classes of B, C, D, and E in Taiwan. 3. Effect of station-pair distance is seen at short periods (PGA and Sa0.3). 4. No significant different is found in site amplifications of crustal and subduction earthquakes. The result could be a reference for the Fa and Fv in Taiwan's building code.

Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation

PubMed Central

Jing, Yun; Tao, Molei; Clement, Greg T.

2011-01-01

A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green’s function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed. PMID:21302985

The Effect of Crack Orientation on the Nonlinear Interaction of a P-wave with an S-wave

DOE PAGES

TenCate, J. A.; Malcolm, A. E.; Feng, X.; ...

2016-06-06

Cracks, joints, fluids, and other pore-scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore-scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presencemore » and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low-amplitude P wave probe by a high-amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.« less

Observation of aftershocks of the 2003 Tokachi-Oki earthquake for estimation of local site effects

NASA Astrophysics Data System (ADS)

Yamanaka, Hiroaki; Motoki, Kentaro; Etoh, Kiminobu; Murayama, Masanari; Komaba, Nobuhiko

2004-03-01

Observation of aftershocks of the 2003 Tokachi-Oki earthquake was conducted in the southern part of the Tokachi basin in Hokkaido, Japan for estimation of local site effects. We installed accelerographs at 12 sites in Chokubetsu, Toyokoro, and Taiki areas, where large strong motion records were obtained during the main shock at stations of the K-NET and KiK-net. The stations of the aftershock observation are situated with different geological conditions and some of the sites were installed on Pleistocene layers as reference sites. The site amplifications are investigated using spectral ratio of S-waves from the aftershocks. The S-wave amplification factor is dominant at a period of about 1 second at the site near the KiK-net site in Toyokoro. This amplification fits well with calculated 1D amplification of S-wave in alluvial layers with a thickness of 50 meters. In addition to the site effects, we detected nonlinear amplification of the soft soils only during the main shock. The site effects at the strong motion site of the K-NET at Chokubetsu have a dominate peak at a period of 0.4 seconds. This amplification is due to soft soils having a thickness of about 13 meters. Contrary to the results at the two areas, site effects are not significantly different at the stations in the Taiki area, because of similarity on surface geological conditions.

Theoretical and Analog Studies of the Effects of Nonlinear Stability Derivatives on the Longitudinal Motions of an Aircraft in Response to Step Control Deflections and to the Influence of Proportional Automatic Control

NASA Technical Reports Server (NTRS)

Curfman, Howard J , Jr

1955-01-01

Through theoretical and analog results the effects of two nonlinear stability derivatives on the longitudinal motions of an aircraft have been investigated. Nonlinear functions of pitching-moment and lift coefficients with angle of attack were considered. Analog results of aircraft motions in response to step elevator deflections and to the action of the proportional control systems are presented. The occurrence of continuous hunting oscillations was predicted and demonstrated for the attitude stabilization system with proportional control for certain nonlinear pitching-moment variations and autopilot adjustments.

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

Some Thoughts on Stability in Nonlinear Periodic Focusing Systems

DOE R&D Accomplishments Database

McMillan, E. M.

1967-09-05

A brief discussion is given of the long-term stability of particle motions through periodic focusing structures containing lumped nonlinear elements. A method is presented whereby one can specify the nonlinear elements in such a way as to generate a variety of structures in which the motion has long-term stability.

On the mechanical modeling of tensegrity columns subject to impact loading

NASA Astrophysics Data System (ADS)

Amendola, Ada; Favata, Antonino; Micheletti, Andrea

2018-04-01

A physical model of a tensegrity columns is additively manufactured in a titanium alloy. After removing sacrificial supports, such a model is post-tensioned through suitable insertion of Spectra cables. The wave dynamics of the examined system is first experimentally investigated by recording the motion through high-speed cameras assisted by a digital image correlation algorithm, which returns time-histories of the axial displacements of the bases of each prism of the column. Next, the experimental response is mechanically simulated by means of two different models: a stick-and-spring model accounting for the presence of bending-stiff connections between the 3D-printed elements (mixed bending-stretching response), and a tensegrity model accounting for a purely stretching response. The comparison of theory and experiment reveals that the presence of bending-stiff connections weakens the nonlinearity of the wave dynamics of the system. A stretching-dominated response instead supports highly compact solitary waves in the presence of small prestress and negligible bending stiffness of connections.

Middle atmosphere electrical energy coupling

NASA Technical Reports Server (NTRS)

Hale, L. C.

1989-01-01

The middle atmosphere (MA) has long been known as an absorber of radio waves, and as a region of nonlinear interactions among waves. The region of highest transverse conductivity near the top of the MA provides a common return for global thunderstorm, auroral Birkeland, and ionospheric dynamo currents, with possibilities for coupling among them. Their associated fields and other transverse fields map to lower altitudes depending on scale size. Evidence now exists for motion-driven aerosol generators, and for charge trapped at the base of magnetic field lines, both capable of producing large MA electric fields. Ionospheric Maxwell currents (curl H) parallel to the magnetic field appear to map to lower altitudes, with rapidly time-varying components appearing as displacement currents in the stratosphere. Lightning couples a (primarily ELF and ULF) current transient to the ionosphere and magnetosphere whose wave shape is largely dependent on the MA conductivity profile. Electrical energy is of direct significance mainly in the upper MA, but electrodynamic transport of minor constituents such as smoke particles or CN may be important at other altitudes.

On the nonlinear stability of viscous modes within the Rayleigh problem on an infinite flat plate

NASA Technical Reports Server (NTRS)

Webb, J. C.; Otto, S. R.; Lilley, G. M.

1994-01-01

The stability has been investigated of the unsteady flow past an infinite flat plate when it is moved impulsively from rest, in its own plane. For small times the instantaneous stability of the flow depends on the linearized equations of motion which reduce in this problem to the Orr-Sommerfeld equation. It is known that the flow for certain values of Reynolds number, frequency and wave number is unstable to Tollmien-Schlichting waves, as in the case of the Blasius boundary layer flow past a flat plate. With increase in time, the unstable waves only undergo growth for a finite time interval, and this growth rate is itself a function of time. The influence of finite amplitude effects is studied by solving the full Navier-Stokes equations. It is found that the stability characteristics are markedly changed both by the consideration of the time evolution of the flow, and by the introduction of finite amplitude effects.

Quality of motion considerations in numerical analysis of motion restoring implants of the spine.

PubMed

Bowden, Anton E; Guerin, Heather L; Villarraga, Marta L; Patwardhan, Avinash G; Ochoa, Jorge A

2008-06-01

Motion restoring implants function in a dynamic environment that encompasses the full range of spinal kinematics. Accurate assessment of the in situ performance of these devices using numerical techniques requires model verification and validation against the well-established nonlinear quality of motion of the spine, as opposed to the previous norm of matching kinematic endpoint metrics such as range of motion and intervertebral disc pressure measurements at a single kinematic reference point. Experimental data was obtained during cadaveric testing of nine three-functional spinal unit (L3-S1) lumbar spine segments. Each specimen was tested from 8 Nm of applied flexion moment to 6 Nm of applied extension moment with an applied 400 N compressive follower preload. A nonlinear kinematic curve representing the spinal quality of motion (applied moment versus angular rotation) for the index finite element model was constructed and compared to the kinematic responses of the experimental specimens. The effect of spinal soft tissue structure mechanical behaviors on the fidelity of the model's quality of motion to experimental data was assessed by iteratively modifying the material representations of annulus fibrosus, nucleus pulposus, and ligaments. The present work demonstrated that for this model, the annulus fibrosus played a small role in the nonlinear quality of motion of the model, whereas changes in ligament representations had a large effect, as validated against the full kinematic range of motion. An anisotropic continuum representation of the annulus fibrosus was used, along with nonlinear fabric representations of the ligaments and a hyperelastic representation of the nucleus pulposus. Our results suggest that improvements in current methodologies broadly used in numerical simulations of the lumbar spine are needed to fully describe the highly nonlinear motion of the spine.

Modelling of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

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

2014-04-01

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

On the Nonlinear Dynamics of a Tunable Shock Micro-switch

NASA Astrophysics Data System (ADS)

Azizi, Saber; Javaheri, Hamid; Ghanati, Parisa

2016-12-01

A tunable shock micro-switch based on piezoelectric excitation is proposed in this study. This model includes a clamped-clamped micro-beam sandwiched with two piezoelectric layers throughout the entire length. Actuation of the piezoelectric layers via a DC voltage leads to an initial axial force in the micro-beam and directly affects on its overall bending stiffness; accordingly enables two-side tuning of both the trigger time and threshold shock. The governing motion equation, in the presence of an electrostatic actuation and a shock wave, is derived using Hamilton's principle. We employ the finite element method based on the Galerkin technique to obtain the temporal and phase responses subjected to three different shock waves including half sine, triangular and rectangular forms. Subsequently, we investigate the effect of the piezoelectric excitations on the threshold shock amplitude and trigger time.

Narrow bandwidth detection of vibration signature using fiber lasers

DOEpatents

Moore, Sean; Soh, Daniel B.S.

2018-05-08

The various technologies presented herein relate to extracting a portion of each pulse in a series of pulses reflected from a target to facilitate determination of a Doppler-shifted frequency for each pulse and, subsequently, a vibration frequency for the series of pulses. Each pulse can have a square-wave configuration, whereby each pulse can be time-gated to facilitate discarding the leading edge and the trailing edge (and associated non-linear effects) of each pulse and accordingly, capture of the central portion of the pulse from which the Doppler-shifted frequency, and ultimately, the vibration frequency of the target can be determined. Determination of the vibration velocity facilitates identification of the target being in a state of motion. The plurality of pulses can be formed from a laser beam (e.g., a continuous wave), the laser beam having a narrow bandwidth.

Ultrasonic nonlinear guided wave inspection of microscopic damage in a composite structure

NASA Astrophysics Data System (ADS)

Zhang, Li; Borigo, Cody; Owens, Steven; Lissenden, Clifford; Rose, Joseph; Hakoda, Chris

2017-02-01

Sudden structural failure is a severe safety threat to many types of military and industrial composite structures. Because sudden structural failure may occur in a composite structure shortly after macroscale damage initiates, reliable early diagnosis of microdamage formation in the composite structure is critical to ensure safe operation and to reduce maintenance costs. Ultrasonic guided waves have been widely used for long-range defect detection in various structures. When guided waves are generated under certain excitation conditions, in addition to the traditional linear wave mode (known as the fundamental harmonic wave mode), a number of nonlinear higher-order harmonic wave modes are also be generated. Research shows that the nonlinear parameters of a higher-order harmonic wave mode could have excellent sensitivity to microstructural changes in a material. In this work, we successfully employed a nonlinear guided wave structural health monitoring (SHM) method to detect microscopic impact damage in a 32-layer carbon/epoxy fiber-reinforced composite plate. Our effort has demonstrated that, utilizing appropriate transducer design, equipment, excitation signals, and signal processing techniques, nonlinear guided wave parameter measurements can be reliably used to monitor microdamage initiation and growth in composite structures.

Containerless Ripple Turbulence

NASA Astrophysics Data System (ADS)

Putterman, Seth; Wright, William; Duval, Walter; Panzarella, Charles

2002-11-01

One of the longest standing unsolved problems in physics relates to the behavior of fluids that are driven far from equilibrium such as occurs when they become turbulent due to fast flow through a grid or tidal motions. In turbulent flows the distribution of vortex energy as a function of the inverse length scale [or wavenumber 'k'] of motion is proportional to 1/k5/3 which is the celebrated law of Kolmogorov. Although this law gives a good description of the average motion, fluctuations around the average are huge. This stands in contrast with thermally activated motion where large fluctuations around thermal equilibrium are highly unfavorable. The problem of turbulence is the problem of understanding why large fluctuations are so prevalent which is also called the problem of 'intermittency'. Turbulence is a remarkable problem in that its solution sits simultaneously at the forefront of physics, mathematics, engineering and computer science. A recent conference [March 2002] on 'Statistical Hydrodynamics' organized by the Los Alamos Laboratory Center for Nonlinear Studies brought together researchers in all of these fields. Although turbulence is generally thought to be described by the Navier-Stokes Equations of fluid mechanics the solution as well as its existence has eluded researchers for over 100 years. In fact proof of the existence of such a solution qualifies for a 1 M millennium prize. As part of our NASA funded research we have proposed building a bridge between vortex turbulence and wave turbulence. The latter occurs when high amplitude waves of various wavelengths are allowed to mutually interact in a fluid. In particular we have proposed measuring the interaction of ripples [capillary waves] that run around on the surface of a fluid sphere suspended in a microgravity environment. The problem of ripple turbulence poses similar mathematical challenges to the problem of vortex turbulence. The waves can have a high amplitude and a strong nonlinear interaction. Furthermore, the steady state distribution of energy again follows a Kolmogorov scaling law; in this case the ripple energy is distributed according to 1/k 7/4. Again, in parallel with vortex turbulence ripple turbulence exhibits intermittency. The problem of ripple turbulence presents an experimental opportunity to generate data in a controlled, benchmarked system. In particular the surface of a sphere is an ideal environment to study ripple turbulence. Waves run around the sphere and interact with each other, and the effect of walls is eliminated. In microgravity this state can be realized for over 2 decades of frequency. Wave turbulence is a physically relevant problem in its own right. It has been studied on the surface of liquid hydrogen and its application to Alfven waves in space is a source of debate. Of course, application of wave turbulence perspectives to ocean waves has been a major success. The experiment which we plan to run in microgravity is conceptually straightforward. Ripples are excited on the surface of a spherical drop of fluid and then their amplitude is recorded with appropriate photography. A key challenge is posed by the need to stably position a 10cm diameter sphere of water in microgravity. Two methods are being developed. Orbitec is using controlled puffs of air from at least 6 independent directions to provided the positioning force. This approach has actually succeeded to position and stabilize a 4cm sphere during a KC 135 segment. Guigne International is using the radiation pressure of high frequency sound. These transducers have been organized into a device in the shape of a dodecahedron. This apparatus 'SPACE DRUMS' has already been approved for use for combustion synthesis experiments on the International Space Station. A key opportunity presented by the ripple turbulence data is its use in driving the development of codes to simulate its properties.

Containerless Ripple Turbulence

NASA Technical Reports Server (NTRS)

Putterman, Seth; Wright, William; Duval, Walter; Panzarella, Charles

2002-01-01

One of the longest standing unsolved problems in physics relates to the behavior of fluids that are driven far from equilibrium such as occurs when they become turbulent due to fast flow through a grid or tidal motions. In turbulent flows the distribution of vortex energy as a function of the inverse length scale [or wavenumber 'k'] of motion is proportional to 1/k(sup 5/3) which is the celebrated law of Kolmogorov. Although this law gives a good description of the average motion, fluctuations around the average are huge. This stands in contrast with thermally activated motion where large fluctuations around thermal equilibrium are highly unfavorable. The problem of turbulence is the problem of understanding why large fluctuations are so prevalent which is also called the problem of 'intermittency'. Turbulence is a remarkable problem in that its solution sits simultaneously at the forefront of physics, mathematics, engineering and computer science. A recent conference [March 2002] on 'Statistical Hydrodynamics' organized by the Los Alamos Laboratory Center for Nonlinear Studies brought together researchers in all of these fields. Although turbulence is generally thought to be described by the Navier-Stokes Equations of fluid mechanics the solution as well as its existence has eluded researchers for over 100 years. In fact proof of the existence of such a solution qualifies for a 1 M$ millennium prize. As part of our NASA funded research we have proposed building a bridge between vortex turbulence and wave turbulence. The latter occurs when high amplitude waves of various wavelengths are allowed to mutually interact in a fluid. In particular we have proposed measuring the interaction of ripples [capillary waves] that run around on the surface of a fluid sphere suspended in a microgravity environment. The problem of ripple turbulence poses similar mathematical challenges to the problem of vortex turbulence. The waves can have a high amplitude and a strong nonlinear interaction. Furthermore, the steady state distribution of energy again follows a Kolmogorov scaling law; in this case the ripple energy is distributed according to 1/k (sup 7/4). Again, in parallel with vortex turbulence ripple turbulence exhibits intermittency. The problem of ripple turbulence presents an experimental opportunity to generate data in a controlled, benchmarked system. In particular the surface of a sphere is an ideal environment to study ripple turbulence. Waves run around the sphere and interact with each other, and the effect of walls is eliminated. In microgravity this state can be realized for over 2 decades of frequency. Wave turbulence is a physically relevant problem in its own right. It has been studied on the surface of liquid hydrogen and its application to Alfven waves in space is a source of debate. Of course, application of wave turbulence perspectives to ocean waves has been a major success. The experiment which we plan to run in microgravity is conceptually straightforward. Ripples are excited on the surface of a spherical drop of fluid and then their amplitude is recorded with appropriate photography. A key challenge is posed by the need to stably position a 10cm diameter sphere of water in microgravity. Two methods are being developed. Orbitec is using controlled puffs of air from at least 6 independent directions to provided the positioning force. This approach has actually succeeded to position and stabilize a 4cm sphere during a KC 135 segment. Guigne International is using the radiation pressure of high frequency sound. These transducers have been organized into a device in the shape of a dodecahedron. This apparatus 'SPACE DRUMS' has already been approved for use for combustion synthesis experiments on the International Space Station. A key opportunity presented by the ripple turbulence data is its use in driving the development of codes to simulate its properties.

Nonlinear Whistler Wave Physics in the Radiation Belts

NASA Astrophysics Data System (ADS)

Crabtree, Chris

2016-10-01

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

Modelling of Charles Darwin's tsunami reports

NASA Astrophysics Data System (ADS)

Galiev, Shamil

2010-05-01

Darwin landed at Valdivia and Concepcion, Chile, just before, during, and after a great 1835 earthquake. He described his impressions and results of the earthquake-induced natural catastrophe in The Voyage of the Beagle. His description of the tsunami could easily be read as a report from Indonesia or Sri Lanka, after the catastrophic tsunami of 26 December 2004. In particular, Darwin emphasised the dependence of earthquake-induced waves on a form of the coast and the coastal depth: ‘… Talcuhano and Callao are situated at the head of great shoaling bays, and they have always suffered from this phenomenon; whereas, the town of Valparaiso, which is seated close on the border of a profound ocean... has never been overwhelmed by one of these terrific deluges…' . He reports also, that ‘… the whole body of the sea retires from the coast, and then returns in great waves of overwhelming force ...' (we cite the Darwin's sentences following researchspace. auckland. ac. nz/handle/2292/4474). The coastal evolution of a tsunami was analytically studied in many publications (see, for example, Synolakis, C.E., Bernard, E.N., 2006. Philos. Trans. R. Soc., Ser. A, 364, 2231-2265; Tinti, S., Tonini, R. 205. J.Fluid Mech., 535, 11-21). However, the Darwin's reports and the influence of the coastal depth on the formation and the evolution of the steep front and the profile of tsunami did not practically discuss. Recently, a mathematical theory of these phenomena was presented in researchspace. auckland. ac. nz/handle/2292/4474. The theory describes the waves which are excited due to nonlinear effects within a shallow coastal zone. The tsunami elevation is described by two components: . Here is the linear (prime) component. It describes the wave coming from the deep ocean. is the nonlinear component. This component may become very important near the coastal line. After that the theory of the shallow waves is used. This theory yields the linear equation for and the weakly-nonlinear equation for . The last equation contains the forcing term which is generated by nonlinearity and depends on . The nonlinear shock-like solution for is constructed which is valid within the narrow coastal zone. Then the tsunami evolution near a coast is studied. It is found that the coastal evolution strongly depends on the profile of the bottom and the distance from the coastline. Far from this the wave surface is smooth and the wave is long enough. The wave profile begins to change quickly, if the coastal water is shallow. The steep (discontinuous) front of the tsunami can be generated. The water level reduces ahead of the front, or the ebb can appear there. Then this front begins to move away from the coast - into the ocean. This direction is opposite to the motion of the whole wave. The amplitude of the front is increased. The water wall is formed. This process explains the catastrophic effect of a tsunami, when a water-wall appears instantly. The wave, having two steep peaks, may be generated in the case of very shallow water. In contrast with this, the tsunami, practically, does not change, if the coastal water is deep. On the whole, the conclusions agree with the Darwin's reports.

Nonlinear surface waves at ferrite-metamaterial waveguide structure

NASA Astrophysics Data System (ADS)

Hissi, Nour El Houda; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Shabat, Mohammed Musa; Atangana, Jacques

2016-09-01

A new ferrite slab made of a metamaterial (MTM), surrounded by a nonlinear cover cladding and a ferrite substrate, was shown to support unusual types of electromagnetic surface waves. We impose the boundary conditions to derive the dispersion relation and others necessary to formulate the proposed structure. We analyse the dispersion properties of the nonlinear surface waves and we calculate the associated propagation index and the film-cover interface nonlinearity. In the calculation, several sets of the permeability of the MTM are considered. Results show that the waves behaviour depends on the values of the permeability of the MTM, the thickness of the waveguide and the film-cover interface nonlinearity. It is also shown that the use of the singular solutions to the electric field equation allows to identify several new properties of surface waves which do not exist in conventional waveguide.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

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

Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures.

PubMed

Khusnutdinova, Karima R; Samsonov, Alexander M; Zakharov, Alexey S

2009-05-01

We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

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.

Laboratory and theoretical models of planetary-scale instabilities and waves

NASA Technical Reports Server (NTRS)

Hart, John E.; Toomre, Juri

1990-01-01

Meteorologists and planetary astronomers interested in large-scale planetary and solar circulations recognize the importance of rotation and stratification in determining the character of these flows. In the past it has been impossible to accurately model the effects of sphericity on these motions in the laboratory because of the invariant relationship between the uni-directional terrestrial gravity and the rotation axis of an experiment. Researchers studied motions of rotating convecting liquids in spherical shells using electrohydrodynamic polarization forces to generate radial gravity, and hence centrally directed buoyancy forces, in the laboratory. The Geophysical Fluid Flow Cell (GFFC) experiments performed on Spacelab 3 in 1985 were analyzed. Recent efforts at interpretation led to numerical models of rotating convection with an aim to understand the possible generation of zonal banding on Jupiter and the fate of banana cells in rapidly rotating convection as the heating is made strongly supercritical. In addition, efforts to pose baroclinic wave experiments for future space missions using a modified version of the 1985 instrument led to theoretical and numerical models of baroclinic instability. Rather surprising properties were discovered, which may be useful in generating rational (rather than artificially truncated) models for nonlinear baroclinic instability and baroclinic chaos.

Local magnetohydrodynamic instabilities and the wave-driven dynamo in accretion disks

NASA Technical Reports Server (NTRS)

Vishniac, Ethan T.; Diamond, Patrick

1992-01-01

We consider the consequences of magnetic buoyancy and the magnetic shearing instability (MSI) on the strength and organization of the magnetic field in a thin accretion disk. We discuss a model in which the wave-driven dynamo growth rate is balanced by the dissipative effects of the MSI. As in earlier work, the net helicity is due to small advective motions driven by nonlinear interactions between internal waves. Assuming a simple model of the internal wave spectrum generated from the primary m = 1 internal waves, we find that the magnetic energy density saturates at about (H/r) exp 4/3 times the local pressure (where H is the disk thickness and r is its radius). On very small scales the shearing instability will produce an isotropic fluctuating field. For a stationary disk this is equivalent to a dimensionless 'viscosity' of about (H/r) exp 4/3. The vertical and radial diffusion coefficients will be comparable to each other. Magnetic buoyancy will be largely suppressed by the turbulence due to the MSI. We present a rough estimate of its effects and find that it removes magnetic flux from the disk at a rate comparable to that caused by turbulent diffusion.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Evaluation of crack status in a meter-size concrete structure using the ultrasonic nonlinear coda wave interferometry.

PubMed

Legland, Jean-Baptiste; Zhang, Yuxiang; Abraham, Odile; Durand, Olivier; Tournat, Vincent

2017-10-01

The field of civil engineering is in need of new methods of non-destructive testing, especially in order to prevent and monitor the serious deterioration of concrete structures. In this work, experimental results are reported on fault detection and characterization in a meter-scale concrete structure using an ultrasonic nonlinear coda wave interferometry (NCWI) method. This method entails the nonlinear mixing of strong pump waves with multiple scattered probe (coda) waves, along with analysis of the net effect using coda wave interferometry. A controlled damage protocol is implemented on a post-tensioned, meter-scale concrete structure in order to generate cracking within a specific area being monitored by NCWI. The nonlinear acoustic response due to the high amplitude of acoustic modulation yields information on the elastic nonlinearities of concrete, as evaluated by two specific nonlinear observables. The increase in nonlinearity level corresponds to the creation of a crack with a network of microcracks localized at its base. In addition, once the crack closes as a result of post-tensioning, the residual nonlinearities confirm the presence of the closed crack. Last, the benefits and applicability of this NCWI method to the characterization and monitoring of large structures are discussed.

Consistent nonlinear deterministic and stochastic evolution equations for deep to shallow water wave shoaling

NASA Astrophysics Data System (ADS)

Vrecica, Teodor; Toledo, Yaron

2015-04-01

One-dimensional deterministic and stochastic evolution equations are derived for the dispersive nonlinear waves while taking dissipation of energy into account. The deterministic nonlinear evolution equations are formulated using operational calculus by following the approach of Bredmose et al. (2005). Their formulation is extended to include the linear and nonlinear effects of wave dissipation due to friction and breaking. The resulting equation set describes the linear evolution of the velocity potential for each wave harmonic coupled by quadratic nonlinear terms. These terms describe the nonlinear interactions between triads of waves, which represent the leading-order nonlinear effects in the near-shore region. The equations are translated to the amplitudes of the surface elevation by using the approach of Agnon and Sheremet (1997) with the correction of Eldeberky and Madsen (1999). The only current possibility for calculating the surface gravity wave field over large domains is by using stochastic wave evolution models. Hence, the above deterministic model is formulated as a stochastic one using the method of Agnon and Sheremet (1997) with two types of stochastic closure relations (Benney and Saffman's, 1966, and Hollway's, 1980). These formulations cannot be applied to the common wave forecasting models without further manipulation, as they include a non-local wave shoaling coefficients (i.e., ones that require integration along the wave rays). Therefore, a localization method was applied (see Stiassnie and Drimer, 2006, and Toledo and Agnon, 2012). This process essentially extracts the local terms that constitute the mean nonlinear energy transfer while discarding the remaining oscillatory terms, which transfer energy back and forth. One of the main findings of this work is the understanding that the approximated non-local coefficients behave in two essentially different manners. In intermediate water depths these coefficients indeed consist of rapidly oscillating terms, but as the water depth becomes shallow they change to an exponential growth (or decay) behavior. Hence, the formerly used localization technique cannot be justified for the shallow water region. A new formulation is devised for the localization in shallow water, it approximates the nonlinear non-local shoaling coefficient in shallow water and matches it to the one fitting to the intermediate water region. This allows the model behavior to be consistent from deep water to intermediate depths and up to the shallow water regime. Various simulations of the model were performed for the cases of intermediate, and shallow water, overall the model was found to give good results in both shallow and intermediate water depths. The essential difference between the shallow and intermediate nonlinear shoaling physics is explained via the dominating class III Bragg resonances phenomenon. By inspecting the resonance conditions and the nature of the dispersion relation, it is shown that unlike in the intermediate water regime, in shallow water depths the formation of resonant interactions is possible without taking into account bottom components. References Agnon, Y. & Sheremet, A. 1997 Stochastic nonlinear shoaling of directional spectra. J. Fluid Mech. 345, 79-99. Benney, D. J. & Saffman, P. G. 1966 Nonlinear interactions of random waves. Proc. R. Soc. Lond. A 289, 301-321. Bredmose, H., Agnon, Y., Madsen, P.A. & Schaffer, H.A. 2005 Wave transformation models with exact second-order transfer. European J. of Mech. - B/Fluids 24 (6), 659-682. Eldeberky, Y. & Madsen, P. A. 1999 Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves. Coastal Engineering 38, 1-24. Kaihatu, J. M. & Kirby, J. T. 1995 Nonlinear transformation of waves in infinite water depth. Phys. Fluids 8, 175-188. Holloway, G. 1980 Oceanic internal waves are not weak waves. J. Phys. Oceanogr. 10, 906-914. Stiassnie, M. & Drimer, N. 2006 Prediction of long forcing waves for harbor agitation studies. J. of waterways, port, coastal and ocean engineering 132(3), 166-171. Toledo, Y. & Agnon, Y. 2012 Stochastic evolution equations with localized nonlinear shoaling coefficients. European J. of Mech. - B/Fluids 34, 13-18.

Fractional Whirl Motion in Wave Journal Bearings

NASA Technical Reports Server (NTRS)

Dimofte, Florin; Hendricks, Robert C.

1996-01-01

Unloaded gas, plain journal bearings experience sub-synchronous whirl motion due to fluid film instabilities and wall contact usually occurs immediately after the onset of the whirl motion. An alternative is the wave journal bearing which significantly improves bearing stability. The predicted threshold where the sub-synchronous whirl motion starts was well confirmed by the experimental observation. In addition, both a two-wave and a three-wave journal bearing can operate free of sub-synchronous whirl motion over a large range in speeds. When the sub-synchronous whirl motion occurs, both the two-wave and three-wave bearing can run in a whirl orbit well within the bearing clearance. At large clearances and wave amplitudes a two-wave bearing, unliKe other bearings, can exhibit a sub-synchronous whirl movement at both low and high speeds, but can run extremely stable and without whirl at intermediate speeds. Moreover, in these cases, the whirl frequencies are close to a quarter of the synchronous speed. The three-wave bearing can exhibit sub-synchronous whirl motion only after a specific threshold when the speed increases and the whirl frequencies are close to half of the synchronous speed.

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

PubMed

Shukla, P K; Eliasson, B

2007-08-31

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

Planning for coordinated space and ground-based ionospheric modification experiments

NASA Technical Reports Server (NTRS)

Lee, M. C.; Burke, William J.; Carlson, Herbert C.; Heckscher, John L.; Kossey, Paul A.; Weber, E. J.; Kuo, S. P.

1990-01-01

The planning and conduction of coordinated space and ground-based ionospheric modification experiments are discussed. The purpose of these experiments is to discuss: (1) the nonlinear VLF wave interaction with the ionospheric plasmas; and (2) the nonlinear propagation of VLF waves in the HF-modified ionosphere. It is expected that the HF-induced ionospheric density striations can render the nonlinear mode conversion of VLF waved into lower hybrid waves. Lower hybrid waves can also be excited parametrically by the VLF waves in the absence of the density striations if the VLF waves are intense enough. Laboratory experiments are planned for crosschecking the results obtained from the field experiments.

Excitations of breathers and rogue wave in the Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Qi, Jian-Wen; Duan, Liang; Yang, Zhan-Ying; Yang, Wen-Li

2018-01-01

We study the excitations of breathers and rogue wave in a classical Heisenberg spin chain with twist interaction, which is governed by a fourth-order integrable nonlinear Schrödinger equation. The dynamics of these waves have been extracted from an exact solution. In particular, the corresponding existence conditions based on the parameters of perturbation wave number K, magnon number N, background wave vector ks and amplitude c are presented explicitly. Furthermore, the characteristics of magnetic moment distribution corresponding to these nonlinear waves are also investigated in detail. Finally, we discussed the state transition of three types nonlinear localized waves under the different excitation conditions.

NONLINEAR OPTICAL EFFECTS AND FIBER OPTICS: Theory of four-wave mixing in photorefractive media when the response of a medium is nonlinear in respect of the modulation parameter

NASA Astrophysics Data System (ADS)

Zozulya, A. A.

1988-12-01

A theoretical model is constructed for four-wave mixing in a photorefractive crystal where a transmission grating is formed by the drift-diffusion nonlinearity mechanism in the absence of an external electrostatic field and the response of the medium is nonlinear in respect of the modulation parameter. A comparison is made with a model in which the response of the medium is linear in respect of the modulation parameter. Theoretical models of four-wave and two-wave mixing are also compared with experiments.

Optical wave turbulence and the condensation of light

NASA Astrophysics Data System (ADS)

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

2009-11-01

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

Nonlinear model of a rotating hub-beams structure: Equations of motion

NASA Astrophysics Data System (ADS)

Warminski, Jerzy

2018-01-01

Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.

Numerical analysis of two and three dimensional buoyancy driven water-exit of a circular cylinder

NASA Astrophysics Data System (ADS)

Moshari, Shahab; Nikseresht, Amir Hossein; Mehryar, Reza

2014-06-01

With the development of the technology of underwater moving bodies, the need for developing the knowledge of surface effect interaction of free surface and underwater moving bodies is increased. Hence, the two-phase flow is a subject which is interesting for many researchers all around the world. In this paper, the non-linear free surface deformations which occur during the water-exit of a circular cylinder due to its buoyancy are solved using finite volume discretization based code, and using Volume of Fluid (VOF) scheme for solving two phase flow. Dynamic mesh model is used to simulate dynamic motion of the cylinder. In addition, the effect of cylinder mass in presence of an external force is studied. Moreover, the oblique exit and entry of a circular cylinder with two exit angles is simulated. At last, water-exit of a circular cylinder in six degrees of freedom is simulated in 3D using parallel processing. The simulation errors of present work (using VOF method) for maximum velocity and height of a circular cylinder are less than the corresponding errors of level set method reported by previous researchers. Oblique exit shows interesting results; formation of waves caused by exit of the cylinder, wave motion in horizontal direction and the air trapped between the waves are observable. In 3D simulation the visualization of water motion on the top surface of the cylinder and the free surface breaking on the front and back faces of the 3D cylinder at the exit phase are observed which cannot be seen in 2D simulation. Comparing the results, 3D simulation shows better agreement with experimental data, specially in the maximum height position of the cylinder.

Contrast gain control in first- and second-order motion perception.

PubMed

Lu, Z L; Sperling, G

1996-12-01

A novel pedestal-plus-test paradigm is used to determine the nonlinear gain-control properties of the first-order (luminance) and the second-order (texture-contrast) motion systems, that is, how these systems' responses to motion stimuli are reduced by pedestals and other masking stimuli. Motion-direction thresholds were measured for test stimuli consisting of drifting luminance and texture-contrast-modulation stimuli superimposed on pedestals of various amplitudes. (A pedestal is a static sine-wave grating of the same type and same spatial frequency as the moving test grating.) It was found that first-order motion-direction thresholds are unaffected by small pedestals, but at pedestal contrasts above 1-2% (5-10 x pedestal threshold), motion thresholds increase proportionally to pedestal amplitude (a Weber law). For first-order stimuli, pedestal masking is specific to the spatial frequency of the test. On the other hand, motion-direction thresholds for texture-contrast stimuli are independent of pedestal amplitude (no gain control whatever) throughout the accessible pedestal amplitude range (from 0 to 40%). However, when baseline carrier contrast increases (with constant pedestal modulation amplitude), motion thresholds increase, showing that gain control in second-order motion is determined not by the modulator (as in first-order motion) but by the carrier. Note that baseline contrast of the carrier is inherently independent of spatial frequency of the modulator. The drastically different gain-control properties of the two motion systems and prior observations of motion masking and motion saturation are all encompassed in a functional theory. The stimulus inputs to both first- and second-order motion process are normalized by feedforward, shunting gain control. The different properties arise because the modulator is used to control the first-order gain and the carrier is used to control the second-order gain.

Kuznetsov-Ma waves train generation in a left-handed material

NASA Astrophysics Data System (ADS)

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

2015-03-01

We analyze the behavior of an electromagnetic wave which propagates in a left-handed material. Second-order dispersion and cubic-quintic nonlinearities are considered. This behavior of an electromagnetic wave is modeled by a nonlinear Schrödinger equation which is solved by collective coordinates theory in order to characterize the light pulse intensity profile. More so, a specific frequency range has been outlined where electromagnetic wave behavior will be investigated. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton. When the quintic nonlinearity comes into play, it provokes strong and long internal perturbations which lead to Benjamin-Feir instability. This phenomenon, also called modulational instability, induces appearance of a Kuznetsov-Ma waves train. We numerically verify the validity of Kuznetsov-Ma theory by presenting physical conditions which lead to Kuznetsov-Ma waves train generation. Thereafter, some properties of such waves train are also verified.

Experimental Measurement of the Nonlinear Interaction between Counterpropagating Alfv'en Waves in the LaPD

NASA Astrophysics Data System (ADS)

Schroeder, J. W. R.; Drake, D. J.; Howes, G. G.; Skiff, F.; Kletzing, C. A.; Carter, T. A.; Dorfman, S.; Auerbach, D.

2012-10-01

Turbulence plays an important role in the transport of mass and energy in many space and astrophysical plasmas ranging from galaxy clusters to Earth's magnetosphere. One active topic of research is the application of idealized Alfv'enic turbulence models to plasma conditions relevant to space and astrophysical plasmas. Alfv'enic turbulence models based on incompressible magnetohydrodynamics (MHD) contain a nonlinear interaction that drives the cascade of energy to smaller scales. We describe experiments at the Large Plasma Device (LaPD) that focus on the interaction of an Alfv'en wave traveling parallel to the mean magnetic field with a counterpropagating Alfv'en wave. Theory predicts the nonlinear interaction of the two primary waves will produce a secondary daughter Alfv'en wave. In this study, we present the first experimental identification of the daughter wave generated by nonlinear interactions between the primary Alfv'en waves.

Effect of Forcing Function on Nonlinear Acoustic Standing Waves

NASA Technical Reports Server (NTRS)

Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce

2003-01-01

Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.

Linear and Nonlinear Coupling of Electrostatic Drift and Acoustic Perturbations in a Nonuniform Bi-Ion Plasma with Non-Maxwellian Electrons

NASA Astrophysics Data System (ADS)

Ali, Gul-e.; Ahmad, Ali; Masood, W.; Mirza, Arshad M.

2017-12-01

Linear and nonlinear coupling of drift and ion acoustic waves are studied in a nonuniform magnetized plasma comprising of Oxygen and Hydrogen ions with nonthermal distribution of electrons. It has been observed that different ratios of ion number densities and kappa and Cairns distributed electrons significantly modify the linear dispersion characteristics of coupled drift-ion acoustic waves. In the nonlinear regime, KdV (for pure drift waves) and KP (for coupled drift-ion acoustic waves) like equations have been derived to study the nonlinear evolution of drift solitary waves in one and two dimensions. The dependence of drift solitary structures on different ratios of ion number densities and nonthermal distribution of electrons has also been explored in detail. It has been found that the ratio of the diamagnetic drift velocity to the velocity of the nonlinear structure determines the existence regimes for the drift solitary waves. The present investigation may be beneficial to understand the formation of solitons in the ionospheric F-region.

The role of nonlinear critical layers in boundary layer transition

NASA Technical Reports Server (NTRS)

Goldstein, M.E.

1995-01-01

Asymptotic methods are used to describe the nonlinear self-interaction between pairs of oblique instability modes that eventually develops when initially linear spatially growing instability waves evolve downstream in nominally two-dimensional laminar boundary layers. The first nonlinear reaction takes place locally within a so-called 'critical layer', with the flow outside this layer consisting of a locally parallel mean flow plus a pair of oblique instability waves - which may or may not be accompanied by an associated plane wave. The amplitudes of these waves, which are completely determined by nonlinear effects within the critical layer, satisfy either a single integro-differential equation or a pair of integro-differential equations with quadratic to quartic-type nonlinearities. The physical implications of these equations are discussed.

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.

Identification of aerodynamic models for maneuvering aircraft

NASA Technical Reports Server (NTRS)

Chin, Suei; Lan, C. Edward

1990-01-01

Due to the requirement of increased performance and maneuverability, the flight envelope of a modern fighter is frequently extended to the high angle-of-attack regime. Vehicles maneuvering in this regime are subjected to nonlinear aerodynamic loads. The nonlinearities are due mainly to three-dimensional separated flow and concentrated vortex flow that occur at large angles of attack. Accurate prediction of these nonlinear airloads is of great importance in the analysis of a vehicle's flight motion and in the design of its flight control system. A satisfactory evaluation of the performance envelope of the aircraft may require a large number of coupled computations, one for each change in initial conditions. To avoid the disadvantage of solving the coupled flow-field equations and aircraft's motion equations, an alternate approach is to use a mathematical modeling to describe the steady and unsteady aerodynamics for the aircraft equations of motion. Aerodynamic forces and moments acting on a rapidly maneuvering aircraft are, in general, nonlinear functions of motion variables, their time rate of change, and the history of maneuvering. A numerical method was developed to analyze the nonlinear and time-dependent aerodynamic response to establish the generalized indicial function in terms of motion variables and their time rates of change.

Lagrangian methods in nonlinear plasma wave interaction

NASA Technical Reports Server (NTRS)

Crawford, F. W.

1980-01-01

Analysis of nonlinear plasma wave interactions is usually very complicated, and simplifying mathematical approaches are highly desirable. The application of averaged-Lagrangian methods offers a considerable reduction in effort, with improved insight into synchronism and conservation (Manley-Rowe) relations. This chapter indicates how suitable Lagrangian densities have been defined, expanded, and manipulated to describe nonlinear wave-wave and wave-particle interactions in the microscopic, macroscopic and cold plasma models. Recently, further simplifications have been introduced by the use of techniques derived from Lie algebra. These and likely future developments are reviewed briefly.

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.

Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-09-01

Nonlinear two-dimensional Kadomtsev-Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech-tanh, sinh-cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.

Inverse four-wave-mixing and self-parametric amplification effect in optical fibre

PubMed Central

Turitsyn, Sergei K.; Bednyakova, Anastasia E.; Fedoruk, Mikhail P.; Papernyi, Serguei B.; Clements, Wallace R.L.

2015-01-01

An important group of nonlinear processes in optical fibre involves the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and self-action of the propagating optical field (self-phase modulation and modulation instability). Here, we present a new nonlinear self-action effect, self-parametric amplification (SPA), which manifests itself as optical spectrum narrowing in normal dispersion fibre, leading to very stable propagation with a distinctive spectral distribution. The narrowing results from an inverse four-wave mixing, resembling an effective parametric amplification of the central part of the spectrum by energy transfer from the spectral tails. SPA and the observed stable nonlinear spectral propagation with random temporal waveform can find applications in optical communications and high power fibre lasers with nonlinear intra-cavity dynamics. PMID:26345290

Nonlinear ultrasonic imaging with X wave

NASA Astrophysics Data System (ADS)

Du, Hongwei; Lu, Wei; Feng, Huanqing

2009-10-01

X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.

Wave-particle interaction in the Faraday waves.

PubMed

Francois, N; Xia, H; Punzmann, H; Shats, M

2015-10-01

Wave motion in disordered Faraday waves is analysed in terms of oscillons or quasi-particles. The motion of these oscillons is measured using particle tracking tools and it is compared with the motion of fluid particles on the water surface. Both the real floating particles and the oscillons, representing the collective fluid motion, show Brownian-type dispersion exhibiting ballistic and diffusive mean squared displacement at short and long times, respectively. While the floating particles motion has been previously explained in the context of two-dimensional turbulence driven by Faraday waves, no theoretical description exists for the random walk type motion of oscillons. It is found that the r.m.s velocity ⟨μ̃(osc)⟩(rms) of oscillons is directly related to the turbulent r.m.s. velocity ⟨μ̃⟩(rms) of the fluid particles in a broad range of vertical accelerations. The measured ⟨μ̃(osc)⟩(rms) accurately explains the broadening of the frequency spectra of the surface elevation observed in disordered Faraday waves. These results suggest that 2D turbulence is the driving force behind both the randomization of the oscillons motion and the resulting broadening of the wave frequency spectra. The coupling between wave motion and hydrodynamic turbulence demonstrated here offers new perspectives for predicting complex fluid transport from the knowledge of wave field spectra and vice versa.

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

NASA Astrophysics Data System (ADS)

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

2007-11-01

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

Amplification of nonlinear surface waves by wind

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

Leblanc, Stephane

2007-10-15

A weakly nonlinear analysis is conducted to study the evolution of slowly varying wavepackets with small but finite amplitudes, that evolve at the interface between air and water under the effect of wind. In the inviscid assumption, wave envelopes are governed by cubic nonlinear Schroedinger or Davey-Stewartson equations forced by a linear term corresponding to Miles' mechanism of wave generation. Under fair wind, it is shown that Stokes waves grow exponentially and that Benjamin-Feir instability becomes explosive.

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 extraordinary wave in dense plasma

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

Krasovitskiy, V. B., E-mail: krasovit@mail.ru; Turikov, V. A.

2013-10-15

Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. Themore » possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.« less

Nonlinear modulation of an extraordinary wave under the conditions of parametric decay

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

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

2012-06-15

A self-consistent set of Hamilton equations describing nonlinear saturation of the amplitude of oscillations excited under the conditions of parametric decay of an elliptically polarized extraordinary wave in cold plasma is solved analytically and numerically. It is shown that the exponential increase in the amplitude of the secondary wave excited at the half-frequency of the primary wave changes into a reverse process in which energy is returned to the primary wave and nonlinear oscillations propagating across the external magnetic field are generated. The system of 'slow' equations for the amplitudes, obtained by averaging the initial equations over the high-frequency period,more » is used to describe steady-state nonlinear oscillations in plasma.« less

An ansatz for solving nonlinear partial differential equations in mathematical physics.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd

2016-01-01

In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

Coupled rotor and fuselage equations of motion

NASA Technical Reports Server (NTRS)

Warmbrodt, W.

1979-01-01

The governing equations of motion of a helicopter rotor coupled to a rigid body fuselage are derived. A consistent formulation is used to derive nonlinear periodic coefficient equations of motion which are used to study coupled rotor/fuselage dynamics in forward flight. Rotor/fuselage coupling is documented and the importance of an ordering scheme in deriving nonlinear equations of motion is reviewed. The nature of the final equations and the use of multiblade coordinates are discussed.

Nonlinear dispersion effects in elastic plates: numerical modelling and validation

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Phase 1 Validation Testing and Simulation for the WEC-Sim Open Source Code

NASA Astrophysics Data System (ADS)

Ruehl, K.; Michelen, C.; Gunawan, B.; Bosma, B.; Simmons, A.; Lomonaco, P.

2015-12-01

WEC-Sim is an open source code to model wave energy converters performance in operational waves, developed by Sandia and NREL and funded by the US DOE. The code is a time-domain modeling tool developed in MATLAB/SIMULINK using the multibody dynamics solver SimMechanics, and solves the WEC's governing equations of motion using the Cummins time-domain impulse response formulation in 6 degrees of freedom. The WEC-Sim code has undergone verification through code-to-code comparisons; however validation of the code has been limited to publicly available experimental data sets. While these data sets provide preliminary code validation, the experimental tests were not explicitly designed for code validation, and as a result are limited in their ability to validate the full functionality of the WEC-Sim code. Therefore, dedicated physical model tests for WEC-Sim validation have been performed. This presentation provides an overview of the WEC-Sim validation experimental wave tank tests performed at the Oregon State University's Directional Wave Basin at Hinsdale Wave Research Laboratory. Phase 1 of experimental testing was focused on device characterization and completed in Fall 2015. Phase 2 is focused on WEC performance and scheduled for Winter 2015/2016. These experimental tests were designed explicitly to validate the performance of WEC-Sim code, and its new feature additions. Upon completion, the WEC-Sim validation data set will be made publicly available to the wave energy community. For the physical model test, a controllable model of a floating wave energy converter has been designed and constructed. The instrumentation includes state-of-the-art devices to measure pressure fields, motions in 6 DOF, multi-axial load cells, torque transducers, position transducers, and encoders. The model also incorporates a fully programmable Power-Take-Off system which can be used to generate or absorb wave energy. Numerical simulations of the experiments using WEC-Sim will be presented. These simulations highlight the code features included in the latest release of WEC-Sim (v1.2), including: wave directionality, nonlinear hydrostatics and hydrodynamics, user-defined wave elevation time-series, state space radiation, and WEC-Sim compatibility with BEMIO (open source AQWA/WAMI/NEMOH coefficient parser).

Origins of spectral broadening of incoherent waves: Catastrophic process of coherence degradation

NASA Astrophysics Data System (ADS)

Xu, G.; Garnier, J.; Rumpf, B.; Fusaro, A.; Suret, P.; Randoux, S.; Kudlinski, A.; Millot, G.; Picozzi, A.

2017-08-01

We revisit the mechanisms underlying the process of spectral broadening of incoherent optical waves propagating in nonlinear media on the basis of nonequilibrium thermodynamic considerations. A simple analysis reveals that a prerequisite for the existence of a significant spectral broadening of the waves is that the linear part of the energy (Hamiltonian) has different contributions of opposite signs. It turns out that, at variance with the expected soliton turbulence scenario, an increase of the amount of disorder (incoherence) in the system does not require the generation of a coherent soliton structure. We illustrate the idea by considering the propagation of two wave components in an optical fiber with opposite dispersion coefficients. A wave turbulence approach to the problem reveals that the increase of kinetic energy in one component is offset by the negative reduction in the other component, so that the waves exhibit, as a general rule, virtually unlimited spectral broadening. More precisely, a self-similar solution of the kinetic equations reveals that the spectra of the incoherent waves tend to relax toward a homogeneous distribution in the wake of a front that propagates in frequency space with a decelerating velocity. We discuss this catastrophic process of spectral broadening in the light of different important phenomena, in particular supercontinuum generation, soliton turbulence, wave condensation, and the runaway motion of mechanical systems composed of positive and negative masses.

Longitudinal nonlinear wave propagation through soft tissue.

PubMed

Valdez, M; Balachandran, B

2013-04-01

In this paper, wave propagation through soft tissue is investigated. A primary aim of this investigation is to gain a fundamental understanding of the influence of soft tissue nonlinear material properties on the propagation characteristics of stress waves generated by transient loadings. Here, for computational modeling purposes, the soft tissue is modeled as a nonlinear visco-hyperelastic material, the geometry is assumed to be one-dimensional rod geometry, and uniaxial propagation of longitudinal waves is considered. By using the linearized model, a basic understanding of the characteristics of wave propagation is developed through the dispersion relation and in terms of the propagation speed and attenuation. In addition, it is illustrated as to how the linear system can be used to predict brain tissue material parameters through the use of available experimental ultrasonic attenuation curves. Furthermore, frequency thresholds for wave propagation along internal structures, such as axons in the white matter of the brain, are obtained through the linear analysis. With the nonlinear material model, the authors analyze cases in which one of the ends of the rods is fixed and the other end is subjected to a loading. Two variants of the nonlinear model are analyzed and the associated predictions are compared with the predictions of the corresponding linear model. The numerical results illustrate that one of the imprints of the nonlinearity on the wave propagation phenomenon is the steepening of the wave front, leading to jump-like variations in the stress wave profiles. This phenomenon is a consequence of the dependence of the local wave speed on the local deformation of the material. As per the predictions of the nonlinear material model, compressive waves in the structure travel faster than tensile waves. Furthermore, it is found that wave pulses with large amplitudes and small elapsed times are attenuated over shorter spans. This feature is due to the elevated strain-rates introduced at the end of the structure where the load is applied. In addition, it is shown that when steep wave fronts are generated in the nonlinear viscoelastic material, energy dissipation is focused in those wave fronts implying deposition of energy in a highly localized region of the material. Novel mechanisms for brain tissue damage are proposed based on the results obtained. The first mechanism is related to the dissipation of energy at steep wave fronts, while the second one is related to the interaction of steep wave fronts with axons encountered on its way through the structure. Copyright © 2013 Elsevier Ltd. All rights reserved.

Bright, dark and W-shaped solitons with extended nonlinear Schrödinger's equation for odd and even higher-order terms

NASA Astrophysics Data System (ADS)

Bendahmane, Issam; Triki, Houria; Biswas, Anjan; Saleh Alshomrani, Ali; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj

2018-02-01

We present solitary wave solutions of an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms by using an ansatz method. The including high-order dispersion terms have significant physical applications in fiber optics, the Heisenberg spin chain, and ocean waves. Exact envelope solutions comprise bright, dark and W-shaped solitary waves, illustrating the potentially rich set of solitary wave solutions of the extended model. Furthermore, we investigate the properties of these solitary waves in nonlinear and dispersive media. Moreover, specific constraints on the system parameters for the existence of these structures are discussed exactly. The results show that the higher-order dispersion and nonlinear effects play a crucial role for the formation and properties of propagating waves.

Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas

NASA Technical Reports Server (NTRS)

Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.

1997-01-01

We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.

Nonlinear tunneling of bright and dark rogue waves in combined nonlinear Schrödinger and Maxwell-Bloch systems

NASA Astrophysics Data System (ADS)

Raju, Thokala Soloman; Pal, Ritu

2018-05-01

We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.

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.

Effects of orography on planetary scale flow

NASA Technical Reports Server (NTRS)

Smith, R. B.

1986-01-01

The earth's orography is composed of a wide variety of scales, each contributing to the spectrum of atmospheric motions. A well studied subject (originating with Charney and Eliassen) is the direct forcing of planetary scale waves by the planetary scale orography: primarily the Tibetan plateau and the Rockies. However, because of the non-linear terms in the equations of dynamic meteorology, even the smallest scales of mountain induced flow can contribute to the planetary scale if the amplitude of the small scale disturbance is sufficintly large. Two possible mechanisms for this are illustrated. First, preferentially located lee cyclones can force planetary waves by their meridional transport of heat and momentum (Hansen and Chen). Recent theories are helping to explain the phenomena of lee cyclogenesis (e.g., Smith, 1984, J.A.S.). Second, mesoscale mountain wave and severe downslope wind phenomena produce such a large local drag, that planetary scale waves can be produced. The mechanism of upscale transfer is easy to understand in this case as the standing planetary scale wave has a wavelength which depends on the mean structure of the atmosphere, and not on the width of the mountain (just as in small scale lee wave theory). An example of a theoretical description of a severe wind flow with very large drag is shown.

Kinetic-scale fluctuations resolved with the Fast Plasma Investigation on NASA's Magnetospheric Multiscale mission.

NASA Astrophysics Data System (ADS)

Gershman, D. J.; Figueroa-Vinas, A.; Dorelli, J.; Goldstein, M. L.; Shuster, J. R.; Avanov, L. A.; Boardsen, S. A.; Stawarz, J. E.; Schwartz, S. J.; Schiff, C.; Lavraud, B.; Saito, Y.; Paterson, W. R.; Giles, B. L.; Pollock, C. J.; Strangeway, R. J.; Russell, C. T.; Torbert, R. B.; Moore, T. E.; Burch, J. L.

2017-12-01

Measurements from the Fast Plasma Investigation (FPI) on NASA's Magnetospheric Multiscale (MMS) mission have enabled unprecedented analyses of kinetic-scale plasma physics. FPI regularly provides estimates of current density and pressure gradients of sufficient accuracy to evaluate the relative contribution of terms in plasma equations of motion. In addition, high-resolution three-dimensional velocity distribution functions of both ions and electrons provide new insights into kinetic-scale processes. As an example, for a monochromatic kinetic Alfven wave (KAW) we find non-zero, but out-of-phase parallel current density and electric field fluctuations, providing direct confirmation of the conservative energy exchange between the wave field and particles. In addition, we use fluctuations in current density and magnetic field to calculate the perpendicular and parallel wavelengths of the KAW. Furthermore, examination of the electron velocity distribution inside the KAW reveals a population of electrons non-linearly trapped in the kinetic-scale magnetic mirror formed between successive wave peaks. These electrons not only contribute to the wave's parallel electric field but also account for over half of the density fluctuations within the wave, supplying an unexpected mechanism for maintaining quasi-neutrality in a KAW. Finally, we demonstrate that the employed wave vector determination technique is also applicable to broadband fluctuations found in Earth's turbulent magnetosheath.

Soliton Turbulence in Shallow Water Ocean Surface Waves

NASA Astrophysics Data System (ADS)

Costa, Andrea; Osborne, Alfred R.; Resio, Donald T.; Alessio, Silvia; Chrivı, Elisabetta; Saggese, Enrica; Bellomo, Katinka; Long, Chuck E.

2014-09-01

We analyze shallow water wind waves in Currituck Sound, North Carolina and experimentally confirm, for the first time, the presence of soliton turbulence in ocean waves. Soliton turbulence is an exotic form of nonlinear wave motion where low frequency energy may also be viewed as a dense soliton gas, described theoretically by the soliton limit of the Korteweg-deVries equation, a completely integrable soliton system: Hence the phrase "soliton turbulence" is synonymous with "integrable soliton turbulence." For periodic-quasiperiodic boundary conditions the ergodic solutions of Korteweg-deVries are exactly solvable by finite gap theory (FGT), the basis of our data analysis. We find that large amplitude measured wave trains near the energetic peak of a storm have low frequency power spectra that behave as ˜ω-1. We use the linear Fourier transform to estimate this power law from the power spectrum and to filter densely packed soliton wave trains from the data. We apply FGT to determine the soliton spectrum and find that the low frequency ˜ω-1 region is soliton dominated. The solitons have random FGT phases, a soliton random phase approximation, which supports our interpretation of the data as soliton turbulence. From the probability density of the solitons we are able to demonstrate that the solitons are dense in time and highly non-Gaussian.

Active Control of Solar Array Dynamics During Spacecraft Maneuvers

NASA Technical Reports Server (NTRS)

Ross, Brant A.; Woo, Nelson; Kraft, Thomas G.; Blandino, Joseph R.

2016-01-01

Recent NASA mission plans require spacecraft to undergo potentially significant maneuvers (or dynamic loading events) with large solar arrays deployed. Therefore there is an increased need to understand and possibly control the nonlinear dynamics in the spacecraft system during such maneuvers. The development of a nonlinear controller is described. The utility of using a nonlinear controller to reduce forces and motion in a solar array wing during a loading event is demonstrated. The result is dramatic reductions in system forces and motion during a 10 second loading event. A motion curve derived from the simulation with the closed loop controller is used to obtain similar benefits with a simpler motion control approach.

Development of a non-linear simulation for generic hypersonic vehicles - ASUHS1

NASA Technical Reports Server (NTRS)

Salas, Juan; Lovell, T. Alan; Schmidt, David K.

1993-01-01

A nonlinear simulation is developed to model the longitudinal motion of a vehicle in hypersonic flight. The equations of motion pertinent to this study are presented. Analytic expressions for the aerodynamic forces acting on a hypersonic vehicle which were obtained from Newtonian Impact Theory are further developed. The control surface forces are further examined to incorporate vehicle elastic motion. The purpose is to establish feasible equations of motion which combine rigid body, elastic, and aeropropulsive dynamics for use in nonlinear simulations. The software package SIMULINK is used to implement the simulation. Also discussed are issues needing additional attention and potential problems associated with the implementation (with proposed solutions).

Improved Shear Wave Motion Detection Using Pulse-Inversion Harmonic Imaging with a Phased Array Transducer

PubMed Central

Song, Pengfei; Zhao, Heng; Urban, Matthew W.; Manduca, Armando; Pislaru, Sorin V.; Kinnick, Randall R.; Pislaru, Cristina; Greenleaf, James F.; Chen, Shigao

2013-01-01

Ultrasound tissue harmonic imaging is widely used to improve ultrasound B-mode imaging quality thanks to its effectiveness in suppressing imaging artifacts associated with ultrasound reverberation, phase aberration, and clutter noise. In ultrasound shear wave elastography (SWE), because the shear wave motion signal is extracted from the ultrasound signal, these noise sources can significantly deteriorate the shear wave motion tracking process and consequently result in noisy and biased shear wave motion detection. This situation is exacerbated in in vivo SWE applications such as heart, liver, and kidney. This paper, therefore, investigated the possibility of implementing harmonic imaging, specifically pulse-inversion harmonic imaging, in shear wave tracking, with the hypothesis that harmonic imaging can improve shear wave motion detection based on the same principles that apply to general harmonic B-mode imaging. We first designed an experiment with a gelatin phantom covered by an excised piece of pork belly and show that harmonic imaging can significantly improve shear wave motion detection by producing less underestimated shear wave motion and more consistent shear wave speed measurements than fundamental imaging. Then, a transthoracic heart experiment on a freshly sacrificed pig showed that harmonic imaging could robustly track the shear wave motion and give consistent shear wave speed measurements while fundamental imaging could not. Finally, an in vivo transthoracic study of seven healthy volunteers showed that the proposed harmonic imaging tracking sequence could provide consistent estimates of the left ventricular myocardium stiffness in end-diastole with a general success rate of 80% and a success rate of 93.3% when excluding the subject with Body Mass Index (BMI) higher than 25. These promising results indicate that pulse-inversion harmonic imaging can significantly improve shear wave motion tracking and thus potentially facilitate more robust assessment of tissue elasticity by SWE. PMID:24021638

Planning for coordinated space and ground-based ionospheric modification experiments

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

Lee, M.C.

1990-10-01

The planning and conducting of coordinated space and ground-based ionospheric modification experiments are discussed. The purpose of these experiments is to investigate (1) the nonlinear VLF wave interaction with the ionospheric plasmas, and (2) the nonlinear propagation of VLF waves in the HF-modified ionosphere. It is expected that the HY-induced ionospheric density striations can render the nonlinear mode conversion of VLF waves into lower hybrid waves. Lower hybrid waves can also be excited parametrically by the VLF waves in the absence of the density striations if the VLF waves are intense enough. Laboratory experiments are planned for crosschecking the resultsmore » obtained from the field experiments.« less

Orbital stability of solitary waves for generalized Boussinesq equation with two nonlinear terms

NASA Astrophysics Data System (ADS)

Zhang, Weiguo; Li, Xiang; Li, Shaowei; Chen, Xu

2018-06-01

This paper investigates the orbital stability and instability of solitary waves for the generalized Boussinesq equation with two nonlinear terms. Firstly, according to the theory of Grillakis-Shatah-Strauss orbital stability, we present the general results to judge orbital stability of the solitary waves. Further, we deduce the explicit expression of discrimination d‧‧(c) to judge the stability of the two solitary waves, and give the stable wave speed interval. Moreover, we analyze the influence of the interaction between two nonlinear terms on the stable wave speed interval, and give the maximal stable range for the wave speed. Finally, some conclusions are given in this paper.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Parametric traveling wave amplifier with a low pump frequency

NASA Astrophysics Data System (ADS)

Marchenko, V. F.; Streltsov, A. M.; Zhmurov, S. E.

1983-01-01

Consideration is given to the model of a parametric traveling wave amplifier with a cubic nonlinearity in the form of an LF filter with MOS varactors. The operation of the amplifier is analyzed with allowance for wave damping and nonlinearity saturation, and the nonlinear mode of operation is examined. Experimental results are discussed, with emphasis on the amplitude-frequency response characteristics.

Properties of Nonlinear Dynamo Waves

NASA Technical Reports Server (NTRS)

Tobias, S. M.

1997-01-01

Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.

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

PubMed Central

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

2016-01-01

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

Nonlinear viscous higher harmonics generation due to incident and reflecting internal wave beam collision

NASA Astrophysics Data System (ADS)

Aksu, Anil A.

2017-09-01

In this paper, we have considered the non-linear effects arising due to the collision of incident and reflected internal wave beams. It has already been shown analytically [Tabaei et al., "Nonlinear effects in reflecting and colliding internal wave beams," J. Fluid Mech. 526, 217-243 (2005)] and numerically [Rodenborn et al., "Harmonic generation by reflecting internal waves," Phys. Fluids 23, 026601 (2011)] that the internal wave beam collision generates the higher harmonics and mean flow in a linear stratification. In this paper, similar to previous analytical work, small amplitude wave theory is employed; however, it is formulated from energetics perspective which allows considering internal wave beams as the product of slowly varying amplitude and fast complex exponential. As a result, the mean energy propagation equation for the second harmonic wave is obtained. Finally, a similar dependence on the angle of incidence is obtained for the non-linear energy transfer to the second harmonic with previous analyses. A possible physical mechanism for this angle dependence on the second harmonic generation is also discussed here. In addition to previous studies, the viscous effects are also included in the mean energy propagation equation for the incident, the reflecting, and the second harmonic waves. Moreover, even though the mean flow obtained here is only confined to the interaction region, it is also affected by viscosity via the decay in the incident and the reflecting internal wave beams. Furthermore, a framework for the non-linear harmonic generation in non-linear stratification is also proposed here.

Nonlinear Ion Harmonics in the Paul Trap with Added Octopole Field: Theoretical Characterization and New Insight into Nonlinear Resonance Effect.

PubMed

Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu

2016-02-01

The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.

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.

Self-action of propagating and standing Lamb waves in the plates exhibiting hysteretic nonlinearity: Nonlinear zero-group velocity modes.

PubMed

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

2017-09-01

An analytical theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous plate material on the Lamb waves near the S 1 zero group velocity point is developed. The theory predicts that the main effect of the hysteretic quadratic nonlinearity consists in the modification of the frequency and the induced absorption of the Lamb modes. The effects of the nonlinear self-action in the propagating and standing Lamb waves are expected to be, respectively, nearly twice and three times stronger than those in the plane propagating acoustic waves. The theory is restricted to the simplest hysteretic nonlinearity, which is influencing only one of the Lamé moduli of the materials. However, possible extensions of the theory to the cases of more general hysteretic nonlinearities are discussed as well as the perspectives of its experimental testing. Applications include nondestructive evaluation of micro-inhomogeneous and cracked plates. Copyright © 2017 Elsevier B.V. All rights reserved.

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.

Stress evaluation of metallic material under steady state based on nonlinear critically refracted longitudinal wave

NASA Astrophysics Data System (ADS)

Mao, Hanling; Zhang, Yuhua; Mao, Hanying; Li, Xinxin; Huang, Zhenfeng

2018-06-01

This paper presents the study of applying the nonlinear ultrasonic wave to evaluate the stress state of metallic materials under steady state. The pre-stress loading method is applied to guarantee components with steady stress. Three kinds of nonlinear ultrasonic experiments based on critically refracted longitudinal wave are conducted on components which the critically refracted longitudinal wave propagates along x, x1 and x2 direction. Experimental results indicate the second and third order relative nonlinear coefficients monotonically increase with stress, and the normalized relationship is consistent with simplified dislocation models, which indicates the experimental result is logical. The combined ultrasonic nonlinear parameter is proposed, and three stress evaluation models at x direction are established based on three ultrasonic nonlinear parameters, which the estimation error is below 5%. Then two stress detection models at x1 and x2 direction are built based on combined ultrasonic nonlinear parameter, the stress synthesis method is applied to calculate the magnitude and direction of principal stress. The results show the prediction error is within 5% and the angle deviation is within 1.5°. Therefore the nonlinear ultrasonic technique based on LCR wave could be applied to nondestructively evaluate the stress of metallic materials under steady state which the magnitude and direction are included.

Extensions of the Ferry shear wave model for active linear and nonlinear microrheology

PubMed Central

Mitran, Sorin M.; Forest, M. Gregory; Yao, Lingxing; Lindley, Brandon; Hill, David B.

2009-01-01

The classical oscillatory shear wave model of Ferry et al. [J. Polym. Sci. 2:593-611, (1947)] is extended for active linear and nonlinear microrheology. In the Ferry protocol, oscillation and attenuation lengths of the shear wave measured from strobe photographs determine storage and loss moduli at each frequency of plate oscillation. The microliter volumes typical in biology require modifications of experimental method and theory. Microbead tracking replaces strobe photographs. Reflection from the top boundary yields counterpropagating modes which are modeled here for linear and nonlinear viscoelastic constitutive laws. Furthermore, bulk imposed strain is easily controlled, and we explore the onset of normal stress generation and shear thinning using nonlinear viscoelastic models. For this paper, we present the theory, exact linear and nonlinear solutions where possible, and simulation tools more generally. We then illustrate errors in inverse characterization by application of the Ferry formulas, due to both suppression of wave reflection and nonlinearity, even if there were no experimental error. This shear wave method presents an active and nonlinear analog of the two-point microrheology of Crocker et al. [Phys. Rev. Lett. 85: 888 - 891 (2000)]. Nonlocal (spatially extended) deformations and stresses are propagated through a small volume sample, on wavelengths long relative to bead size. The setup is ideal for exploration of nonlinear threshold behavior. PMID:20011614

Rotational motions for teleseismic surface waves

NASA Astrophysics Data System (ADS)

Lin, Chin-Jen; Huang, Han-Pang; Pham, Nguyen Dinh; Liu, Chun-Chi; Chi, Wu-Cheng; Lee, William H. K.

2011-08-01

We report the findings for the first teleseismic six degree-of-freedom (6-DOF) measurements including three components of rotational motions recorded by a sensitive rotation-rate sensor (model R-1, made by eentec) and three components of translational motions recorded by a traditional seismometer (STS-2) at the NACB station in Taiwan. The consistent observations in waveforms of rotational motions and translational motions in sections of Rayleigh and Love waves are presented in reference to the analytical solution for these waves in a half space of Poisson solid. We show that additional information (e.g., Rayleigh wave phase velocity, shear wave velocity of the surface layer) might be exploited from six degree-of-freedom recordings of teleseismic events at only one station. We also find significant errors in the translational records of these teleseismic surface waves due to the sensitivity of inertial translation sensors (seismometers) to rotational motions. The result suggests that the effects of such errors need to be counted in surface wave inversions commonly used to derive earthquake source parameters and Earth structure.

Localized spatially nonlinear matter waves in atomic-molecular Bose-Einstein condensates with space-modulated nonlinearity

PubMed Central

Yao, Yu-Qin; Li, Ji; Han, Wei; Wang, Deng-Shan; Liu, Wu-Ming

2016-01-01

The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning. PMID:27403634

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

Lomdahl, P.S.; Kerr, W.C.

The original proposal by Professor A.S. Davydov of a soliton mechanism for localization and transport of energy along linear chain molecules provided the impetus for several research efforts which have explored the properties of these nonlinear entities in differing degrees of realism. The general conclusion from all of this work is that the nonlinear equations of motion which have been used to describe these systems have soliton-like solutions when they are solved in the deterministic limit. This limit corresponds to the absolute zero of temperature, because it ignores the influence of random thermal perturbations on the system. However, the questionsmore » of existence and importance of the Davydov soliton remain controversial when non-zero temperature effects are taken into account, because numerical simulations and theoretical calculations done by independent research groups have reached diametrically opposed conclusions. Our 1985 paper was the first to simulate thermal perturbations at biologically relevant temperature (300 K). Since publishing that paper, we have done simulations for collisions of phonon wave packets with Davydov solitons and have also taken into account the presence of multiple quanta of the high frequency oscillator field in the Davydov equations of motion. We present these results here. However, for the major question about the temperature effects on the Davydov soliton, our conclusions remain unchanged. 5 refs., 6 figs., 1 tab.« less

Quantum model of a hysteresis in a single-domain magnetically soft ferromagnetic

NASA Astrophysics Data System (ADS)

Ignatiev, V. K.; Lebedev, N. G.; Orlov, A. A.

2018-01-01

A quantum model of a single-domain magnetically soft ferromagnetic is proposed. The α-Fe crystal in a state of the saturation magnetization and a variable magnetic field is considered as a sample. The method of an effective Hamiltonian, including the operators of the Zeeman energy, the spin-orbit interaction and the interaction with the crystal field, is used in the model. An expansion of trial single-electron wave function in a series in small parameter of the spin-orbit interaction is suggested to account for the magnetic anisotropy. Within the framework of the Heisenberg representation, the nonlinear equations of motion for the magnetization and the orbital moment of single domain are obtained. Parameters of the modelling Hamiltonian are found from a comparison with experimental data on the magnetic anisotropy of iron. A phenomenological term of the magnetic friction is introduced into equation of the magnetization motion. Nonlinear equations are solved numerically by the Runge-Kutta method. A dependence of the single domain magnetization on magnetic field intensity has a characteristic form of a hysteresis loop which parameters are quantitatively coordinated with experimental data of researches of magnetic properties of nanoparticles of iron and iron oxide. The method is extended for modelling the magnetization dynamics of multi-domain ferromagnetic in the approximation of a strong crystal field.

Evidence for self-refraction in a convergence zone: NPE (Nonlinear progressive wave equation) model results

NASA Technical Reports Server (NTRS)

Mcdonald, B. Edward; Plante, Daniel R.

1989-01-01

The nonlinear progressive wave equation (NPE) model was developed by the Naval Ocean Research and Development Activity during 1982 to 1987 to study nonlinear effects in long range oceanic propagation of finite amplitude acoustic waves, including weak shocks. The NPE model was applied to propagation of a generic shock wave (initial condition provided by Sandia Division 1533) in a few illustrative environments. The following consequences of nonlinearity are seen by comparing linear and nonlinear NPE results: (1) a decrease in shock strength versus range (a well-known result of entropy increases at the shock front); (2) an increase in the convergence zone range; and (3) a vertical meandering of the energy path about the corresponding linear ray path. Items (2) and (3) are manifestations of self-refraction.

Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.

PubMed

Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G

2016-12-02

We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.

Modelization of highly nonlinear waves in coastal regions

NASA Astrophysics Data System (ADS)

Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre

2015-04-01

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