Analytical and numerical investigation of nonlinear internal gravity waves
Directory of Open Access Journals (Sweden)
S. P. Kshevetskii
2001-01-01
Full Text Available The propagation of long, weakly nonlinear internal waves in a stratified gas is studied. Hydrodynamic equations for an ideal fluid with the perfect gas law describe the atmospheric gas behaviour. If we neglect the term Ͽ dw/dt (product of the density and vertical acceleration, we come to a so-called quasistatic model, while we name the full hydro-dynamic model as a nonquasistatic one. Both quasistatic and nonquasistatic models are used for wave simulation and the models are compared among themselves. It is shown that a smooth classical solution of a nonlinear quasistatic problem does not exist for all t because a gradient catastrophe of non-linear internal waves occurs. To overcome this difficulty, we search for the solution of the quasistatic problem in terms of a generalised function theory as a limit of special regularised equations containing some additional dissipation term when the dissipation factor vanishes. It is shown that such solutions of the quasistatic problem qualitatively differ from solutions of a nonquasistatic nature. It is explained by the fact that in a nonquasistatic model the vertical acceleration term plays the role of a regularizator with respect to a quasistatic model, while the solution qualitatively depends on the regularizator used. The numerical models are compared with some analytical results. Within the framework of the analytical model, any internal wave is described as a system of wave modes; each wave mode interacts with others due to equation non-linearity. In the principal order of a perturbation theory, each wave mode is described by some equation of a KdV type. The analytical model reveals that, in a nonquasistatic model, an internal wave should disintegrate into solitons. The time of wave disintegration into solitons, the scales and amount of solitons generated are important characteristics of the non-linear process; they are found with the help of analytical and numerical investigations. Satisfactory
2015-09-30
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...interaction of surface and internal gravity waves in the South China Sea. We will seek answers to the following questions: 1) How does the wind-wave
Rotation-induced nonlinear wavepackets in internal waves
Energy Technology Data Exchange (ETDEWEB)
Whitfield, A. J., E-mail: ashley.whitfield.12@ucl.ac.uk; Johnson, E. R., E-mail: e.johnson@ucl.ac.uk [Department of Mathematics, University College London, London WC1E 6BT (United Kingdom)
2014-05-15
The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets. It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.
Nonlinear internal wave effects on acoustic propagation and scattering
McMahon, Kara Grace
Experimental observations and theoretical studies show that nonlinear internal waves occur widely in shallow water and cause acoustic propagation effects including ducting and mode coupling. Horizontal ducting results when acoustic modes travel between internal wave fronts that form waveguide boundaries. For small grazing angles between a mode trajectory and a front, an interference pattern may arise that is a horizontal Lloyd mirror pattern. An analytic description for this feature is provided, along with comparisons between results from the formulated model predicting a horizontal Lloyd mirror pattern and an adiabatic mode parabolic equation. Different waveguide models are considered, including boxcar and jump sound speed profiles where change in sound speed is assumed 12 m/s. Modifications to the model are made to include multiple and moving fronts. The focus of this analysis is on different front locations relative to the source, as well as on the number of fronts and their curvatures and speeds. Curvature influences mode incidence angles and thereby changes the interference patterns. For sources oriented so that the front appears concave, the areas with interference patterns shrink as curvature increases, while convexly oriented fronts cause patterns to expand. Curvature also influence how energy is distributed in the internal wave duct. For certain curvatures and duct widths energy forms a whispering gallery or becomes fully ducted. Angular constraints which indicate when to expect these phenomena are presented. Results are compared to propagation calculations and were found to agree in most examples. In some cases trailing internal waves are present in the duct and disturb horizontal propagation. This type of propagation is characterized as a scattering process as a result of broken internal wave fronts between the lead waves. Traditionally this is handled in regimes where adiabatic normal modes are valid using sound speed perturbations to describe energy
Internal wave energy flux from density perturbations in nonlinear stratifications
Lee, Frank M.; Allshouse, Michael R.; Swinney, Harry L.; Morrison, P. J.
2017-11-01
Tidal flow over the topography at the bottom of the ocean, whose density varies with depth, generates internal gravity waves that have a significant impact on the energy budget of the ocean. Thus, understanding the energy flux (J = p v) is important, but it is difficult to measure simultaneously the pressure and velocity perturbation fields, p and v . In a previous work, a Green's-function-based method was developed to calculate the instantaneous p, v , and thus J , given a density perturbation field for a constant buoyancy frequency N. Here we extend the previous analytic Green's function work to include nonuniform N profiles, namely the tanh-shaped and linear cases, because background density stratifications that occur in the ocean and some experiments are nonlinear. In addition, we present a finite-difference method for the general case where N has an arbitrary profile. Each method is validated against numerical simulations. The methods we present can be applied to measured density perturbation data by using our MATLAB graphical user interface EnergyFlux. PJM was supported by the U.S. Department of Energy Contract DE-FG05-80ET-53088. HLS and MRA were supported by ONR Grant No. N000141110701.
The Development of Nonlinear Surface and Internal Wave Groups.
1982-11-01
porn (1971a3 observed groups of large amplitude waves propagating in Massachusetts Bay that seemed to rom tidal interaction with a submarine sill...provides a plan view of the tank and a platform for pictures or movies (Fig. 2.2). For these experiments the measurements from 18 wave height sensors
Initial-value problem for the Gardner equation applied to nonlinear internal waves
Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim
2017-04-01
The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of
Lin, Ying-Tsong; McMahon, Kara G; Lynch, James F; Siegmann, William L
2013-01-01
The acoustic ducting effect by curved nonlinear gravity waves in shallow water is studied through idealized models in this paper. The internal wave ducts are three-dimensional, bounded vertically by the sea surface and bottom, and horizontally by aligned wavefronts. Both normal mode and parabolic equation methods are taken to analyze the ducted sound field. Two types of horizontal acoustic modes can be found in the curved internal wave duct. One is a whispering-gallery type formed by the sound energy trapped along the outer and concave boundary of the duct, and the other is a fully bouncing type due to continual reflections from boundaries in the duct. The ducting condition depends on both internal-wave and acoustic-source parameters, and a parametric study is conducted to derive a general pattern. The parabolic equation method provides full-field modeling of the sound field, so it includes other acoustic effects caused by internal waves, such as mode coupling/scattering and horizontal Lloyd's mirror interference. Two examples are provided to present internal wave ducts with constant curvature and meandering wavefronts.
Nonlinear internal wave at the interface of two-layer liquid due to a moving hydrofoil
Wang, Zhen; Wu, Changhong; Zou, Li; Wang, Qianxi; Ding, Qi
2017-07-01
This paper is concerned with the internal wave at the interface of two layers of liquids due to a hydrofoil in the lower layer liquid. The two-layer fluid is assumed moving parallel to the interface at different velocities. The stratified flow is modeled based on the incompressible potential flow theory, with the nonlinear boundary conditions at the interface. Boundary integral equations are formulated for the fully nonlinear interfacial wave generated by the hydrofoil. The numerical model results in a set of nonlinear algebra equations, which are solved using the quasi-Newton method. We show that the quasi-Newton method is more efficient than Newton's method, which is often used for solving these types of equations in the literature. The wave profiles were analyzed in terms of the location and thickness of the hydrofoil, the Froude number, and the ratio of the densities of the two fluids. The computations show that the interfacial wave amplitude showed a trend first of increase and then of decrease with the distance between the hydrofoil and the still interface.
Characterizing the nonlinear internal wave climate in the northeastern South China Sea
Directory of Open Access Journals (Sweden)
S. R. Ramp
2010-09-01
Full Text Available Four oceanographic moorings were deployed in the South China Sea from April 2005 to June 2006 along a transect extending from the Batanes Province, Philippines in the Luzon Strait to just north of Dong-Sha Island on the Chinese continental slope. The purpose of the array was to observe and track large-amplitude nonlinear internal waves (NIWs from generation to shoaling over the course of one full year. The basin and slope moorings observed velocity, temperature (T and salinity (S at 1–3 min intervals to observe the waves without aliasing. The Luzon mooring observed velocity at 15 min and T and S at 3 min, primarily to resolve the tidal forcing in the strait.
The observed waves travelled WNW towards 282–288 degrees with little variation. They were predominantly mode-1 waves with orbital velocities exceeding 100 cm s^{−1} and thermal displacements exceeding 100 m. Consistent with earlier authors, two types of waves were observed: the a-waves arrived diurnally and had a rank-ordered packet structure. The b-waves arrived in between, about an hour later each day similar to the pattern of the semi-diurnal tide. The b-waves were weaker than the a-waves, usually consisted of just one large wave, and were often absent in the deep basin, appearing as NIW only upon reaching the continental slope. The propagation speed of both types of waves was 323±31 cm s^{−1} in the deep basin and 222±18 cm s^{−1} over the continental slope. These speeds were 11–20% faster than the theoretical mode-1 wave speeds for the observed stratification, roughly consistent with the additional contribution from the nonlinear wave amplitude. The observed waves were clustered around the time of the spring tide at the presumed generation site in the Luzon Strait, and no waves were observed at neap tide. A remarkable feature was the distinct lack of waves during the winter months, December 2005 through February
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Observation of sound focusing and defocusing due to propagating nonlinear internal waves.
Luo, J; Badiey, M; Karjadi, E A; Katsnelson, B; Tskhoidze, A; Lynch, J F; Moum, J N
2008-09-01
Fluctuations of the low frequency sound field in the presence of an internal solitary wave packet during the Shallow Water '06 experiment are analyzed. Acoustic, environmental, and on-board ship radar image data were collected simultaneously before, during, and after a strong internal solitary wave packet passed through the acoustic track. Preliminary analysis of the acoustic wave temporal intensity fluctuations agrees with previously observed phenomena and the existing theory of the horizontal refraction mechanism, which causes focusing and defocusing when the acoustic track is nearly parallel to the front of the internal waves [J. Acoust. Soc. Am., 122(2), pp. 747-760 (2007)].
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
International Nuclear Information System (INIS)
Gao, Q. D.; Budny, R. V.
2015-01-01
By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (T i,e ) and toroidal velocity (V ϕ ) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition
2010-03-08
angles, J. Geophys. Res., 81(12), 1960- 1964, 1976. Kudryavtsev ,V., D. Akimov, J. Johannessen, and B. Chapron, On radar imaging of current...the generation of internal wave microwave surface signatures include Alpers (1985), Lyzenga and Bennett (1988), Thompson, 1988, and Kudryavtsev et...1999. Kudryavtsev , V., D. Akimov, J. Johannessen, and B. Chapron, On radar imaging of current features: 1. Model and comparison with observations
2015-09-30
by internal wave surface currents, a process that can be validated with both in-situ observations and synthetic aperature radar (SAR) imagery which...spectrum? How does this affect the detectability of ISWs in SAR imagery? 5) How does the seasonal variability of ISW currents impact the surface gravity...LZSNFS for 2014/02/01 00Z. It shows an intrusion of Kuroshio southwest off Taiwan as often obsevered during winter season. RESULTS A 1.5 year-long
Grigorev, Valery A; Katsnelson, Boris G; Lynch, James F
2016-11-01
Analyses of fluctuations of low frequency signals (300 ± 30 Hz) propagating in shallow water in the presence of nonlinear internal waves (NIWs) in the Shallow Water 2006 experiment are carried out. Signals were received by a vertical line array at a distance of ∼20 km from the source. A NIW train was moving totally inside of the acoustic track, and the angle between the wave front of the NIW and the acoustic track in the horizontal plane was ∼10°. It is shown that the spectrum of the sound intensity fluctuations contains peaks corresponding to the coupling of pairs of propagating modes. Analysis of spectra at different hydrophone depths, and also summed over depth allows the authors to estimate attenuation in the bottom sediments.
Katsnelson, Boris; Grigorev, Valery; Lynch, James F
2008-09-01
The fluctuations of intensity of broadband pulses in the midfrequency range (2-4.5 kHz) propagating in shallow water in the presence of intense internal waves moving approximately along the acoustic track are considered. These pulses were received by two separate single hydrophones placed at different distances from the source (approximately 4 and approximately 12 km) and in different directions. It is shown that the frequency spectra of the fluctuations for these hydrophones have different predominating frequencies corresponding with the directions of the acoustic track. Comparisons of experimental results with theoretical estimates demonstrate good consistency.
Periodic waves in nonlinear metamaterials
International Nuclear Information System (INIS)
Liu, Wen-Jun; Xiao, Jing-Hua; Yan, Jie-Yun; Tian, Bo
2012-01-01
Periodic waves are presented in this Letter. With symbolic computation, equations for monochromatic waves are studied, and analytic periodic waves are obtained. Factors affecting properties of periodic waves are analyzed. Nonlinear metamaterials, with the continuous distribution of the dielectric permittivity obtained, are different from the ones with the discrete distribution. -- Highlights: ► Equations for the monochromatic waves in transverse magnetic polarization have been studied. ► Analytic periodic waves for the equations have been obtained. ► Periodic waves are theoretically presented and studied in the nonlinear metamaterials.
Nonlinear waves and weak turbulence
Zakharov, V E
1997-01-01
This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method.
Directory of Open Access Journals (Sweden)
K. O'Driscoll
2017-09-01
Full Text Available Numerical solutions of the Korteweg–de Vries (KdV and extended Korteweg–de Vries (eKdV equations are used to model the transformation of a sinusoidal internal tide as it propagates across the continental shelf. The ocean is idealized as being a two-layer fluid, justified by the fact that most of the oceanic internal wave signal is contained in the gravest mode. The model accounts for nonlinear and dispersive effects but neglects friction, rotation and mean shear. The KdV model is run for a number of idealized stratifications and unique realistic topographies to study the role of the nonlinear and dispersive effects. In all model solutions the internal tide steepens forming a sharp front from which a packet of nonlinear solitary-like waves evolve. Comparisons between KdV and eKdV solutions are made. The model results for realistic topography and stratification are compared with observations made at moorings off Massachusetts in the Middle Atlantic Bight. Some features of the observations compare well with the model. The leading face of the internal tide steepens to form a shock-like front, while nonlinear high-frequency waves evolve shortly after the appearance of the jump. Although not rank ordered, the wave of maximum amplitude is always close to the jump. Some features of the observations are not found in the model. Nonlinear waves can be very widely spaced and persist over a tidal period.
Nonlinear effects in water waves
International Nuclear Information System (INIS)
Janssen, P.A.E.M.
1989-05-01
This set of lecture notes on nonlinear effects in water waves was written on the occasion of the first ICTP course on Ocean Waves and Tides held from 26 September until 28 October 1988 in Trieste, Italy. It presents a summary and unification of my knowledge on nonlinear effects of gravity waves on an incompressible fluid without vorticity. The starting point of the theory is the Hamiltonian for water waves. The evolution equations of both weakly nonlinear, shallow water and deep water gravity waves are derived by suitable approximation of the energy of the waves, resulting in the Korteweg-de Vries equation and the Zakharov equation, respectively. Next, interesting properties of the KdV equation (solitons) and the Zakharov equation (instability of a finite amplitude wave train) are discussed in some detail. Finally, the evolution of a homogeneous, random wave field due to resonant four wave processes is considered and the importance of this process for ocean wave prediction is pointed out. 38 refs, 21 figs
Nonlinear ambipolar diffusion waves
Energy Technology Data Exchange (ETDEWEB)
Mendonca, J.T.; Rowlands, G.
1985-07-01
The evolution of a plasma perturbation in a neutral gas is considered using the ambipolar diffusion approximation. A nonlinear diffusion equation is derived and, in the one-dimensional case, exact solutions of shock type are obtained.
Toberman, Matthew; Inall, Mark; Boyd, Tim; Dumount, Estelle; Griffiths, Colin
2017-07-01
The tidally modulated outflow of brackish water from a sea loch forms a thin surface layer that propagates into the coastal ocean as a buoyant gravity current, transporting nutrients and sediments, as well as fresh water, heat and momentum. The fresh intrusion both propagates into and generates a strongly stratified environment which supports trains of nonlinear internal waves (NLIWs). NLIWs are shown to propagate ahead of this buoyancy input in response to propagation of the outflow water into the stratified environment generated by the previous release as well as in the opposing direction after the reflection from steep bathymetry. Oblique aerial photographs were taken and photogrammetric rectification led to the identification of the buoyant intrusion and the subsequent generation of NLIWs. An autonomous underwater vehicle (AUV) was deployed on repeated reciprocal transects in order to make simultaneous CTD, ADCP, and microstructure shear measurements of the evolution of these phenomena in conjunction with conventional mooring measurements. AUV-based temperature and salinity signals of NLIWs of depression were observed together with increased turbulent kinetic energy dissipation rates of over 2 orders of magnitude within and in the wake of the NLIWs. Repeated measurements allow a unique opportunity to investigate the horizontal structure of these phenomena. Simple metric scaling demonstrates that these processes are likely to be feature of many fjordic systems located on the west coast of Scotland but may also play a key role in the assimilation of the outflow from many tidally dominated fjordic systems throughout the world.
New approaches to nonlinear waves
2016-01-01
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the app...
Nonlinear gravity-capillary water waves
Jiang, Lei
1997-11-01
Two-dimensional gravity-capillary water waves are analyzed using a fully-nonlinear Cauchy-integral method with spectral accuracy. Standing waves are generated in experiments by vertical oscillation and measured by a non-intrusive optical system along with a wave probe. Nonlinear resonance of standing waves with non-wetting contact line effects are discussed in detail. Amplitude- dependent wave frequency and damping in a glass rectangular tank suggest a new contact-line model. A new type of sideband resonance due to modulated forcing is discovered and explained by weakly-nonlinear analysis. This analytical solution is verified by our numerical simulations and physical experiments. New standing waveforms with dimpled or sharp crests are observed in experiments and computations. These new waveforms have strong symmetry breaking in time as a result of nonlinear harmonic interaction. With increasing wave steepness, steep standing waves experience period- tripling with three distinct forms: sharp crest, dimpled or flat crest, and round crest. Significant breaking occurs in the sharp-crest mode and the dimpled-crest mode. Using a complex-demodulation technique, I find that these breaking waves are related to the same 1:2 internal resonance (harmonic interaction) that causes the new steep waveforms. Novel approaches are used to estimate the (breaking and non-breaking) wave dissipation in steep and breaking standing waves. The breaking events (spray, air entrainment, and plunging) approximately double the wave dissipation. Weak capillarity significantly affects the limiting wave height and the form of standing waves, as demonstrated by both computations and small-scale Faraday-wave experiments. Capillary ripple generation on traveling waves is shown to be significant even at moderate wave steepness. The ubiquitous horizontal asymmetry of traveling waves is shown to be critical to capillary ripple generation. Two new asymmetric modes are identified and are shown to have an
Nonlinear waves in solar plasmas - a review
International Nuclear Information System (INIS)
Ballai, I
2006-01-01
Nonlinearity is a direct consequence of large scale dynamics in the solar plasmas. When nonlinear steepening of waves is balanced by dispersion, solitary waves are generated. In the vicinity of resonances, waves can steepen into nonlinear waves influencing the efficiency of energy deposition. Here we review recent theoretical breakthroughs that have lead to a greater understanding of many aspects of nonlinear waves arising in homogeneous and inhomogeneous solar plasmas
Oscillating nonlinear acoustic shock waves
DEFF Research Database (Denmark)
Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth
2016-01-01
We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... that at resonance a stationary state arise consisting of multiple oscillating shock waves. Off resonance driving leads to a nearly linear oscillating ground state but superimposed by bursts of a fast oscillating shock wave. Based on a travelling wave ansatz for the fluid velocity potential with an added 2'nd order...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...... in Fourier space and equipartition, the role of inhomogeneities and complex geometry and the importance of coupled systems....
Nonlinear waves and pattern dynamics
Pelinovsky, Efim; Mutabazi, Innocent
2018-01-01
This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physi...
Nonlinear positron acoustic solitary waves
International Nuclear Information System (INIS)
Tribeche, Mouloud; Aoutou, Kamel; Younsi, Smain; Amour, Rabia
2009-01-01
The problem of nonlinear positron acoustic solitary waves involving the dynamics of mobile cold positrons is addressed. A theoretical work is presented to show their existence and possible realization in a simple four-component plasma model. The results should be useful for the understanding of the localized structures that may occur in space and laboratory plasmas as new sources of cold positrons are now well developed.
Mathur, Manikandan; Peacock, Thomas
2010-03-19
Internal waves are a ubiquitous and significant means of momentum and energy transport in the oceans, atmosphere, and astrophysical bodies. Here, we show that internal wave propagation in nonuniform density stratifications, which are prevalent throughout nature, has a direct mathematical analogy with the classical optical problem of a Fabry-Perot multiple-beam light interferometer. We rigorously establish this correspondence, and furthermore provide the first experimental demonstration of an internal wave interferometer, based on the theory of resonant transmission of internal waves.
Nonlinear wave interactions of kinetic sound waves
Directory of Open Access Journals (Sweden)
G. Brodin
2015-08-01
Full Text Available We reconsider the nonlinear resonant interaction between three electrostatic waves in a magnetized plasma. The general coupling coefficients derived from kinetic theory are reduced here to the low-frequency limit. The main contribution to the coupling coefficient we find in this way agrees with the coefficient recently presented in Annales Geophysicae. But we also deduce another contribution which sometimes can be important, and which qualitatively agrees with that of an even more recent paper. We have thus demonstrated how results derived from fluid theory can be improved and generalized by means of kinetic theory. Possible extensions of our results are outlined.
Nonlinear Electron Waves in Strongly Magnetized Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans; Juul Rasmussen, Jens
1980-01-01
Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...
Nonlinear lattice waves in heterogeneous media
International Nuclear Information System (INIS)
Laptyeva, T V; Ivanchenko, M V; Flach, S
2014-01-01
We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry–André localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations. (topical review)
Nonlinear evolution of astrophysical Alfven waves
Spangler, S. R.
1984-01-01
Nonlinear Alfven waves were studied using the derivative nonlinear Schrodinger equation as a model. The evolution of initial conditions, such as envelope solitons, amplitude-modulated waves, and band-limited noise was investigated. The last two furnish models for naturally occurring Alfven waves in an astrophysical plasma. A collapse instability in which a wave packet becomes more intense and of smaller spatial extent was analyzed. It is argued that this instability leads to enhanced plasma heating. In studies in which the waves are amplified by an electron beam, the instability tends to modestly inhibit wave growth.
Linear superposition solutions to nonlinear wave equations
International Nuclear Information System (INIS)
Liu Yu
2012-01-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed
Waves in geophysical fluids tsunamis, rogue waves, internal waves and internal tides
Schneider, Wilhelm; Trulsen, Karsten
2006-01-01
Waves in Geophysical Fluids describes: the forecasting and risk evaluation of tsunamis by tectonic motion, land slides, explosions, run-up, and maps the tsunami sources in the world's oceans; stochastic Monte-Carlo simulations and focusing mechanisms for rogue waves, nonlinear wave models, breather formulas, and the kinematics of the Draupner wave; the full story about the discovery of the very large oceanic internal waves, how the waves are visible from above through the signatures on the sea surface, and how to compute them; observations of energetic internal tides and hot spots from several field campaigns in all parts of the world's oceans, with interpretation of spectra. An essential work for students, scientists and engineers working with the fundamental and applied aspects of ocean waves.
Wave Height Distribution for Nonlinear Swell Waves in Deep an Depth Limited Wave Conditions
DEFF Research Database (Denmark)
Nørgaard, Jørgen Harck; Andersen, Thomas Lykke; Knudsen, Jannie Elkær
2017-01-01
This paper presents initial results from an on-going study on the influence from wave nonlinearity on the wave height distribution in deep- and depth-limited nonlinear wave conditions. A fully nonlinear VOF model, IH-2VOF, is applied to model the propagation of irregular waves on a sloping sea bed...... from deep to shallow water, including the effects of wave breaking. Different wave nonlinearities are evaluated in the model and the effects of the wave nonlinearity, described by the so-called Ursell-number, on the wave height distributions along the sloping sea bed are evaluated. The widely used...
Nonlinear dynamics of resistive electrostatic drift waves
DEFF Research Database (Denmark)
Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.
1999-01-01
The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... polarity, i.e. a pair of electrostatic convective cells....
Control methods for localization of nonlinear waves.
Porubov, Alexey; Andrievsky, Boris
2017-03-06
A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).
Nonlinear interactions of counter-travelling waves
International Nuclear Information System (INIS)
Matsuuchi, Kazuo
1980-01-01
Nonlinear interactions between two waves travelling in opposite directions are investigated. When a nonlinear Klein-Gordon equation is adopted as a model equation, it is shown that such a wave system is governed by a simple set of equations for their complex amplitudes. Steady progressive waves governed by this set are investigated for various cases classified according to the signs of the coefficients. It is then found that one wave travelling in one direction appears from a certain point and the other travelling in the opposite direction has a constant amplitude from that point. This phenomenon may be regarded as a sort of reflection in spite of no rigid boundary. (author)
Evolution Of Nonlinear Waves in Compressing Plasma
Energy Technology Data Exchange (ETDEWEB)
P.F. Schmit, I.Y. Dodin, and N.J. Fisch
2011-05-27
Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size {Delta} during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches {Delta}. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
Experiments on nonlinear cross waves
Lichter, S.; Shemer, L.
1986-12-01
Surface water waves are generated by a paddle-type wavemaker operating at one end of a long tank. In addition to a progressing wave field at the forcing frequency, a subharmonic cross wave is generated in the neighborhood of the wavemaker. At lower forcing amplitudes there is a Benjamin-Feir instability of the progressing wave. At large forcing amplitudes, the fundamental decays rapidly along the channel. The cross wave dominates the near field and is strongly modulated on a slow time scale. During each modulation period a soliton propagates away from the wavemaker. The near-field standing cross wave undergoes a transformation into a progressing wave in the far field.
Nonlinear Electrostatic Wave Equations for Magnetized Plasmas
DEFF Research Database (Denmark)
Dysthe, K.B.; Mjølhus, E.; Pécseli, Hans
1984-01-01
The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed.......The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed....
Wave Height Distribution for Nonlinear Swell Waves in Deep an Depth-Limited Wave Conditions
DEFF Research Database (Denmark)
Nørgaard, Jørgen Harck; Andersen, Thomas Lykke; Knudsen, Jannie Elkær
2017-01-01
This paper presents initial results from an on-going study on the influence from wave nonlinearity on the wave height distribution in deep- and depth-limited nonlinear wave conditions. A fully nonlinear VOF model, IH-2VOF, is applied to model the propagation of irregular waves on a sloping sea bed...... Battjes & Groenendijk (2000) shallow water wave height distribution is concluded in the present study to significantly underpredict the low-exceedance wave heights in case of very nonlinear waves. A modification of the Battjess & Groenendijk (2000) distribution is suggested in order to include the effects...... from deep to shallow water, including the effects of wave breaking. Different wave nonlinearities are evaluated in the model and the effects of the wave nonlinearity, described by the so-called Ursell-number, on the wave height distributions along the sloping sea bed are evaluated. The widely used...
Toward An Internal Gravity Wave Spectrum In Global Ocean Models
2015-05-14
Toward an internal gravity wave spectrum in global ocean models Malte Müller1,2, Brian K. Arbic3, James G. Richman4, Jay F. Shriver4, Eric L. Kunze5...fields and tides are beginning to display realistic internal gravity wave spectra, especially as model resolution increases. This paper examines...able to simulate the internal gravity wave spectrum and the extent to which nonlinear internal wave-wave interactions contribute to the simulated
Variation principle for nonlinear wave propagation
International Nuclear Information System (INIS)
Watanabe, T.; Lee, Y.C.; Nishikawa, Kyoji; Hojo, H.; Yoshida, Y.
1976-01-01
Variation principle is derived which determines stationary nonlinear propagation of electrostatic waves in the self-consistent density profile. Example is given for lower-hybrid waves and the relation to the variation principle for the Lagrangian density of electromagnetic fluids is discussed
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
Solitary waves on nonlinear elastic rods. I
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1984-01-01
Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...
Berg, Robert F.
1996-01-01
Near the liquid-vapor critical point, density stratification supports internal gravity waves which affect 1-g viscosity measurements in the CVX (Critical Viscosity of Xenon) experiment. Two internal-wave modes were seen in the horizontal viscometer. The frequencies of the two modes had different temperature dependences: with decreasing temperature, the higher frequency increased monotonically from 0.7 to 2.8 Hz, but the lower frequency varied non-monotonically, with a maximum of 1.0 Hz at 20 mK above the critical temperature. The measured frequencies agree with independently calculated frequencies to within 15%.
Topological horseshoes in travelling waves of discretized nonlinear wave equations
International Nuclear Information System (INIS)
Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming
2014-01-01
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes
Nonlocal nonlinear coupling of kinetic sound waves
Directory of Open Access Journals (Sweden)
O. Lyubchyk
2014-11-01
Full Text Available We study three-wave resonant interactions among kinetic-scale oblique sound waves in the low-frequency range below the ion cyclotron frequency. The nonlinear eigenmode equation is derived in the framework of a two-fluid plasma model. Because of dispersive modifications at small wavelengths perpendicular to the background magnetic field, these waves become a decay-type mode. We found two decay channels, one into co-propagating product waves (forward decay, and another into counter-propagating product waves (reverse decay. All wavenumbers in the forward decay are similar and hence this decay is local in wavenumber space. On the contrary, the reverse decay generates waves with wavenumbers that are much larger than in the original pump waves and is therefore intrinsically nonlocal. In general, the reverse decay is significantly faster than the forward one, suggesting a nonlocal spectral transport induced by oblique sound waves. Even with low-amplitude sound waves the nonlinear interaction rate is larger than the collisionless dissipation rate. Possible applications regarding acoustic waves observed in the solar corona, solar wind, and topside ionosphere are briefly discussed.
Nonlinear transient wave propagation in homgeneous plasmas
International Nuclear Information System (INIS)
Thomsen, K.
1983-01-01
The transient phenomena associated with the propagation of nonlinear high frequency waves in homogeneous and isotropic or anisotropic plasma are considered. The basic equation for the different wave types included in this analysis are derived by using a two-fluid description of the plasma. Before discussing the importance of different nonlinearities the main results from a linear treatment are given. Generation of harmonic and local changes in the plasma frequency caused by ponderomotive forces are the nonlinear phenomena which are included in the nonlinear treatment. Generation of harmonics is only important for extraordinary waves and this case is discussed in detail. The density perturbations are described either as forced non-dispersive or as forced dispersive low frequency electrostatic waves. The differences between these two descriptions are first considered analytically then by a numerical analysis of the problem with the influence of the density variations on the propagation of the high frequency wave included. A one-dimensional description is used in all cases. (Auth.)
Nonlinear wave equation with intrinsic wave particle dualism
International Nuclear Information System (INIS)
Klein, J.J.
1976-01-01
A nonlinear wave equation derived from the sine-Gordon equation is shown to possess a variety of solutions, the most interesting of which is a solution that describes a wave packet travelling with velocity usub(e) modulating a carrier wave travelling with velocity usub(c). The envelop and carrier wave speeds agree precisely with the group and phase velocities found by de Broglie for matter waves. No spreading is exhibited by the soliton, so that it behaves exactly like a particle in classical mechanics. Moreover, the classically computed energy E of the disturbance turns out to be exactly equal to the frequency ω of the carrier wave, so that the Planck relation is automatically satisfied without postulating a particle-wave dualism. (author)
Jefrey, A
1964-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
Solitary waves on nonlinear elastic rods. II
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1987-01-01
In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results...
NONLINEAR MHD WAVES IN A PROMINENCE FOOT
Energy Technology Data Exchange (ETDEWEB)
Ofman, L. [Catholic University of America, Washington, DC 20064 (United States); Knizhnik, K.; Kucera, T. [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States); Schmieder, B. [LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris-Diderot, Sorbonne Paris Cit, 5 place Jules Janssen, F-92195 Meudon (France)
2015-11-10
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{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.
NONLINEAR MHD WAVES IN A PROMINENCE FOOT
International Nuclear Information System (INIS)
Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.
2015-01-01
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
2006-01-01
Internal waves are waves that travel within the interior of a fluid. The waves propagate at the interface or boundary between two layers with sharp density differences, such as temperature. They occur wherever strong tides or currents and stratification occur in the neighborhood of irregular topography. They can propagate for several hundred kilometers. The ASTER false-color VNIR image off the island of Tsushima in the Korea Strait shows the signatures of several internal wave packets, indicating a northern propagation direction. With its 14 spectral bands from the visible to the thermal infrared wavelength region, and its high spatial resolution of 15 to 90 meters (about 50 to 300 feet), ASTER images Earth to map and monitor the changing surface of our planet. ASTER is one of five Earth-observing instruments launched December 18, 1999, on NASA's Terra satellite. The instrument was built by Japan's Ministry of Economy, Trade and Industry. A joint U.S./Japan science team is responsible for validation and calibration of the instrument and the data products. The broad spectral coverage and high spectral resolution of ASTER provides scientists in numerous disciplines with critical information for surface mapping, and monitoring of dynamic conditions and temporal change. Example applications are: monitoring glacial advances and retreats; monitoring potentially active volcanoes; identifying crop stress; determining cloud morphology and physical properties; wetlands evaluation; thermal pollution monitoring; coral reef degradation; surface temperature mapping of soils and geology; and measuring surface heat balance. The U.S. science team is located at NASA's Jet Propulsion Laboratory, Pasadena, Calif. The Terra mission is part of NASA's Science Mission Directorate. Size: 60 by 120 kilometers (37.2 by 74.4 miles) Location: 34.6 degrees North latitude, 129.5 degrees East longitude Orientation: North at top Image Data: ASTER bands 3, 2, and 1 Original Data Resolution: 90
Nonlinear water waves: introduction and overview
Constantin, A.
2017-12-01
For more than two centuries progress in the study of water waves proved to be interdependent with innovative and deep developments in theoretical and experimental directions of investigation. In recent years, considerable progress has been achieved towards the understanding of waves of large amplitude. Within this setting one cannot rely on linear theory as nonlinearity becomes an essential feature. Various analytic methods have been developed and adapted to come to terms with the challenges encountered in settings where approximations (such as those provided by linear or weakly nonlinear theory) are ineffective. Without relying on simpler models, progress becomes contingent upon the discovery of structural properties, the exploitation of which requires a combination of creative ideas and state-of-the-art technical tools. The successful quest for structure often reveals unexpected patterns and confers aesthetic value on some of these studies. The topics covered in this issue are both multi-disciplinary and interdisciplinary: there is a strong interplay between mathematical analysis, numerical computation and experimental/field data, interacting with each other via mutual stimulation and feedback. This theme issue reflects some of the new important developments that were discussed during the programme `Nonlinear water waves' that took place at the Isaac Newton Institute for Mathematical Sciences (Cambridge, UK) from 31st July to 25th August 2017. A cross-section of the experts in the study of water waves who participated in the programme authored the collected papers. These papers illustrate the diversity, intensity and interconnectivity of the current research activity in this area. They offer new insight, present emerging theoretical methodologies and computational approaches, and describe sophisticated experimental results. This article is part of the theme issue 'Nonlinear water waves'.
Nonlinear wave forces on large ocean structures
Huang, Erick T.
1993-04-01
This study explores the significance of second-order wave excitations on a large pontoon and tests the feasibility of reducing a nonlinear free surface problem by perturbation expansions. A simulation model has been developed based on the perturbation expansion technique to estimate the wave forces. The model uses a versatile finite element procedure for the solution of the reduced linear boundary value problems. This procedure achieves a fair compromise between computation costs and physical details by using a combination of 2D and 3D elements. A simple hydraulic model test was conducted to observe the wave forces imposed on a rectangle box by Cnoidal waves in shallow water. The test measurements are consistent with the numerical predictions by the simulation model. This result shows favorable support to the perturbation approach for estimating the nonlinear wave forces on shallow draft vessels. However, more sophisticated model tests are required for a full justification. Both theoretical and experimental results show profound second-order forces that could substantially impact the design of ocean facilities.
Nonlinear waves in waveguides with stratification
Leble, Sergei B
1991-01-01
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Nonlinear waves in collisionless gravitating systems
Energy Technology Data Exchange (ETDEWEB)
Polyachenko, V.L.; Shukhman, I.G.
1979-09-01
Nonlinear equations are derived for the gravitational potential in collisionless systems modeling galaxies. Solutions in the form of solitary waves (solitons) are obtained and their stability is tested. Systems composed of both stars and gas are also discussed. The dependence of the critical wavelength on the perturbation amplitude is established for the classical Jeans problem (an infinite, homogeneous world model) and for its two- and one-dimensional analogs in the collisionless case.
Neutron optical tests of nonlinear wave mechanics
International Nuclear Information System (INIS)
Gahler, R.; Klein, A.G.; Zeilinger, A.
1979-01-01
The free-space propagation of matter waves is analysed with a view to placing an upper limit on the strength of possible non-linear terms in the Schrodinger equation. Such additional terms of the form psiF(/psi/ 2 ) were introduced by Bialynicki-Birula and Mycielski in order to counteract the spreading of wave packets, thereby allowing solutions which behave macroscopically like classical particles. For the particularly interesting case of a logarithmic nonlinearity, of the form F=-b ln/psi/ 2 it is found that the free-space propagation of slow neutrons places a very stringent upper limit on the magnitude of b. Precise measurements of Fresnel diffraction with slow neutrons do not give any evidence for nonlinear effects and allows the deduction of an upper limit for b -15 eV about 3 orders of magnitude smaller than the lower bound proposed by the above authors, making such nonlinearities extremely unlikely in the real world
Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
A method for generating highly nonlinear periodic waves in physical wave basins
DEFF Research Database (Denmark)
Zhang, Haiwen; Schäffer, Hemming A.; Bingham, Harry B.
2006-01-01
This abstract describes a new method for generating nonlinear waves of constant form in physical wave basins. The idea is to combine fully dispersive linear wavemaker theory with nonlinear shallow water wave generation theory; and use an exact nonlinear theory as the target. We refer to the method...... as an ad-hoc unified wave generation theory, since there is no rigorous analysis behind the idea which is simply justified by the improved results obtained for the practical generation of steady nonlinear waves....
Nonlinear multi-frequency electromagnetic wave propagation phenomena
Valovik, Dmitry V.
2017-11-01
A generalisation of the concept of monochromatic electromagnetic waves guided by layered waveguide structures filled with non-linear medium is introduced. This generalisation leads to guided waves of a novel type: a non-linear multi-frequency guided wave. The existence of such waves, in particular guide structures, is proven using the perturbation method. Numerical experiments are presented for non-linear 1- and 2-frequency guided waves in plane and cylindrical (with a circular cross-section) waveguides. Numerically, a novel non-linear effect is found for particular cases of non-linear multi-frequency guided waves. The suggested generalisation gives not only a unified approach to treat various electromagnetic wave propagation problems but also paves the way to study non-linear interactions of guided waves.
On the nonlinear shaping mechanism for gravity wave spectrum in the atmosphere
Directory of Open Access Journals (Sweden)
I. P. Chunchuzov
2009-11-01
Full Text Available The nonlinear mechanism of shaping of a high vertical wave number spectral tail in the field of a few discrete internal gravity waves in the atmosphere is studied in this paper. The effects of advection of fluid parcels by interacting gravity waves are taken strictly into account by calculating wave field in Lagrangian variables, and performing a variable transformation from Lagrangian to Eulerian frame. The vertical profiles and vertical wave number spectra of the Eulerian displacement field are obtained for both the case of resonant and non-resonant wave-wave interactions. The evolution of these spectra with growing parameter of nonlinearity of the internal wave field is studied and compared to that of a broad band spectrum of gravity waves with randomly independent amplitudes and phases. The calculated vertical wave number spectra of the vertical displacements or relative temperature fluctuations are found to be consistent with the observed spectra in the middle atmosphere.
Linear and Nonlinear Electrostatic Waves in Unmagnetized Dusty Plasmas
International Nuclear Information System (INIS)
Mamun, A. A.; Shukla, P. K.
2010-01-01
A rigorous and systematic theoretical study has been made of linear and nonlinear electrostatic waves propagating in unmagnetized dusty plasmas. The basic features of linear and nonlinear electrostatic waves (particularly, dust-ion-acoustic and dust-acoustic waves) for different space and laboratory dusty plasma conditions are described. The experimental observations of such linear and nonlinear features of dust-ion-acoustic and dust-acoustic waves are briefly discussed.
Copepod Behavior Response in an Internal Wave Apparatus
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.
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws......Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Integrability and Linear Stability of Nonlinear Waves
Degasperis, Antonio; Lombardo, Sara; Sommacal, Matteo
2018-03-01
It is well known that the linear stability of solutions of 1+1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N× N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N=3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.
Weakly nonlinear electron plasma waves in collisional plasmas
DEFF Research Database (Denmark)
Pecseli, H. L.; Rasmussen, J. Juul; Tagare, S. G.
1986-01-01
The nonlinear evolution of a high frequency plasma wave in a weakly magnetized, collisional plasma is considered. In addition to the ponderomotive-force-nonlinearity the nonlinearity due to the heating of the electrons is taken into account. A set of nonlinear equations including the effect...
International Conference on Applications in Nonlinear Dynamics
Longhini, Patrick; Palacios, Antonio
2017-01-01
This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
Internal Wave Generation by Convection
Lecoanet, Daniel Michael
In nature, it is not unusual to find stably stratified fluid adjacent to convectively unstable fluid. This can occur in the Earth's atmosphere, where the troposphere is convective and the stratosphere is stably stratified; in lakes, where surface solar heating can drive convection above stably stratified fresh water; in the oceans, where geothermal heating can drive convection near the ocean floor, but the water above is stably stratified due to salinity gradients; possible in the Earth's liquid core, where gradients in thermal conductivity and composition diffusivities maybe lead to different layers of stable or unstable liquid metal; and, in stars, as most stars contain at least one convective and at least one radiative (stably stratified) zone. Internal waves propagate in stably stratified fluids. The characterization of the internal waves generated by convection is an open problem in geophysical and astrophysical fluid dynamics. Internal waves can play a dynamically important role via nonlocal transport. Momentum transport by convectively excited internal waves is thought to generate the quasi-biennial oscillation of zonal wind in the equatorial stratosphere, an important physical phenomenon used to calibrate global climate models. Angular momentum transport by convectively excited internal waves may play a crucial role in setting the initial rotation rates of neutron stars. In the last year of life of a massive star, convectively excited internal waves may transport even energy to the surface layers to unbind them, launching a wind. In each of these cases, internal waves are able to transport some quantity--momentum, angular momentum, energy--across large, stable buoyancy gradients. Thus, internal waves represent an important, if unusual, transport mechanism. This thesis advances our understanding of internal wave generation by convection. Chapter 2 provides an underlying theoretical framework to study this problem. It describes a detailed calculation of the
Monsoon regulation of Lombok Strait internal waves
Matthews, J. P.; Aiki, H.; Masuda, S.; Awaji, T.; Ishikawa, Y.
2011-05-01
We use satellite imagery and numerical modeling to investigate the characteristics of Lombok Strait nonlinear internal waves in relation to the dominant monsoon seasonality. Two basic wave types are identified, the first of which represents the well-known arc-like internal wave (AIW) that radiates uniformly away from its generation region near the sill in regular sequences of ranked solitons. This component is best defined to the north of the strait and is the main focus of our paper. A second type (termed here the "irregular internal wave") manifests to the south in association with extensive throughflow plumes and appears in distorted, braided assemblages with orientations that are incompatible with uniform outward motion from the sill. Synthetic aperture radar (SAR) data show that the northward-propagating AIWs are often observed during the boreal winter monsoon, when the southward throughflow weakens. A potential cause of this seasonal behavior is revealed by advanced numerical modeling, which indicates that strong southward throughflows during the southeast monsoon greatly constrain the northward tidal influx, particularly near the surface, thereby inhibiting embryonic wave growth at the leading edge of the intrusion and producing comparatively weak internal wave release. This new mechanism operates alongside other possible seasonal influences on SAR internal wave detection relating, for example, to wind or stratification. Our findings suggest that long-term modifications to the Lombok Strait throughflow, due to evolution of the monsoon and/or the El Niño-Southern Oscillation, could retune the energy, composition, and directionality of internal wavefields radiated from the passage.
New travelling wave solutions for nonlinear stochastic evolution ...
Indian Academy of Sciences (India)
expansion method to look for travelling wave solutions of nonlinear partial differential equations. It is interesting to mention that, in this method the sign of the parameters can be used to judge the numbers and types of travelling wave solutions.
Manipulating acoustic wave reflection by a nonlinear elastic metasurface
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.
Four Wave Mixing using Intermodal Nonlinearities
DEFF Research Database (Denmark)
Rishøj, Lars Søgaard
99.8 % of the power from the fundamental mode to a specific HOM in the custom designed fiber. Furthermore, it is demonstrated that stable propagation in the considered fiber is possible, without deterioration from mode coupling. Finally, modulation instability and multiple FWM signal and idler lines......The nonlinear process of four-wave mixing (FWM) enables coupling of energy between wavelengths. This is useful for both optical amplification and wavelength conversion. A crucial prerequisite for the process is phase matching. This PhD project investigates how higher order modes (HOMs) in fibers...... can be used as an additional degree of freedom to fulfill this phase matching requirement. The design of a specialty few moded fiber is discussed. This fiber allows for FWM between a pump in the Ytterbium gain region with a signal at telecommunication wavelengths, hereby generating a new wavelength...
Solitary wave solutions of two-dimensional nonlinear Kadomtsev ...
Indian Academy of Sciences (India)
2017-09-13
Sep 13, 2017 ... Home; Journals; Pramana – Journal of Physics; Volume 89; Issue 3. Solitary wave solutions of ... 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 ...
Nonlinear Alfvén Waves in a Vlasov Plasma
DEFF Research Database (Denmark)
Bell, T.F.
1965-01-01
Stationary solutions to the nonlinear Vlasov—Boltzmann equations are considered which represent one-dimensional electromagnetic waves in a hot magnetoplasma. These solutions appear in arbitrary reference frames as circularly polarized, sinusoidal waves of unlimited amplitude, i.e., as nonlinear A...
Variational Boussinesq model for strongly nonlinear dispersive waves
Lawrence, C.; Adytia, D.; van Groesen, E.
2018-01-01
For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq model with optimized dispersion is derived and a simple Finite Element implementation is described. Improving a previous weakly nonlinear version, high waves over flat and varying bottom are shown to be
Thermal conductivity of nonlinear waves in disordered chains
Indian Academy of Sciences (India)
Abstract. We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity (). We ﬁnd ...
Nonlinear heat and particle transport due to collisional drift waves
Energy Technology Data Exchange (ETDEWEB)
Nishi-kawa, K.I.; Hatori, T.; Terashima, Y.
1977-03-01
The nonlinear evolution of unstable modes which govern transport processes in magnetically confined plasmas were investigated. A nonlinear theory of unstable collisional drift wave, and the consequent nonlinear transport were extended to include electron and ion temperature gradients. Thermal transport properties are discussed and basic equations are given.
Nonlinear waves in bipolar complex viscous astroclouds
Karmakar, P. K.; Haloi, A.
2017-05-01
A theoretical evolutionary model to analyze the dynamics of strongly nonlinear waves in inhomogeneous complex astrophysical viscous clouds on the gravito-electrostatic scales of space and time is procedurally set up. It compositionally consists of warm lighter electrons and ions (Boltzmanian); and cold massive bi-polar dust grains (inertial fluids) alongside vigorous neutral dynamics in quasi-neutral hydrodynamic equilibrium. Application of the Sagdeev pseudo-potential method reduces the inter-coupled structure equations into a pair of intermixed forced Korteweg-de Vries-Burgers (f-KdVB) equations. The force-terms are self-consistently sourced by inhomogeneous gravito-electrostatic interplay. A numerical illustrative shape-analysis based on judicious astronomical parametric platform shows the electrostatic waves evolving as compressive dispersive shock-like eigen-modes. A unique transition from quasi-monotonic to non-monotonic oscillatory compressive shock-like patterns is found to exist. In contrast, the self-gravitational and effective perturbations grow purely as non-monotonic compressive oscillatory shock-like structures with no such transitory features. It is seen that the referral frame velocity acts as amplitude-reducing agent (stabilizing source) for the electrostatic fluctuations solely. A comparison in the prognostic light of various earlier satellite-based observations and in-situ measurements is presented. The paper ends up with synoptic highlights on the main implications and non-trivial applications in the interstellar space and cosmic plasma environments leading to bounded structure formation.
Tsunamis - harbor oscillations induced by nonlinear transient long waves
Lepelletier, Thierry G. (Thierry Georges)
1980-01-01
The process of excitation of harbors and bays by transient nonlinear long waves is investigated theoretically and experimentally. In addition, nonlinear shallow water waves generated in a closed rectangular basin by the motion of the basin are also examined. Two numerical methods based on finite element techniques are used to solve the weakly nonlinear-dispersive-dissipative equations of motion and are applied to the basin excitation problem and the transient harbor oscillation problem, ...
Generation of dispersion in nondispersive nonlinear waves in thermal equilibrium.
Lee, Wonjung; Kovačič, Gregor; Cai, David
2013-02-26
In this work, we examine the important theoretical question of whether dispersion relations can arise from purely nonlinear interactions among waves that possess no linear dispersive characteristics. Using two prototypical examples of nondispersive waves, we demonstrate how nonlinear interactions can indeed give rise to effective dispersive-wave-like characteristics in thermal equilibrium. Physically, these example systems correspond to the strong nonlinear coupling limit in the theory of wave turbulence. We derive the form of the corresponding dispersion relation, which describes the effective dispersive structures, using the generalized Langevin equations obtained in the Zwanzig-Mori projection framework. We confirm the validity of this effective dispersion relation in our numerical study using the wavenumber-frequency spectral analysis. Our work may provide insight into an important connection between highly nonlinear turbulent wave systems, possibly with no discernible dispersive properties, and the dispersive nature of the corresponding renormalized waves.
Introduction to Wave Propagation in Nonlinear Fluids and Solids
Drumheller, Douglas S.
1998-02-01
Waves occur widely in nature and have innumerable commercial uses. Waves are responsible for the sound of speech, meteors igniting the atmosphere, radio and television broadcasting, medical diagnosis using ultrasound. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models for a variety of gases, liquids, and solids. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Students at an advanced undergraduate/graduate level will find this text a clear and comprehensive introduction to the study of nonlinear wave phenomena, and it will also be valuable as a professional reference in engineering and applied physics.
Nonlinear interaction of waves in an inhomogeneous plasma
International Nuclear Information System (INIS)
Istomin, Ya.N.
1988-01-01
Nonlinear wave processes in a weakly inhomogeneous plasma are considered. A quasilinear equation is derived which takes into account the effect of the waves on resonance particles, provided that the inhomogeneity appreciably affects the nature of the resonance interaction. Three-wave interaction is investigated under the same conditions. As an example, the nonlinear interaction in a relativistic plasma moving along a strong curvilinear magnetic field is considered
Agapitov, O. V.; Krasnoselskikh, V; Mozer, F. S.; Artemyev, A.V.; Volokitin, A.S.
2015-01-01
International audience; Huge numbers of different nonlinear structures (double layers, electron holes, nonlinear whistlers, etc., referred to as Time Domain Structures, TDS) have been observed by the electric field experiment on the Van Allen Probes. Some of them are associated with whistler waves. Such TDS often emerge on the forward edges of the whistler wave packets and form chains. The parametric decay of a whistler wave into a whistler wave propagating in the opposite direction and an el...
Acoustic field distribution of sawtooth wave with nonlinear SBE model
Energy Technology Data Exchange (ETDEWEB)
Liu, Xiaozhou, E-mail: xzliu@nju.edu.cn; Zhang, Lue; Wang, Xiangda; Gong, Xiufen [Key Laboratory of Modern Acoustics, Ministry of Education, Institute of Acoustics, Nanjing University, Nanjing 210093 (China)
2015-10-28
For precise prediction of the acoustic field distribution of extracorporeal shock wave lithotripsy with an ellipsoid transducer, the nonlinear spheroidal beam equations (SBE) are employed to model acoustic wave propagation in medium. To solve the SBE model with frequency domain algorithm, boundary conditions are obtained for monochromatic and sawtooth waves based on the phase compensation. In numerical analysis, the influence of sinusoidal wave and sawtooth wave on axial pressure distributions are investigated.
Nonlinear evolution of the modulational instability of whistler waves
DEFF Research Database (Denmark)
Karpman, V.I.; Hansen, F.R.; Huld, T.
1990-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves is investigated in two spatial dimensions by numerical simulations. The long time evolution of the modulational instability shows a quasirecurrent behavior with a slow spreading...... of the energy, originally confined to the lowest wave numbers, to larger and larger wave numbers resulting in an apparently chaotic or random wave field. © 1990 The American Physical Society...
Nonlinear physics of shear Alfvén waves
Zonca, Fulvio; Chen, Liu
2014-02-01
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These "nonlinear equilibria" or "phase-space zonal structures" dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
Nonlinear physics of shear Alfvén waves
International Nuclear Information System (INIS)
Zonca, Fulvio; Chen, Liu
2014-01-01
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These 'nonlinear equilibria' or 'phase-space zonal structures' dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results
Nonlinear Whistler Wave Physics in the Radiation Belts
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
Nonlinear density waves in a marginally stable gravitating disk
International Nuclear Information System (INIS)
Korchagin, V.I.
1986-01-01
The evolution of short nonlinear density waves in a disk at the stability limit is studied for arbitrary values of the radial wave number k/sub r/. For waves with wave numbers that do not lie at the minimum of the dispersion curve, the behavior of the amplitude is described by a nonlinear parabolic equation; however, stationary soliton solutions cannot exist in such a system since there is no dispersion spreading of a packet. For wave numbers lying at the minimum of the dispersion curve, soliton structures with determined amplitude are possible. In stable gravitating disks and in a disk at the stability limit, two physically different types of soliton can exist
The effect of nonlinear traveling waves on rotating machinery
Jauregui-Correa, Juan Carlos
2013-08-01
The effect of the housing stiffness on nonlinear traveling waves is presented in this work. It was found that the housing controls the synchronization of nonlinear elements and it allows nonlinear waves to travel through the structure. This phenomenon was observed in a gearbox with a soft housing, and the phenomenon was reproduced with a lump-mass dynamic model. The model included a pair of gears, the rolling bearings and the housing. The model considered all the nonlinear effects. Numerical and experimental results were analyzed with a time-frequency method using the Morlet wavelet function. A compound effect was observed when the nonlinear waves travel between the gears and the bearings: the waves increased the dynamic load amplitude and add another periodic load.
Superposed nonlinear waves in coherently coupled Bose–Einstein condensates
Energy Technology Data Exchange (ETDEWEB)
Babu Mareeswaran, R.; Kanna, T., E-mail: kanna_phy@bhc.edu.in
2016-09-23
We study the dynamics of superposed nonlinear waves in coherently coupled Gross–Pitaevskii (CCGP) equations with constant (autonomous system) and time varying (non-autonomous system) nonlinearity coefficients. By employing a linear transformation, the autonomous CCGP system is converted into two separate scalar nonlinear Schrödinger equations and we show that linear superposition of different nonlinear wave solutions of these scalar equations results into several kinds of nonlinear coherent structures namely, coexisting rogue wave-Ma breather, Akhmediev–Ma breathers, collision and bound states of Ma breathers and solitons. Next, the non-autonomous CCGP system is converted into an autonomous CCGP system with a similarity transformation. We show an interesting possibility of soliton compression and appearance of creeping solitons for kink-like and periodically modulated nonlinearity coefficient. - Highlights: • Coherently coupled Gross–Pitaevskii equations with constant and time-dependent nonlinearities are considered. • Novel superposed nonlinear structures are reported. • Breather collision and nontrivial twin-peak rogue wave are explored. • Co-existing breathers and rogue waves are observed. • Creeping solitons and compression mechanism, respectively for periodically modulated and kink-like nonlinearity are identified.
Traveling wave solutions of a highly nonlinear shallow water equation
Geyer, A.; Quirchmayr, Ronald
2018-01-01
Motivated by the question whether higher-order nonlinear model equations, which go beyond the Camassa-Holm regime of moderate amplitude waves, could point us to new types of waves profiles, we study the traveling wave solutions of a quasilinear evolution equation which models the propagation of
Nonlinear interaction of the surface waves at a plasma boundary
International Nuclear Information System (INIS)
Dolgopolov, V.V.; El-Naggar, I.A.; Hussein, A.M.; Khalil, Sh.M.
1976-01-01
Amplitudes of electromagnetic waves with combination frequencies, radiating from the plasma boundary due to nonlinear interaction of the surface waves, have been found. Previous papers on this subject did not take into account that the tangential components of the electric field of waves with combination frequencies were discontinuous at the plasma boundary. (Auth.)
Generation of Caustics and Rogue Waves from Nonlinear Instability.
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.
Nonlinear acoustic waves in micro-inhomogeneous solids
Nazarov, Veniamin
2014-01-01
Nonlinear Acoustic Waves in Micro-inhomogeneous Solids covers the broad and dynamic branch of nonlinear acoustics, presenting a wide variety of different phenomena from both experimental and theoretical perspectives. The introductory chapters, written in the style of graduate-level textbook, present a review of the main achievements of classic nonlinear acoustics of homogeneous media. This enables readers to gain insight into nonlinear wave processes in homogeneous and micro-inhomogeneous solids and compare it within the framework of the book. The subsequent eight chapters covering: Physical m
Energetics of borelike internal waves
Henyey, Frank S.; Hoering, Antje
1997-02-01
The net integrated energy flux into a train of internal waves is evaluated in a two-layer model. The nonzero value for this integral results from the difference in the stratification between the initial and final state, similar to the energy supply to a surface bore. We apply this expression to waves measured by Wesson and Gregg [1988] in the Strait of Gibraltar and to waves measured by Farmer and Smith [1980] in Knight Inlet. We find the energy supply to be important to the energetics, but the data do not allow a definitive test of the conjecture that the primary energy balance is between this supply and dissipation. We contrast our conjecture to the solitary-wave considerations of Bogucki and Garrett [1993].
Rogue and shock waves in nonlinear dispersive media
Resitori, Stefania; Baronio, Fabio
2016-01-01
This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists ...
Nonlinear Wave-Particle Interactions in Radiation Belt Physics
Summers, D.; Tang, R.; Omura, Y.; Miyashita, Y.
2010-12-01
Earth's radiation belts have undergone considerable theoretical and experimental investigation since their discovery in 1958 by James Van Allen and colleagues.Much of our understanding of wave-particle interactions in the radiation belts has been based on the linear theory of plasma waves and quasi-linear diffusion.There is recent evidence ,however,that fully nonlinear aspects of wave-particle interactions may play an essential role in radiation belt physics.This evidence is in the form of increasingly refined wave and particle data,and,in parallel,recently developed nonlinear wave growth theory supported by self-consistent particle simulations.We examine the nonlinear spatio-temporal evolution of whistler-mode chorus emissions in the Earth's inner magnetosphere.Chorus waves with rising frequency are generated at the magnetic equator,and propagate to higher latitudes.During propagation,nonlinear wave evolution occurs due to interaction with resonant electrons.From model equations we reproduce the time evolution of the chorus wave at the equator.By taking into account the adiabatic variation of the off-equatorial energetic particle distribution,we determine the resonant current.Then by solving general wave equations numerically we obtain the time evolution of the chorus wave frequency and amplitude along the static dipole magnetic field.Further,we incorporate the effects of nonlinear wave growth into the calculation of the Kennel-Petschek limit for the stably-trapped particle flux in a planetary magnetosphere.Using the model chorus equations we estimate nonlinear growth rates for a range of input parameters.By calculating the resulting total wave gain,we are able to estimate the self-limiting particle flux.We compare our new theoretical results for the limiting flux with particle observations at Earth and Saturn.
Nonlinear Trivelpiece--Gould waves: Recurrence, harmonic cascade, and sidebands
Energy Technology Data Exchange (ETDEWEB)
Cabral, J.A.C.; Lapao, L.M.; Mendonca, J.T. (Centro de Electrodinamica, Instituto Superior Tecnico, 1096 Lisboa Codex (Portugal))
1993-03-01
A theoretical and experimental study of Trivelpiece--Gould waves propagating in a magnetized plasma column is presented in this paper. In the experiments, these waves are excited by a radio frequency (rf) source, which also serves to create the plasma. Observation of nonlinear effects includes space and time recurrence effects, a wave spectrum containing a large number (up to 25) harmonics, and low-frequency sidebands. The theoretical model explains the recurrence effects as a consequence of multiple nonlinear interactions between the fundamental wave and its harmonics. A good agreement is found between theory and the experiments.
Wave-breaking and generic singularities of nonlinear hyperbolic equations
International Nuclear Information System (INIS)
Pomeau, Yves; Le Berre, Martine; Guyenne, Philippe; Grilli, Stephan
2008-01-01
Wave-breaking is studied analytically first and the results are compared with accurate numerical simulations of 3D wave-breaking. We focus on the time dependence of various quantities becoming singular at the onset of breaking. The power laws derived from general arguments and the singular behaviour of solutions of nonlinear hyperbolic differential equations are in excellent agreement with the numerical results. This shows the power of the analysis by methods using generic concepts of nonlinear science. (open problem)
Strongly nonlinear waves in a chain of Teflon beads
Daraio, C.; Nesterenko, V. F.; Herbold, E. B.; Jin, S.
2005-01-01
One-dimensional “sonic vacuum” type phononic crystals were assembled from a chain of polytetrafluoroethylene (PTFE,Teflon) spheres with different diameters in a Teflon holder. It was demonstrated that this polymer-based sonic vacuum, with exceptionally low elastic modulus of particles, supports propagation of strongly nonlinear solitary waves with a very low speed. These solitary waves can be described using the classical nonlinear Hertz law despite the viscoelastic nature of the polymer and ...
Optical rogue waves and soliton turbulence in nonlinear fibre optics
DEFF Research Database (Denmark)
Genty, G.; Dudley, J. M.; de Sterke, C. M.
2009-01-01
We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required.......We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required....
Nonlinear mechanism of tsunami wave generation by atmospheric disturbances
Pelinovsky, E.; Talipova, T.; Kurkin, A.; Kharif, C.
2001-01-01
The problem of tsunami wave generation by variable meteo-conditions is discussed. The simplified linear and nonlinear shallow water models are derived, and their analytical solutions for a basin of constant depth are discussed. The shallow-water model describes well the properties of the generated tsunami waves for all regimes, except the resonance case. The nonlinear-dispersive model based on the forced Korteweg-de Vries equation ...
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
arising in mathematical physics. Keywords. Exact travelling wave solutions; nonlinear physical models; Kudryashov method. PACS Nos 02.30.Jr; 02.70.Wz; 04.20.Jb. 1. Introduction. The study of nonlinear partial differential equations is an active area of research in applied mathematics, theoretical physics and engineering ...
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report ...
Nonlinear waves in electron–positron–ion plasmas including charge ...
Indian Academy of Sciences (India)
2017-01-04
Jan 4, 2017 ... Recently, it has been suggested that the nonlinear study of wave propagation can be helpful to under- stand nonlinear structures similar to the broadband electrostatic noise (BEN) observed in the Earth's mag- netosphere by numerous satellites (spacecrafts) such as. Geotail [8], Polar [9],Viking [10], FAST ...
New travelling wave solutions for nonlinear stochastic evolution ...
Indian Academy of Sciences (India)
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic ...
Defocusing regimes of nonlinear waves in media with negative dispersion
DEFF Research Database (Denmark)
Bergé, L.; Kuznetsov, E.A.; Juul Rasmussen, J.
1996-01-01
Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schrodinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called critical dimension cannot collapse in finite time...
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
Abstract. The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and ...
New travelling wave solutions for nonlinear stochastic evolution
Indian Academy of Sciences (India)
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic ...
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...
Periodic and solitary wave solutions of cubic–quintic nonlinear ...
Indian Academy of Sciences (India)
odic, double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena. Keywords. Variable coefficient reaction-diffusion equation; solitary wave solution; cubic–quintic nonlinearity. PACS No.
International Nuclear Information System (INIS)
Zhang Zaiyun; Liu Zhenhai; Miao Xiujin; Chen Yuezhong
2011-01-01
In this Letter, we investigate the perturbed nonlinear Schroedinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.
Symbolic computation of nonlinear wave interactions on MACSYMA
International Nuclear Information System (INIS)
Bers, A.; Kulp, J.L.; Karney, C.F.F.
1976-01-01
In this paper the use of a large symbolic computation system - MACSYMA - in determining approximate analytic expressions for the nonlinear coupling of waves in an anisotropic plasma is described. MACSYMA was used to implement the solutions of a fluid plasma model nonlinear partial differential equations by perturbation expansions and subsequent iterative analytic computations. By interacting with the details of the symbolic computation, the physical processes responsible for particular nonlinear wave interactions could be uncovered and appropriate approximations introduced so as to simplify the final analytic result. Details of the MACSYMA system and its use are discussed and illustrated. (Auth.)
Nonlinear waves in electron–positron–ion plasmas including charge ...
Indian Academy of Sciences (India)
2017-01-04
Jan 4, 2017 ... The introduction of the Poisson equation increased the Mach number required to generate the waveforms but the driving electric field E0 was reduced. The results are compared with satellite observations. Keywords. Nonlinear waves; low frequency; ion-acoustic waves. PACS Nos 52.35.Qz; 52.35.Fp; 52.35 ...
Efficient algorithms for non-linear four-wave interactions
Van Vledder, G.P.
2012-01-01
This paper addresses the on-going activities in the development of efficient methods for computing the non-linear four-wave interactions in operational discrete third-generation wind-wave models. It is generally assumed that these interactions play an important role in the evolution of wind
Transfer and scattering of wave packets by a nonlinear trap.
Li, Kai; Kevrekidis, P G; Malomed, Boris A; Frantzeskakis, D J
2011-11-01
In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by "nonlinear tweezers," as well as the scattering of coherent linear wave packets on the stationary localized nonlinearity. The use of a nonlinear trap for dragging allows one to pick up and transfer the relevant structures without grabbing surrounding "radiation." A stability border for the dragged modes is identified by means of analytical estimates and systematic simulations. In the framework of the scattering problem, the shares of trapped, reflected, and transmitted wave fields are found. Quasi-Airy stationary modes with a divergent norm, which may be dragged by a nonlinear trap moving at a constant acceleration, are briefly considered too.
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...... does not exist - one needs to use the nonlocal description, because the nonlocal response function does not converge towards a delta-function. Also, we use the nonlocal theory to show for the first time that the coupling to second harmonic is able to generate an X-shape in the fundamental field despite...
Exact and explicit solitary wave solutions to some nonlinear equations
International Nuclear Information System (INIS)
Jiefang Zhang
1996-01-01
Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative Φ 4 -model equation, the generalized Fisher equation, and the elastic-medium wave equation
Nonlinear periodic space-charge waves in plasma
International Nuclear Information System (INIS)
Kovalev, V. A.
2009-01-01
A solution is obtained in the form of coupled nonlinear periodic space-charge waves propagating in a magnetoactive plasma. The wave spectrum in the vicinity of the critical point, where the number of harmonics increases substantially, is found to fall with harmonic number as ∝ s -1/3 . Periodic space-charge waves are invoked to explain the zebra pattern in the radio emission from solar flares.
Nonlinear shallow water waves: A fractional order approach
Directory of Open Access Journals (Sweden)
Sarmad Arshad
2016-03-01
Full Text Available Nonlinear partial differential equations governing the obscure phenomena of shallow water waves are discussed in this article. Time fractional model is considered to understand the upcoming solutions on the basis of all historical states of the solution. A semi-analytic technique, Homotopy Perturbation Transform Method (HPTM is used in conjunction with a numerical technique to validate the approximate solutions. With the aid of graphical interpretation, the favorable wave parameters, to avoid wave breaking are estimated.
Nonlinear evolution of oblique whistler waves in radiation belts
Sharma, R. P.; Nandal, P.; Yadav, N.; Sharma, Swati
2017-02-01
Magnetic power spectrum and formation of coherent structures have been investigated in the present work applicable to Van Allen radiation belt. The nonlinear interaction of high frequency oblique whistler wave and low frequency magnetosonic wave has been investigated. Simulation was performed of the coupled equation of these two waves. The nonlinear interaction of these waves leads to the formation of the localized structures. These resulting localized structures are of complex nature. The associated magnetic power spectrum has also been studied. Dispersive nonlinear processes account for the high frequency part of the spectrum. The resulting magnetic power spectrum shows a scaling of k^{ - 4.5}. The energy transfer process from injection scales to smaller scales is explained by the results.
Modeling nonlinear acoustic waves in media with inhomogeneities in the coefficient of nonlinearity
Demi, L.; Verweij, M.D.; Van Dongen, K.W.A.
2010-01-01
The refraction and scattering of nonlinear acoustic waves play an important role in the realistic application of medical ultrasound. One cause of these effects is the tissue dependence of the nonlinear medium behavior. A method that is able to model those effects is essential for the design of
Nonlinear excitation of geodesic acoustic modes by drift waves
International Nuclear Information System (INIS)
Chakrabarti, N.; Singh, R.; Kaw, P. K.; Guzdar, P. N.
2007-01-01
In this paper, two mode-coupling analyses for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by drift waves are presented. The first approach is a coherent parametric process, which leads to a three-wave resonant interaction. This investigation allows for the drift waves and the GAMs to have comparable scales. The second approach uses the wave-kinetic equations for the drift waves, which then couples to the GAMs. This requires that the GAM scale length be large compared to the wave packet associated with the drift waves. The resonance conditions for these two cases lead to specific predictions of the radial wave number of the excited GAMs
Nonlinear Waves on Stochastic Support: Calcium Waves in Astrocyte Syncytia
Jung, P.; Cornell-Bell, A. H.
Astrocyte-signaling has been observed in cell cultures and brain slices in the form of Calcium waves. Their functional relevance for neuronal communication, brain functions and diseases is, however, not understood. In this paper, the propagation of intercellular calcium waves is modeled in terms of waves in excitable media on a stochastic support. We utilize a novel method to decompose the spatiotemporal patterns into space-time clusters (wave fragments). Based on this cluster decomposition, a statistical description of wave patterns is developed.
Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains
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.
Harmonic generation by internal waves in a thermohaline staircase with rotation
Wunsch, Scott
2017-11-01
Thermohaline staircases, generated by double-diffusive convection, are found in many regions of the ocean. Oceanic internal waves interact with these staircases. Recent results show that, in linear theory, internal waves with sufficiently long wavelengths are transmitted through the staircase, while short wavelengths may be reflected. However, nonlinear self-interaction of internal waves with the sharp density jumps within the staircase is expected to generate double-wavenumber harmonics of the incident waves. This effect removes energy from the incident waves, reducing the transmitted energy in some cases. Energy transferred to the harmonic waves may also impact the stability of the staircase. Here, weakly nonlinear theory is used to explore the implications of this nonlinear effect on the dynamics of internal waves in oceanic thermohaline staircases. Rotation is included, and variations with latitude are considered.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
International Nuclear Information System (INIS)
Tataronis, J. A.
2004-01-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfven continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named ''accumulation continuum'' and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory
Constrained non-linear waves for offshore wind turbine design
International Nuclear Information System (INIS)
Rainey, P J; Camp, T R
2007-01-01
Advancements have been made in the modelling of extreme wave loading in the offshore environment. We give an overview of wave models used at present, and their relative merits. We describe a method for embedding existing non-linear solutions for large, regular wave kinematics into linear, irregular seas. Although similar methods have been used before, the new technique is shown to offer advances in computational practicality, repeatability, and accuracy. NewWave theory has been used to constrain the linear simulation, allowing best possible fit with the large non-linear wave. GH Bladed was used to compare the effect of these models on a generic 5 MW turbine mounted on a tripod support structure
Propagation of nonlinear waves in bi-inductance nonlinear transmission lines
Kengne, Emmanuel; Lakhssassi, Ahmed
2014-10-01
We consider a one-dimensional modified complex Ginzburg-Landau equation, which governs the dynamics of matter waves propagating in a discrete bi-inductance nonlinear transmission line containing a finite number of cells. Employing an extended Jacobi elliptic functions expansion method, we present new exact analytical solutions which describe the propagation of periodic and solitary waves in the considered network.
International Nuclear Information System (INIS)
Romeo, Francesco; Rega, Giuseppe
2006-01-01
Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration
Energy Technology Data Exchange (ETDEWEB)
Romeo, Francesco [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: francesco.romeo@uniromal.it; Rega, Giuseppe [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: giuseppe.rega@uniromal.it
2006-02-01
Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration.
Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations
Zhang, Linghai
2017-10-01
The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 0 is a positive constant, if 0 mathematical neuroscience.
2015-09-30
1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Observation of the Near-seabed Velocity and Particles...turbulence interaction and/or the dynamic pressure perturbation induced by ISWs cause the resuspension and redistribution of sediment particles and...likely form the continuous sediment waves on the seafloor [Ma et al., 2008 and Reeder et al., 2011]. To our knowledge, there are no direct observations
Nonlinear Alfvén wave dynamics in plasmas
Sarkar, Anwesa; Chakrabarti, Nikhil; Schamel, Hans
2015-07-01
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
Energy Technology Data Exchange (ETDEWEB)
Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)
2015-03-31
This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.
Numerical modelling of nonlinear full-wave acoustic propagation
Energy Technology Data Exchange (ETDEWEB)
Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx [Grupo de Acústica y Vibraciones, Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Ciudad Universitaria, Apartado Postal 70-186, C.P. 04510, México D.F., México (Mexico)
2015-10-28
The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on a GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.
Exact traveling wave solutions for system of nonlinear evolution equations.
Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H
2016-01-01
In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.
Nonlinear acoustic wave equations with fractional loss operators.
Prieur, Fabrice; Holm, Sverre
2011-09-01
Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations. © 2011 Acoustical Society of America
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...
Averaging approximation to singularly perturbed nonlinear stochastic wave equations
Lv, Yan; Roberts, A. J.
2012-06-01
An averaging method is applied to derive effective approximation to a singularly perturbed nonlinear stochastic damped wave equation. Small parameter ν > 0 characterizes the singular perturbation, and να, 0 ⩽ α ⩽ 1/2, parametrizes the strength of the noise. Some scaling transformations and the martingale representation theorem yield the effective approximation, a stochastic nonlinear heat equation, for small ν in the sense of distribution.
Nonlinear coseismic infrasound waves in the upper atmosphere and ionosphere
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.
Ulysses Observations of Nonlinear Wave-wave Interactions in the ...
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... The Ulysses Unified Radio and Plasma Wave Experiment (URAP) has observed Langmuir, ion-acoustic and associated solar type III radio emissions in the interplanetary medium. Bursts of 50-300 Hz (in the spacecraft frame) electric field signals, corresponding to long-wavelength ion-acoustic waves are ...
International Nuclear Information System (INIS)
El Naggar, I.A.; Hussein, A.M.; Khalil, Sh.M.
1992-09-01
Electromagnetic waves radiated with combination frequencies from a semi-bounded plasma due to nonlinear interaction of radiation with surface wave (both of P-polarization) has been investigated. Waves are radiated both into vacuum and plasma are found to be P-polarized. We take into consideration the continuity at the plasma boundary of the tangential components of the electric field of the waves. The case of normal incidence of radiation and rarefield plasma layer is also studied. (author). 7 refs
Nonlinear fast sausage waves in homogeneous magnetic flux tubes
Mikhalyaev, Badma B.; Ruderman, Michael S.
2015-12-01
> We consider fast sausage waves in straight homogeneous magnetic tubes. The plasma motion is described by the ideal magnetohydrodynamic equations in the cold plasma approximation. We derive the nonlinear Schrödinger equation describing the nonlinear evolution of an envelope of a carrier wave. The coefficients of this equation are expressed in terms Bessel and modified Bessel functions. They are calculated numerically for various values of parameters. In particular, we show that the criterion for the onset of the modulational or Benjamin-Fair instability is satisfied. The implication of the obtained results for solar physics is discussed.
Nonlinearly driven oscillations in the gyrotron traveling-wave amplifier
International Nuclear Information System (INIS)
Chiu, C. C.; Pao, K. F.; Yan, Y. C.; Chu, K. R.; Barnett, L. R.; Luhmann, N. C. Jr.
2008-01-01
By delivering unprecedented power and gain, the gyrotron traveling-wave amplifier (gyro-TWT) offers great promise for advanced millimeter wave radars. However, the underlying physics of this complex nonlinear system is yet to be fully elucidated. Here, we report a new phenomenon in the form of nonlinearly driven oscillations. A zero-drive stable gyro-TWT is shown to be susceptible to a considerably reduced dynamic range at the band edge, followed by a sudden transition into driven oscillations and then a hysteresis effect. An analysis of this unexpected behavior and its physical interpretation are presented.
Stability of nonlinear ion sound waves and solitons in plasmas
International Nuclear Information System (INIS)
Infeld, E.; Rowlands, G.
1979-01-01
Large amplitude ion acoustic waves and solitons in two component plasmas are investigated for stability. The soliton solutions are found to be stable, while the nonlinear waves are always unstable, though for a significant range of parameters they are only unstable to fully three-dimensional perturbations. The results in one dimension are compared with those obtained from the Korteweg-de Vries equation, which gives stability for non linear waves and solitons. Agreement is surprisingly good for Mach numbers less than about 1.5 A three-dimensional generalization of the Korteweg-de Vries equation is considered but this leads to stability for all non linear solutions and hence is not a good model for nonlinear waves. It is, however, reasonable in the soliton limit. (author)
Internal wave shoaling in Mamala Bay, Oahu, Hawaii
Smith, K.; Merrifield, M. A.
2016-02-01
Internal waves shoaling in nearshore systems are an important factor in the internal wave energy budget. The Hawaiian Island Ridge is known as a site of strong internal tide generation, but the propagation of the internal tide energy into the island nearshore regions is less well studied. An array of three moorings with vertical thermistor chains was deployed in Mamala Bay, off the south shore of Oahu. The deepest mooring at 500 m, which also was equipped with a downward-looking ADCP, observed large breaking semidiurnal internal tides along the boundary. While these did not occur consistently, they were associated with significant mixing. The shallowest mooring, at 90 m, observed small but frequent internal bores along the bottom not linked with tidal phase. The middle mooring, at 300 m, displayed elevated energy in a high frequency band (6-40 cpd) close to the slope. This may be explained as the concentration of high frequency energy due to nonlinear interactions along the near-critical slope. While some of the nearshore internal wave observations can be attributed to internal waves from remote sources propagating in the onshore direction, a significant portion is due to locally generated internal waves propagating in the alongshore direction, leading to complex interactions on the south Oahu slope.
Design Wave Load Prediction by Non-Linear Strip Theories
DEFF Research Database (Denmark)
Jensen, Jørgen Juncher
1998-01-01
Some methods for predicting global stochastic wave load responses in ships are presented. The methods take into account the elastic behaviour of the ship and at least some of the non-linearities in the wave-induced loadings.Numerical rsults obtained for actual ships are reviewed with special...... emphasis on their usefulness in design procedures covering both extreme responses and fatigue damage predictions....
On the pressure field of nonlinear standing water waves
Schwartz, L. W.
1980-01-01
The pressure field produced by two dimensional nonlinear time and space periodic standing waves was calculated as a series expansion in the wave height. The high order series was summed by the use of Pade approximants. Calculations included the pressure variation at great depth, which was considered to be a likely cause of microseismic activity, and the pressure distribution on a vertical barrier or breakwater.
On the so called rogue waves in nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Y. Charles Li
2016-04-01
Full Text Available The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schrodinger equation (NLS provides a mechanism. A Peregrine wave solution can be obtained by taking the infinite spatial period limit to the homoclinic solutions. In this article, from the perspective of the phase space structure of these homoclinic orbits in the infinite dimensional phase space where the NLS defines a dynamical system, we examine the observability of these homoclinic orbits (and their approximations. Our conclusion is that these approximate homoclinic orbits are the most observable solutions, and they should correspond to the most common deep ocean waves rather than the rare rogue waves. We also discuss other possibilities for the mechanism of a rogue wave: rough dependence on initial data or finite time blow up.
Some nonlinear processes relevant to the beat wave accelerator
International Nuclear Information System (INIS)
Bingham, R.; Mori, W.B.
1985-03-01
The beat wave accelerator depends on the generation of a large amplitude plasma wave with a phase velocity close to the velocity of light c. The plasma wave (ωsub(p), ksub(p)) is generated by beating colinear laser beams (ω 1 , k 1 ) and (ω 2 ,k 2 ) with ωsub(p) = ω 1 -ω 2 , ksub(p) = k 1 -k 2 . Since the process involves both large amplitude transverse and longitudinal waves, various nonlinear instabilities associated with either wave may occur. The object of the article is to discuss some of the processes that may compete with the beat wave generation listing their threshold and growth rate. (author)
Parameter spaces for linear and nonlinear whistler-mode waves
International Nuclear Information System (INIS)
Summers, Danny; Tang, Rongxin; Omura, Yoshiharu; Lee, Dong-Hun
2013-01-01
We examine the growth of magnetospheric whistler-mode waves which comprises a linear growth phase followed by a nonlinear growth phase. We construct time-profiles for the wave amplitude that smoothly match at the transition between linear and nonlinear wave growth. This matching procedure can only take place over a limited “matching region” in (N h /N 0 ,A T )-space, where A T is the electron thermal anisotropy, N h is the hot (energetic) electron number density, and N 0 is the cold (background) electron number density. We construct this matching region and determine how the matching wave amplitude varies throughout the region. Further, we specify a boundary in (N h /N 0 ,A T )-space that separates a region where only linear chorus wave growth can occur from the region in which fully nonlinear chorus growth is possible. We expect that this boundary should prove of practical use in performing computationally expensive full-scale particle simulations, and in interpreting experimental wave data
Rouseff, Daniel; Tang, Dajun; Williams, Kevin L; Wang, Zhongkang; Moum, James N
2008-09-01
Preliminary results are presented from an analysis of mid-frequency acoustic transmission data collected at range 550 m during the Shallow Water 2006 Experiment. The acoustic data were collected on a vertical array immediately before, during, and after the passage of a nonlinear internal wave on 18 August, 2006. Using oceanographic data collected at a nearby location, a plane-wave model for the nonlinear internal wave's position as a function of time is developed. Experimental results show a new acoustic path is generated as the internal wave passes above the acoustic source.
Head-on collision of internal waves with trapped cores
Maderich, Vladimir; Jung, Kyung Tae; Terletska, Kateryna; Kim, Kyeong Ok
2017-12-01
The dynamics and energetics of a head-on collision of internal solitary waves (ISWs) with trapped cores propagating in a thin pycnocline were studied numerically within the framework of the Navier-Stokes equations for a stratified fluid. The peculiarity of this collision is that it involves trapped masses of a fluid. The interaction of ISWs differs for three classes of ISWs: (i) weakly non-linear waves without trapped cores, (ii) stable strongly non-linear waves with trapped cores, and (iii) shear unstable strongly non-linear waves. The wave phase shift of the colliding waves with equal amplitude grows as the amplitudes increase for colliding waves of classes (i) and (ii) and remains almost constant for those of class (iii). The excess of the maximum run-up amplitude, normalized by the amplitude of the waves, over the sum of the amplitudes of the equal colliding waves increases almost linearly with increasing amplitude of the interacting waves belonging to classes (i) and (ii); however, it decreases somewhat for those of class (iii). The colliding waves of class (ii) lose fluid trapped by the wave cores when amplitudes normalized by the thickness of the pycnocline are in the range of approximately between 1 and 1.75. The interacting stable waves of higher amplitude capture cores and carry trapped fluid in opposite directions with little mass loss. The collision of locally shear unstable waves of class (iii) is accompanied by the development of instability. The dependence of loss of energy on the wave amplitude is not monotonic. Initially, the energy loss due to the interaction increases as the wave amplitude increases. Then, the energy losses reach a maximum due to the loss of potential energy of the cores upon collision and then start to decrease. With further amplitude growth, collision is accompanied by the development of instability and an increase in the loss of energy. The collision process is modified for waves of different amplitudes because of the exchange
Waves in nonlinear pre-stressed materials
Schneider, Wilhelm; Saccomandi, G
2007-01-01
The papers in this book provide a unique state-of-the-art multidisciplinary overview on the subject of waves in pre-stressed materials through the interaction of several topics, ranging from the mathematical modelling of incremental material response (elastic and inelastic), to the analysis of the governing differential equations and boundary-value problems, and to computational methods for the solution to these problems, with particular reference to industrial, geophysical, and biomechanical applications. A complete view on the title subject is proposed, including: The basic and fundamental theoretical issues (mechanical modelling, exact solutions, asymptotic methods, numerical treatment); A unified introduction to wave propagation (small on large and large on large); A look toward classical (such as geophysics and the mechanics of rubber-like solids) and emergent (such as biomechanics) applications.
30th International Symposium on Shock Waves
Sadot, Oren; Igra, Ozer
2017-01-01
These proceedings collect the papers presented at the 30th International Symposium on Shock Waves (ISSW30), which was held in Tel-Aviv Israel from July 19 to July 24, 2015. The Symposium was organized by Ortra Ltd. The ISSW30 focused on the state of knowledge of the following areas: Nozzle Flow, Supersonic and Hypersonic Flows with Shocks, Supersonic Jets, Chemical Kinetics, Chemical Reacting Flows, Detonation, Combustion, Ignition, Shock Wave Reflection and Interaction, Shock Wave Interaction with Obstacles, Shock Wave Interaction with Porous Media, Shock Wave Interaction with Granular Media, Shock Wave Interaction with Dusty Media, Plasma, Magnetohyrdrodynamics, Re-entry to Earth Atmosphere, Shock Waves in Rarefied Gases, Shock Waves in Condensed Matter (Solids and Liquids), Shock Waves in Dense Gases, Shock Wave Focusing, Richtmyer-Meshkov Instability, Shock Boundary Layer Interaction, Multiphase Flow, Blast Waves, Facilities, Flow Visualization, and Numerical Methods. The two volumes serve as a reference ...
Travelling wave solutions to nonlinear physical models by means of ...
Indian Academy of Sciences (India)
This paper presents the ﬁrst integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established ﬁrst integrals, exact solutions are successfully ...
Blowing-up semilinear wave equation with exponential nonlinearity ...
Indian Academy of Sciences (India)
Indian Acad. Sci. (Math. Sci.) Vol. 123, No. 3, August 2013, pp. 365–372. c Indian Academy of Sciences. Blowing-up semilinear wave equation with exponential nonlinearity in two space dimensions. T SAANOUNI. Department of Mathematics, Faculty of Sciences of Tunis,. University of Tunis El Manar, El Manar 2092, Tunisia.
Periodic and solitary wave solutions of cubic–quintic nonlinear ...
Indian Academy of Sciences (India)
physics pp. 1253–1258. Periodic and solitary wave solutions of cubic–quintic nonlinear reaction-diffusion equation with variable convection coefficients. S B BHARDWAJ1,2,∗ ... 3Department of Mathematics, National Institute of Technology, Delhi 110 040, India. 4Department of .... 3.1 Fractional transform soliton solutions.
Weakly Nonlinear Waves with Slowly-Varying Speed | Chikwendu ...
African Journals Online (AJOL)
A previously developed method of generating uniformly valid, multiple- scale asymptotic expansions for the solution of weakly nonlinear one-dimensional wave equations is applied to problems with slowly-varying speed. The method is also shown to be applicable specifically to periodic initial data.
Nonlinear propagation of weakly relativistic ion-acoustic waves in ...
Indian Academy of Sciences (India)
2016-10-06
Oct 6, 2016 ... Abstract. This work presents theoretical and numerical discussion on the dynamics of ion-acoustic solitary wave for weakly relativistic regime in unmagnetized plasma comprising non-extensive electrons, Boltzmann positrons and relativistic ions. In order to analyse the nonlinear propagation phenomena, ...
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
Solitary wave solutions to nonlinear evolution equations in ...
Indian Academy of Sciences (India)
where u(x,y,t) is a travelling wave solution of nonlinear partial differential equation. We use the ... The ordinary differential equation (9) is then integrated as long as all terms contain derivatives, where we neglect ...... In addition to deterministic perturbation terms, stochastic perturbation terms will also be taken into account.
Travelling wave solutions to nonlinear physical models by means
Indian Academy of Sciences (India)
This paper presents the ﬁrst integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established ﬁrst integrals, exact solutions are successfully ...
An inhomogeneous wave equation and non-linear Diophantine approximation
DEFF Research Database (Denmark)
Beresnevich, V.; Dodson, M. M.; Kristensen, S.
2008-01-01
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...
Breathers and rogue waves: Demonstration with coupled nonlinear ...
Indian Academy of Sciences (India)
Abstract. Different types of breathers and rogue waves (RWs) are some of the important coher- ent structures which have been recently realized in several physical phenomena in hydrodynamics, nonlinear optics, Bose–Einstein condensates, etc. Mathematically, they have been deduced in non- linear Schrödinger (NLS) ...
Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations
Directory of Open Access Journals (Sweden)
Waheed A. Ahmed
2017-11-01
Full Text Available Approximate symmetries of a class of perturbed nonlinear wave equations are computed using two newly-developed methods. Invariant solutions associated with the approximate symmetries are constructed for both methods. Symmetries and solutions are compared through discussing the advantages and disadvantages of each method.
Nonlinear wave propagation studies, dispersion modeling, and signal parameters correction
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk
..: ..., 2004, 00. [European Workshop on FP6-AERONEWS /1./. Naples (IT), 13.09.2004-16.09.2004] EU Projects: European Commission(XE) 502927 - AERO-NEWS Institutional research plan: CEZ:AV0Z2076919 Keywords : nodestructive testing * nonlinear elastic wave spectroscopy Subject RIV: BI - Acoustics
Periodic and solitary wave solutions of cubic–quintic nonlinear ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 86; Issue 6. Periodic and solitary wave solutions of cubic–quintic nonlinear reaction-diffusion equation with variable convection coefficients. BHARDWAJ S B SINGH RAM MEHAR SHARMA KUSHAL MISHRA S C. Regular Volume 86 Issue 6 June 2016 pp 1253-1258 ...
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a -transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In...
Dispersive shock waves in nonlinear and atomic optics
Kamchatnov, Anatoly
2017-10-01
A brief review is given of dispersive shock waves observed in nonlinear optics and dynamics of Bose-Einstein condensates. The theory of dispersive shock waves is developed on the basis of Whitham modulation theory for various situations taking place in these two fields. In particular, the full classification is established for types of wave structures evolving from initial discontinuities for propagation of long light pulses in fibers with account of steepening effect and for dynamics of the polarization mode in two-component Bose-Einstein condensates.
Dispersive shock waves in nonlinear and atomic optics
Directory of Open Access Journals (Sweden)
Kamchatnov Anatoly
2017-01-01
Full Text Available A brief review is given of dispersive shock waves observed in nonlinear optics and dynamics of Bose-Einstein condensates. The theory of dispersive shock waves is developed on the basis of Whitham modulation theory for various situations taking place in these two fields. In particular, the full classification is established for types of wave structures evolving from initial discontinuities for propagation of long light pulses in fibers with account of steepening effect and for dynamics of the polarization mode in two-component Bose-Einstein condensates.
Nonlinear heat and particle transport due to collisional drift waves
Energy Technology Data Exchange (ETDEWEB)
Nishi-Kawa, K.I.; Hatori, T.; Terashima, Y.
1978-07-01
A nonlinear analysis of collisional drift instability is developed in a slab model based on the two fluid equations, where inhomogeneities in electron and ion temperatures and unperturbed current are included in addition to ion inertia, finite ion gyroradius, and viscosity. A systematic expansion is introduced by taking epsilon=vertical-barkappavertical-barl as a smallness parameter, where kappa is the degree of density gradient and l is the linear scale of the slab along the density gradient. The nonlinear development of the drift wave near marginal stability is studied on the basis of the model equations. A new feature, hard excitation, has been found, which is due to the effects of the nonlinear frequency shift and the electron temperature gradient. The saturation amplitude is calculated, and the expressions for wave-associated particle and heat fluxes are obtained. A comparison of the expressions with the experimental results of a stellerator device is also made.
Nonlinear Waves and Solitons on Contours and Closed Surfaces
Ludu, Andrei
2007-01-01
The present volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the manifolds considered. Emphasis on the relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given. The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics. Nonlinear Waves and Solitons on Contours and Closed Surfaces provides graduate students and researchers in mathematics, physics and engineering with a ready tut...
96 International Conference on Nonlinear Programming
1998-01-01
About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for second derivative approximations in trust region methods". 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "Primal-dual methods for nonconvex optimization" by...
NONLINEAR GRAVITATIONAL-WAVE MEMORY FROM BINARY BLACK HOLE MERGERS
International Nuclear Information System (INIS)
Favata, Marc
2009-01-01
Some astrophysical sources of gravitational waves can produce a 'memory effect', which causes a permanent displacement of the test masses in a freely falling gravitational-wave detector. The Christodoulou memory is a particularly interesting nonlinear form of memory that arises from the gravitational-wave stress-energy tensor's contribution to the distant gravitational-wave field. This nonlinear memory contributes a nonoscillatory component to the gravitational-wave signal at leading (Newtonian-quadrupole) order in the waveform amplitude. Previous computations of the memory and its detectability considered only the inspiral phase of binary black hole coalescence. Using an 'effective-one-body' (EOB) approach calibrated to numerical relativity simulations, as well as a simple fully analytic model, the Christodoulou memory is computed for the inspiral, merger, and ringdown. The memory will be very difficult to detect with ground-based interferometers, but is likely to be observable in supermassive black hole mergers with LISA out to redshifts z ∼< 2. Detection of the nonlinear memory could serve as an experimental test of the ability of gravity to 'gravitate'.
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.
Ulysses Observations of Nonlinear Wave-wave Interactions in the ...
Indian Academy of Sciences (India)
tribpo
gsfc.nasa.gov. Abstract. The Ulysses Unified Radio and Plasma Wave Experiment. (URAP) has observed Langmuir, ion-acoustic and associated solar type III radio emissions in the interplanetary medium. Bursts of 50-300 Hz (in the spacecraft ...
CISM Course on Nonlinear Waves in Real Fluids
1991-01-01
The study of materials which exhibit new and unconventional properties is of central importance for the devel- opment of advanced and refined technologies in many fields of engineering science. In this connection there has been a rapidly growing interest in real fluid effects on wave phenomena in the past few years. A prominent example is provided by Bethe-Zel'dovich-Thompson (BZT) fluids which have the distinguishing feature that they exhibit negative nonlinearity over a finite range of temperature and pressures in the pure vapour phase. However, two phase flows with and without phase change are an even richer source of new unexpected and previously thought impossible phenomena. Topics covered by this volume include waves in gases near the critical point, waves in retrograde fluids, temperature waves in superfluid helium and density waves in suspensions of particles in liquids. Clearly, the aim of the various contributions is twofold. First, they are intended to provide scientists and engineers working in th...
Nonlinear Passive Control of a Wave Energy Converter Subject to Constraints in Irregular Waves
Directory of Open Access Journals (Sweden)
Liguo Wang
2015-06-01
Full Text Available This paper investigates a passive control method of a point absorbing wave energy converter by considering the displacement and velocity constraints under irregular waves in the time domain. A linear generator is used as a power take-off unit, and the equivalent damping force is optimized to improve the power production of the wave energy converter. The results from nonlinear and linear passive control methods are compared, and indicate that the nonlinear passive control method leads to the excitation force in phase with the velocity of the converter that can significantly improve the energy production of the converter.
Interference effects in the nonlinear charge density wave dynamics
International Nuclear Information System (INIS)
Jelcic, D.; Batistic, I.; Bjelis, A.
1987-12-01
The main features of the nonlinear charge density wave transport in the external dc-ac field are shown to be the natural consequences of resonant phase slip diffusion. This process is treated numerically within the time dependent Landau-Ginzburg model, developed by Gor'kov. The resonances in the ac field are manifested as Shapiro steps in I-V characteristics, present at all rational ratios of internal frequency of current oscillations and external ac frequency. The origin of Shapiro steps, as well as their forms and heights, are cosidered in detail. In particular, it is shown that close to resonances the phase slip voltage acquires a highly nonsinusoidal modulation which leads to the appearance of low frequency and satellite peaks in the Fourier spectrum. Taking into account the interference of adjacent phase slips and the segment or domain structure of physical samples, we interpret the finite width of steps, side wings, synchronization, incomplete and complete mode locking and some other effects observed in numerous experiments on NbSe 3 and other CDW materials. (author). 36 refs, 12 figs
Nonlinear damping of drift waves by strong flow curvature
International Nuclear Information System (INIS)
Sidikman, K.L.; Carreras, B.A.; Garcia, L.; Diamond, P.H.
1993-01-01
A single-equation model has been used to study the effect of a fixed poloidal flow (V 0 ) on turbulent drift waves. The electron dynamics come from a laminar kinetic equation in the dissipative trapped-electron regime. In the past, the authors have assumed that the mode frequency is close to the drift-wave frequency. Trapped-electron density fluctuations are then related to potential fluctuations by an open-quotes iδclose quotes term. Flow shear (V 0 ') and curvature (V 0 double-prime) both have a stabilizing effect on linear modes for this open-quotes iδclose quotes model. However, in the nonlinear regime, single-helicity effects inhibit the flow damping. Neither V 0 ' nor V 0 double-prime produces a nonlinear damping effect. The above assumption on the frequency can be relaxed by including the electron time-response in the linear part of the evolution. In this time-dependent model, instability drive due to trapped electrons is reduced when mode frequency is greater than drift-wave frequency. Since V 0 double-prime produces such a frequency shift, its linear effect is enhanced. There is also nonlinear damping, since single-helicity effects do not eliminate the shift. Renormalized theory for this model predicts nonlinear stability for sufficiently large curvature. Single-helicity calculations have already shown nonlinear damping, and this strong V 0 double-prime regime is being explored. In the theory, the Gaussian shape of the nonlinear diffusivity is expanded to obtain a quadratic potential. The implications of this assumption will be tested by solving the full renormalized equation using a shooting method
2010-09-30
Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING
Nonlinear problems in fluid dynamics and inverse scattering: Nonlinear waves and inverse scattering
Ablowitz, Mark J.
1994-12-01
Research investigations involving the fundamental understanding and applications of nonlinear wave motion and related studies of inverse scattering and numerical computation have been carried out and a number of significant results have been obtained. A class of nonlinear wave equations which can be solved by the inverse scattering transform (IST) have been studied, including the Kadaomtsev-Petviashvili (KP) equation, the Davey-Stewartson equation, and the 2+1 Toda system. The solutions obtained by IST correspond to the Cauchy initial value problem with decaying initial data. We have also solved two important systems via the IST method: a 'Volterra' system in 2+1 dimensions and a new one dimensional nonlinear equation which we refer to as the Toda differential-delay equation. Research in computational chaos in moderate to long time numerical simulations continues.
Controlling wave propagation through nonlinear engineered granular systems
Leonard, Andrea
We study the fundamental dynamic behavior of a special class of ordered granular systems in order to design new, structured materials with unique physical properties. The dynamic properties of granular systems are dictated by the nonlinear, Hertzian, potential in compression and zero tensile strength resulting from the discrete material structure. Engineering the underlying particle arrangement of granular systems allows for unique dynamic properties, not observed in natural, disordered granular media. While extensive studies on 1D granular crystals have suggested their usefulness for a variety of engineering applications, considerably less attention has been given to higher-dimensional systems. The extension of these studies in higher dimensions could enable the discovery of richer physical phenomena not possible in 1D, such as spatial redirection and anisotropic energy trapping. We present experiments, numerical simulation (based on a discrete particle model), and in some cases theoretical predictions for several engineered granular systems, studying the effects of particle arrangement on the highly nonlinear transient wave propagation to develop means for controlling the wave propagation pathways. The first component of this thesis studies the stress wave propagation resulting from a localized impulsive loading for three different 2D particle lattice structures: square, centered square, and hexagonal granular crystals. By varying the lattice structure, we observe a wide range of properties for the propagating stress waves: quasi-1D solitary wave propagation, fully 2D wave propagation with tunable wave front shapes, and 2D pulsed wave propagation. Additionally the effects of weak disorder, inevitably present in real granular systems, are investigated. The second half of this thesis studies the solitary wave propagation through 2D and 3D ordered networks of granular chains, reducing the effective density compared to granular crystals by selectively placing wave
4th International Conference on Nonlinear Mechanics
Maugin, G
2003-01-01
The mechanics of electromagnetic materials and structures has been developing rapidly with extensive applications in, e. g. , electronics industry, nuclear engineering, and smart materials and structures. Researchers in this interdisciplinary field are with diverse background and motivation. The Symposium on the Mechanics of Electromagnetic Materials and Structures of the Fourth International Conference on Nonlinear Mechanics in Shanghai, China in August 13-16, 2002 provided an opportunity for an intimate gathering of researchers and exchange of ideas. This volume contains papers based on most of the presentations at the symposium, and articles from a few invited contributors. These papers reflect some of the recent activities in the mechanics of electromagnetic materials and structures. The first twelve papers are in the order in which they were listed in the program of the conference. These are followed by six invited papers in alphabetical order of the last names of the first authors. We would like to exte...
Traveling wave solutions and conservation laws for nonlinear evolution equation
Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa
2018-02-01
In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated.
Renormalized Compton scattering and nonlinear damping of collisionless drift waves
International Nuclear Information System (INIS)
Krommes, J.A.
1979-05-01
A kinetic theory for the nonlinear damping of collisionless drift waves in a shear-free magnetic field is presented. The general formalism is a renormalized version of induced scattering on the ions and reduces correctly to weak turbulence theory. The approximation studied explicitly reduces to Compton scattering, systematizes thee earlier calculations of Dupree and Tetreault (DT) [Phys. Fluids 21, 425 (1978)], and extends that theory to finite ion gyroradius. Certain conclusions differ significantly from those of DT
Nonlinear wave time dependent dynamic evolution in solar flux tubes
Fedun, V.; Erdelyi, R.
2005-12-01
The aim of the present work is to investigate the excitation, time dependent dynamic evolution and interaction of weakly nonlinear propagating (i.e. solitary) waves on vertical cylindrical magnetic flux tubes in a compressible solar atmospheric plasma. The axisymmetric flux tube has a field strength of 1000 G at its footpoint what is typical for photospheric regions. Solitons are excited by a footpoint driver. The propagation of the nonlinear signal is investigated by solving numerically a set of fully nonlinear 2D MHD equations in cylindrical coordinates. For the initial conditions the solutions of the linear dispersion relation for wave modes (in the present case we focus on the sausage mode) in a magnetic flux tube is applied. This dispersion relation is solved numerically for a range of plasma parameters. We compare our results with the works of Roberts [1], Wilson [2] (dispersion relation), Molotovshchikov [3] (nonlinear slow sausage waves) and Weisshaar [4] (numerical solutions of the Leibovich-Prichard-Roberts equation). (1) We found solitary solutions and investigate solitary propagating with external sound speed by solving the full MHD equations. (2) We also found a solitary wave propagating with the tube speed. A natural application of our studies may be spicule formation in the chromosphere, as suggested by Roberts [5], where it was demonstrated theoretically, that a solar photospheric magnetic flux tube can support the propagation of solitons governed by the Benjamin-Ono (slow mode) equations. Future possible improvements in modeling and the relevance of the photospheric chromospheric transition region coupling by spicules is suggested. [1] B. Roberts and A. Webb, Sol. Phys., 1978, v. 56, p. 5 [2] P.R. Wilson, Astron. Astrophys., 1980, v. 87, p. 121 [3] A.L. Molotovshchikov and M.S. Ruderman, Sol. Phys., 1987, v. 109, p. 247 [4] E. Weisshaar, Phys. Fluids A, 1989, v. 1(8), p. 1406 [5] B. Roberts and A. Mangeney, Royal Astronomical Society, Monthly
Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
2016-08-03
Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures E. Kim,1 F. Li,1 C. Chong,2 G. Theocharis ,3 J. Yang,1 and P.G. Kevrekidis2...Kevrekidis, IMA J. Appl. Math. 76, 389 (2011). [4] G. Theocharis , N. Boechler, and C. Daraio, in Phononic Crystals and Metamaterials, Ch. 6, Springer...9] N. Boechler, G. Theocharis , and C. Daraio, Nature Ma- terials 10, 665 (2011). [10] F. Li, P. Anzel, J. Yang, P.G. Kevrekidis, and C. Daraio, Nat
Internal waves and temperature fronts on slopes
Directory of Open Access Journals (Sweden)
S. A. Thorpe
Full Text Available Time series measurements from an array of temperature miniloggers in a line at constant depth along the sloping boundary of a lake are used to describe the `internal surf zone' where internal waves interact with the sloping boundary. More small positive temperature time derivatives are recorded than negative, but there are more large negative values than positive, giving the overall distribution of temperature time derivatives a small negative skewness. This is consistent with the internal wave dynamics; fronts form during the up-slope phase of the motion, bringing cold water up the slope, and the return flow may become unstable, leading to small advecting billows and weak warm fronts. The data are analysed to detect `events', periods in which the temperature derivatives exceed a set threshold. The speed and distance travelled by `events' are described. The motion along the slope may be a consequence of (a instabilities advected by the flow (b internal waves propagating along-slope or (c internal waves approaching the slope from oblique directions. The propagation of several of the observed 'events' can only be explained by (c, evidence that the internal surf zone has some, but possibly not all, the characteristics of the conventional 'surface wave' surf zone, with waves steepening as they approach the slope at oblique angles.
Key words. Oceanography: general (benthic boundary layers; limnology, Oceanography: physical (internal and inertial waves
4th International Conference on Structural Nonlinear Dynamics and Diagnosis
2018-01-01
This book presents contributions on the most active lines of recent advanced research in the field of nonlinear mechanics and physics selected from the 4th International Conference on Structural Nonlinear Dynamics and Diagnosis. It includes fifteen chapters by outstanding scientists, covering various aspects of applications, including road tanker dynamics and stability, simulation of abrasive wear, energy harvesting, modeling and analysis of flexoelectric nanoactuator, periodic Fermi–Pasta–Ulam problems, nonlinear stability in Hamiltonian systems, nonlinear dynamics of rotating composites, nonlinear vibrations of a shallow arch, extreme pulse dynamics in mode-locked lasers, localized structures in a photonic crystal fiber resonator, nonlinear stochastic dynamics, linearization of nonlinear resonances, treatment of a linear delay differential equation, and fractional nonlinear damping. It appeals to a wide range of experts in the field of structural nonlinear dynamics and offers researchers and engineers a...
Linear and nonlinear wave propagation in rarefied plasmas
International Nuclear Information System (INIS)
Ballai, I.; Erdelyi, R.; Voitenko, Y.; Goossens, M.
2002-01-01
Small-amplitude magnetohydrodynamic waves are studied in a dilute collisionless plasma with an anisotropic plasma pressure. The parallel and perpendicular pressure components are defined by two polytropic pressure laws. Previous results obtained within the framework of the Chew-Goldberger-Low double-adiabatic and double-isothermal models are recovered for specific values of the polytropic indices. The double-polytropic model can be considered as an extension of its single-polytropic counterpart model. Dispersion relations for the linear waves are derived and analyzed in the presence of pressure anisotropy. Particular cases of linear and nonlinear waves in a magnetic slab with double-polytropic plasma are investigated. The presence of the effective parallel and perpendicular sound speeds in the slab gives rise to a complicated interplay between kink and sausage modes supported by the slab. The behavior of weakly nonlinear waves in the slab are governed by the Benjamin-Ono equation. The soliton-like solution of this equation may be accelerated or retarded depending on the values of parallel and perpendicular sound speeds. The solitons are always accelerated in the magnetically dominated slab
Directory of Open Access Journals (Sweden)
S.-D. Zhang
2000-10-01
Full Text Available By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Energy Technology Data Exchange (ETDEWEB)
Lepri, Stefano, E-mail: stefano.lepri@isc.cnr.it [Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Pikovsky, Arkady [Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str 24/25, Potsdam (Germany); Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
Accretion disk viscosity and internal waves in disks
Huang, Min
1992-01-01
Recently, Vishniac, Jin and Diamond suggested that internal waves in accretion disks play a critical role in generating magnetic fields, and consequently are indirectly responsible for angular momentum transfer in thin, conducting, and non-self-gravitational disk systems. A project in which we will construct a quantitative model of the internal wave spectrum in accretion disks is started. It includes two aspects of work. The physical properties of the waves in a thin, non-self-gravitational, and non-magnetized accretion disk with realistic vertical structure is cataloged and examined. Besides the low frequency internal waves discovered by Vishniac and Diamond, it was found that sound waves with low frequency and low axisymmetry (with small absolute value of m) are capable of a driving dynamo because they are (1) well confined in a layer with thickness 2(absolute value of m)H where H is the disk scale height; (2) highly dispersive so they may survive the strong dissipation caused by the coherent nonlinear interaction their high frequency partners experience; and (3) elliptically polarized because they are confined in the z-direction. As a first step towards constructing a quantitative theory of this dynamo effect, a framework of calculating resonant nonlinear interaction among waves in disk is established. We are developing a numerical code which will compute the steady spectrum of the wave field in this framework. For simplicity, we only include the low frequency internal waves suggested by Vishniac and Diamond in the present stage. In the vicinity of the static state, the time step whose length is determined by the evolution of the modes with the largest amplitudes is too large for the modes with smaller amplitudes and overshooting occurs. Through nonlinear coupling, this overshooting is amplified and appears as a numerical instability affecting the evolution of the large amplitude modes. Shorter time steps may delay the appearance of the instability but not cure
Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media
Luna, Manuel
2011-05-01
Solitary wave formation is a well studied nonlinear phenomenon arising in propagation of dispersive nonlinear waves under suitable conditions. In non-homogeneous materials, dispersion may happen due to effective reflections between the material interfaces. This dispersion has been used along with nonlinearities to find solitary wave formation using the one-dimensional p-system. These solitary waves are called stegotons. The main goal in this work is to find two-dimensional stegoton formation. To do so we consider the nonlinear two-dimensional p-system with variable coefficients and solve it using finite volume methods. The second goal is to obtain effective equations that describe the macroscopic behavior of the variable coefficient system by a constant coefficient one. This is done through a homogenization process based on multiple-scale asymptotic expansions. We compare the solution of the effective equations with the finite volume results and find a good agreement. Finally, we study some stability properties of the homogenized equations and find they and one-dimensional versions of them are unstable in general.
Asymmetric wave propagation through nonlinear PT-symmetric oligomers
D'Ambroise, J.; Kevrekidis, P. G.; Lepri, S.
2012-11-01
In the present paper, we consider nonlinear PT-symmetric dimers and trimers (more generally, oligomers) embedded within a linear Schrödinger lattice. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear PT symmetric oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states and interestingly find them to be unstable except in the vicinity of the linear limit. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties persists in the case of such wavepackets, as well. The role of potential asymmetries in the nonlinearity or in the gain/loss pattern is also considered. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Harmonic Wave Generated by Contact Acoustic Nonlinearity in Obliquely Incident Ultrasonic Wave
Energy Technology Data Exchange (ETDEWEB)
Yun, Dong Seok; Choi, Sung Ho; Kim, Chung Seok; Jhang, Kyung Young [Hangyang University, Seoul (Korea, Republic of)
2012-08-15
The objective of this study is to image the harmonic wave generated by contact acoustic nonlinearity in obliquely incident ultrasonic wave for early detection of closed cracks. A closed crack has been simulated by contacting two aluminum block specimens producing solid-solid contact interfaces and then acoustic nonlinearity has been imaged with contact pressure. Sampling phased array(SPA) and synthetic aperture focusing technique(SAFT) are used for imaging techniques. The amplitude of the fundamental frequency decreased with applying pressure. But, the amplitude of second harmonic increased with pressure and was a maximum amplitude at the simulation point of closed crack. Then, the amplitude of second harmonic decreased. As a result, harmonic imaging of contact acoustic nonlinearity is possible and it is expected to be apply for early detection of initial cracks.
New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schroedinger Equation
International Nuclear Information System (INIS)
Yang Qin; Dai Chaoqing; Zhang Jiefang
2005-01-01
Some new exact travelling wave and period solutions of discrete nonlinear Schroedinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.
Glimpses of Kolmogorov's spectral energy dynamics in nonlinear acoustic waves
Gupta, Prateek; Scalo, Carlo
2017-11-01
Gupta, Lodato, and Scalo (AIAA 2017) have demonstrated the existence of an equilibrium spectral energy cascade in shock waves formed as a result of continued modal thermoacoustic amplification consistent with Kolmogorov's theory for high-Reynolds-number hydrodynamic turbulence. In this talk we discuss the derivation of a perturbation energy density norm that guarantees energy conservation during the nonlinear wave steepening process, analogous to inertial subrange turbulent energy cascade dynamics. The energy cascade is investigated via a bi-spectral analysis limited to wave-numbers and frequencies lower than the ones associated with the shock, analogous to the viscous dissipation length scale in turbulence. The proposed norm is derived by recombining second-order nonlinear acoustic equations and is positive definite; moreover, it decays to zero in the presence of viscous dissipation and is hence classifiable as a Lyapunov function of acoustic perturbation variables. The cumulative energy spectrum wavenumber distribution demonstrates a -3/2 decay law in the inertial range. The governing equation for the thus-derived energy norm highlights terms responsible for energy cascade towards higher harmonics, analogous to vortex stretching terms in hydrodynamic turbulence.
Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains
Energy Technology Data Exchange (ETDEWEB)
Pascoe, D. J.; Goddard, C. R.; Nakariakov, V. M., E-mail: D.J.Pascoe@warwick.ac.uk [Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)
2017-10-01
Quasi-periodic rapidly propagating wave trains are frequently observed in extreme ultraviolet observations of the solar corona, or are inferred by the quasi-periodic modulation of radio emission. The dispersive nature of fast magnetohydrodynamic waves in coronal structures provides a robust mechanism to explain the detected quasi-periodic patterns. We perform 2D numerical simulations of impulsively generated wave trains in coronal plasma slabs and investigate how the behavior of the trapped and leaky components depend on the properties of the initial perturbation. For large amplitude compressive perturbations, the geometrical dispersion associated with the waveguide suppresses the nonlinear steepening for the trapped wave train. The wave train formed by the leaky components does not experience dispersion once it leaves the waveguide and so can steepen and form shocks. The mechanism we consider can lead to the formation of multiple shock fronts by a single, large amplitude, impulsive event and so can account for quasi-periodic features observed in radio spectra.
Nonlinear waves and solitons on contours and closed surfaces
Ludu, Andrei
2012-01-01
This volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given. The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics. This book is intended for graduate students and researchers in mathematics, physics and engineering. This new edition has been thoroughly revised, expanded and updated.
28th International Symposium on Shock Waves
2012-01-01
The University of Manchester hosted the 28th International Symposium on Shock Waves between 17 and 22 July 2011. The International Symposium on Shock Waves first took place in 1957 in Boston and has since become an internationally acclaimed series of meetings for the wider Shock Wave Community. The ISSW28 focused on the following areas: Blast Waves, Chemically Reacting Flows, Dense Gases and Rarefied Flows, Detonation and Combustion, Diagnostics, Facilities, Flow Visualisation, Hypersonic Flow, Ignition, Impact and Compaction, Multiphase Flow, Nozzle Flow, Numerical Methods, Propulsion, Richtmyer-Meshkov, Shockwave Boundary Layer Interaction, Shock Propagation and Reflection, Shock Vortex Interaction, Shockwave Phenomena and Applications, as well as Medical and Biological Applications. The two Volumes contain the papers presented at the symposium and serve as a reference for the participants of the ISSW 28 and individuals interested in these fields.
Hitting probabilities for nonlinear systems of stochastic waves
Dalang, Robert C
2015-01-01
The authors consider a d-dimensional random field u = \\{u(t,x)\\} that solves a non-linear system of stochastic wave equations in spatial dimensions k \\in \\{1,2,3\\}, driven by a spatially homogeneous Gaussian noise that is white in time. They mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent \\beta. Using Malliavin calculus, they establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of \\mathbb{R}^d, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that ap
Linear and nonlinear analysis of density wave instability phenomena
International Nuclear Information System (INIS)
Ambrosini, Walter
1999-01-01
In this paper the mechanism of density-wave oscillations in a boiling channel with uniform and constant heat flux is analysed by linear and nonlinear analytical tools. A model developed on the basis of a semi-implicit numerical discretization of governing partial differential equations is used to provide information on the transient distribution of relevant variables along the channel during instabilities. Furthermore, a lumped parameter model and a distributed parameter model developed in previous activities are also adopted for independent confirmation of the observed trends. The obtained results are finally put in relation with the picture of the phenomenon proposed in classical descriptions. (author)
Propagation of shear wave in nonlinear and dissipative medium
International Nuclear Information System (INIS)
Jeambrun, D.
1995-01-01
The civil engineering projects, like nuclear installations, submitted to vibrations or seismic motions, require the study of the soil behaviour underlying the site under intensive dynamic loading. In order to understand in depth the soil damping phenomenon, a propagation of a shear seismic wave in a dissipative medium has been numerically simulated. The computer code, based on a nonlinear hysteretic model using Newmark-Wilson and Newton-Raphson algorithms and variable spatial steps, passes through the difficulties related to acceleration discontinuities. The simulation should allow the identification of the soil parameters by comparison with in situ measures. (author)
Optimal Control Of Nonlinear Wave Energy Point Converters
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Zhou, Qiang; Kramer, Morten
2013-01-01
In this paper the optimal control law for a single nonlinear point absorber in irregular sea-states is derived, and proven to be a closed-loop controller with feedback from measured displacement, velocity and acceleration of the floater. However, a non-causal integral control component dependent...... on future velocities appears in the optimal control law, rendering the optimal control law less useful for real time implementation. To circumvent this problem a causal closed-loop controller with the same feedback information is proposed, based on a slight modification of the optimal control law. The basic...... idea behind the control strategy is to enforce the stationary velocity response of the absorber into phase with the wave excitation force at any time. The controller is optimal under monochromatic wave excitation. It is demonstrated that the devised causal controller, in plane irregular sea states...
Nonlinear travelling waves in rotating Hagen–Poiseuille flow
Pier, Benoît; Govindarajan, Rama
2018-03-01
The dynamics of viscous flow through a rotating pipe is considered. Small-amplitude stability characteristics are obtained by linearizing the Navier–Stokes equations around the base flow and solving the resulting eigenvalue problems. For linearly unstable configurations, the dynamics leads to fully developed finite-amplitude perturbations that are computed by direct numerical simulations of the complete Navier–Stokes equations. By systematically investigating all linearly unstable combinations of streamwise wave number k and azimuthal mode number m, for streamwise Reynolds numbers {{Re}}z ≤slant 500 and rotational Reynolds numbers {{Re}}{{Ω }} ≤slant 500, the complete range of nonlinear travelling waves is obtained and the associated flow fields are characterized.
Nonlinear wave-beam kinetic equilibrium in decelerating systems
International Nuclear Information System (INIS)
Grishin, V.K.; Shaposhnikova, E.N.
1981-01-01
The equilibrium state of the wave-beam system arising during the interaction of a particle beam and excited electromagnetic wave has been investigated on the basis of the analysis of the exact polution of a non-linear self-consistent linear equation using the complete system of conservation laws. A waveguide with a dielectric filler, into which a monoenergetic particle beam magnetized in a transverse plane is continuously injected, is used as a model of an decelerating system. A dispersion equation describing the system state and expression for the evaluation of efficiency of the beam energy conversion to the field energy have been obtained. It is concluded that larae fields and high efficiency of energy conversion are achieved during the marked beam reconstruction. States with different values of current and beam velocity but similar amplitudes of a longitudinal field are possible in the system considered [ru
Nonlinear beat excitation of low frequency wave in degenerate plasmas
Mir, Zahid; Shahid, M.; Jamil, M.; Rasheed, A.; Shahbaz, A.
2018-03-01
The beat phenomenon due to the coupling of two signals at slightly different frequencies that generates the low frequency signal is studied. The linear dispersive properties of the pump and sideband are analyzed. The modified nonlinear dispersion relation through the field coupling of linear modes against the beat frequency is derived in the homogeneous quantum dusty magnetoplasmas. The dispersion relation is used to derive the modified growth rate of three wave parametric instability. Moreover, significant quantum effects of electrons through the exchange-correlation potential, the Bohm potential, and the Fermi pressure evolved in macroscopic three wave interaction are presented. The analytical results are interpreted graphically describing the significance of the work. The applications of this study are pointed out at the end of introduction.
Directory of Open Access Journals (Sweden)
Yu-Hua Zhang
2017-01-01
Full Text Available Residual stress has significant influence on the performance of mechanical components, and the nondestructive estimation of residual stress is always a difficult problem. This study applies the relative nonlinear coefficient of critical refraction longitudinal (LCR wave to nondestructively characterize the stress state of materials; the feasibility of residual stress estimation using the nonlinear property of LCR wave is verified. The nonlinear ultrasonic measurements based on LCR wave are conducted on components with known stress state to calculate the relative nonlinear coefficient. Experimental results indicate that the relative nonlinear coefficient monotonically increases with prestress and the increment of relative nonlinear coefficient is about 80%, while the wave velocity only decreases about 0.2%. The sensitivity of the relative nonlinear coefficient for stress is much higher than wave velocity. Furthermore, the dependence between the relative nonlinear coefficient and deformation state of components is found. The stress detection resolution based on the nonlinear property of LCR wave is 10 MPa, which has higher resolution than wave velocity. These results demonstrate that the nonlinear property of LCR wave is more suitable for stress characterization than wave velocity, and this quantitative information could be used for residual stress estimation.
Quantifying wave-breaking dissipation using nonlinear phase-resolved wave-field simulations
Qi, Y.; Xiao, W.; Yue, D. K. P.
2014-12-01
We propose to understand and quantify wave-breaking dissipation in the evolution of general irregular short-crested wave-fields using direct nonlinear phase-resolved simulations based on a High-Order Spectral (HOS) method (Dommermuth & Yue 1987). We implement a robust phenomenological-based energy dissipation model in HOS to capture the effect of wave-breaking dissipation on the overall wave-field evolution (Xiao et al 2013). The efficacy of this model is confirmed by direct comparisons against measurements for the energy loss in 2D and 3D breaking events. By comparing simulated wave-fields with and without the dissipation model in HOS, we obtain the dissipation field δ(x,y,t), which provides the times, locations and intensity of wave breaking events (δ>δc). This is validated by comparison of HOS simulations with Airborne Terrain Mapper (ATM) measurements in the recent ONR Hi-Res field experiment. Figure (a) shows one frame of simulated wave-field (with dissipation model). Figure (b) is the corresponding measurement from ATM, where a large wave breaking event was captured. Figure (c) is the 3D view of the simulated wave-field with the colored region representing dissipation with δ>δc. The HOS predicted high-dissipation area is found to agree well with the measured breaking area. Based on HOS predicted high-dissipation area (δ>δc), we calculate Λ(c) (Phillips 1985), the distribution of total length of breaking wave front per unit surface area per unit increment of breaking velocity c. Figure (d) shows the distribution Λ(c) calculated from HOS. For breaking speeds c greater than 5m/s, the simulated Λ(c) is in qualitative agreement with Phillips theoretical power-law of Λ(c)~c-6. From δ(x,y,t), we further quantify wave breaking by calculating the whitecap coverage rate Wr(t) and energy dissipation rate ΔE'(t), and study the evolution of Wr and ΔE' to understand the role of wave breaking in nonlinear wave-field evolution. We obtain HOS simulations
High-order finite difference solution for 3D nonlinear wave-structure interaction
DEFF Research Database (Denmark)
Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter
2010-01-01
This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme...... OceanWave3D presented in [1, 2]. A nonlinear decomposition of the solution into incident and scattered fields is used to increase the efficiency of the wave-structure interaction problem resolution. Application of the method to the diffraction of nonlinear waves around a fixed, bottom mounted circular...
Nonlinear interactions of electromagnetic waves with the auroral ionosphere
Wong, Alfred Y.
1999-09-01
The ionosphere provides us with an opportunity to perform plasma experiments in an environment with long confinement times, very large-scale lengths, and no confining walls. The auroral ionosphere with its nearly vertical magnetic field geometry is uniquely endowed with large amount of free energy from electron and ion precipitation along the magnetic field and mega-ampere current across the magnetic field. To take advantage of this giant outdoor laboratory, two facilities HAARP and HIPAS, with frequencies ranging from the radio to optical bands, are now available for active probing of and interaction with this interesting region. The ponderomotive pressures from the self-consistent wave fields have produced significant local perturbations of density and particle distributions at heights where the incident EM frequency matches a plasma resonance. This paper will review theory and experiments covering the nonlinear phenomena of parametric decay instability to wave collapse processes. At HF frequencies plasma lenses can be created by preconditioning pulses to focus what is a normally divergent beam into a high-intensity spot to further enhance nonlinear phenomena. At optical wavelengths a large rotating liquid metal mirror is used to focus laser pulses up to a given height. Such laser pulses are tuned to the same wavelengths of selected atomic and molecular resonances, with resulting large scattering cross sections. Ongoing experiments on dual-site experiments and excitation of ELF waves will be presented. The connection of such basic studies to environmental applications will be discussed. Such applications include the global communication using ELF waves, the ozone depletion and remediation and the control of atmospheric CO2 through the use of ion cyclotron resonant heating.
Energy Technology Data Exchange (ETDEWEB)
Tsuchiya, T. [Dia Consultants Company, Tokyo (Japan)
1996-10-01
Nonlinear full-wave tomography (FWT) is under investigation to improve the estimation accuracy of Vp/Vs distributions. Full-wave tomography is one of the underground structure exploration methods mainly using Tarantola`s nonlinear local optimization method (LOM). Numerical experiment for FWT was carried out assuming relatively weak nonlinear underground structure. In the case of inversion by local optimization method, adequate preconditioning is important. Utilization of geological information is also effective in estimating low-frequency components of a model. As far as data are obtained under proper observation arrangement, even in actual field, precise estimation of Vp/Vs distributions is possible by FWT using explosion in a hole as wave source. In full-wave tomography, selection of observation arrangement is essential for both Vp and Vs. However, the proper arrangement is different between Vp and Vs. Approach to different analyses for Vp and Vs is also necessary by using only proper data for Vp and Vs among obtained data sets. 4 figs.
Mass, momentum, and energy flux conservation between linear and nonlinear steady-state wave groups
Liu, Zeng; Xu, Dali; Liao, Shijun
2017-12-01
This paper provides a mass, momentum, and energy flux conservation analysis between the linear and nonlinear steady-state wave groups. Convergent high-order solutions for nonlinear wave groups with multiple steady-state near resonances in deep water have been obtained by means of the homotopy analysis method. The small divisors associated with nearly resonant components are transformed to singularities that are originally caused by exact resonances by a piecewise auxiliary linear operator. Both two primary components and other nearly resonant ones are considered in the initial guess to search for finite amplitude wave groups. It is found that as nonlinearity of wave groups increases, more wave components appear in the spectrum due to the nearly resonant interactions. The nonlinear wave fields change from the initial bi-chromatic waves that contain only two nontrivial primary components into the steady-state resonant waves that contain both two primary components and other nearly resonant ones. The conservation of mean rates of mass, momentum, and energy fluxes is established between the nonlinear wave groups and linear waves that are combined by two primary components with the same frequencies as in nonlinear wave groups. Comparison of the linear and nonlinear wave fields shows that the nearly resonant components influence the wave field distribution significantly: the nonlinear free surfaces have more peaked crests, steeper troughs, and more flatten wave nodes, and the related velocities at the crests and troughs increase more rapidly with the nonlinearity. All of these findings are helpful to enrich and deepen our understanding about nonlinear wave groups.
Massachusetts Bay - Internal wave packets digitized from SAR imagery
National Oceanic and Atmospheric Administration, Department of Commerce — This feature class contains internal wave packets digitized from SAR imagery at 1:350,000 scale in Massachusetts Bay. Internal waves are nonsinusoidal waves that...
XXIII International Conference on Nonlinear Dynamics of Electronic Systems
Stoop, Ruedi; Stramaglia, Sebastiano
2017-01-01
This book collects contributions to the XXIII international conference “Nonlinear dynamics of electronic systems”. Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry.
29th International Symposium on Shock Waves
Ranjan, Devesh
2015-01-01
This proceedings present the results of the 29th International Symposium on Shock Waves (ISSW29) which was held in Madison, Wisconsin, U.S.A., from July 14 to July 19, 2013. It was organized by the Wisconsin Shock Tube Laboratory, which is part of the College of Engineering of the University of Wisconsin-Madison. The ISSW29 focused on the following areas: Blast Waves, Chemically Reactive Flows, Detonation and Combustion, Facilities, Flow Visualization, Hypersonic Flow, Ignition, Impact and Compaction, Industrial Applications, Magnetohydrodynamics, Medical and Biological Applications, Nozzle Flow, Numerical Methods, Plasmas, Propulsion, Richtmyer-Meshkov Instability, Shock-Boundary Layer Interaction, Shock Propagation and Reflection, Shock Vortex Interaction, Shock Waves in Condensed Matter, Shock Waves in Multiphase Flow, as well as Shock Waves in Rarefield Flow. The two Volumes contain the papers presented at the symposium and serve as a reference for the participants of the ISSW 29 and individuals interes...
Directory of Open Access Journals (Sweden)
Heng Wang
2016-01-01
Full Text Available By using the method of dynamical system, the exact travelling wave solutions of the higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms are studied. Based on this method, all phase portraits of the system in the parametric space are given with the aid of the Maple software. All possible bounded travelling wave solutions, such as solitary wave solutions, kink and anti-kink wave solutions, and periodic travelling wave solutions, are obtained, respectively. The results presented in this paper improve the related previous conclusions.
X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Balyan, M. K., E-mail: mbalyan@ysu.am [Yerevan State University, Faculty of Physics (Armenia)
2016-12-15
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.
2D wave-front shaping in optical superlattices using nonlinear volume holography.
Yang, Bo; Hong, Xu-Hao; Lu, Rong-Er; Yue, Yang-Yang; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan
2016-07-01
Nonlinear volume holography is employed to realize arbitrary wave-front shaping during nonlinear processes with properly designed 2D optical superlattices. The concept of a nonlinear polarization wave in nonlinear volume holography is investigated. The holographic imaging of irregular patterns was performed using 2D LiTaO3 crystals with fundamental wave propagating along the spontaneous polarization direction, and the results agree well with the theoretical predictions. This Letter not only extends the application area of optical superlattices, but also offers an efficient method for wave-front shaping technology.
Rayleigh scattering and nonlinear inversion of elastic waves
Energy Technology Data Exchange (ETDEWEB)
Gritto, Roland [Univ. of California, Berkeley, CA (United States)
1995-12-01
Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of -100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to k_{p}R = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.
Directory of Open Access Journals (Sweden)
R. Maugé
2008-03-01
Full Text Available A set of evolution equations is derived for the modal coefficients in a weakly nonlinear nonhydrostatic internal-tide generation problem. The equations allow for the presence of large-amplitude topography, e.g. a continental slope, which is formally assumed to have a length scale much larger than that of the internal tide. However, comparison with results from more sophisticated numerical models show that this restriction can in practice be relaxed. It is shown that a topographically induced coupling between modes occurs that is distinct from nonlinear coupling. Nonlinear effects include the generation of higher harmonics by reflection from boundaries, i.e. steeper tidal beams at frequencies that are multiples of the basic tidal frequency. With a seasonal thermocline included, the model is capable of reproducing the phenomenon of local generation of internal solitary waves by a tidal beam impinging on the seasonal thermocline.
Saprykina, Ya. V.; Kuznetsov, S. Yu.; Divinskii, B. V.
2017-05-01
Using data from laboratory, field, and numerical experiments, we investigated regularities in changes in the relative limit height of breaking waves (the breaking index) from peculiarities of nonlinear wave transformations and type of wave breaking. It is shown that the value of the breaking index depends on the relative part of the wave energy in the frequency range of the second nonlinear harmonic. If this part is more than 35%, then the breaking index can be taken as a constant equal to 0.6. These waves are spilling breaking waves, asymmetric on the horizontal axis, and are almost symmetric on the vertical axis. If this part of the energy is less than 35%, then the breaking index increases with increasing energy in the frequency range of the second harmonic. These waves are plunging breaking waves, asymmetric on the vertical axis, and are almost symmetric on the horizontal axis. It is revealed that the breaking index depends on the asymmetry of waves on the vertical axis, determined by the phase shift between the first and second nonlinear harmonic (biphase). It is shown that the relation between the amplitudes of the second and first nonlinear harmonics for an Ursell number less than 1 corresponds to Stokes' second-order wave theory. The empirical dependences of the breaking index on the parameters of nonlinear transformation of waves are proposed.
Dynamics of electron wave packet in a disordered chain with delayed nonlinear response
International Nuclear Information System (INIS)
Zhu Hongjun; Xiong Shijie
2010-01-01
We investigate the dynamics of one electron wave packet in a linear chain with random on-site energies and a nonadiabatic electron-phonon interaction which is described by a delayed cubic nonlinear term in the time-dependent Schroedinger equation. We show that in the regime where the wave packet is delocalized in the case with only the delayed nonlinearity, the wave packet becomes localized when the disorder is added and the localization is enhanced by increasing the disorder. In the regime where the self-trapping phenomenon occurs in the case with only the delayed nonlinearity, by adding the disorder the general dynamical features of the wave packet do not change if the nonlinearity parameter is small, but the dynamics shows the subdiffusive behavior if the nonlinearity parameter is large. The numerical results demonstrate complicated wave packet dynamics of systems with both the disorder and nonlinearity.
A general theory of two-wave mixing in nonlinear media
DEFF Research Database (Denmark)
Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael
2009-01-01
A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave...... to the previous theory of two-wave mixing, the theory presented here is more general and the application of the theory to the photorefractive materials, Kerr media and semiconductor broad-area amplifiers are described....
Nonlinear waves in Poynting-flux dominated outflows
Mochol, Iwona
2012-11-01
Rotating, compact objects power some of the most spectacular phenomena in astrophysics, e.g., gamma-ray bursts, active galactic nuclei and pulsar winds. The energy is carried by Poynting flux, and the system is usually modelled using relativistic magnetohydrodynamics (MHD). However, in the relatively low density medium expected around some of these objects, the MHD approximation breaks down, allowing new, large-amplitude waves to propagate. We discuss the role of these waves in two astrophysical contexts: In blazar jets, we show that a magnetic shear, launched together with a plasma from the black hole magnetosphere, begins to accelerate particles at a large distance from its source. The resulting non-thermal emission can, nevertheless, be modulated on very short timescales, which can explain the rapid variability of the TeV gamma-ray flux observed from some blazars. In pulsar winds, we analyze the radial propagation of superluminal modes, including their damping by radiation reaction and by interaction with an external photon field. We discuss their effect on the structure of the pulsar wind termination shock, presenting new solutions in which the nonlinear wave is asymptotically matched to the constant pressure surroundings. The observational implications of these solutions are discussed for both isolated pulsars, and pulsars in binary systems.
Numerical simulation of the nonlinear dynamics of packets of spiral density waves
International Nuclear Information System (INIS)
Korchagin, V.I.
1987-01-01
In a numerical experiment, the behavior of nonlinear packets of spiral density waves in a gas disk has been investigated for different initial wave amplitudes. If the amplitude of the density perturbations is small (<5%), the wave packet is drawn toward the center or toward the periphery of the disk in accordance with the linear theory. The behavior of linear packets of waves with wavelength comparable to the disk radius (R/sub d//lambda = 4) exhibits good agreement with the conclusions of the linear theory of tightly wound spiral waves. The dynamics of wave packets with initial density amplitudes 16, 30, 50% demonstrates the nonlinear nature of the behavior. THe behavior is governed by whether or not the nonlinear effects of higher than third order in the wave amplitude play a part. If the wave packet dynamics is determined by the cubic nonlinearity, the results of the numerical experiment are in qualitative and quantitative agreement with the nonlinear theory of short waves, although the characteristic scale of the packet and the wavelength are of the order of the disk radius. In the cases when the nonlinear effects of higher orders in the amplitude play an important part, the behavior of a packet does not differ qualitatively from the behavior predicted by the theory of cubic nonlinearity, but the nonlinear spreading of the packet takes place more rapidly
DEFF Research Database (Denmark)
Schløer, Signe; Bredmose, Henrik; Bingham, Harry B.
2016-01-01
and nonlinear irregular wave realizations are calculated using the fully nonlinear potential flow wave model OceanWave3D [1]. The linear and nonlinear wave realizations are compared using both a static analysis on a fixed monopile and dynamic calculations with the aeroelastic code Flex5 [2]. The conclusion from...
Dense Gravity Currents with Breaking Internal Waves
Tanimoto, Yukinobu; Hogg, Charlie; Ouellette, Nicholas; Koseff, Jeffrey
2017-11-01
Shoaling and breaking internal waves along a pycnocline may lead to mixing and dilution of dense gravity currents, such as cold river inflows into lakes or brine effluent from desalination plants in near-coastal environments. In order to explore the interaction between gravity currents and breaking interfacial waves a series of laboratory experiments was performed in which a sequence of internal waves impinge upon a shelf-slope gravity current. The waves are generated in a two-layer thin-interface ambient water column under a variety of conditions characterizing both the waves and the gravity currents. The mixing of the gravity current is measured through both intrusive (CTD probe) and nonintrusive (Planar-laser inducted fluorescence) techniques. We will present results over a full range of Froude number (characterizing the waves) and Richardson number (characterizing the gravity current) conditions, and will discuss the mechanisms by which the gravity current is mixed into the ambient environment including the role of turbulence in the process. National Science Foundation.
Variational space–time (dis)continuous Galerkin method for nonlinear free surface water waves
Gagarina, Elena; Ambati, V.R.; van der Vegt, Jacobus J.W.; Bokhove, Onno
2014-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles’ variational principle for water waves together with a finite element
Variational space-time (dis)continuous Galerkin method for nonlinear free surface waves
Gagarina, Elena; van der Vegt, Jacobus J.W.; Ambati, V.R.; Bokhove, Onno
A new variational finite element method is developed for nonlinear free surface gravity water waves. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a space-time finite element discretization that is
Computation of nonlinear water waves with a high-order Boussinesq model
DEFF Research Database (Denmark)
Fuhrman, David R.; Madsen, Per A.; Bingham, Harry
2005-01-01
-crested waves in shallow/deep water, resulting in hexagonal/rectangular surface patterns; crescent waves, resulting from unstable perturbations of plane progressive waves; and highly-nonlinear wave-structure interactions. The emphasis is on physically demanding problems, and in eachcase qualitative and (when...
Identification and modeling of internal waves
Digital Repository Service at National Institute of Oceanography (India)
Murty, T.V.R.; Sadhuram, Y.; Rao, M.M.M.; SujithKumar, S.; Maneesha, K.; Sandhya, K.S.; Prakash, S.S.; Chandramouli, P.; Murthy, K.S.R.
) and Bhimili (17°35.486’N, 83°42.322’E) at sonic depth 100 m during different seasons using time series CTD (hourly), current meter and indigenously developed thermister chain (at an interval of 2 minutes) to study the Internal Wave (IW) characteristics. Sound...
Lipschitz Metrics for a Class of Nonlinear Wave Equations
Bressan, Alberto; Chen, Geng
2017-12-01
The nonlinear wave equation {u_{tt}-c(u)(c(u)u_x)_x=0} determines a flow of conservative solutions taking values in the space {H^1(R)}. However, this flow is not continuous with respect to the natural H 1 distance. The aim of this paper is to construct a new metric which renders the flow uniformly Lipschitz continuous on bounded subsets of {H^1(R)}. For this purpose, H 1 is given the structure of a Finsler manifold, where the norm of tangent vectors is defined in terms of an optimal transportation problem. For paths of piecewise smooth solutions, one can carefully estimate how the weighted length grows in time. By the generic regularity result proved in [7], these piecewise regular paths are dense and can be used to construct a geodesic distance with the desired Lipschitz property.
Shoaling internal solitary waves of depression over gentle slopes
Rivera, Gustavo; Diamessis, Peter
2017-11-01
The shoaling of an internal solitary wave (ISW) of depression over gentle slopes is explored through fully nonlinear and non-hydrostatic simulations using a high resolution/accuracy deformed spectral multidomain penalty method. During shoaling, the wave does not disintegrate as in the case of steeper slope but, instead, maintains its symmetric shape. At the core of the wave, an unstable region forms, characterized by the entrapment of heavier-over-light fluid. The formation of this convective instability is attributed to the vertical stretching by the ISW of the near-surface vorticity layer associated with the baroclinic background current. According to recent field observations in the South China Sea, the unstable region drives localized turbulent mixing within the wave, estimated to be up to four times larger than that in the open ocean, in the form of a recirculating trapped core. In this talk, emphasis is placed on the structure of the unstable region and the persistence of a possible recirculating core using simulations which capture 2D wave propagation combined with 3D representation of the transition to turbulence. As such, a preliminary understanding of the underlying fluid mechanics and the potential broader oceanic significance of ISWs with trapped cores is offered. Financial support gratefully acknowledged to NSF OCE Grant 1634257.
Theory of Nonlinear Guided Electromagnetic Waves in a Plane Two-Layered Dielectric Waveguide
Directory of Open Access Journals (Sweden)
Valeria Yu. Kurseeva
2017-01-01
Full Text Available Propagation of transverse electric electromagnetic waves in a homogeneous plane two-layered dielectric waveguide filled with a nonlinear medium is considered. The original wave propagation problem is reduced to a nonlinear eigenvalue problem for an equation with discontinuous coefficients. The eigenvalues are propagation constants (PCs of the guided waves that the waveguide supports. The existence of PCs that do not have linear counterparts and therefore cannot be found with any perturbation method is proven. PCs without linear counterparts correspond to a novel propagation regime that arises due to the nonlinearity. Numerical results are also presented; the comparison between linear and nonlinear cases is made.
Kinematic parameters of internal waves of the second mode in the South China Sea
Kurkina, Oxana; Talipova, Tatyana; Soomere, Tarmo; Giniyatullin, Ayrat; Kurkin, Andrey
2017-10-01
Spatial distributions of the main properties of the mode function and kinematic and non-linear parameters of internal waves of the second mode are derived for the South China Sea for typical summer conditions in July. The calculations are based on the Generalized Digital Environmental Model (GDEM) climatology of hydrological variables, from which the local stratification is evaluated. The focus is on the phase speed of long internal waves and the coefficients at the dispersive, quadratic and cubic terms of the weakly non-linear Gardner model. Spatial distributions of these parameters, except for the coefficient at the cubic term, are qualitatively similar for waves of both modes. The dispersive term of Gardner's equation and phase speed for internal waves of the second mode are about a quarter and half, respectively, of those for waves of the first mode. Similarly to the waves of the first mode, the coefficients at the quadratic and cubic terms of Gardner's equation are practically independent of water depth. In contrast to the waves of the first mode, for waves of the second mode the quadratic term is mostly negative. The results can serve as a basis for expressing estimates of the expected parameters of internal waves for the South China Sea.
Kinematic parameters of internal waves of the second mode in the South China Sea
Directory of Open Access Journals (Sweden)
O. Kurkina
2017-10-01
Full Text Available Spatial distributions of the main properties of the mode function and kinematic and non-linear parameters of internal waves of the second mode are derived for the South China Sea for typical summer conditions in July. The calculations are based on the Generalized Digital Environmental Model (GDEM climatology of hydrological variables, from which the local stratification is evaluated. The focus is on the phase speed of long internal waves and the coefficients at the dispersive, quadratic and cubic terms of the weakly non-linear Gardner model. Spatial distributions of these parameters, except for the coefficient at the cubic term, are qualitatively similar for waves of both modes. The dispersive term of Gardner's equation and phase speed for internal waves of the second mode are about a quarter and half, respectively, of those for waves of the first mode. Similarly to the waves of the first mode, the coefficients at the quadratic and cubic terms of Gardner's equation are practically independent of water depth. In contrast to the waves of the first mode, for waves of the second mode the quadratic term is mostly negative. The results can serve as a basis for expressing estimates of the expected parameters of internal waves for the South China Sea.
Initial boundary value problems of nonlinear wave equations in an exterior domain
International Nuclear Information System (INIS)
Chen Yunmei.
1987-06-01
In this paper, we investigate the existence and uniqueness of the global solutions to the initial boundary value problems of nonlinear wave equations in an exterior domain. When the space dimension n >= 3, the unique global solution of the above problem is obtained for small initial data, even if the nonlinear term is fully nonlinear and contains the unknown function itself. (author). 10 refs
Theoretical investigation of nonlinear ultrasonic wave modulation spectroscopy at crack interface
Czech Academy of Sciences Publication Activity Database
Kober, Jan; Převorovský, Zdeněk
2014-01-01
Roč. 61, January (2014), s. 10-15 ISSN 0963-8695 Institutional support: RVO:61388998 Keywords : ultrasonic testing * nonlinear wave modulation spectroscopy * classical nonlinearity * hysteretic nonlinearity * crack characterization Subject RIV: BI - Acoustics Impact factor: 2.225, year: 2014 http://www.sciencedirect.com/science/article/pii/S0963869513001175
Resonantly driven nonlinear density waves in protostellar disks
Yuan, Chi; Cassen, Pat
1994-01-01
Recent observations of binary, pre-main-sequence, solar-type stars provide evidence that such systems may coexist with circumstellar disks. The binary disk systems, besides being of general interest for the study of star formation, potentially provide useful tests of companion-disk interaction theories prominent in current hypotheses of planet formation. In this paper, we apply an asymptotic analysis of the nonlinear, resonant interaction of a stellar companion with a disk to understand the dependence of such interactions on the properties of the system: the binary mass ratio, the physical properties of the disk, and the effective dissipation (treated herein as viscosity). The method is based on a WKBJ approximation and exploits the conditions that the disk is thin and much less massive than the primary, but does not require that the companion-induced disturbance be small. Both isothermal and adiabatic responses are treated. Only circular orbit resonances are considered in this paper. It is demonstrated that the temperature of the disk as well as the relative mass of the companion affects the degree of nonlinearity, and that nonlinearity promotes high wave compression ratios, long wavelengths, and increased propagation distances. Nevertheless, the total torque exerted between the companion and the disk is well represented by linear theory. The amplitudes of density disturbances are reduced by viscosity and nonisothermality. Because resonant interactions are generally strong and capable of driving rapid evolution, one might expect observations of systems undergoing strong, resonant-driven evolution to be rare. In this connection, it is pointed out that the m = 1 resonance is distinguished by being anomalously weaker than the others and is therefore of observational interest. It is speculated that, in conditions of intrinsically small dissipation, the propagation of resonant-driven density waves is limited by the tendency of their wavelength to diminish with distance
International Conference on Differential Equations and Nonlinear Mechanics
2001-01-01
The International Conference on Differential Equations and Nonlinear Mechanics was hosted by the University of Central Florida in Orlando from March 17-19, 1999. One of the conference days was dedicated to Professor V. Lakshmikantham in th honor of his 75 birthday. 50 well established professionals (in differential equations, nonlinear analysis, numerical analysis, and nonlinear mechanics) attended the conference from 13 countries. Twelve of the attendees delivered hour long invited talks and remaining thirty-eight presented invited forty-five minute talks. In each of these talks, the focus was on the recent developments in differential equations and nonlinear mechanics and their applications. This book consists of 29 papers based on the invited lectures, and I believe that it provides a good selection of advanced topics of current interest in differential equations and nonlinear mechanics. I am indebted to the Department of Mathematics, College of Arts and Sciences, Department of Mechanical, Materials and Ae...
High-order Boussinesq-type modelling of nonlinear wave phenomena in deep and shallow water
DEFF Research Database (Denmark)
Madsen, Per A.; Fuhrman, David R.
2010-01-01
In this work, we start with a review of the development of Boussinesq theory for water waves covering the period from 1872 to date. Previous reviews have been given by Dingemans,1 Kirby,2,3 and Madsen & Schäffer.4 Next, we present our most recent high-order Boussinesq-type formulation valid...... for fully nonlinear and highly dispersive waves traveling over a rapidly varying bathymetry. Finally, we cover applications of this Boussinesq model, and we study a number of nonlinear wave phenomena in deep and shallow water. These include (1) Kinematics in highly nonlinear progressive deep-water waves; (2...
Numerical Simulation of Nonlinear Ultrasonic Waves Due to Bi-material Interface Contact
International Nuclear Information System (INIS)
Hirose, S; Saitoh, T
2014-01-01
Boundary integral equations are formulated to investigate nonlinear waves generated by a debonding interface of bi-material subjected to an incident plane wave. For the numerical simulation, the IRK (Implicit Runge-Kutta method) based CQ-BEM (Convolution Quadrature-Boundary Element Method) is developed. The interface conditions for a debonding area, consisting of three phases of separation, stick, and slip, are developed for the simulation of nonlinear ultrasonic waves. Numerical results are obtained and discussed for normal incidence of a plane longitudinal wave onto the nonlinear interface with a static compressive stress
Internal Decoupling in Nonlinear Process Control
Directory of Open Access Journals (Sweden)
Jens G. Balchen
1988-07-01
Full Text Available A simple method has been investigated for the total or partial removal of the effect of non-linear process phenomena in multi-variable feedback control systems. The method is based upon computing the control variables which will drive the process at desired rates. It is shown that the effect of model errors in the linearization of the process can be partly removed through the use of large feedback gains. In practice there will be limits on how large gains can he used. The sensitivity to parameter errors is less pronounced and the transient behaviour is superior to that of ordinary PI controllers.
Internal Gravity Waves in the Magnetized Solar Atmosphere. I. Magnetic Field Effects
Energy Technology Data Exchange (ETDEWEB)
Vigeesh, G.; Steiner, O. [Kiepenheuer-Institut für Sonnenphysik, Schöneckstrasse 6, D-79104 Freiburg (Germany); Jackiewicz, J., E-mail: vigeesh@leibniz-kis.de [New Mexico State University, Department of Astronomy, P.O. Box 30001, MSC 4500, Las Cruces, NM 88003 (United States)
2017-02-01
Observations of the solar atmosphere show that internal gravity waves are generated by overshooting convection, but are suppressed at locations of magnetic flux, which is thought to be the result of mode conversion into magnetoacoustic waves. Here, we present a study of the acoustic-gravity wave spectrum emerging from a realistic, self-consistent simulation of solar (magneto)convection. A magnetic field free, hydrodynamic simulation and a magnetohydrodynamic (MHD) simulation with an initial, vertical, homogeneous field of 50 G flux density were carried out and compared with each other to highlight the effect of magnetic fields on the internal gravity wave propagation in the Sun’s atmosphere. We find that the internal gravity waves are absent or partially reflected back into the lower layers in the presence of magnetic fields and argue that the suppression is due to the coupling of internal gravity waves to slow magnetoacoustic waves still within the high- β region of the upper photosphere. The conversion to Alfvén waves is highly unlikely in our model because there is no strongly inclined magnetic field present. We argue that the suppression of internal waves observed within magnetic flux concentrations may also be due to nonlinear breaking of internal waves due to vortex flows that are ubiquitously present in the upper photosphere and the chromosphere.
Bhardwaj, Divyanshu; Guha, Anirban
2018-01-01
Theoretical studies on linear shear instabilities often use simple velocity and density profiles (e.g., constant, piecewise) for obtaining good qualitative and quantitative predictions of the initial disturbances. Furthermore, such simple profiles provide a minimal model for obtaining a mechanistic understanding of otherwise elusive shear instabilities. However, except a few specific cases, the efficacy of simple profiles has remained limited to the linear stability paradigm. In this work, we have proposed a general framework that can simulate the fully nonlinear evolution of a variety of stratified shear instabilities as well as wave-wave and wave-topography interaction problems having simple piecewise constant and/or linear profiles. To this effect, we have modified the classical vortex method by extending the Birkhoff-Rott equation to multiple interfaces and, furthermore, have incorporated background shear across a density interface. The latter is more subtle and originates from the understanding that Bernoulli's equation is not just limited to irrotational flows but can be modified to make it applicable for piecewise linear velocity profiles. We have solved diverse problems that can be essentially reduced to the multiple interacting interfaces paradigm, e.g., spilling and plunging breakers, stratified shear instabilities like Holmboe and Taylor-Caulfield, jet flows, and even wave-topography interaction problems like Bragg resonance. Free-slip boundary being a vortex sheet, its effect can also be effectively captured using vortex method. We found that the minimal models capture key nonlinear features, e.g., wave breaking features like cusp formation and roll-ups, which are observed in experiments and/or extensive simulations with smooth, realistic profiles.
Nonlinear internal friction, chaos, fractal and musical instruments
International Nuclear Information System (INIS)
Sun, Z.Q.; Lung, C.W.
1995-08-01
Nonlinear and structure sensitive internal friction phenomena in materials are used for characterizing musical instruments. It may be one of the most important factors influencing timbre of instruments. As a nonlinear dissipated system, chaos and fractals are fundamental peculiarities of sound spectra. It is shown that the concept of multi range fractals can be used to decompose the frequency spectra of melody. New approaches are suggested to improve the fabrication, property characterization and physical understanding of instruments. (author). 18 refs, 4 figs
International Nuclear Information System (INIS)
Abdou, M.A.
2008-01-01
The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics
The nonlinear equatorial Kelvin wave. [in coastal currents of El Nino and Gulf of Guinea
Boyd, J. P.
1980-01-01
Using the method of strained coordinates, a uniformly valid approximation to the nonlinear equatorial Kelvin wave is derived. It is shown that nonlinear effects are negligible for the Kelvin waves associated with the Gulf of Guinea upwelling. The Kelvin waves involved in El Nino, however, are significantly distorted both in shape and speed. The leading edge is smoothed and expanded rather than steepened, but the trailing edge will form sharp fronts and eventually break.
REVIEWS OF TOPICAL PROBLEMS: Waves in systems with cross-diffusion as a new class of nonlinear waves
Tsyganov, Mikhail A.; Biktashev, V. N.; Brindley, J.; Holden, A. V.; Ivanitsky, Genrikh R.
2007-03-01
Research on spatially extended excitable systems with cross-diffusion components is reviewed. Particular attention is given to the new phenomena of the quasi-soliton and half-soliton interaction of excitation waves, which are specific to such systems and occur along with the standard nonsoliton wave interaction that causes the waves to mutually annihilate. A correlation is shown to exist between interaction regimes and wave profile shapes. One example of a cross-diffusion system is population systems with taxes. Based on the mathematical models of and experimental work with bacterial populations, waves in excitable cross-diffusion systems can be identified as a new class of nonlinear waves.
International Nuclear Information System (INIS)
Khalil, Sh.M.; El-Sherif, N.; El-Siragy, N.M.; Tanta Univ.; El-Naggar, I.A.; Alexandria Univ.
1985-01-01
Investigation is made for nonlinear interaction between incident radiation and a surface wave in a magnetized plasma layer. Both interacting waves are of P polarization. The generated currents and fields at combination frequencies are obtained analytically. Unlike the S-polarized interacting waves, the magnetic field affects the fundamental waves and leads to an amplification of generated waves when their frequencies approach the cyclotron frequency. (author)
Internal wave structures in abyssal cataract flows
Makarenko, Nikolay; Liapidevskii, Valery; Morozov, Eugene; Tarakanov, Roman
2014-05-01
We discuss some theoretical approaches, experimental results and field data concerning wave phenomena in ocean near-bottom stratified flows. Such strong flows of cold water form everywhere in the Atlantic abyssal channels, and these currents play significant role in the global water exchange. Most interesting wave structures arise in a powerful cataract flows near orographic obstacles which disturb gravity currents by forced lee waves, attached hydraulic jumps, mixing layers etc. All these effects were observed by the authors in the Romanche and Chain fracture zones of Atlantic Ocean during recent cruises of the R/V Akademik Ioffe and R/V Akademik Sergei Vavilov (Morozov et al., Dokl. Earth Sci., 2012, 446(2)). In a general way, deep-water cataract flows down the slope are similar to the stratified flows examined in laboratory experiments. Strong mixing in the sill region leads to the splitting of the gravity current into the layers having the fluids with different densities. Another peculiarity is the presence of critical layers in shear flows sustained over the sill. In the case under consideration, this critical level separates the flow of near-bottom cold water from opposite overflow. In accordance with known theoretical models and laboratory measurements, the critical layer can absorb and reflect internal waves generated by the topography, so the upward propagation of these perturbations is blocked from above. High velocity gradients were registered downstream in the vicinity of cataract and it indicates the existence of developed wave structures beyond the sill formed by intense internal waves. This work was supported by RFBR (grants No 12-01-00671-a, 12-08-10001-k and 13-08-10001-k).
The Fate and Impact of Internal Waves in Nearshore Ecosystems.
Woodson, C B
2018-01-03
Internal waves are widespread features of global oceans that play critical roles in mixing and thermohaline circulation. Similarly to surface waves, internal waves can travel long distances, ultimately breaking along continental margins. These breaking waves can transport deep ocean water and associated constituents (nutrients, larvae, and acidic low-oxygen waters) onto the shelf and locally enhance turbulence and mixing, with important effects on nearshore ecosystems. We are only beginning to understand the role internal waves play in shaping nearshore ecosystems. Here, I review the physics of internal waves in shallow waters and identify two commonalities among internal waves in the nearshore: exposure to deep offshore waters and enhanced turbulence and mixing. I relate these phenomena to important ecosystem processes ranging from extreme events to fertilization success to draw general conclusions about the influence of internal waves on ecosystems and the effects of internal waves in a changing climate.
The Fate and Impact of Internal Waves in Nearshore Ecosystems
Woodson, C. B.
2018-01-01
Internal waves are widespread features of global oceans that play critical roles in mixing and thermohaline circulation. Similarly to surface waves, internal waves can travel long distances, ultimately breaking along continental margins. These breaking waves can transport deep ocean water and associated constituents (nutrients, larvae, and acidic low-oxygen waters) onto the shelf and locally enhance turbulence and mixing, with important effects on nearshore ecosystems. We are only beginning to understand the role internal waves play in shaping nearshore ecosystems. Here, I review the physics of internal waves in shallow waters and identify two commonalities among internal waves in the nearshore: exposure to deep offshore waters and enhanced turbulence and mixing. I relate these phenomena to important ecosystem processes ranging from extreme events to fertilization success to draw general conclusions about the influence of internal waves on ecosystems and the effects of internal waves in a changing climate.
Internal wave turbulence near a Texel beach.
Directory of Open Access Journals (Sweden)
Hans van Haren
Full Text Available A summer bather entering a calm sea from the beach may sense alternating warm and cold water. This can be felt when moving forward into the sea ('vertically homogeneous' and 'horizontally different', but also when standing still between one's feet and body ('vertically different'. On a calm summer-day, an array of high-precision sensors has measured fast temperature-changes up to 1 °C near a Texel-island (NL beach. The measurements show that sensed variations are in fact internal waves, fronts and turbulence, supported in part by vertical stable stratification in density (temperature. Such motions are common in the deep ocean, but generally not in shallow seas where turbulent mixing is expected strong enough to homogenize. The internal beach-waves have amplitudes ten-times larger than those of the small surface wind waves. Quantifying their turbulent mixing gives diffusivity estimates of 10(-4-10(-3 m(2 s(-1, which are larger than found in open-ocean but smaller than wave breaking above deep sloping topography.
Homogeneous internal wave turbulence driven by tidal flows
Le Reun, Thomas; Favier, Benjamin; Le Bars, Michael; Erc Fludyco Team
2017-11-01
We propose a novel investigation of the stability of strongly stratified planetary fluid layers undergoing periodic tidal distortion in the limit where rotational effects are negligible compared to buoyancy. With the help of a local model focusing on a small fluid area compared to the global layer, we find that periodic tidal distortion drives a parametric subharmonic resonance of internal. This instability saturates into an homogeneous internal wave turbulence pervading the whole fluid interior: the energy is injected in the unstable waves which then feed a succession of triadic resonances also generating small spatial scales. As the timescale separation between the forcing and Brunt-Väisälä is increased, the temporal spectrum of this turbulence displays a -2 power law reminiscent of the Garrett and Munk spectrum measured in the oceans (Garett & Munk 1979). Moreover, in this state consisting of a superposition of waves in weak non-linear interaction, the mixing efficiency is increased compared to classical, Kolmogorov-like stratified turbulence. This study is of wide interest in geophysical fluid dynamics ranging from oceanic turbulence and tidal heating in icy satellites to dynamo action in partially stratified planetary cores as it could be the case in the Earth. We acknowledge support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 681835-FLUDYCO-ERC-2015-CoG).
Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves
Fibich, G.; Ilan, B.; Tsynkov, S.
2002-01-01
The critical nonlinear Schrodinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L(sub 2) norm of the initial solution) is sufficiently high, then the NLS model predicts that the beam will self-focus to a point (i.e.. collapse) at a finite propagation distance. Mathematically, this behavior corresponds to the formation of a singularity in the solution of the NLS. A key question which has been open for many years is whether the solution to the NLH, i.e., the 'parent' equation, may nonetheless exist and remain regular everywhere, in particular for those initial conditions (input powers) that lead to blowup in the NLS. In the current study, we address this question by introducing linear damping into both models and subsequently comparing the numerical solutions of the damped NLH (boundary-value problem) with the corresponding solutions of the damped NLS (initial-value problem). Linear damping is introduced in much the same way as done when analyzing the classical constant-coefficient Helmholtz equation using the limiting absorption principle. Numerically, we have found that it provides a very efficient tool for controlling the solutions of both the NLH and NHS. In particular, we have been able to identify initial conditions for which the NLS solution does become singular. whereas the NLH solution still remains regular everywhere. We believe that our finding of a larger domain of existence for the NLH than that for the NLS is accounted for by precisely those mechanisms, that have been neglected when deriving the NLS from the NLH, i.e., nonparaxiality and backscattering.
Nonlinear wave modulation of cylindrical and spherical quantum ion-acoustic solitary waves
Sabry, R.; El-Labany, S. K.; Shukla, P. K.
2008-12-01
Cylindrical and spherical amplitude modulation of quantum ion-acoustic (QIA) envelope solitary waves in a dense quantum plasma comprised of electrons and ions is investigated. For this purpose, a one-dimensional quantum hydrodynamic model and the Poisson equation are considered. By using the standard reductive perturbation technique, a modified nonlinear Schrödinger equation with the geometrical and the quantum effects is derived. The effect of quantum corrections and the effect due to the cylindrical and spherical geometries on the propagation of the QIA envelope solitary waves are examined. It is shown that there exists a modulation instability period depending on the quantum parameter, which does not exist for the one-dimensional classical case.
Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials
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
Bulk nonlinear elastic strain waves in a bar with nanosize inclusions
DEFF Research Database (Denmark)
Gula, Igor A.; Samsonov (†), Alexander M.
2018-01-01
We propose a mathematical model for propagation of the long nonlinearly elastic longitudinal strain waves in a bar, which contains nanoscale structural inclusions. The model is governed by a nonlinear doubly dispersive equation (DDE) with respect to the one unknown longitudinal strain function. We...... obtained the travelling wave solutions to DDE, and, in particular, the strain solitary wave solution, which was shown to be significantly affected by parameters of the inclusions. Moreover we found some critical inaccuracies, committed in papers by others in the derivation of a constitutive equation...... for the long strain waves in a microstructured medium, revised them, and showed an importance of improvements for correct estimation of wave parameters....
Compound waves in a higher order nonlinear model of thermoviscous fluids
DEFF Research Database (Denmark)
Rønne Rasmussen, Anders; Sørensen, Mads Peter; Gaididei, Yuri B.
2016-01-01
A generalized traveling wave ansatz is used to investigate compound shock waves in a higher order nonlinear model of a thermoviscous fluid. The fluid velocity potential is written as a traveling wave plus a linear function of space and time. The latter offers the possibility of predicting...
The effect of non-linear wave in front of vertical wall using bi ...
African Journals Online (AJOL)
of waves in front of a vertical wall are examined, using the new theoretical approach of a bi-parametric distribution, proposed by Ejinkonye [1] to investigate the effect of nonlinearity for the mechanics of the sea waves. The most probable value of the wave steepness is assumed to be = 0.055. From the subsequent calculation ...
Strongly nonlinear evolution of low-frequency wave packets in a dispersive plasma
Vasquez, Bernard J.
1993-01-01
The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p Schrodinger (DNLS) equation.
Directory of Open Access Journals (Sweden)
O. Onishchenko
2013-03-01
Full Text Available In this paper, we have investigated vortex structures (e.g. convective cells of internal gravity waves (IGWs in the earth's atmosphere with a finite vertical temperature gradient. A closed system of nonlinear equations for these waves and the condition for existence of solitary convective cells are obtained. In the atmosphere layers where the temperature decreases with height, the presence of IGW convective cells is shown. The typical parameters of such structures in the earth's atmosphere are discussed.
Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves
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 Maps and their Applications 2011 International Workshop
Fournier-Prunaret, Daniele; Ueta, Tetsushi; Nishio, Yoshifumi
2014-01-01
In the field of Dynamical Systems, nonlinear iterative processes play an important role. Nonlinear mappings can be found as immediate models for many systems from different scientific areas, such as engineering, economics, biology, or can also be obtained via numerical methods permitting to solve non-linear differential equations. In both cases, the understanding of specific dynamical behaviors and phenomena is of the greatest interest for scientists. This volume contains papers that were presented at the International Workshop on Nonlinear Maps and their Applications (NOMA 2011) held in Évora, Portugal, on September 15-16, 2011. This kind of collaborative effort is of paramount importance in promoting communication among the various groups that work in dynamical systems and networks in their research theoretical studies as well as for applications. This volume is suitable for graduate students as well as researchers in the field.
Directory of Open Access Journals (Sweden)
Xiao-Fang Zhong
2017-12-01
Full Text Available The irregular wave disturbance attenuation problem for jacket-type offshore platforms involving the nonlinear characteristics is studied. The main contribution is that a digital-control-based approximation of optimal wave disturbances attenuation controller (AOWDAC is proposed based on iteration control theory, which consists of a feedback item of offshore state, a feedforward item of wave force and a nonlinear compensated component with iterative sequences. More specifically, by discussing the discrete model of nonlinear offshore platform subject to wave forces generated from the Joint North Sea Wave Project (JONSWAP wave spectrum and linearized wave theory, the original wave disturbances attenuation problem is formulated as the nonlinear two-point-boundary-value (TPBV problem. By introducing two vector sequences of system states and nonlinear compensated item, the solution of introduced nonlinear TPBV problem is obtained. Then, a numerical algorithm is designed to realize the feasibility of AOWDAC based on the deviation of performance index between the adjacent iteration processes. Finally, applied the proposed AOWDAC to a jacket-type offshore platform in Bohai Bay, the vibration amplitudes of the displacement and the velocity, and the required energy consumption can be reduced significantly.
Wave propagation in photonic crystals and metamaterials: Surface waves, nonlinearity and chirality
Energy Technology Data Exchange (ETDEWEB)
Wang, Bingnan [Iowa State Univ., Ames, IA (United States)
2009-01-01
nonlinear SRRs are built and modeled to study the nonlinearity in magnetic metamaterials and the results will be presented in Chapter 3. Negative refractive index n is one of the major target in the research of metamaterials. Negative n can be obtained with a metamaterial with both ϵ and μ negative. As an alternative, negative index for one of the circularly polarized waves could be achieved with metamaterials having a strong chirality ?. In this case neither ϵ} nor μ negative is required. My work on chiral metamaterials will be presented in Chapter 4.
Nonlinear evolution of a baroclinic wave and imbalanced dissipation
Nadiga, Balu
2015-11-01
The question of how ocean circulation equilibrates in the presence of continuous large-scale forcing and a tendency of geostrophic turbulence to confine energy to large and intermediate scales is considered. By considering the nonlinear evolution of an unstable baroclinic wave at small Rossby and Froude numbers (small aspect ratio domain) at high resolutions, it is shown that submesoscale instabilities provide an interior pathway between the energetic oceanic mesoscales and smaller unbalanced scales. An estimate of the magnitude of this pathway is presented. Phenomenology-wise, mesoscale shear and strain resulting from the primary baroclinic instability drive frontogenesis; fronts in turn support ageostrophic secondary circulation and instabilities. These two processes together lead to a quick rise in dissipation rate which then reaches a peak and begins to fall as frontogenesis slows down; eventually balanced and imbalanced modes decouple. Dissipation of balanced energy by imbalanced processes is shown to scale exponentially with Rossby number of the base flow. Further, a break is seen in the total energy (TE) spectrum at small scales with a transition from k-3 to k - 5 / 3 reminiscent of the atmospheric spectra of Nastrom & Gage. For details see JFM 756, 965-1006.
Nonlinear dynamics of wind waves: multifractal phase/time effects
Directory of Open Access Journals (Sweden)
R. H. Mellen
1994-01-01
Full Text Available In addition to the bispectral coherence method, phase/time analysis of analytic signals is another promising avenue for the investigation of phase effects in wind waves. Frequency spectra of phase fluctuations obtained from both sea and laboratory experiments follow an F-β power law over several decades, suggesting that a fractal description is appropriate. However, many similar natural phenomena have been shown to be multifractal. Universal multifractals are quantified by two additional parameters: the Lévy index 0 α 2 for the type of multifractal and the co-dimension 0 C1 1 for intermittence. The three parameters are a full statistical measure the nonlinear dynamics. Analysis of laboratory flume data is reported here and the results indicate that the phase fluctuations are 'hard multifractal' (α > 1. The actual estimate is close to the limiting value α = 2, which is consistent with Kolmogorov's lognormal model for turbulent fluctuations. Implications for radar and sonar backscattering from the sea surface are briefly considered.
Modeling Nonlinear Acoustic Standing Waves in Resonators: Theory and Experiments
Raman, Ganesh; Li, Xiaofan; Finkbeiner, Joshua
2004-01-01
The overall goal of the cooperative research with NASA Glenn is to fundamentally understand, computationally model, and experimentally validate non-linear acoustic waves in enclosures with the ultimate goal of developing a non-contact acoustic seal. The longer term goal is to transition the Glenn acoustic seal innovation to a prototype sealing device. Lucas and coworkers are credited with pioneering work in Resonant Macrosonic Synthesis (RMS). Several Patents and publications have successfully illustrated the concept of Resonant Macrosonic Synthesis. To utilize this concept in practical application one needs to have an understanding of the details of the phenomenon and a predictive tool that can examine the waveforms produced within resonators of complex shapes. With appropriately shaped resonators one can produce un-shocked waveforms of high amplitude that would result in very high pressures in certain regions. Our goal is to control the waveforms and exploit the high pressures to produce an acoustic seal. Note that shock formation critically limits peak-to-peak pressure amplitudes and also causes excessive energy dissipation. Proper shaping of the resonator is thus critical to the use of this innovation.
Energy Technology Data Exchange (ETDEWEB)
Arevalo, Edward, E-mail: arevalo@temf.tu-darmstadt.d [Technische Universitaet Darmstadt, Institut fuer Theorie elektromagnetischer Felder, TEMF, Schlossgartenstr. 8, D-64289 Darmstadt (Germany)
2009-09-21
The effect of instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schroedinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed to derive closed-form expressions for small-amplitude solitary waves. The notion that the existence of nonlinear solitary waves in discrete systems is a signature of the modulation instability is used. With the help of this notion we conjecture that instability effects on moving solitons can be qualitative estimated from the analytical solutions. Results from numerical simulations are presented to support this conjecture.
Vertically varying Eulerian mean currents induced by internal coastal Kelvin waves
Weber, Jan Erik H.
2017-02-01
The lost momentum in spatially damped internal Kelvin waves reappears as Eulerian mean currents through the action of the nonlinear wave-wave interaction terms. A novel expression is derived for the steady balance between the frictional force on the coastally trapped horizontal Eulerian mean flow, and the forcing from the wavefield in terms of the mean wave Reynolds stresses and the horizontal divergence of the Stokes drift. The forcing can be expressed in terms of orthogonal eigenfunctions for internal waves, yielding the vertical variation of the Eulerian mean flow. For arbitrary values of the Brunt-Väisälä frequency N, it is shown that the wave forcing on the Eulerian mean is always negative, yielding a Poiseuille type flow. Therefore, unlike the Stokes drift velocity in internal Kelvin waves which exhibits a backward drift for the first mode in the region of maximum N, the wave-induced horizontal Eulerian mean current is always in the direction of the waves. The results are illustrated by an example from Van Mijenfjorden in Svalbard, which is an arctic sill fjord where internal waves are generated by the action of the barotropic semidiurnal tide.
The Effect of Surface Topography on the Nonlinear Dynamics of Rossby Waves
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
Directory of Open Access Journals (Sweden)
Mati Goldberg
Full Text Available A new paradigm has recently emerged in brain science whereby communications between glial cells and neuron-glia interactions should be considered together with neurons and their networks to understand higher brain functions. In particular, astrocytes, the main type of glial cells in the cortex, have been shown to communicate with neurons and with each other. They are thought to form a gap-junction-coupled syncytium supporting cell-cell communication via propagating Ca(2+ waves. An identified mode of propagation is based on cytoplasm-to-cytoplasm transport of inositol trisphosphate (IP(3 through gap junctions that locally trigger Ca(2+ pulses via IP(3-dependent Ca(2+-induced Ca(2+ release. It is, however, currently unknown whether this intracellular route is able to support the propagation of long-distance regenerative Ca(2+ waves or is restricted to short-distance signaling. Furthermore, the influence of the intracellular signaling dynamics on intercellular propagation remains to be understood. In this work, we propose a model of the gap-junctional route for intercellular Ca(2+ wave propagation in astrocytes. Our model yields two major predictions. First, we show that long-distance regenerative signaling requires nonlinear coupling in the gap junctions. Second, we show that even with nonlinear gap junctions, long-distance regenerative signaling is favored when the internal Ca(2+ dynamics implements frequency modulation-encoding oscillations with pulsating dynamics, while amplitude modulation-encoding dynamics tends to restrict the propagation range. As a result, spatially heterogeneous molecular properties and/or weak couplings are shown to give rise to rich spatiotemporal dynamics that support complex propagation behaviors. These results shed new light on the mechanisms implicated in the propagation of Ca(2+ waves across astrocytes and the precise conditions under which glial cells may participate in information processing in the brain.
Evidence for Nonlinear VLF Wave Physics from Van Allen Probe Data
Crabtree, C. E.; Tejero, E. M.; Ganguli, G.; Hospodarsky, G. B.; Kletzing, C.
2015-12-01
VLF waves in the whistler mode branch in the Earth's radiation belts play a critical role in both the acceleration and loss of energetic electrons. VLF waves are often observed with magnetic field amplitudes that are a significant fraction of the background magnetic field suggesting that nonlinear effects may be important. We develop new Bayesian time-series analysis tools to investigate magnetic and electric field data from the EMFISIS instrument on board the Van Allen Probes. We also validate the analysis techniques through laboratory experiments. We apply these tools to Chorus waves to show that the picture of a single coherent plane wave is insufficient to explain EMFISIS data and that nonlinear collective wave interactions play an important role in moderating Chorus wave growth. We also apply these techniques to show that nonlinear induced scattering by thermal electrons can play a significant role in controlling the propagation of large amplitude lightning generated whistlers inside the plasmasphere.
Analytical Solitons for Langmuir Waves in Plasma Physics with Cubic Nonlinearity and Perturbations
Zhou, Qin; Mirzazadeh, M.
2016-09-01
We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schrödinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on the G'/G-expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.
High-order Boussinesq-type modelling of nonlinear wave phenomena in deep and shallow water
DEFF Research Database (Denmark)
Madsen, Per A.; Fuhrman, David R.
2010-01-01
In this work, we start with a review of the development of Boussinesq theory for water waves covering the period from 1872 to date. Previous reviews have been given by Dingemans,1 Kirby,2,3 and Madsen & Schäffer.4 Next, we present our most recent high-order Boussinesq-type formulation valid...... for fully nonlinear and highly dispersive waves traveling over a rapidly varying bathymetry. Finally, we cover applications of this Boussinesq model, and we study a number of nonlinear wave phenomena in deep and shallow water. These include (1) Kinematics in highly nonlinear progressive deep-water waves; (2......) Kinematics in progressive solitary waves; (3) Reflection of solitary waves from a vertical wall; (4) Reflection and diffraction around a vertical plate; (5) Quartet and quintet interactions and class I and II instabilities; (6) Extreme events from focused directionally spread waveelds; (7) Bragg scattering...
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have ... The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.
Surface and Internal Waves due to a Moving Load on a Very Large Floating Structure
Directory of Open Access Journals (Sweden)
Taro Kakinuma
2012-01-01
Full Text Available Interaction of surface/internal water waves with a floating platform is discussed with nonlinearity of fluid motion and flexibility of oscillating structure. The set of governing equations based on a variational principle is applied to a one- or two-layer fluid interacting with a horizontally very large and elastic thin plate floating on the water surface. Calculation results of surface displacements are compared with the existing experimental data, where a tsunami, in terms of a solitary wave, propagates across one-layer water with a floating thin plate. We also simulate surface and internal waves due to a point load, such as an airplane, moving on a very large floating structure in shallow water. The wave height of the surface or internal mode is amplified when the velocity of moving point load is equal to the surface- or internal-mode celerity, respectively.
From solitons to rogue waves in nonlinear left-handed metamaterials.
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.
Stimulated Raman scattering and ion dynamics: the role of Langmuir wave non-linearities
International Nuclear Information System (INIS)
Bonnaud, G.; Pesme, D.
1988-02-01
The non-linear evolution of stimulated Raman scattering by coupling of the SRS-driven Langmuir waves to ion acoustic waves is studied numerically, in a homogeneous density laser-irradiated plasma. The coupled wave amplitude behaviour is represented either by envelope equations or by complete wave-like equations. The various physical phenomena which are involved are described. This preliminary work has been presented at the 17th Anomalous Absorption Conference, held in last May, in Lake Tahoe City (USA) [fr
International Nuclear Information System (INIS)
Matsumoto, H.; Kimura, T.
1986-01-01
Triggered by the experimental results of the MINIX, a computer simulation study was initiated on the nonlinear excitation of electrostatic electron cyclotron waves by a monochromatic electromagnetic wave such as the transmitted microwave in the MINIX. The model used assumes that both of the excited waves and exciting (pumping) electromagnetic wave as well as the idler electromagnetic wave propagate in the direction perpendicular to the external magnetic field. The simulation code used for this study was the one-and-two-half dimensional electromagnetic particle code named KEMPO. The simulation result shows the high power electromagnetic wave produces both the backscattered electromagnetic wave and electrostatic electron cyclotron waves as a result of nonlinear parametric instability. Detailed nonlinear microphysics related to the wave excitation is discussed in terms of the nonlinear wave-wave couplings and associated ponderomotive force produced by the high power electromagnetic waves. 2 references, 4 figures
Nonlinear waves from a localized vortex source in strongly correlated fluids
Gupta, Akanksha; Ganesh, Rajaraman; Joy, Ashwin
2017-11-01
Highly charged quasi two-dimensional grain medium (complex plasma) is a remarkable test-bed to study wave like phenomena. Understanding of such wave propagation has many important applications in geophysics, petroleum engineering, and mining, earthquakes, and seismology. In the present study, for the first time, the propagation of nonlinear wave which originates from localized coherent vortex source has been studied using molecular dynamics simulation taking Yukawa liquids as a prototype for strongly correlated fluid. In this work, the coupling of transverse and longitudinal mode, effect of azimuthal speed of vortex source on the linear and nonlinear properties of generated wave will be presented as a function of strong correlation.
Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation
International Nuclear Information System (INIS)
Zhaqilao,
2013-01-01
A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed
Wave instabilities in nonlinear Schrödinger systems with non vanishing background
Trillo, Stefano
2014-01-01
We investigate wave collapse in the generalized nonlinear Schrödinger (NLS) equation and in the presence of a non vanishing background. Through the use of virial identities, we establish a new criterion for blow-up.
Nonlinear standing shear Alfven waves in the Earth`s magnetosphere
Energy Technology Data Exchange (ETDEWEB)
Rankin, R.; Frycz, P.; Tikhonchuk, V.T.; Samson, J. C. [Univ. of Alberta, Edmonton, Alberta (Canada)
1994-11-01
We present theory and numerical simulations of strong nonlinear effects in standing shear Alfven waves (SAWs) in the Earth`s magnetosphere, which is modeled as a finite size box with straight magnetic lines and (partially) reflecting boundaries. In a low beta plasma it is shown that the ponderomotive force can lead to a large-amplitude SAW spatial harmonic generation due to nonlinear coupling between the SAW and a slow magnetosonic wave. The nonlinear coupling leads to secularly growing frequency shifts, and in the case of driven systems, nonlinear dephasing can lead to saturation of the driven wave fields. The results are discussed on the context of their possible relevance to the theory of standing ionospheric cavity wave modes and field line resonances in the high-latitude magnetosphere.
Three-dimensional nonlinear waves under spatial confinement
Azhand, Arash
2016-01-01
The aim of my thesis is to study the evolution of scroll waves under spatial confinement both experimentally as well as numerically. Scroll waves represent three-dimensional (3D) analogs of spiral waves. In the simplest case, the central axis around which a scroll wave rotates is a straight line. The line is named the filament of the scroll wave, and each infinitesimal cross-section represents the core of a spiral wave. Two specific types of scroll waves are considered: (1) Straight scroll wa...
Using Python to Construct a Scalable Parallel Nonlinear Wave Solver
Mandli, Kyle
2011-01-01
Computational scientists seek to provide efficient, easy-to-use tools and frameworks that enable application scientists within a specific discipline to build and/or apply numerical models with up-to-date computing technologies that can be executed on all available computing systems. Although many tools could be useful for groups beyond a specific application, it is often difficult and time consuming to combine existing software, or to adapt it for a more general purpose. Python enables a high-level approach where a general framework can be supplemented with tools written for different fields and in different languages. This is particularly important when a large number of tools are necessary, as is the case for high performance scientific codes. This motivated our development of PetClaw, a scalable distributed-memory solver for time-dependent nonlinear wave propagation, as a case-study for how Python can be used as a highlevel framework leveraging a multitude of codes, efficient both in the reuse of code and programmer productivity. We present scaling results for computations on up to four racks of Shaheen, an IBM BlueGene/P supercomputer at King Abdullah University of Science and Technology. One particularly important issue that PetClaw has faced is the overhead associated with dynamic loading leading to catastrophic scaling. We use the walla library to solve the issue which does so by supplanting high-cost filesystem calls with MPI operations at a low enough level that developers may avoid any changes to their codes.
Finite-element based perturbation analysis of wave propagation in nonlinear periodic structures
Manktelow, Kevin; Narisetti, Raj K.; Leamy, Michael J.; Ruzzene, Massimo
2013-08-01
Wave propagation in continuous, periodic structures subject to weak nonlinearities is studied using a finite-element discretization of a single unit cell followed by a perturbation analysis. The dispersion analysis is integrated with commercial finite-element analysis (FEA) software to expedite nonlinear analysis of geometrically-complex unit cells. A simple continuous multilayer system is used to illustrate the principle aspects of the procedure. A periodic structure formed by membrane elements on nonlinear elastic supports is used to demonstrate the versatility of the procedure. Weakly nonlinear band diagrams are generated in which amplitude-dependent bandgaps and group velocities are identified. The nonlinear dispersion analysis procedure described, coupled with commercial FEA software, should facilitate the study of wave propagation in a wide-variety of geometrically-complex, nonlinear periodic structures.
DEFF Research Database (Denmark)
Pu, Minhao; Chen, Yaohui; Yvind, Kresten
2014-01-01
Influence of thermal effects induced by nonlinear absorption on four-wave mixing in silicon waveguides is investigated. A conversion bandwidth reduction up to 63% is observed in simulation due to the thermal effects.......Influence of thermal effects induced by nonlinear absorption on four-wave mixing in silicon waveguides is investigated. A conversion bandwidth reduction up to 63% is observed in simulation due to the thermal effects....
Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials
Energy Technology Data Exchange (ETDEWEB)
Ren, Jie [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Li, Nianbei [Tongji Univ., Shanghai Shi (China)
2014-02-18
Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study how to design the novel wave diode devices to realize the non-reciprocal wave propagations. Analytical results reveal that such non-reciprocal wave propagation can be purely induced by asymmetric geometry in nonlinear materials. The detailed numerical simulations are performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect has been demonstrated. The results open a way for making wave diodes efficiently simply through shape engineering.
Blow-Up of Solutions for a Class of Sixth Order Nonlinear Strongly Damped Wave Equation
Directory of Open Access Journals (Sweden)
Huafei Di
2014-01-01
Full Text Available We consider the blow-up phenomenon of sixth order nonlinear strongly damped wave equation. By using the concavity method, we prove a finite time blow-up result under assumptions on the nonlinear term and the initial data.
Statistical analysis of nonlinear wave interactions in simulated Langmuir turbulence data
Directory of Open Access Journals (Sweden)
J. Soucek
2003-03-01
Full Text Available We present a statistical analysis of strong turbulence of Langmuir and ion-sound waves resulting from beam-plasma interaction. The analysis is carried out on data sets produced by a numerical simulation of one-dimensional Zakharov’s equations. The nonlinear wave interactions are studied using two different approaches: high-order spectra and Volterra models. These methods were applied to identify two and three wave processes in the data, and the Volterra model was furthermore employed to evaluate the direction and magnitude of energy transfer between the wave modes in the case of Langmuir wave decay. We demonstrate that these methods allow one to determine the relative importance of strongly and weakly turbulent processes. The statistical validity of the results was thoroughly tested using surrogated data set analysis.Key words. Space plasma physics (wave-wave interactions; experimental and mathematical techniques; nonlinear phenomena
Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Kartashov, Yaroslav V [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain); Egorov, Alexey A [Physics Department, M V Lomonosov Moscow State University, 119899, Moscow (Russian Federation); Vysloukh, Victor A [Departamento de Fisica y Matematicas, Universidad de las Americas-Puebla, Santa Catarina Martir, 72820, Puebla, Cholula (Mexico); Torner, Lluis [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain)
2004-05-01
We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in the appearance of stability (instability) bands in a focusing (defocusing) medium, which is in sharp contrast with the properties of periodic waves in Kerr media. One of the key results discovered is the stabilization of multicolour periodic waves in quadratic media. In particular, dark-type waves are shown to be metastable, while bright-type waves are completely stable in a broad range of energy flows and material parameters. This yields the first known example of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons. Such results open the way to the experimental observation of the corresponding self-sustained periodic wave patterns.
Nonlinear evolution of perturbations in a thin fluid layer during wave formation
Prokudina, L. A.
2014-03-01
A mathematical model is presented for the state of a free surface of a thin fluid layer (a fluid film) in heat-mass-exchange processes of condensation and evaporation. The wave motion of a fluid film is studied under inhomogeneous surface tension. Nonlinear development of perturbations belonging to a continuous band of wave numbers on the surface of a thin fluid layer is investigated within the framework of a non-linear parabolic equation. It is shown that wave packets with carrier wave lying near the harmonic of maximum increment become self-ordered; as a result, a monochromatic wave is generated on the surface of the fluid film. When a wave packet is generated in the neighborhood of the neutral stability curve, one can observe a phenomenon of directed energy transfer to the waves in the neighborhood of the harmonic of maximum increment.
Three Waves of International Student Mobility (1999-2020)
Choudaha, Rahul
2017-01-01
This article analyses the changes in international student mobility from the lens of three overlapping waves spread over seven years between 1999 and 2020. Here a wave is defined by the key events and trends impacting international student mobility within temporal periods. Wave I was shaped by the terrorist attacks of 2001 and enrolment of…
Bed failure induced by internal solitary waves
Rivera-Rosario, Gustavo A.; Diamessis, Peter J.; Jenkins, James T.
2017-07-01
The pressure field inside a porous bed induced by the passage of an Internal Solitary Wave (ISW) of depression is examined using high-accuracy numerical simulations. The velocity and density fields are obtained by solving the Dubreil-Jacotin-Long Equation, for a two-layer, continuously stratified water column. The total wave-induced pressure across the surface of the bed is computed by vertically integrating for the hydrostatic and nonhydrostatic contributions. The bed is assumed to be a continuum composed of either sand or silt, with a small amount of trapped gas. Results show variations in pore-water pressure penetrating deeper into more conductive materials and remaining for a prolonged period after the wave has passed. In order to quantify the potential for failure, the vertical pressure gradient is compared against the buoyant weight of the bed. The pressure gradient exceeds this weight for weakly conductive materials. Failure is further enhanced by a decrease in bed saturation, consistent with studies in surface-wave induced failure. In deeper water, the ISW-induced pressure is stronger, causing failure only for weakly conductive materials. The pressure associated with the free-surface displacement that accompanies ISWs is significant, when the water depth is less than 100 m, but has little influence when it is greater than 100 m, where the hydrostatic pressure due to the pycnocline displacement is much larger. Since the pore-pressure gradient reduces the specific weight of the bed, results show that particles are easier for the flow to suspend, suggesting that pressure contributes to the powerful resuspension events observed in the field.
Dynamic responses of a riser under combined excitation of internal waves and background currents
Directory of Open Access Journals (Sweden)
Lou Min
2014-09-01
Full Text Available In this study, the dynamic responses of a riser under the combined excitation of internal waves and background currents are studied. A modified Taylor-Goldstein equation is used to calculate the internal waves vertical structures when background currents exist. By imposing rigid-lid boundary condition, the equation is solved by Thompson-Haskell method. Based on the principle of virtual work, a nonlinear differential equation for riser motions is established combined with the modified Morison formula. Using Newmark-β method, the motion equation is solved in time domain. It is observed that the internal waves without currents exhibit dominated effect on dynamic response of a riser in the first two modes. With the effects of the background currents, the motion displacements of the riser will increase significantly in both cases that wave goes along and against the currents. This phenomenon is most obviously observed at the motions in the first mode
Dynamic responses of a riser under combined excitation of internal waves and background currents
Directory of Open Access Journals (Sweden)
Min Lou
2014-09-01
Full Text Available In this study, the dynamic responses of a riser under the combined excitation of internal waves and background currents are studied. A modified Taylor-Goldstein equation is used to calculate the internal waves vertical structures when background currents exist. By imposing rigid-lid boundary condition, the equation is solved by Thompson-Haskell method. Based on the principle of virtual work, a nonlinear differential equation for riser motions is established combined with the modified Morison formula. Using Newmark-β method, the motion equation is solved in time domain. It is observed that the internal waves without currents exhibit dominated effect on dynamic response of a riser in the first two modes. With the effects of the background currents, the motion displacements of the riser will increase significantly in both cases that wave goes along and against the currents. This phenomenon is most obviously observed at the motions in the first mode.
Dynamic responses of a riser under combined excitation of internal waves and background currents
Lou, Min; Yu, Chenglong
2014-09-01
In this study, the dynamic responses of a riser under the combined excitation of internal waves and background currents are studied. A modified Taylor-Goldstein equation is used to calculate the internal waves vertical structures when background currents exist. By imposing rigid-lid boundary condition, the equation is solved by Thompson-Haskell method. Based on the principle of virtual work, a nonlinear differential equation for riser motions is established combined with the modified Morison formula. Using Newmark-β method, the motion equation is solved in time domain. It is observed that the internal waves without currents exhibit dominated effect on dynamic response of a riser in the first two modes. With the effects of the background currents, the motion displacements of the riser will increase significantly in both cases that wave goes along and against the currents. This phenomenon is most obviously observed at the motions in the first mode
DEFF Research Database (Denmark)
Stroescu, Ionut Emanuel; Sørensen, Lasse; Frigaard, Peter Bak
2016-01-01
A non-linear stretching method was implemented for stream function theory to solve wave kinematics for physical conditions close to breaking waves in shallow waters, with wave heights limited by the water depth. The non-linear stretching method proves itself robust, efficient and fast, showing good...
Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.
2010-01-01
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices. By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite number of exact soliton solutions in terms of the Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite bandgap of the optical-lattice-induced spectrum. Starting from the exact solutions, we employ the relaxation met...
New travelling wave solutions for nonlinear stochastic evolution ...
Indian Academy of Sciences (India)
The investigation of exact solutions of nonlinear evolution equations play an important role in the study of nonlinear physical phenomena. In the past several decades, many powerful methods such as differential transform method [1,2], the extended tanh method. [3,4], the exp-function method [5–8], variational iteration ...
Blowing-up semilinear wave equation with exponential nonlinearity ...
Indian Academy of Sciences (India)
H1-norm. Hence, it is legitimate to consider an exponential nonlinearity. Moreover, the choice of an exponential nonlinearity emerges from a possible control of solutions via a. Moser–Trudinger type inequality [1, 16, 19]. In fact, Nakamura and Ozawa [17] proved global well-posedness and scattering for small Cauchy data in ...
Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.
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.
The soliton transform and a possible application to nonlinear Alfven waves in space
Hada, T.; Hamilton, R. L.; Kennel, C. F.
1993-01-01
The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.
Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 1
International Nuclear Information System (INIS)
Krivitsky, V.S.; Vladimirov, S.V.
1991-01-01
An expression is obtained for the collision integral describing the simultaneous interaction of plasma particles with resonant and non-resonant waves. It is shown that this collision integral is determined by two processes: a 'direct' nonlinear interaction of particles and waves, and the influence of the non-stationary of the system. The expression for the nonlinear collision integral is found to be quite different from the expression for a quasi-linear collision integral; in particular, the nonlinear integral contains higher-order derivatives of the distribution function with respect to momentum than the quasi-linear one. (author)
Non-Linear Langmuir Wave Modulation in Collisionless Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans
1977-01-01
in the expressions concerning the modulation instability of a plane Langmuir wave. When the Vlasov equation for the ions is applied, a Langmuir wave is modulationally unstable for arbitrary perturbations independent of the unperturbed wave amplitude, in contrast to what is found for fluid ions. A simple analogy...
Ultrasonic nonlinear guided wave inspection of microscopic damage in a composite structure
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.
Rogue wave solutions of the nonlinear Schrödinger eqution with ...
Indian Academy of Sciences (India)
In this paper, a unified formula of a series of rogue wave solutions for the standard (1+1)-dimensional nonlinear Schrödinger equation is obtained through exp-function method. Further, by means of an appropriate transformation and previously obtained solutions, rogue wave solutions of the variable coefficient Schrödinger ...
Nonlinear sausage-wave propagation in a magnetic slab in an incompressible fluid
Ruderman, M. S.
1993-04-01
Long nonlinear sausage-wave propagation in a magnetic slab in an incompressible plasma is considered. The governing equation is derived with the aid of the reductive perturbation method. The solutions of this equation in the form of periodic waves of permanent shape are found numerically.
Plasma heating by non-linear wave-Plasma interaction | Echi ...
African Journals Online (AJOL)
We simulate the non-linear interaction of waves with magnetized tritium plasma with the aim of determining the parameter values that characterize the response of the plasma. The wave-plasma interaction has a non-conservative Hamiltonian description. The resulting system of Hamilton's equations is integrated numerically ...
Rogue wave solutions of the nonlinear Schrödinger equation with ...
Indian Academy of Sciences (India)
solutions of the variable coefficient Schrödinger equation are also obtained. Two free functions of time t and several arbitrary parameters are involved to generate a large number of wave structures. Keywords. Nonlinear Schrödinger equation; exp-function method; breather soliton; rogue wave. PACS Nos 02.30.Jr; 05.45.
Nonlinear Ultrasonic Techniques to Monitor Radiation Damage in RPV and Internal Components
Energy Technology Data Exchange (ETDEWEB)
Jacobs, Laurence [Georgia Inst. of Technology, Atlanta, GA (United States); Kim, Jin-Yeon [Georgia Inst. of Technology, Atlanta, GA (United States); Qu, Jisnmin [Northwestern Univ., Evanston, IL (United States); Ramuhalli, Pradeep [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Wall, Joe [Electric Power Research Inst. (EPRI), Knoxville, TN (United States)
2015-11-02
The objective of this research is to demonstrate that nonlinear ultrasonics (NLU) can be used to directly and quantitatively measure the remaining life in radiation damaged reactor pressure vessel (RPV) and internal components. Specific damage types to be monitored are irradiation embrittlement and irradiation assisted stress corrosion cracking (IASCC). Our vision is to develop a technique that allows operators to assess damage by making a limited number of NLU measurements in strategically selected critical reactor components during regularly scheduled outages. This measured data can then be used to determine the current condition of these key components, from which remaining useful life can be predicted. Methods to unambiguously characterize radiation related damage in reactor internals and RPVs remain elusive. NLU technology has demonstrated great potential to be used as a material sensor – a sensor that can continuously monitor a material’s damage state. The physical effect being monitored by NLU is the generation of higher harmonic frequencies in an initially monochromatic ultrasonic wave. The degree of nonlinearity is quantified with the acoustic nonlinearity parameter, β, which is an absolute, measurable material constant. Recent research has demonstrated that nonlinear ultrasound can be used to characterize material state and changes in microscale characteristics such as internal stress states, precipitate formation and dislocation densities. Radiation damage reduces the fracture toughness of RPV steels and internals, and can leave them susceptible to IASCC, which may in turn limit the lifetimes of some operating reactors. The ability to characterize radiation damage in the RPV and internals will enable nuclear operators to set operation time thresholds for vessels and prescribe and schedule replacement activities for core internals. Such a capability will allow a more clear definition of reactor safety margins. The research consists of three tasks: (1
Lee, Seung-Heon; Lu, Jian; Lee, Seung-Jun; Han, Jae-Hyun; Jeong, Chan-Uk; Lee, Seung-Chul; Li, Xian; Jazbinšek, Mojca; Yoon, Woojin; Yun, Hoseop; Kang, Bong Joo; Rotermund, Fabian; Nelson, Keith A; Kwon, O-Pil
2017-08-01
Highly efficient nonlinear optical organic crystals are very attractive for various photonic applications including terahertz (THz) wave generation. Up to now, only two classes of ionic crystals based on either pyridinium or quinolinium with extremely large macroscopic optical nonlinearity have been developed. This study reports on a new class of organic nonlinear optical crystals introducing electron-accepting benzothiazolium, which exhibit higher electron-withdrawing strength than pyridinium and quinolinium in benchmark crystals. The benzothiazolium crystals consisting of new acentric core HMB (2-(4-hydroxy-3-methoxystyryl)-3-methylbenzo[d]thiazol-3-ium) exhibit extremely large macroscopic optical nonlinearity with optimal molecular ordering for maximizing the diagonal second-order nonlinearity. HMB-based single crystals prepared by simple cleaving method satisfy all required crystal characteristics for intense THz wave generation such as large crystal size with parallel surfaces, moderate thickness and high optical quality with large optical transparency range (580-1620 nm). Optical rectification of 35 fs pulses at the technologically very important wavelength of 800 nm in 0.26 mm thick HMB crystal leads to one order of magnitude higher THz wave generation efficiency with remarkably broader bandwidth compared to standard inorganic 0.5 mm thick ZnTe crystal. Therefore, newly developed HMB crystals introducing benzothiazolium with extremely large macroscopic optical nonlinearity are very promising materials for intense broadband THz wave generation and other nonlinear optical applications. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Shoji, Masafumi; Miyoshi, Yoshizumi; Katoh, Yuto; Keika, Kunihiro; Angelopoulos, Vassilis; Kasahara, Satoshi; Asamura, Kazushi; Nakamura, Satoko; Omura, Yoshiharu
2017-09-01
Electromagnetic plasma waves are thought to be responsible for energy exchange between charged particles in space plasmas. Such an energy exchange process is evidenced by phase space holes identified in the ion distribution function and measurements of the dot product of the plasma wave electric field and the ion velocity. We develop a method to identify ion hole formation, taking into consideration the phase differences between the gyromotion of ions and the electromagnetic ion cyclotron (EMIC) waves. Using this method, we identify ion holes in the distribution function and the resulting nonlinear EMIC wave evolution from Time History of Events and Macroscale Interactions during Substorms (THEMIS) observations. These ion holes are key to wave growth and frequency drift by the ion currents through nonlinear wave-particle interactions, which are identified by a computer simulation in this study.
A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation.
Bou Matar, Olivier; Guerder, Pierre-Yves; Li, YiFeng; Vandewoestyne, Bart; Van Den Abeele, Koen
2012-05-01
A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb's problem and plane wave nonlinear propagation.
Non-Linear Numerical Modeling and Experimental Testing of a Point Absorber Wave Energy Converter
DEFF Research Database (Denmark)
Zurkinden, Andrew Stephen; Ferri, Francesco; Beatty, S.
2014-01-01
the calculation of the non-linear hydrostatic restoring moment by a cubic polynomial function fit to laboratory test results. Moreover, moments due to viscous drag are evaluated on the oscillating hemisphere considering the horizontal and vertical drag force components. The influence on the motions of this non.......e. H/λ≤0.02. For steep waves, H/λ≥0.04 however, the relative velocities between the body and the waves increase thus requiring inclusion of the non-linear hydrostatic restoring moment to effectively predict the dynamics of the wave energy converter. For operation of the device with a passively damping...
Bulk Nonlinear Elastic Strain Waves in a Bilayer Coaxial Cylindrical Rod
Gula, I. A.; Samsonov, A. M.
2017-12-01
The problem of the propagation of long nonlinear elastic strain waves in a bilayer coaxial cylindrical rod with an ideal contact between the layers has been considered. Expressions for transverse displacements through longitudinal displacements have been derived. The former satisfies free boundary conditions and continuity conditions for displacements and stresses at the interlayer interface with the desired accuracy. It has been shown how these expressions generalize the well-known plane-section and Love hypotheses for an isotropic homogeneous rod. An equation for the propagation of a nonlinearly elastic strain longitudinal wave has been derived, and its particular solution in the form of a solitary traveling wave has been studied.
Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Samiran, E-mail: sran_g@yahoo.com [Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata-700 009 (India); Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata-700064 (India)
2016-08-15
The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.
Nonlinear wave breaking in self-gravitating viscoelastic quantum fluid
Energy Technology Data Exchange (ETDEWEB)
Mitra, Aniruddha, E-mail: anibabun@gmail.com [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India); Roychoudhury, Rajkumar, E-mail: rajdaju@rediffmail.com [Advanced Centre for Nonlinear and Complex Phenomena, 1175 Survey Park, Kolkata 700075 (India); Department of Mathematics, Bethune College, Kolkata 700006 (India); Bhar, Radhaballav [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India); Khan, Manoranjan, E-mail: mkhan.ju@gmail.com [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India)
2017-02-12
The stability of a viscoelastic self-gravitating quantum fluid has been studied. Symmetry breaking instability of solitary wave has been observed through ‘viscosity modified Ostrovsky equation’ in weak gravity limit. In presence of strong gravitational field, the solitary wave breaks into shock waves. Response to a Gaussian perturbation, the system produces quasi-periodic short waves, which in terns predicts the existence of gravito-acoustic quasi-periodic short waves in lower solar corona region. Stability analysis of this dynamical system predicts gravity has the most prominent effect on the phase portraits, therefore, on the stability of the system. The non-existence of chaotic solution has also been observed at long wavelength perturbation through index value theorem. - Highlights: • In weak gravitational field, viscoelastic quantum fluid exhibits symmetry breaking instability. • Gaussian perturbation produces quasi-periodic gravito-acoustic waves into the system. • There exists no chaotic state of the system against long wavelength perturbations.
Spectro-spatial analysis of wave packet propagation in nonlinear acoustic metamaterials
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.
Zhao, Youxuan; Li, Feilong; Cao, Peng; Liu, Yaolu; Zhang, Jianyu; Fu, Shaoyun; Zhang, Jun; Hu, Ning
2017-08-01
Since the identification of micro-cracks in engineering materials is very valuable in understanding the initial and slight changes in mechanical properties of materials under complex working environments, numerical simulations on the propagation of the low frequency S 0 Lamb wave in thin plates with randomly distributed micro-cracks were performed to study the behavior of nonlinear Lamb waves. The results showed that while the influence of the randomly distributed micro-cracks on the phase velocity of the low frequency S 0 fundamental waves could be neglected, significant ultrasonic nonlinear effects caused by the randomly distributed micro-cracks was discovered, which mainly presented as a second harmonic generation. By using a Monte Carlo simulation method, we found that the acoustic nonlinear parameter increased linearly with the micro-crack density and the size of micro-crack zone, and it was also related to the excitation frequency and friction coefficient of the micro-crack surfaces. In addition, it was found that the nonlinear effect of waves reflected by the micro-cracks was more noticeable than that of the transmitted waves. This study theoretically reveals that the low frequency S 0 mode of Lamb waves can be used as the fundamental waves to quantitatively identify micro-cracks in thin plates. Copyright © 2017 Elsevier B.V. All rights reserved.
Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices
Gao, Xuzhen; Zeng, Jianhua
2018-02-01
The nonlinear lattice — a new and nonlinear class of periodic potentials — was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting — the cubic and quintic model — by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully "nonlinear quasi-crystal". A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov-Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode — the fundamental and vortex solitons — are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross-Pitaevskii equation or nonlinear Schrödinger equation, the predicted localized modes thus may be implemented in Bose-Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.
Modeling Non-linear Ocean Wave Amplification in Coastal Settings
Harrington, J. P.; Cox, R.; Brennan, J.; Clancy, C.; Herterich, J.; Dias, F.
2016-12-01
Coastal boulder deposits occur in many locations worldwide, along high-energy coastlines. They contain clasts with masses >100 t in some cases, deposited many m above high water and many tens of m inland, often at the top of steep cliffs. The clasts are moved by storm waves, despite being at elevations and inshore distances that should be unreachable by recorded sea states. The question is, therefore, how are storm waves amplified to the extent needed to transport megagravel inshore? As climate changes, with the risk of increased storminess, it is important to understand this issue, as it is central to understanding inland transmission of fluid forces during storm events. Numerical modeling is a powerful technique for exploring this complex problem. We used a conformal mapping solution to Euler's equations to explore runup of 2D wave trains against a vertical barrier (simulating a coastal cliff). Previous research showed that modeled wave trains passing over flat bathymetry experience vertical runup up to 6 times the initial wave amplitude for both short- (3 times water depth) and long- (125 times depth) wavelength waves. We increased the model complexity by including a bathymetric step, causing an abrupt depth decrease before the cliff. We found that the uneven bathymetry further amplified both short- and long-wavelength waves. Short-wavelength simulations were hampered by our code's limitations in solving Euler's equations for steep waves, and crashed before reaching maximum runups: ongoing work focuses on solving the computational problems. These problems did not affect the long-wavelength simulations, however, which returned maximum runup values up to 10 times initial amplitude. The key message is that bathymetric effects can drive large wave-height amplifications. This suggests that enhanced runup for long-wavelength waves caused by variable bathymetry could be a key factor in cases where ocean waves overtop steep cliffs and transport boulders well above high
Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System
Li, Hailiang; Wang, Yi; Yang, Tong; Zhong, Mingying
2018-04-01
The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133-179, 2004) and Liu et al. (Physica D 188:178-192, 2004), we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665-725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.
Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory
Gnutzmann, Sven; Waltner, Daniel
2016-03-01
In this paper we present a general framework for solving the stationary nonlinear Schrödinger equation (NLSE) on a network of one-dimensional wires modeled by a metric graph with suitable matching conditions at the vertices. A formal solution is given that expresses the wave function and its derivative at one end of an edge (wire) nonlinearly in terms of the values at the other end. For the cubic NLSE this nonlinear transfer operation can be expressed explicitly in terms of Jacobi elliptic functions. Its application reduces the problem of solving the corresponding set of coupled ordinary nonlinear differential equations to a finite set of nonlinear algebraic equations. For sufficiently small amplitudes we use canonical perturbation theory, which makes it possible to extract the leading nonlinear corrections over large distances.
Towards nonlinear wave reconstruction and prediction from synthetic radar images
Wijaya, Andreas Parama
2016-01-01
The use of remotely wave sensing by a marine radar is increasingly needed to provide wave information for the sake of safety and operational effectiveness in many offshore activities. Reconstruction of radar images needs to be carried out since radar images are a poor representation of the sea
Nonlinear wave propagation through a ferromagnet with damping in ...
Indian Academy of Sciences (India)
magnetic waves in a ferromagnet can be reduced to an integro-differential equation. Keywords. Solitons; integro-differential equations; reductive perturbation method. PACS Nos 41.20 Jb; 05.45 Yv; 03.50 De; 78.20 Ls. 1. Introduction. The phenomenon of propagation of electromagnetic waves in ferromagnets are not only.
Interpretation of nonlinearity in wind generated ocean surface waves
Digital Repository Service at National Institute of Oceanography (India)
Varkey, M.J.
This study attempts to resolve a mix-up between a physical process and its mathematical interpretation in the context of wind waves on ocean surface. Wind generated wave systems, are conventionally interpreted as a result of interaction of a number...
Nonlinear wave propagation through a ferromagnet with damping in ...
Indian Academy of Sciences (India)
wavelength in (2+1) dimensions. The purpose of the present work is to study the property of electromagnetic waves of long wavelength propagating through an isotropic ferromagnet in the classical continuum limit in (2+1) dimensions taking into account the dissipative effect. By using the long wave approximation of the ...
Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.
2010-09-01
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.
International Nuclear Information System (INIS)
Zhang Jiefang; Meng Jianping; Wu Lei; Li Yishen; Malomed, Boris A.
2010-01-01
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.
Dynamics of unstable sound waves in a non-equilibrium medium at the nonlinear stage
Khrapov, Sergey; Khoperskov, Alexander
2018-03-01
A new dispersion equation is obtained for a non-equilibrium medium with an exponential relaxation model of a vibrationally excited gas. We have researched the dependencies of the pump source and the heat removal on the medium thermodynamic parameters. The boundaries of sound waves stability regions in a non-equilibrium gas have been determined. The nonlinear stage of sound waves instability development in a vibrationally excited gas has been investigated within CSPH-TVD and MUSCL numerical schemes using parallel technologies OpenMP-CUDA. We have obtained a good agreement of numerical simulation results with the linear perturbations dynamics at the initial stage of the sound waves growth caused by instability. At the nonlinear stage, the sound waves amplitude reaches the maximum value that leads to the formation of shock waves system.
Identification of nonlinear coupling in wave turbulence at the surface of water
Campagne, Antoine; Hassaini, Roumaissa; Redor, Ivan; Aubourg, Quentin; Sommeria, Joël; Mordant, Nicolas
2017-11-01
The Weak Turbulence Theory is a theory, in the limit of vanishing nonlinearity, that derive analytically statistical features of wave turbulence. The stationary spectrum for the surface elevation in the case of gravity waves, is predicted to E(k) k - 5 / 2 . This spectral exponent -5/2 remains elusive in all experiments. in which the measured exponent is systematically lower than the prediction. Furthermore in the experiments the weaker the nonlinearity the further the spectral exponent is from the prediction. In order to investigate the reason for this observation we developed an experiment in the CORIOLIS facility in Grenoble. It is a 13m-diameter circular pool filled with water with a 70 cm depth. We generate wave turbulence by using two wedge wavemakers. Surface elevation measurements are performed by a stereoscopic optical technique and by capacitive probes. The nonlinear coupling at work in this system are analyzed by computing 3- and 4-wave correlations of the Fourier wave amplitudes in frequency. Theory predicts that coupling should occur through 4-wave resonant interaction. In our data, strong 3-wave correlations are observed in addition to the 4-wave correlation. Most our observations are consistent with field observation in the Black Sea (Leckler et al. 2015). This project has received funding from the European Research Council (ERC, Grant Agreement No 647018-WATU).
Observing and modeling nonlinear dynamics in an internal combustion engine
International Nuclear Information System (INIS)
Daw, C.S.; Kennel, M.B.; Finney, C.E.; Connolly, F.T.
1998-01-01
We propose a low-dimensional, physically motivated, nonlinear map as a model for cyclic combustion variation in spark-ignited internal combustion engines. A key feature is the interaction between stochastic, small-scale fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Residual cylinder gas from each cycle alters the in-cylinder fuel-air ratio and thus the combustion efficiency in succeeding cycles. The model close-quote s simplicity allows rapid simulation of thousands of engine cycles, permitting statistical studies of cyclic-variation patterns and providing physical insight into this technologically important phenomenon. Using symbol statistics to characterize the noisy dynamics, we find good quantitative matches between our model and experimental time-series measurements. copyright 1998 The American Physical Society
A Numerical Implementation of a Nonlinear Mild Slope Model for Shoaling Directional Waves
Directory of Open Access Journals (Sweden)
Justin R. Davis
2014-02-01
Full Text Available We describe the numerical implementation of a phase-resolving, nonlinear spectral model for shoaling directional waves over a mild sloping beach with straight parallel isobaths. The model accounts for non-linear, quadratic (triad wave interactions as well as shoaling and refraction. The model integrates the coupled, nonlinear hyperbolic evolution equations that describe the transformation of the complex Fourier amplitudes of the deep-water directional wave field. Because typical directional wave spectra (observed or produced by deep-water forecasting models such as WAVEWATCH III™ do not contain phase information, individual realizations are generated by associating a random phase to each Fourier mode. The approach provides a natural extension to the deep-water spectral wave models, and has the advantage of fully describing the shoaling wave stochastic process, i.e., the evolution of both the variance and higher order statistics (phase correlations, the latter related to the evolution of the wave shape. The numerical implementation (a Fortran 95/2003 code includes unidirectional (shore-perpendicular propagation as a special case. Interoperability, both with post-processing programs (e.g., MATLAB/Tecplot 360 and future model coupling (e.g., offshore wave conditions from WAVEWATCH III™, is promoted by using NetCDF-4/HD5 formatted output files. The capabilities of the model are demonstrated using a JONSWAP spectrum with a cos2s directional distribution, for shore-perpendicular and oblique propagation. The simulated wave transformation under combined shoaling, refraction and nonlinear interactions shows the expected generation of directional harmonics of the spectral peak and of infragravity (frequency <0.05 Hz waves. Current development efforts focus on analytic testing, development of additional physics modules essential for applications and validation with laboratory and field observations.
Evidence and effects of a wave-driven nonlinear current in the equatorial electrojet
Directory of Open Access Journals (Sweden)
M. Oppenheim
1997-07-01
Full Text Available Ionospheric two-stream waves and gradient-drift waves nonlinearly drive a large-scale (D.C. current in the E-region ionosphere. This current flows parallel to, and with a comparable magnitude to, the fundamental Pedersen current. Evidence for the existence and magnitude of wave-driven currents derives from a theoretical understanding of E-region waves, supported by a series of nonlinear 2D simulations of two-stream waves and by data collected by rocket instruments in the equatorial electrojet. Wave-driven currents will modify the large-scale dynamics of the equatorial electrojet during highly active periods. A simple model shows how a wave-driven current appreciably reduces the horizontally flowing electron current of the electrojet. This reduction may account for the observation that type-I radar echoes almost always have a Doppler velocity close to the acoustic speed, and also for the rocket observation that electrojet regions containing gradient-drift waves do not appear also to contain horizontally propagating two-stream waves. Additionally, a simple model of a gradient-drift instability shows that wave-driven currents can cause nonsinusoidal electric fields similar to those measured in situ.
Nonlinear wave energy modelling in the surf zone
Directory of Open Access Journals (Sweden)
Th. V. Karambas
1996-01-01
Full Text Available Breaking wave energy in the surf zone is modelled through the incorporation of the time dependent energy balance equation in a non linear dispersive wave propagation model. The energy equations solved simultaneously with the momentum and continuity equation. Turbulence effects and the non uniform horizontal velocity distribution due to breaking is introduced in both the energy and momentum equations. The dissipation term is a function of the velocity defect derived from a turbulent analysis. The resulting system predicts both wave characteristics (surface elevation and velocity and the energy distribution inside surf zone. The model is validated against experimental data and analytical expressions.
Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice
International Nuclear Information System (INIS)
Abdullaev, F. Kh.; Tomio, Lauro; Gammal, A.; Luz, H. L. F. da
2007-01-01
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation
Three-wave interaction in two-component quadratic nonlinear lattices
DEFF Research Database (Denmark)
Konotop, V. V.; Cunha, M. D.; Christiansen, Peter Leth
1999-01-01
We investigate a two-component lattice with a quadratic nonlinearity and find with the multiple scale technique that integrable three-wave interaction takes place between plane wave solutions when these fulfill resonance conditions. We demonstrate that. energy conversion and pulse propagation known...... from three-wave interaction is reproduced in the lattice and that exact phase matching of parametric processes can be obtained in non-phase-matched lattices by tilting the interacting plane waves with respect to each other. [S1063-651X(99)15110-9]....
Nonlinear Evolution Equations for Broader Bandwidth Wave Packets in Crossing Sea States
Directory of Open Access Journals (Sweden)
S. Debsarma
2014-01-01
Full Text Available Two coupled nonlinear equations are derived describing the evolution of two broader bandwidth surface gravity wave packets propagating in two different directions in deep water. The equations, being derived for broader bandwidth wave packets, are applicable to more realistic ocean wave spectra in crossing sea states. The two coupled evolution equations derived here have been used to investigate the instability of two uniform wave trains propagating in two different directions. We have shown in figures the behaviour of the growth rate of instability of these uniform wave trains for unidirectional as well as for bidirectional perturbations. The figures drawn here confirm the fact that modulational instability in crossing sea states with broader bandwidth wave packets can lead to the formation of freak waves.
Nonlinear Modeling and Analysis of Pressure Wave inside CEUP Fuel Pipeline
Directory of Open Access Journals (Sweden)
Qaisar Hayat
2014-01-01
Full Text Available Operating conditions dependent large pressure variations are one of the working characteristics of combination electronic unit pump (CEUP fuel injection system for diesel engines. We propose a precise and accurate nonlinear numerical model of pressure inside HP fuel pipeline of CEUP using wave equation (WE including both viscous and frequency dependent frictions. We have proved that developed hyperbolic approximation gives more realistic description of pressure wave as compared to classical viscous damped wave equation. Frictional effects of various frequencies on pressure wave have been averaged out across valid frequencies to represent the combined effect of all frequencies on pressure wave. Dynamic variations of key fuel properties including density, acoustic wave speed, and bulk modulus with varying pressures have also been incorporated. Based on developed model we present analysis on effect of fuel pipeline length on pressure wave propagation and variation of key fuel properties with both conventional diesel and alternate fuel rapeseed methyl ester (RME for CEUP pipeline.
On the solution of the equations for nonlinear interaction of three damped waves
International Nuclear Information System (INIS)
1976-01-01
Three-wave interactions are analyzed in a coherent wave description assuming different linear damping (or growth) of the individual waves. It is demonstrated that when two of the coefficients of dissipation are equal, the set of equations can be reduced to a single equivalent equation, which in the nonlinearly unstable case, where one wave is undamped, asymptotically takes the form of an equation defining the third Painleve transcendent. It is then possible to find an asymptotic expansion near the time of explosion. This solution is of principal interest since it indicates that the solution of the general three-wave system, where the waves undergo different individual dissipations, belongs to a higher class of functions, which reduces to Jacobian elliptic functions only in the case where all waves suffer the same damping [fr
Optimized nonlinear inversion of surface-wave dispersion data
International Nuclear Information System (INIS)
Raykova, Reneta B.
2014-01-01
A new code for inversion of surface wave dispersion data is developed to obtain Earth’s crustal and upper mantle velocity structure. The author developed Optimized Non–Linear Inversion ( ONLI ) software, based on Monte-Carlo search. The values of S–wave velocity VS and thickness h for a number of horizontal homogeneous layers are parameterized. Velocity of P–wave VP and density ρ of relevant layers are calculated by empirical or theoretical relations. ONLI explores parameters space in two modes, selective and full search, and the main innovation of software is evaluation of tested models. Theoretical dispersion curves are calculated if tested model satisfied specific conditions only, reducing considerably the computation time. A number of tests explored impact of parameterization and proved the ability of ONLI approach to deal successfully with non–uniqueness of inversion problem. Key words: Earth’s structure, surface–wave dispersion, non–linear inversion, software
NONLINEAR ULTRASONIC WAVE MODULATION TOMOGRAPHY FOR DAMAGED ZONE LOCATION
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk
-, - (2008), s. 14-17 ISSN 1213-3825. [WCNDT /17./. Šanghaj, 24.10.2008-28.10.2008] Institutional research plan: CEZ:AV0Z20760514 Keywords : nonlinear ultrasonic spectroscopy * defects localization * aircraft structure Subject RIV: BI - Acoustics
Solitary wave solutions of two-dimensional nonlinear Kadomtsev ...
Indian Academy of Sciences (India)
Aly R Seadawy
2017-09-13
Sep 13, 2017 ... We considered the two-dimensional DASWs in colli- sionless, unmagnetized cold plasma consisting of dust fluid, ions and electrons. The dynamics of DASWs is governed by the normalized fluid equations of nonlin- ear continuity (1), nonlinear motion of system (2) and. (3) and linear Poisson equation (4) as.
Solitary wave solutions to nonlinear evolution equations in ...
Indian Academy of Sciences (India)
This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of ...
Breathers and rogue waves: Demonstration with coupled nonlinear ...
Indian Academy of Sciences (India)
. ∗ and M LAKSHMANAN. Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University,. Tiruchirappalli 620 024, India. ∗. Corresponding author. E-mail: velan@cnld.bdu.ac.in. DOI: 10.1007/s12043-015-0937-4; ePublication: ...
Relativistic nonlinearity and wave-guide propagation of rippled laser ...
Indian Academy of Sciences (India)
In the present paper we have investigated the self-focusing behaviour of radially symmetrical rippled Gaussian laser beam propagating in a plasma. Considering the nonlinearity to arise ... ripple as well as on the beam width. Values of critical power has been calculated for different values of the position parameter of ripple.
Solitary wave solutions of selective nonlinear diffusion-reaction ...
Indian Academy of Sciences (India)
An auto-Bäcklund transformation derived in the homogeneous balance method is employed to obtain several new exact solutions of certain kinds of nonlinear diffusion-reaction (D-R) equations. These equations arise in a variety of problems in physical, chemical, biological, social and ecological sciences.
Relativistic nonlinearity and wave-guide propagation of rippled laser ...
Indian Academy of Sciences (India)
Abstract. In the present paper we have investigated the self-focusing behaviour of radially sym- metrical rippled Gaussian laser beam propagating in a plasma. Considering the nonlinearity to arise from relativistic phenomena and following the approach of Akhmanov et al, which is based on the. WKB and paraxial-ray ...
Nonlinear coherent four-wave-mixing in optical microscopy
Potma, Eric O.; Boeij, Wim P. de; Wiersma, Douwe A.
2000-01-01
We present a detailed theoretical analysis of the imaging properties of coherent nonlinear microscopes. We have developed a model that allows calculation of the generation and propagation of coherent signals under high numerical aperture (NA) conditions without invoking the slowly varying envelope
Nonlinear wave damping due to multi-plasmon resonances
Brodin, G.; Ekman, R.; Zamanian, J.
2018-02-01
For short wavelengths, it is well known that the linearized Wigner–Moyal equation predicts wave damping due to wave-particle interaction, where the resonant velocity shifted from the phase velocity by a velocity {v}q={{\\hslash }}k/2m. Here {{\\hslash }} is the reduced Planck constant, k is the wavenumber and m is the electron mass. Going beyond linear theory, we find additional resonances with velocity shifts {{nv}}q,n=2,3, \\ldots , giving rise to a new wave-damping mechanism that we term multi-plasmon damping, as it can be seen as the simultaneous absorption (or emission) of multiple plasmon quanta. Naturally this wave damping is not present in classical plasmas. For a temperature well below the Fermi temperature, if the linear (n = 1) resonant velocity is outside the Fermi sphere, the number of linearly resonant particles is exponentially small, while the multi-plasmon resonances can be located in the bulk of the distribution. We derive sets of evolution equations for the case of two-plasmon and three-plasmon resonances for Langmuir waves in the simplest case of a fully degenerate plasma. By solving these equations numerically for a range of wave-numbers we find the corresponding damping rates, and we compare them to results from linear theory to estimate the applicability. Finally, we discuss the effects due to a finite temperature.
Generation and growth rates of nonlinear distortions in a traveling wave tube.
Wöhlbier, John G; Dobson, Ian; Booske, And John H
2002-11-01
The structure of a steady state multifrequency model of a traveling wave tube amplifier is exploited to describe the generation of intermodulation frequencies and calculate their growth rates. The model describes the evolution of Fourier coefficients of circuit and electron beam quantities and has the form of differential equations with quadratic nonlinearities. Intermodulation frequencies are sequentially generated by the quadratic nonlinearities in a series solution of the differential equations. A formula for maximum intermodulation growth rates is derived and compared to simulation results.
Global existence and decay of solutions of a nonlinear system of wave equations
Said-Houari, Belkacem
2012-03-01
This work is concerned with a system of two wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we show that our problem has a unique local solution. Also, we prove that, for some restrictions on the initial data, the rate of decay of the total energy is exponential or polynomial depending on the exponents of the damping terms in both equations.
Strongly nonlinear wave dynamics in a chain of polymer coated beads
Daraio, C.; Nesterenko, V. F.
2006-01-01
Strongly nonlinear phononic crystals were assembled from a chain of Parylene-C coated steel spheres in a polytetrafluoroethylene (PTFE) holder. This system exhibits strongly nonlinear properties and extends the range of materials supporting "sonic vacuum" type behavior. The combination of a high density core and a soft (low elastic modulus) coating ensures a relatively low velocity of wave propagation. The beads contact interaction caused by the deformation of the Parylene coating can be desc...
Construction of the wave operator for non-linear dispersive equations
Tsuruta, Kai Erik
In this thesis, we will study non-linear dispersive equations. The primary focus will be on the construction of the positive-time wave operator for such equations. The positive-time wave operator problem arises in the study of the asymptotics of a partial differential equation. It is a map from a space of initial data X into itself, and is loosely defined as follows: Suppose that for a solution ψlin to the dispersive equation with no non-linearity and initial data ψ +, there exists a unique solution ψ to the non-linear equation with initial data ψ0 such that ψ behaves as ψ lin as t → infinity. Then the wave operator is the map W+ that takes ψ + to ψ0. By its definition, W+ is injective. An important additional question is whether or not the map is also surjective. If so, then every non-linear solution emanating from X behaves, in some sense, linearly as it evolves (this is known as asymptotic completeness). Thus, there is some justification for treating these solutions as their much simpler linear counterparts. The main results presented in this thesis revolve around the construction of the wave operator(s) at critical non-linearities. We will study the "semi-relativistic" Schrodinger equation as well as the Klein-Gordon-Schrodinger system on R2 . In both cases, we will impose fairly general quadratic non-linearities for which conservation laws cannot be relied upon. These non-linearities fall below the scaling required to employ such tools as the Strichartz estimates. We instead adapt the "first iteration method" of Jang, Li, and Zhang to our setting which depends crucially on the critical decay of the non-linear interaction of the linear evolution. To see the critical decay in our problem, careful analysis is needed to treat the regime where one has spatial and/or time resonance.
Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng
2004-01-01
Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair
Generation and growth rates of nonlinear distortions in a traveling wave tube
International Nuclear Information System (INIS)
Woehlbier, John G.; Dobson, Ian; Booske, John H.
2002-01-01
The structure of a steady state multifrequency model of a traveling wave tube amplifier is exploited to describe the generation of intermodulation frequencies and calculate their growth rates. The model describes the evolution of Fourier coefficients of circuit and electron beam quantities and has the form of differential equations with quadratic nonlinearities. Intermodulation frequencies are sequentially generated by the quadratic nonlinearities in a series solution of the differential equations. A formula for maximum intermodulation growth rates is derived and compared to simulation results
Couston, Louis-Alexandre; Lecoanet, Daniel; Favier, Benjamin; Le Bars, Michael
2017-11-01
We investigate via direct numerical simulations the spontaneous generation and reversals of mean zonal flows in a stably-stratified fluid layer lying above a turbulent convective fluid. Contrary to the leading idealized theories of mean flow generation by self-interacting internal waves, the emergence of a mean flow in a convectively-generated internal gravity wave field is not always possible because nonlinear interactions of waves of different frequencies can disrupt the mean flow generation mechanism. Strong mean flows thus emerge when the divergence of the Reynolds stress resulting from the nonlinear interactions of internal waves produces a strong enough anti-diffusive acceleration for the mean flow, which, as we will demonstrate, is the case when the Prandtl number is sufficiently low, or when the energy input into the internal wavefield by the convection and density stratification are sufficiently large. Implications for mean zonal flow production as observed in the equatorial stratospheres of the Earth, Saturn and Jupiter, and possibly occurring in other geophysical systems such as planetary and stellar interiors will be briefly discussed. Funding provided by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program through Grant Agreement No. 681835-FLUDYCO-ERC-2015-CoG.
Wave-vortex interactions in the nonlinear Schrödinger equation
Guo, Yuan; Bühler, Oliver
2014-02-01
This is a theoretical study of wave-vortex interaction effects in the two-dimensional nonlinear Schrödinger equation, which is a useful conceptual model for the limiting dynamics of superfluid quantum condensates at zero temperature. The particular wave-vortex interaction effects are associated with the scattering and refraction of small-scale linear waves by the straining flows induced by quantized point vortices and, crucially, with the concomitant nonlinear back-reaction, the remote recoil, that these scattered waves exert on the vortices. Our detailed model is a narrow, slowly varying wavetrain of small-amplitude waves refracted by one or two vortices. Weak interactions are studied using a suitable perturbation method in which the nonlinear recoil force on the vortex then arises at second order in wave amplitude, and is computed in terms of a Magnus-type force expression for both finite and infinite wavetrains. In the case of an infinite wavetrain, an explicit asymptotic formula for the scattering angle is also derived and cross-checked against numerical ray tracing. Finally, under suitable conditions a wavetrain can be so strongly refracted that it collapses all the way onto a zero-size point vortex. This is a strong wave-vortex interaction by definition. The conditions for such a collapse are derived and the validity of ray tracing theory during the singular collapse is investigated.
Benoit, Michel; Yates, Marissa L.; Raoult, Cécile
2017-04-01
Efficient and accurate numerical models simulating wave propagation are required for a variety of engineering projects including the evaluation of coastal risks, the design of protective coastal structures, and the estimation of the potential for marine renewable energy devices. Nonlinear and dispersive effects are particularly significant in the coastal zone where waves interact with the bottom, the shoreline, and coastal structures. The main challenge in developing a numerical models is finding a compromise between computational efficiency and the required accuracy of the simulated wave field. Here, a potential approach is selected and the (fully nonlinear) water wave problem is formulated using the Euler-Zakharov equations (Zakharov, 1968) describing the temporal evolution of the free surface elevation and velocity potential. The proposed model (Yates and Benoit, 2015) uses a spectral approach in the vertical (i.e. the vertical variation of the potential is approximated by a linear combination of the first NT+1 Chebyshev polynomials, following the work of Tian and Sato (2008)). The Zakharov equations are integrated in time using a fourth-order Runge-Kutta scheme with a constant time step. At each sub-timestep, the Laplace Boundary Value Problem (BVP) is solved to estimate the free surface vertical velocity using the spectral approach, with typical values of NT between 5 to 8 for practical applications. The 1DH version of the code is validated with comparisons to the experimental data set of Becq-Girard et al. (1999), which studied the propagation of irregular waves over a beach profile with a submerged bar. The nonlinear and dispersive capacities of the model are verified with the correct representation of wave-wave interactions, in particular the transfer of energy between different harmonic components during wave propagation (analysis of the transformation of the variance spectrum along the channel). Evolution of wave skewness, asymmetry and kurtosis along the
Su, Zhenpeng; Zhu, Hui; Xiao, Fuliang; Zheng, Huinan; Shen, Chao; Wang, Yuming; Wang, Shui
2013-06-01
Electromagnetic ion cyclotron (EMIC) waves are long suggested to account for the rapid loss of radiation belt relativistic electrons. Here we perform both theoretical analysis and numerical simulation to comprehensively investigate the nonlinear interaction between EMIC wave and relativistic electrons. In particular, we emphasize the dependence of nonlinear processes on the electron initial latitude. The nonlinear phase trapping yields negative equatorial pitch angle transport, with efficiency varying over the electron initial latitude, implying that it can increase the loss rate predicted by quasilinear theory. The nonlinear channel effect phase bunching produces positive equatorial pitch angle transport, less dependent on the electron initial latitude, suggesting that it can decrease the loss rate predicted by quasilinear theory. The nonlinear cluster effect phase bunching alternately causes positive and negative equatorial pitch angle transport, quasi-periodically dependent on the electron initial latitude, suggesting that it can either decrease or increase the loss rate predicted by the quasilinear theory. Such latitudinal dependence of nonlinear processes should be taken into account in the evaluation of radiation belt electron loss rate driven by EMIC waves.
Energy Technology Data Exchange (ETDEWEB)
Mitsotakis, Dimitrios, E-mail: dmitsot@gmail.com [Victoria University of Wellington, School of Mathematics, Statistics and Operations Research, PO Box 600, Wellington 6140 (New Zealand); Dutykh, Denys, E-mail: Denys.Dutykh@univ-savoie.fr [LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, Campus Scientifique, F-73376 Le Bourget-du-Lac Cedex (France); Assylbekuly, Aydar, E-mail: asylbekuly@mail.ru [Khoja Akhmet Yassawi International Kazakh–Turkish University, Faculty of Natural Science, Department of Mathematics, 161200 Turkestan (Kazakhstan); Zhakebayev, Dauren, E-mail: daurjaz@mail.ru [Al-Farabi Kazakh National University, Faculty of Mechanics and Mathematics, Department of Mathematical and Computer Modelling, 050000 Almaty (Kazakhstan)
2017-05-25
In this Letter we consider long capillary–gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott–Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well. - Highlights: • A model for long capillary–gravity weakly dispersive and fully nonlinear water waves is derived. • Shallow capillary–gravity waves are classified using phase plane analysis. • Peaked travelling waves are found in the critical regime. • The dynamics of peakons in Serre–Green–Naghdi equations is studied numerically.
A new auxiliary equation and exact travelling wave solutions of nonlinear equations
International Nuclear Information System (INIS)
Sirendaoreji
2006-01-01
A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations
DEFF Research Database (Denmark)
Belleter, Dennis J.W.; Galeazzi, Roberto; Fossen, Thor Inge
2015-01-01
This paper presents a global exponential stability (GES) proof for a signalbased nonlinear wave encounter frequency estimator. The estimator under consideration is a second-order nonlinear observer designed to estimate the frequency of a sinusoid with unknown frequency, amplitude and phase. The GES...... proof extends previous results that only guarantee global K-exponential stability. Typical applications are control and decision-support systems for marine craft, where it is important to know the sea state and wave frequency. The theoretical results are verified experimentally by analyzing data from...
Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation
Karney, C. F. F.
1977-01-01
Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.
Nonlinear self-adjointness and invariant solutions of a 2D Rossby wave equation
Cimpoiasu, Rodica; Constantinescu, Radu
2014-02-01
The paper investigates the nonlinear self-adjointness of the nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane. It is a particular form of Rossby equation which does not possess variational structure and it is studied using a recently method developed by Ibragimov. The conservation laws associated with the infinite-dimensional symmetry Lie algebra models are constructed and analyzed. Based on this Lie algebra, some classes of similarity invariant solutions with nonconstant linear and nonlinear shears are obtained. It is also shown how one of the conservation laws generates a particular wave solution of this equation.
Modified wave operators for nonlinear Schrodinger equations in one and two dimensions
Directory of Open Access Journals (Sweden)
Nakao Hayashi
2004-04-01
Full Text Available We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schr"{o}dinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13
Influence of the nonlinearity on statistical characteristics of long wave runup
Directory of Open Access Journals (Sweden)
P. Denissenko
2011-12-01
Full Text Available Runup of long irregular waves on a plane beach is studied experimentally in the water flume at the University of Warwick. Statistics of wave runup (displacement and velocity of the moving shoreline and their extreme values is analyzed for the incident wave field with the narrow band spectrum for different amplitudes of incident waves (different values of the breaking parameter Br_{σ}. It is shown experimentally that the distribution of the shoreline velocity does not depend on Br_{σ} and coincides with the distribution of the vertical velocity in the incident wave field as it is predicted in the statistical theory of nonlinear long wave runup. Statistics of runup amplitudes shows the same behavior as that of the incident wave amplitudes. However, the distribution of the wave runup on a beach differs from the statistics of the incident wave elevation. The mean sea level at the coast rises with an increase in Br_{σ} causing wave set-up on a beach, which agrees with the theoretical predictions. At the same time values of skewness and kurtosis for wave runup are similar to those for the incident wave field and they might be used for the forecast of sea floods at the coast.
Theoretical Studies of the Oceanic Internal Wave System.
1982-08-31
Kraichnan, which 7s easily implemented in the diagrammatic laguage . We should note that one problem with this *pproach is that it is not currently known...and Hendershott, M. C. (1977) Stochastic closure for nonlinear Roasby waves. J. Fluid Mach. 82, 747-765. Holloway, G. (1978) Order and disorder in
Non-linear wave equations:Mathematical techniques
International Nuclear Information System (INIS)
1978-01-01
An account of certain well-established mathematical methods, which prove useful to deal with non-linear partial differential equations is presented. Within the strict framework of Functional Analysis, it describes Semigroup Techniques in Banach Spaces as well as variational approaches towards critical points. Detailed proofs are given of the existence of local and global solutions of the Cauchy problem and of the stability of stationary solutions. The formal approach based upon invariance under Lie transformations deserves attention due to its wide range of applicability, even if the explicit solutions thus obtained do not allow for a deep analysis of the equations. A compre ensive introduction to the inverse scattering approach and to the solution concept for certain non-linear equations of physical interest are also presented. A detailed discussion is made about certain convergence and stability problems which arise in importance need not be emphasized. (author) [es
Wavelet analysis of the slow non-linear dynamics of wave turbulence
Energy Technology Data Exchange (ETDEWEB)
Miquel, Benjamin; Mordant, Nicolas, E-mail: benjamin.miquel@lps.ens.fr [Laboratoire de Physique Statistique, Ecole Normale Superieure (France)
2011-12-22
In wave turbulence, the derivation of solutions in the frame of the Weak Turbulence Theory relies on the existence of a double time-scale separation: first, between the period of the waves and characteristic nonlinear time t{sub NL} corresponding to energy exchange among waves; and secondly, between t{sub NL} and the characteristic dissipation time t{sub d}. Due to the lack of space and time resolved measurement, this hypothesis have remained unverified so far. We study the turbulence of flexion waves in thin elastic plates. t{sub d} is measured using the decline stage of the turbulence whereas a wavelet analysis is performed to measure the characteristic non-linear time t{sub NL}.
A nonlinear model for the fluidization of marine mud by waves
Energy Technology Data Exchange (ETDEWEB)
Foda, M.A.; Hunt, J.R.; Chou, Hsien-Ter (Univ. of California, Berkeley (United States))
1993-04-15
The authors consider the problem of fluidization of mud deposits in shallow waters due to interactions with water waves. This is of increasing interest because of concerns that water pollutants, including heavy metals, pesticides, etc., are often found near surfaces of mud deposits. The authors look at the question of whether the cohesive properties of mud deposits exhibit nonlinear properties when they experience strains from water wave interactions. It is obvious that with large enough wave interactions the deposits become fluidized, and are not in that case truly nonlinear. In their modeling efforts they try to incorporate these ideas into a cohesive model where the magnitude of the water wave-sediment interaction has an influence on the type of response within the system.
Study of nonlinear waves described by the cubic Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Walstead, A.E.
1980-03-12
The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables.
Statistical analysis of nonlinear wave interaction in simulated Langmuir turbulence data
Czech Academy of Sciences Publication Activity Database
Souček, Jan; Dudok de Wit, T.; Krasnoselskikh, V.; Volokitin, A.
2003-01-01
Roč. 21, - (2003), s. 681-692 ISSN 0992-7689 R&D Projects: GA ČR GA205/01/1064 Grant - others:CNRS(FR) PICS 1175 Institutional research plan: CEZ:AV0Z3042911 Keywords : space plasma physics * wave-wave interactions * experimental and matehmatical techniques * nonlinear phenomena Subject RIV: DG - Athmosphere Sciences, Meteorology Impact factor: 1.031, year: 2003
Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping
Directory of Open Access Journals (Sweden)
Jieqiong Wu
2015-09-01
Full Text Available We study the energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping. The damping is localized in a bounded domain and near infinity, and the principal part of the wave equation has a variable-coefficient. We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.
Solitary waves for a coupled nonlinear Schrodinger system with dispersion management
Directory of Open Access Journals (Sweden)
Panayotis Panayotaros
2010-08-01
Full Text Available We consider a system of coupled nonlinear Schrodinger equations with periodically varying dispersion coefficient that arises in the context of fiber-optics communication. We use Lions's Concentration Compactness principle to show the existence of standing waves with prescribed L^2 norm in an averaged equation that approximates the coupled system. We also use the Mountain Pass Lemma to prove the existence of standing waves with prescribed frequencies.
The influence of damping and source terms on solutions of nonlinear wave equations
Directory of Open Access Journals (Sweden)
Mohammad A. Rammaha
2007-11-01
Full Text Available We discuss in this paper some recent development in the study of nonlinear wave equations. In particular, we focus on those results that deal with wave equations that feature two competing forces.One force is a damping term and the other is a strong source. Our central interest here is to analyze the influence of these forces on the long-time behavior of solutions.
Nonlinear acoustic waves in the viscous thermosphere and ionosphere above earthquake
Czech Academy of Sciences Publication Activity Database
Chum, Jaroslav; Cabrera, M. A.; Mošna, Zbyšek; Fagre, M.; Baše, Jiří; Fišer, Jiří
2016-01-01
Roč. 121, č. 12 (2016), s. 12126-12137 ISSN 2169-9380 R&D Projects: GA ČR(CZ) GC15-07281J Institutional support: RVO:68378289 Keywords : infrasound * seismic waves * ionosphere * nonlinear wave propagation * viscosity * dissipation * remote sensing Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.733, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/2016JA023450/full
Traveling waves in a delayed SIR model with nonlocal dispersal and nonlinear incidence
Zhang, Shou-Peng; Yang, Yun-Rui; Zhou, Yong-Hui
2018-01-01
This paper is concerned with traveling waves of a delayed SIR model with nonlocal dispersal and a general nonlinear incidence. The existence and nonexistence of traveling waves of the system are established respectively by Schauder's fixed point theorem and two-sided Laplace transform. It is also shown that the spread speed c is influenced by the dispersal rate of the infected individuals and the delay τ.
Nonlinear localized dust acoustic waves in a charge varying dusty plasma with nonthermal ions
International Nuclear Information System (INIS)
Tribeche, Mouloud; Amour, Rabia
2007-01-01
A numerical investigation is presented to show the existence, formation, and possible realization of large-amplitude dust acoustic (DA) solitary waves in a charge varying dusty plasma with nonthermal ions. These nonlinear localized structures are self-consistent solutions of the collisionless Vlasov equation with a population of fast particles. The spatial patterns of the variable charge DA solitary wave are significantly modified by the nonthermal effects. The results complement and provide new insights into previously published results on this problem
Travelling wave solutions to nonlinear physical models by means of ...
Indian Academy of Sciences (India)
On the other hand, considerable attention has been given to problem of finding spe- cial types of analytic solutions to understand biological, physical and chemical phenomena modelled by NPDEs. Among the possible solutions, certain solutions may depend only on a single combination of variables such as travelling wave ...
Nonlinear Langmuir Wave Modulation in Weakly Magnetized Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans
1978-01-01
influence on the modulation stability of plane Langmuir waves. As in the unmagnetized case, kinetic results were found to deviate considerably from those obtained by using a fluid description for the ion dynamics. With particular attention to ionospheric phenomena, the effect is included of the spatially...
Unigueness for stochastic non-linear wave equations
Czech Academy of Sciences Publication Activity Database
Ondreját, Martin
2007-01-01
Roč. 67, č. 12 (2007), s. 3287-3310 ISSN 0362-546X R&D Projects: GA ČR GA201/04/0750 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic wave equation * uniqueness Subject RIV: BA - General Mathematics Impact factor: 1.097, year: 2007
Non-linear high-frequency waves in the magnetosphere
Indian Academy of Sciences (India)
forms of solitary bipolar electric field pulses which are called electrostatic solitary waves. (ESW) [1]. Karovsky et al [5] have used a BGK analysis to theoretically describe the high-frequency. ESW. Using counter-streaming electron and ion beams in a computer simulation experi- ment, Omura et al [6] have shown that the ...
ASYMPIOTIC SOLUTIONS OF THE NON-LINEAR WAVE EQUAION
African Journals Online (AJOL)
MIS
1983-09-01
-value case is equivalent to the case of periodic standing waves on the infinite line. In this paper eq. (1.1) is studied on the infinite line for non-periodic ..... and this is an elliptic integral which can be evaluated to give (Byrd and.
Nonlinear Lamb waves for fatigue damage identification in FRP-reinforced steel plates.
Wang, Yikuan; Guan, Ruiqi; Lu, Ye
2017-09-01
A nonlinear Lamb-wave-based method for fatigue crack detection in steel plates with and without carbon fibre reinforcement polymer (CFRP) reinforcement is presented in this study. Both numerical simulation and experimental evaluation were performed for Lamb wave propagation and its interaction with a fatigue crack on these two steel plate types. With the generation of the second harmonic, the damage-induced wave nonlinearities were identified by surface-bonded piezoelectric sensors. Numerical simulation revealed that the damage-induced wave component at the second harmonic was slightly affected by the existence of CFRP laminate, although the total wave energy was decreased because of wave leakage into the CFRP laminate. Due to unavoidable nonlinearity from the experimental environments, it was impractical to directly extract the time-of-flight of the second harmonic for locating the crack. To this end, the correlation coefficient of benchmark and signal with damage at double frequency in the time domain was calculated, based on which an imaging method was introduced to locate the fatigue crack in steel plates with and without CFRP laminates. Copyright © 2017 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Tang Xiaoyan; Shukla, Padma Kant
2008-01-01
Exact solutions, including the periodic travelling and non-travelling wave solutions, are presented for the nonlinear Klein-Gordon equation with imaginary mass. Some arbitrary functions are permitted in the periodic non-travelling wave solutions, which contribute to various high dimensional nonlinear structures
Nonlinear metric perturbation enhancement of primordial gravitational waves.
Bastero-Gil, M; Macias-Pérez, J; Santos, D
2010-08-20
We present the evolution of the full set of Einstein equations during preheating after inflation. We study a generic supersymmetric model of hybrid inflation, integrating fields and metric fluctuations in a 3-dimensional lattice. We take initial conditions consistent with Einstein's constraint equations. The induced preheating of the metric fluctuations is not large enough to backreact onto the fields, but preheating of the scalar modes does affect the evolution of vector and tensor modes. In particular, they do enhance the induced stochastic background of gravitational waves during preheating, giving an energy density in general an order of magnitude larger than that obtained by evolving the tensor fluctuations in an homogeneous background metric. This enhancement can improve the expectations for detection by planned gravitational wave observatories.
A new active absorption system and its performance to linear and non-linear waves
DEFF Research Database (Denmark)
Andersen, Thomas Lykke; Clavero, M.; Frigaard, Peter Bak
2016-01-01
Highlights •An active absorption system for wavemakers has been developed. •The theory for flush mounted gauges has been extended to cover also small gaps. •The new system has been validated in a wave flume with wavemakers in both ends. •A generation and absorption procedure for highly non-linear...
Solitary heat waves in nonlinear lattices with squared on-site potential
Indian Academy of Sciences (India)
Abstract. A model Hamiltonian is proposed for heat conduction in a nonlinear lattice with squared on-site potential using the second quantized operators and averaging the same using a suitable wave function, equations are derived in discrete form for the field amplitude and the prop- erties of heat transfer are examined ...
Experimental Investigation of Nonlinear Coupling of Lower Hybrid Waves on Tore Supra
Czech Academy of Sciences Publication Activity Database
Goniche, M.; Frincu, B.; Ekedahl, A.; Petržílka, Václav; Berger-By, G.; Hillairet, J.; Litaudon, X.; Preynas, M.; Voyer, D.
2012-01-01
Roč. 62, č. 2 (2012), s. 322-332 ISSN 1536-1055 R&D Projects: GA ČR GA202/07/0044 Institutional research plan: CEZ:AV0Z20430508 Keywords : LHwave * plasma * lower hybrid * wave coupling * nonlinear coupling Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 0.517, year: 2012
Nonlinear propagation of dust-acoustic solitary waves in a dusty ...
Indian Academy of Sciences (India)
... Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Pramana – Journal of Physics; Volume 80; Issue 6. Nonlinear propagation of dust-acoustic solitary waves in a dusty plasma with arbitrarily charged dust and trapped electrons. O Rahman A A Mamun. Volume 80 Issue 6 June 2013 pp ...
Rogue wave solutions of the nonlinear Schrödinger equation with ...
Indian Academy of Sciences (India)
physics pp. 1063–1072. Rogue wave solutions of the nonlinear Schrödinger equation with variable coefficients. CHANGFU LIU1,∗, YAN YAN LI1, MEIPING GAO1, ZEPING WANG1,. ZHENGDE DAI2 and CHUANJIAN WANG3. 1School of Mathematics, Wenshan University, Wenshan, 663000, People's Republic of China.
Local numerical modelling of ultrasonic guided waves in linear and nonlinear media
Packo, Pawel; Radecki, Rafal; Kijanka, Piotr; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2017-04-01
Nonlinear ultrasonic techniques provide improved damage sensitivity compared to linear approaches. The combination of attractive properties of guided waves, such as Lamb waves, with unique features of higher harmonic generation provides great potential for characterization of incipient damage, particularly in plate-like structures. Nonlinear ultrasonic structural health monitoring techniques use interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity. Signal processing techniques used in non-destructive evaluation are frequently supported by modeling and numerical simulations in order to facilitate problem solution. This paper discusses known and newly-developed local computational strategies for simulating elastic waves, and attempts characterization of their numerical properties in the context of linear and nonlinear media. A hybrid numerical approach combining advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE) is proposed for unique treatment of arbitrary strain-stress relations. The iteration equations of the method are derived directly from physical principles employing stress and displacement continuity, leading to an accurate description of the propagation in arbitrarily complex media. Numerical analysis of guided wave propagation, based on the newly developed hybrid approach, is presented and discussed in the paper for linear and nonlinear media. Comparisons to Finite Elements (FE) are also discussed.
Hamiltonian Finite Element Discretization for Nonlinear Free Surface WaterWaves
van der Vegt, Jacobus J.W.; Brink, Freekjan; Iszak, Ferenc
2017-01-01
A novel finite element discretization for nonlinear potential flow water waves is presented. Starting from Luke’s Lagrangian formulation we prove that an appropriate finite element discretization preserves the Hamiltonian structure of the potential flow water waveequations, even on general
Explosion of limit cycles and chaotic waves in a simple nonlinear chemical system
DEFF Research Database (Denmark)
Brøns, Morten; Sturis, Jeppe
2001-01-01
A model of an autocatalytic chemical reaction was employed to study the explosion of limit cycles and chaotic waves in a nonlinear chemical system. The bifurcation point was determined using asymptotic analysis and perturbations. Scaling laws for amplitude and period were derived. A strong...
Nonlinear behavior of a monochromatic wave in a one-dimensional Vlasov plasma
International Nuclear Information System (INIS)
Shoucri, M.M.; Gagne, R.R.J.
1978-01-01
The nonlinear evolution of a monochromatic wave in a one-dimensional Vlasov plasma is studied numerically. The numerical results are carried out far enough in time for phase mixing to dominate the asymptotic state of the system. A qualitative comparison with previously reported simulations is given
A robust WENO scheme for nonlinear waves in a moving reference frame
DEFF Research Database (Denmark)
Kontos, Stavros; Bingham, Harry B.; Lindberg, Ole
2016-01-01
For robust nonlinear wave simulation in a moving reference frame, we recast the free surface problem in Hamilton-Jacobi form and propose a Weighted Essentially Non-Oscillatory (WENO) scheme to automatically handle the upwinding of the convective term. A new automatic procedure for deriving the li...
Non-linear wave loads and ship responses by a time-domain strip theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
. Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership...
Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...
Waves, conservation laws and symmetries of a third-order nonlinear ...
African Journals Online (AJOL)
user
Abstract. In this paper a less studied nonlinear partial differential equation of the third-order is under consideration. Important properties concerning advanced character such like conservation laws and the equation of continuity are given. Characteristic wave properties such like dispersion relations and both the group and ...
Self-focusing of electromagnetic surface waves on a nonlinear impedance surface
Energy Technology Data Exchange (ETDEWEB)
Luo, Zhangjie, E-mail: zhangjie-luo-cn@126.com [College of Electronics and Information Engineering, Sichuan University, Chengdu 610064 (China); Applied Electromagnetics Group, Electrical and Computer Engineering Department, University of California, San Diego, California 92093 (United States); Chen, Xing [College of Electronics and Information Engineering, Sichuan University, Chengdu 610064 (China); Long, Jiang; Quarfoth, Ryan; Sievenpiper, Daniel, E-mail: dsievenpiper@eng.ucsd.edu [Applied Electromagnetics Group, Electrical and Computer Engineering Department, University of California, San Diego, California 92093 (United States)
2015-05-25
The self-focusing effect of optical beams has been a popular topic of study for quite a while, but such a nonlinear phenomenon at microwave frequencies has never been realized, partially due to the underdevelopment of nonlinear material. In this research, self-focused electromagnetic (EM) surface waves are demonstrated on a circuit-based, power-dependent impedance surface. The formation of a self-focused beam is investigated using a series of discrete-time simulations, and the result is further validated in measurement. It is experimentally observed that, in contrast to the normal scattering of low-power surface waves, high-power waves propagate through the surface while maintaining narrow beam width, and even converge extremely tightly to create a hot spot with higher power. The result is essentially a nonlinear effect of the surface that compensates for the natural tendency of surface waves to diffract. This intriguing experiment can be extended to various potential EM applications such as power-dependent beam steering antennas and nonlinear microwave propagation or dissipation.
On the statistical properties of the non-linear water waves ...
African Journals Online (AJOL)
In this work we introduce a bi-parametric distribution of nonlinear stochastic processes, in studying the properties of second-order random processes with a narrow-band spectrum. ... such probabilistic based design criterion may result in substantial cost saving if uncertainties in the wave estimates are incorporated.
Periodic nonlinear waves resulting from the contact interaction of a crack
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.
Stochastic wave equation with critical nonlinearities: Temporal regularity and uniqueness
Czech Academy of Sciences Publication Activity Database
Ondreját, Martin
2010-01-01
Roč. 248, č. 7 (2010), s. 1579-1602 ISSN 0022-0396 R&D Projects: GA ČR GA201/07/0237 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic wave equation * Spatially homogeneous Wiener process * Critical growth Subject RIV: BA - General Mathematics Impact factor: 1.261, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/ondrejat-0339543.pdf
Invariant measures for stochastic nonlinear beam and wave equations
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Ondreját, Martin; Seidler, Jan
2016-01-01
Roč. 260, č. 5 (2016), s. 4157-4179 ISSN 0022-0396 R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : stochastic partial differential equation * stochastic beam equation * stochastic wave equation * invariant measure Subject RIV: BA - General Mathematics Impact factor: 1.988, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/ondrejat-0453412.pdf
Coupled equations of electromagnetic waves in nonlinear metamaterial waveguides.
Azari, Mina; Hatami, Mohsen; Meygoli, Vahid; Yousefi, Elham
2016-11-01
Over the past decades, scientists have presented ways to manipulate the macroscopic properties of a material at levels unachieved before, and called them metamaterials. This research can be considered an important step forward in electromagnetics and optics. In this study, higher-order nonlinear coupled equations in a special kind of metamaterial waveguides (a planar waveguide with metamaterial core) will be derived from both electric and magnetic components of the transverse electric mode of electromagnetic pulse propagation. On the other hand, achieving the refractive index in this research is worthwhile. It is also shown that the coupled equations are not symmetric with respect to the electric and magnetic fields, unlike these kinds of equations in fiber optics and dielectric waveguides. Simulations on the propagation of a fundamental soliton pulse in a nonlinear metamaterial waveguide near the resonance frequency (a little lower than the magnetic resonant frequency) are performed to study its behavior. These pulses are recommended to practice in optical communications in controlled switching by external voltage, even in low power.
Chirped self-similar waves for quadratic-cubic nonlinear Schrödinger equation
Pal, Ritu; Loomba, Shally; Kumar, C. N.
2017-12-01
We have constructed analytical self-similar wave solutions for quadratic-cubic Nonlinear Schrödinger equation (QC-NLSE) by means of similarity transformation method. Then, we have investigated the role of chirping on these self-similar waves as they propagate through the tapered graded index waveguide. We have revealed that the chirping leads to interesting features and allows us to control the propagation of self-similar waves. This has been demonstrated for two cases (i) periodically distributed system and (ii) constant choice of system parameters. We expect our results to be useful in designing high performance optical devices.
Ayub, Kamran; Khan, M. Yaqub; Mahmood-Ul-Hassan, Qazi; Ahmad, Jamshad
2017-09-01
Nonlinear mathematical problems and their solutions attain much attention in solitary waves. In soliton theory, an efficient tool to attain various types of soliton solutions is the \\exp (-φ (ζ ))-expansion technique. This article is devoted to find exact travelling wave solutions of Drinfeld-Sokolov equation via a reliable mathematical technique. By using the proposed technique, we attain soliton wave solution of various types. It is observed that the technique under discussion is user friendly with minimum computational work, and can be extended for physical problems of different nature in mathematical physics.
Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems
Trillo, S.
2014-12-03
We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign.
A Fast GPU-accelerated Mixed-precision Strategy for Fully NonlinearWater Wave Computations
DEFF Research Database (Denmark)
Glimberg, Stefan Lemvig; Engsig-Karup, Allan Peter; Madsen, Morten G.
2011-01-01
We present performance results of a mixed-precision strategy developed to improve a recently developed massively parallel GPU-accelerated tool for fast and scalable simulation of unsteady fully nonlinear free surface water waves over uneven depths (Engsig-Karup et.al. 2011). The underlying wave......-preconditioned defect correction method. The improved strategy improves the performance by exploiting architectural features of modern GPUs for mixed precision computations and is tested in a recently developed generic library for fast prototyping of PDE solvers. The new wave tool is applicable to solve and analyze...
Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water
Energy Technology Data Exchange (ETDEWEB)
Jiménez, N.; Picó, R. [Instituto de Investigación para la Gestión Integrada de zonas Costeras, Universitat Politècnica de València, Paranimf 1, 46730 Grao de Gandia, València (Spain); Romero-García, V. [LUNAM Université, Université du Maine, LAUM UMR CNRS 6613, Av. O. Messiaen, 72085 Le Mans (France); Garcia-Raffi, L. M. [Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 València (Spain); Staliunas, K. [ICREA, Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Colom, 11, E-08222 Terrassa, Barcelona (Spain)
2015-11-16
We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10{sup −4}). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.
Fate of internal waves on a shallow shelf
Davis, Kristen; Arthur, Robert; Reid, Emma; Decarlo, Thomas; Cohen, Anne
2017-11-01
Internal waves strongly influence the physical and chemical environment of coastal ecosystems worldwide. We report novel observations from a distributed temperature sensing (DTS) system that tracked the transformation of internal waves from the shelf break to the surf zone over a shelf-slope region of a coral atoll in the South China Sea. The spatially-continuous view of the near-bottom temperature field provided by the DTS offers a perspective of physical processes previously available only in laboratory settings or numerical models. These processes include internal wave reflection off a natural slope, shoreward transport of dense fluid within trapped cores, internal ``tide pools'' (dense water left behind after the retreat of an internal wave), and internal run-down (near-bottom, offshore-directed jets of water preceding a breaking internal wave). Analysis shows that the fate of internal waves on this shelf - whether they are transmitted into shallow waters or reflected back offshore - is mediated by local water column density and shear structure, with important implications for nearshore distributions of energy, heat, and nutrients. We acknowledge the US Army Research Laboratory DoD Supercomputing Resource Center for computer time on Excalibur, which was used for the numerical simulations in this work. Funding for field work supported by Academia Sinica and for K.D. and E.R. from NSF.
Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions
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
The nonlinear interactions between O+ ions and oxygen band EMIC waves
Wang, Zhiqiang; Pan, Zhirui; Zhai, Hao; Gao, Zhuxiu; Sun, Kang; Zhang, Yusheng
2017-07-01
During geomagnetically active times, O+ ions from the ionosphere become an important ion component in the ring current, which changes the dispersion relations and significantly enlarges the growth rate of oxygen band electromagnetic ion cyclotron (EMIC) waves. Motivated by a large number of oxygen band EMIC wave observations in the inner magnetosphere, we study the nonlinear motions of ring current O+ ions caused by the cyclotron resonance with oxygen band EMIC waves. A dimensionless parameter R is used to characterize the competition between wave-induced and adiabatic motions. The numerical calculations based on gyroaveraged test particle equations are performed. For typical 20 keV O+ ions at L = 5, two kinds of nonlinear processes occur simultaneously when αeq > 59° (R loss cone and reduce the overall loss rate estimated from the quasi-linear theory. Instead, phase bunching tends to increase the overall loss rate. The phase-trapped O+ ions have chance to be accelerated drastically, reaching 750% of the initial energy. These O+ ions move forward and backward alternatively along the field lines when they are bouncing back to the equator, forming a periodic energy variation which has not been reported before. The results suggest that the oxygen band EMIC waves, which appear frequently during storms, should be considered in the ring current dynamics in terms of nonlinear acceleration and resonance scattering of ring current particles.
Propagation of multidimensional nonlinear waves and kinematical conservation laws
Prasad, Phoolan
2017-01-01
This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics. Finally, it addresses one of the most challenging problems in fluid dynamics: finding successive positions of a curved shock front. The topics discussed are the outcome of collaborative work that was carried out mainly at the Indian Institute of Science, Bengaluru, India. The theory presented in the book is supported by referring to extensive numerical results. The book is organised into ten chapters. Chapters 1–4 offer a summary of and briefly discuss the theory of hyperbolic partial differential equations and conservation laws. Formulation of equations of a weakly nonlinear wavefront and those of a shock front are briefly explained in Chapter 5, while Chapter 6 addresses KCL theory in space of arbitrary dimensions. The remaining chapters examine various analyses and applications of KCL equations ending in the ultimate goal-propagation of a three-dimensional curved sho...
Flow velocity measurement with the nonlinear acoustic wave scattering
Energy Technology Data Exchange (ETDEWEB)
Didenkulov, Igor, E-mail: din@appl.sci-nnov.ru [Institute of Applied Physics, 46 Ulyanov str., Nizhny Novgorod, 603950 (Russian Federation); Lobachevsky State University of Nizhny Novgorod, 23 Gagarin ave., Nizhny Novgorod, 603950 (Russian Federation); Pronchatov-Rubtsov, Nikolay, E-mail: nikvas@rf.unn.ru [Lobachevsky State University of Nizhny Novgorod, 23 Gagarin ave., Nizhny Novgorod, 603950 (Russian Federation)
2015-10-28
A problem of noninvasive measurement of liquid flow velocity arises in many practical applications. To this end the most often approach is the use of the linear Doppler technique. The Doppler frequency shift of signal scattered from the inhomogeneities distributed in a liquid relatively to the emitted frequency is proportional to the sound frequency and velocities of inhomogeneities. In the case of very slow flow one needs to use very high frequency sound. This approach fails in media with strong sound attenuation because acoustic wave attenuation increases with frequency and there is limit in increasing sound intensity, i.e. the cavitation threshold. Another approach which is considered in this paper is based on the method using the difference frequency Doppler Effect for flows with bubbles. This method is based on simultaneous action of two high-frequency primary acoustic waves with closed frequencies on bubbles and registration of the scattered by bubbles acoustic field at the difference frequency. The use of this method is interesting since the scattered difference frequency wave has much lower attenuation in a liquid. The theoretical consideration of the method is given in the paper. The experimental examples confirming the theoretical equations, as well as the ability of the method to be applied in medical diagnostics and in technical applications on measurement of flow velocities in liquids with strong sound attenuation is described. It is shown that the Doppler spectrum form depends on bubble concentration velocity distribution in the primary acoustic beams crossing zone that allows one to measure the flow velocity distribution.
Nonlinear inverse scattering methods for thermal- wave slice tomography: a wavelet domain approach
Energy Technology Data Exchange (ETDEWEB)
Miller, E.L. [Department of Electrical and Computer Engineering, Northeastern University, 235 Forsyth Building, Boston, Massachusetts02115 (United States); Nicolaides, L.; Mandelis, A. [Photothermal and Optoelectronic Diagnostics Laboratory, Department of Mechanical Engineering, University of Toronto, 5 Kings College Road, Toronto M5S3G8, Ontario (Canada)
1998-06-01
A wavelet domain, nonlinear inverse scattering approach is presented for imaging subsurface defects in a material sample, given observations of scattered thermal waves. Unlike methods using the Born linearization, our inversion scheme is based on the full wave-field model describing the propagation of thermal waves. Multiresolution techniques are employed to regularize and to lower the computational burden of this ill-posed imaging problem. We use newly developed wavelet-based regularization methods to resolve better the edge structures of defects relative to reconstructions obtained with smoothness-type regularizers. A nonlinear approximation to the exact forward-scattering model is introduced to simplify the inversion with little loss in accuracy. We demonstrate this approach on cross-section imaging problems by using synthetically generated scattering data from transmission and backprojection geometries. {copyright} 1998 Optical Society of America
PetClaw: A scalable parallel nonlinear wave propagation solver for Python
Alghamdi, Amal
2011-01-01
We present PetClaw, a scalable distributed-memory solver for time-dependent nonlinear wave propagation. PetClaw unifies two well-known scientific computing packages, Clawpack and PETSc, using Python interfaces into both. We rely on Clawpack to provide the infrastructure and kernels for time-dependent nonlinear wave propagation. Similarly, we rely on PETSc to manage distributed data arrays and the communication between them.We describe both the implementation and performance of PetClaw as well as our challenges and accomplishments in scaling a Python-based code to tens of thousands of cores on the BlueGene/P architecture. The capabilities of PetClaw are demonstrated through application to a novel problem involving elastic waves in a heterogeneous medium. Very finely resolved simulations are used to demonstrate the suppression of shock formation in this system.
Nonlinear Propagation of Mag Waves Through the Transition Region
Jatenco-Pereira, V.; Steinolfson, R. S.; Mahajan, S.; Tajima, T.
1990-11-01
RESUMEN. Una onda de gravitaci5n magneto acustica (GMA), se inicia en el regimen de alta beta cerca de la basa de fot5sfera solar y es segui- da, usando simulaciones numericas, mientras viaja radialmente a traves de la cromosfera, la regi5n de transici6n y dentro de la corona. Se ha' seleccionado parametros iniciales de manera que la beta resulte menor que uno cerca de la parte alta de la regi6n de transici6n. Nuestro interes maximo se concentra en la cantidad y forma del flujo de energia que puede ser llevada por la onda hasta la corona dados una atm6sfera inicial y amplitud de onda especificas. Segun los estudios a la fecha, el flujo de energ1a termico domina, aumentando linealmente con la ampli tud deonda y resulta de aproximadamente i05 ergs/cm2-s en una amplitud de 0.5. El flujo de energia cinetica siempre permanece despreciable, mientras que el flujo de energia magnetica depende de la orientaci5n inicial del campo. Un modo GMA rapido y casi paralelo, el cual es esen- cialmente un modo MHD en la corona se convierte a un modo rapido modificado y a uno lento, cuando la beta atmosferica disminuye a uno. ABSTRACT: A magneto-acoustic-gravity (MAG) wave is initiated in the high-beta regime near the base of the solar photosphere and followed, using numerical siriiulations, as it travels radially through the chromosphere, the transition region, and into the corona. Initial parameters are selected such that beta becomes less than one near the top of the transition region. Our primary interest is in the amount and form of energy flux that can be carried by the wave train into the corona for a specified initial atmosphere and wave amplitude. For the studies conducted to date, the thermal energy flux dominates, it about linearly with wave amplitude and becomes approximately 10 ergs/cm2-s at an amplitude of 0.5. The kinetic energy flux always remains negligible, while the magnetic energy flux depends on the inLtial field orientation. A nearly parallel fast MAG mode, which
Generation of Long Waves using Non-Linear Digital Filters
DEFF Research Database (Denmark)
Høgedal, Michael; Frigaard, Peter; Christensen, Morten
1994-01-01
transform of the 1st order surface elevation and subsequently inverse Fourier transformed. Hence, the methods are unsuitable for real-time applications, for example where white noise are filtered digitally to obtain a wave spectrum with built-in stochastic variabillity. In the present paper an approximative...... method for including the correct 2nd order bound terms in such applications is presented. The technique utilizes non-liner digital filters fitted to the appropriate transfer function is derived only for bounded 2nd order subharmonics, as they laboratory experiments generally are considered the most...
Alberucci, Alessandro; Laudyn, Urszula A; Piccardi, Armando; Kwasny, Michał; Klus, Bartlomiej; Karpierz, Mirosław A; Assanto, Gaetano
2017-07-01
We investigate nonlinear optical propagation of continuous-wave (CW) beams in bulk nematic liquid crystals. We thoroughly analyze the competing roles of reorientational and thermal nonlinearity with reference to self-focusing/defocusing and, eventually, the formation of nonlinear diffraction-free wavepackets, the so-called spatial optical solitons. To this extent we refer to dye-doped nematic liquid crystals in planar cells excited by a single CW beam in the highly nonlocal limit. To adjust the relative weight between the two nonlinear responses, we employ two distinct wavelengths, inside and outside the absorption band of the dye, respectively. Different concentrations of the dye are considered in order to enhance the thermal effect. The theoretical analysis is complemented by numerical simulations in the highly nonlocal approximation based on a semi-analytic approach. Theoretical results are finally compared to experimental results in the Nematic Liquid Crystals (NLC) 4-trans-4'-n-hexylcyclohexylisothiocyanatobenzene (6CHBT) doped with Sudan Blue dye.
Giant nonlinear response at a plasmonic nanofocus drives efficient four-wave mixing
Nielsen, Michael P.; Shi, Xingyuan; Dichtl, Paul; Maier, Stefan A.; Oulton, Rupert F.
2017-12-01
Efficient optical frequency mixing typically must accumulate over large interaction lengths because nonlinear responses in natural materials are inherently weak. This limits the efficiency of mixing processes owing to the requirement of phase matching. Here, we report efficient four-wave mixing (FWM) over micrometer-scale interaction lengths at telecommunications wavelengths on silicon. We used an integrated plasmonic gap waveguide that strongly confines light within a nonlinear organic polymer. The gap waveguide intensifies light by nanofocusing it to a mode cross-section of a few tens of nanometers, thus generating a nonlinear response so strong that efficient FWM accumulates over wavelength-scale distances. This technique opens up nonlinear optics to a regime of relaxed phase matching, with the possibility of compact, broadband, and efficient frequency mixing integrated with silicon photonics.
Island-trapped Waves, Internal Waves, and Island Circulation
2015-09-30
HDSS) with 50 and 140 kHz systems for profiling to ∼700 and 300 m as well as an RDI Ocean Surveyor (OS) 75 kHz acoustic Doppler current profiler ( ADCP ...and a narrowband 150 kHz ADCP . The OS75 was operated in narrowband mode only to provide better statistics over its maximum depth range. In 2013, an...plane were made of the density data from SeaSoar and currents from the OS75 ADCP . Isopycnals show lee waves with a wavelength of about 15 km (Figure 1
Internal waves and the Poincaré equation
Swart, A.N.
2007-01-01
Internal waves are waves propagating through a body of fluid. They are of importance in the field of geophysical fluid mechanics since their enabling mechanisms (density stratification and rotation) are predominant in Earth's oceans and atmosphere. This thesis consists of several chapters. The first
Tomographic reconstruction of internal wave patterns in a paraboloid
Hazewinkel, J.; Maas, L.R.M.; Dalziel, S.B.
2011-01-01
Using tomographic synthetic schlieren, we are able to reconstruct the three-dimensional density field of internal waves. In this study, the waves are radiating from an oscillating sphere positioned eccentrically at the surface of a paraboloidal domain filled with a uniformly stratified fluid. We
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.
The instability of nonlinear surface waves in an electrified liquid jet
International Nuclear Information System (INIS)
Moatimid, Galal M
2009-01-01
We investigate the weakly nonlinear stability of surface waves of a liquid jet. In this work, the liquids are uniformly streaming through two porous media and the gravitational effects are neglected. The system is acted upon by a uniform tangential electric field, that is parallel to the jet axis. The equations of motion are linearly treated and solved in the light of nonlinear boundary conditions. Therefore, the boundary-value problem leads to a nonlinear characteristic second-order differential equation. This characterized equation has a complex nature. The nonlinearity is kept up to the third degree. It is used to judge the behavior of the surface evolution. According to the linear stability theory, we derive the dispersion relation that accounts for the growth waves. The stability criterion is discussed analytically and a stability picture is identified for a chosen sample system. Several special cases are recovered upon appropriate data choices. In order to derive the Ginsburg-Landau equation for the general case, in the nonlinear approach, we used the method of multiple timescales with the aid of the Taylor expansion. This equation describes the competition between nonlinearity and the linear dispersion relation. As a special case for non-porous media where there is no streaming, we obtained the well-known nonlinear Schroedinger equation as it has been derived by others. The stability criteria are expressed theoretically in terms of various parameters of the problem. Stability diagrams are obtained for a set of physical parameters. We found new instability regions in the parameter space. These regions are due to the nonlinear effects.
International Nuclear Information System (INIS)
Lin Chang; Zhang Xiulian
2005-01-01
The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.
International Nuclear Information System (INIS)
Zhang Huiqun
2009-01-01
By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.
Stellwagen Bank National Marine Sanctuary - Internal Wave Analysis Spatial Extent
National Oceanic and Atmospheric Administration, Department of Commerce — This feature class contains the spatial extent of the internal wave analysis. This area of interest was defined in interests of time. A cusory review of the 66 SAR...
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
further simulations we demonstrate few-cycle compressed solitons in extremely short crystals, where spectral phenomena, such as blue/red shifting, nonstationary radiation in accordance with the nonlocal phase-matching condition, and dispersive-wave generation are observed and marked, which helps improve...
A family of nonlinear Schrödinger equations admitting q-plane wave solutions
Nobre, F. D.; Plastino, A. R.
2017-08-01
Nonlinear Schrödinger equations with power-law nonlinearities have attracted considerable attention recently. Two previous proposals for these types of equations, corresponding respectively to the Gross-Pitaievsky equation and to the one associated with nonextensive statistical mechanics, are here unified into a single, parameterized family of nonlinear Schrödinger equations. Power-law nonlinear terms characterized by exponents depending on a real index q, typical of nonextensive statistical mechanics, are considered in such a way that the Gross-Pitaievsky equation is recovered in the limit q → 1. A classical field theory shows that, due to these nonlinearities, an extra field Φ (x → , t) (besides the usual one Ψ (x → , t)) must be introduced for consistency. The new field can be identified with Ψ* (x → , t) only when q → 1. For q ≠ 1 one has a pair of coupled nonlinear wave equations governing the joint evolution of the complex valued fields Ψ (x → , t) and Φ (x → , t). These equations reduce to the usual pair of complex-conjugate ones only in the q → 1 limit. Interestingly, the nonlinear equations obeyed by Ψ (x → , t) and Φ (x → , t) exhibit a common, soliton-like, traveling solution, which is expressible in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics.
An upper ocean current jet and internal waves in a Gulf Stream warm core ring
Joyce, T. M.; Stalcup, M. C.
1984-01-01
On June 22, 1982, the R/V Endeavor, while participating in a multi-ship study of a warm core ring 82B, encountered a strong front in the core of the ring. The vessel was headed on a radial section outward from ring center while a CTD was repeatedly raised and lowered between 10 and 300 m. Current profiles in the upper 100 m were obtained continuously with a Doppler acoustic profiling system. Above the shallow 45 m seasonal thermocline, a current jet of 4 km width was encountered having a central core of relatively light water and a maximum current of 1.1 m/s. This jet was both highly nonlinear and totally unexpected. A high frequency packet of directional internal waves was acoustically observed in the seasonal thermocline at the outer edge of the jet. Vertical velocities were large enough (6 cm/s) as to be directly observable in the Doppler returns. The waves were propagating from the northeast, parallel to the ship track, and orthogonal to the jet toward the center of the warm core ring. While a nonlinear, centrifugal term was required for the force balance of the jet, the high-frequency internal wave packet could be explained with linear, gravest-mode wave dynamics.
Nonlinear propagation of whistler wave and turbulent spectrum in reconnection region of magnetopause
Sharma, R. P.; Pathak, Neha; Yadav, Nitin; Sharma, Prachi
2017-09-01
Whistler waves have ample of observations in the magnetosphere near the dayside magnetopause. Also, the role of whistler waves is well established in the context of magnetic reconnection as well as turbulence generation. In the present work, we examine the combined effect of guide field and nonlinearity in the development of turbulence in magnetic reconnection sites. We have derived the dynamical equation of 3D whistler wave propagating through Harris sheet assuming that background number density and background field are perturbed. The nonlinear dynamical equation is then solved numerically using pseudo-spectral method and finite difference method. Simulation results represent the nonlinear evolution of X-O field line in the presence of nonlinearity, which causes the generation of turbulence. We have also investigated the formation of current sheet/coherent structures as a result of the proposed mechanism. These localized structures have transverse scale size of the order of electron inertial length. When the system reaches quasi steady state, we have evaluated power spectrum in magnetopause and it shows two different scaling having k-3 /2 for k λe1 .The obtained results are consistent with the THEMIS observations. Energy distribution at smaller scales leads to the formation of thermal tail of energetic particles. The energy of these electrons is also calculated and comes out to be in the order of 100 keV.
Nonlinear Wave Radiation and Diffraction by a Near-Surface Body
Ananthakrishnan, P.
1997-11-01
Physics of surface-wave and rigid-body interactions is of importance in naval architecture, in that a good understanding of wave-body interactions is necessary for the design of hulls with minimum ship-motion and resistance characteristics. Particular topics of contemporary research such as generation of spray and breaking waves by a surface ship and control of ship motion in high seas are however highly nonlinear, rendering analysis a challenging task. Using a robust numerical algorithm developed for analyzing fully nonlinear free-surface flow in a viscous fluid (see P. Ananthakrishnan, Three-dimensional wave-body interactions in a viscous fluid, Proc. of ISOPE'97 Conference, Hawaii), we have investigated diffraction and radiation of waves by floating and submerged rigid bodies. In the numerical model, the Navier-Stokes equations subject to exact free-surface and body boundary conditions are solved in primitive variables using a fractional-step finite-difference method which is implemented using curvilinear coordinates. Approximate conditions are however used to model the open boundary and the movement of the contact line. Results presented shed light to a better understanding of generation and ensuing spatial-temporal evolution of vortices under the influence of a free surface, vortical and potential components of hydrodynamics forces, symmetry-breaking in the case of large-amplitude oscillations, generation and damping of super-harmonic waves, and parameter ranges in which effect of viscosity is significant.
Phase-space description of plasma waves. Linear and nonlinear theory
International Nuclear Information System (INIS)
Biro, T.
1992-11-01
We develop an (r,k) phase space description of waves in plasmas by introducing Gaussian window functions to separate short scale oscillations from long scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation also in an inhomogeneous and time varying background plasma, we first discuss the proper form of the current response function. On the analogy of the particle distribution function f(v,r,t), we introduce a wave density N(k,r,t) on phase space. This function is proven to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density' along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible. Within the phase space representation, we obtain a very general formula for the second order nonlinear current in terms of the vector potential. This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasma, including the effects of inhomogeneous turbulence, wave convection and refraction. (author)
Nonlinear piezoelectricity in PZT ceramics for generating ultrasonic phase conjugate waves
Yamamoto; Kokubo; Sakai; Takagi
2000-03-01
We have succeeded in the generation of acoustic phase conjugate waves with nonlinear PZT piezoelectric ceramics and applied them to ultrasonic imaging systems. Our aim is to make a phase conjugator with 100% efficiency. For this purpose, it is important to clarify the mechanism of acoustic phase conjugation through nonlinear piezoelectricity. The process is explained by the parametric interaction via the third-order nonlinear piezoelectricity between the incident acoustic wave at angular frequency omega and the pump electric field at 2 omega. We solved the coupling equations including the third-ordered nonlinear piezoelectricity and theoretically derived the amplitude efficiency of the acoustic phase conjugation. We compared the efficiencies between the theoretical and experimental values for PZT ceramics with eight different compositions. Pb[(Zn1/3Nb2/3)(1 - x)Tix]O3 (X = 0.09, PZNT91/9) piezoelectric single crystals have been investigated for high-performance ultrasonic transducer application, because these have large piezoelectric constants, high electrical-mechanical coupling factors and high dielectric constants. We found that they have third-order nonlinear piezoelectric constants much larger than PZT and are hopeful that the material as a phase conjugator has over 100% efficiency.
Bartoli, Ivan; Nucera, Claudio; Srivastava, Ankit; Salamone, Salvatore; Phillips, Robert; Lanza di Scalea, Francesco; Coccia, Stefano; Sikorsky, Charles S.
2009-03-01
Many bridges, including 90% of the California inventory, are post-tensioned box-girders concrete structures. Prestressing tendons are the main load-carrying components of these and other post-tensioned structures. Despite their criticality, much research is needed to develop and deploy techniques able to provide real-time information on the level of prestress in order to detect dangerous stress losses. In collaboration with Caltrans, UCSD is investigating the combination of ultrasonic guided waves and embedded sensors to provide both prestress level monitoring and defect detection capabilities in concrete-embedded PS tendons. This paper presents a technique based on nonlinear ultrasonic guided waves in the 100 kHz - 2 MHz range for monitoring prestress levels in 7-wire PS tendons. The technique relies on the fact that an axial stress on the tendon generates a proportional radial stress between adjacent wires (interwire stress). In turn, the interwire stress modulates nonlinear effects in ultrasonic wave propagation through both the presence of finite strains and the interwire contact. The nonlinear ultrasonic behavior of the tendon under changing levels of prestress is monitored by tracking higher-order harmonics at (nω) arising under a fundamental guided-wave excitation at (ω). Experimental results will be presented to identify (a) ranges of fundamental excitations at (ω) producing maximum nonlinear response, and (b) optimum lay-out of the transmitting and the receiving transducers within the test tendons. Compared to alternative methods based on linear ultrasonic features, the proposed nonlinear ultrasonic technique appears more sensitive to prestress levels and more robust against changing excitation power at the transmitting transducer or changing transducer/tendon bond conditions.
Nonlinear surge motions of a ship in bi-chromatic following waves
Spyrou, Kostas J.; Themelis, Nikos; Kontolefas, Ioannis
2018-03-01
Unintended motions of a ship operating in steep and long following waves are investigated. A well-known such case is ;surf-riding; where a ship is carried forward by a single wave, an event invoking sometimes lateral instability and even capsize. The dynamics underlying this behavior has been clarified earlier for monochromatic waves. However, the unsteadiness of the phase space associated with ship behavior in a multichromatic sea, combined with the intrinsically strong system nonlinearity, pose new challenges. Here, current theory is extended to cover surging and surf-riding behavior in unidirectional bi-chromatic waves encountering a ship from the stern. Excitation is provided by two unidirectional harmonic wave components having their lengths comparable to the ship length and their frequencies in rational ratio. The techniques applied include (a) continuation analysis; (b) tracking of Lagrangian coherent structures in phase space, approximated through a finite-time Lyapunov exponents' calculation; and (c) large scale simulation. A profound feature of surf-riding in bi-chromatic waves is that it is turned oscillatory. Initially it appears as a frequency-locked motion, ruled by the harmonic wave component dominating the excitation. Transformations of oscillatory surf-riding are realized as the waves become steeper. In particular, heteroclinic tanglings are identified, governing abrupt transitions between qualitatively different motions. Chaotic transients, as well as long-term chaotic motions, exist near to these events. Some extraordinary patterns of ship motion are discovered. These include a counterintuitive low speed motion at very high wave excitation level; and a hybrid motion characterized by a wildly fluctuating velocity. Due to the quite generic nature of the core mathematical model of our investigation, the current results are believed to offer clues about the behavior of a class of nonlinear dynamical systems having in their modeling some analogy with
Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques
International Nuclear Information System (INIS)
Carretero-González, R; Frantzeskakis, D J; Kevrekidis, P G
2008-01-01
The aim of this review is to introduce the reader to some of the physical notions and the mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyse some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g. the linear or the nonlinear limit or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools. (invited article)
Nonlinear Gravitational Waves as Dark Energy in Warped Spacetimes
Directory of Open Access Journals (Sweden)
Reinoud Jan Slagter
2017-02-01
Full Text Available We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1 scalar gauge field (cosmic string on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers of the subsequent orders of the scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution due to the suppression of the n-dependency in the energy momentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This contribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2 breaking of the axially symmetric configuration into a discrete subgroup of rotations of about 180 ∘ . The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2 symmetry, triggers the pressure T z z for discrete values of the azimuthal-angle. There could be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and this could be evidence for the existence of cosmic strings. Careful comparison of this spectrum of extremal values of the first and second order φ-dependency and the distribution of the alignment of the quasar polarizations is necessary. This can be accomplished when more observational data become available. It turns out that, for late time, the vacuum 5D spacetime is conformally invariant if the warp factor fulfils the equation of a vibrating
Electromagnetic internal gravity waves in the Earth's ionospheric E-layer
International Nuclear Information System (INIS)
Kaladze, T.D.; Tsamalashvili, L.V.; Kaladze, D.T.
2011-01-01
In the Earth's ionospheric E-layer existence of the new waves connecting with the electromagnetic nature of internal gravity waves is shown. They represent the mixture of the ordinary internal gravity waves and the new type of dispersive Alfven waves. -- Highlights: ► Existence of electromagnetic internal gravity waves in the ionospheric E-layer is shown. ► Electromagnetic nature of internal gravity waves is described. ► Appearance of the new dispersive Alfven waves is shown.
Nonlinear structures: Cnoidal, soliton, and periodical waves in quantum semiconductor plasma
Energy Technology Data Exchange (ETDEWEB)
Tolba, R. E., E-mail: tolba-math@yahoo.com; El-Bedwehy, N. A., E-mail: nab-elbedwehy@yahoo.com [Department of Mathematics, Faculty of Science Damietta University, New Damietta 34517 (Egypt); Moslem, W. M., E-mail: wmmoslem@hotmail.com [Department of Physics, Faculty of Science Port Said University, Port Said 42521 (Egypt); Centre for Theoretical Physics, The British University in Egypt (BUE), El-Shorouk City, Cairo (Egypt); El-Labany, S. K., E-mail: skellabany@hotmail.com [Department of Physics, Faculty of Science Damietta University, New Damietta 34517 (Egypt); Yahia, M. E., E-mail: meyahia@gmail.com [Faculty of Engineering and Natural Sciences, International University of Sarajevo (IUS), 71210 Ilidža, Sarajevo, Bosnia and Herzegovina (Bosnia and Herzegovina)
2016-01-15
Properties and emerging conditions of various nonlinear acoustic waves in a three dimensional quantum semiconductor plasma are explored. A plasma fluid model characterized by degenerate pressures, exchange correlation, and quantum recoil forces is established and solved. Our analysis approach is based on the reductive perturbation theory for deriving the Kadomtsev-Petviashvili equation from the fluid model and solving it by using Painlevé analysis to come up with different nonlinear solutions that describe different pulse profiles such as cnoidal, soliton, and periodical pulses. The model is then employed to recognize the possible perturbations in GaN semiconductor.
Liepmann, H. W.; Torczynski, J. R.
1983-01-01
Second sound techniques were used to study superfluid helium. Second sound shock waves produced relative velocities in the bulk fluid. Maximum counterflow velocities produced in this way are found to follow the Langer-Fischer prediction for the fundamental critical velocity in its functional dependence on temperature and pressure. Comparison of successive shock and rotating experiments provides strong evidence that breakdown results in vorticity production in the flow behind the shock. Schlieren pictures have verified the planar nature of second sound shocks even after multiple reflections. The nonlinear theory of second sound was repeatedly verified in its prediction of double shocks and other nonlinear phenomena.
Nonlinear features of electrostatic waves in a plasma with nonthermal-Tsallis distributed electrons
Energy Technology Data Exchange (ETDEWEB)
Dutta, Debjit [Department of Mathematics, National Institute of Technology, Agartala, Jiraniya 799046 (India); Sahu, Biswajit, E-mail: biswajit-sahu@yahoo.co.in [Department of Mathematics, West Bengal State University, Barasat, Kolkata 700126 (India)
2016-06-15
Linear and nonlinear properties of electrostatic waves are investigated in an unmagnetized multicomponent plasma system consisting of cold and hot electrons obeying nonthermal-Tsallis distribution and warm ions using the Sagdeev pseudopotential technique. It is found that such a plasma supports soliton, supersoliton, and double layer structures. Also, the present plasma system supports the coexistence of arbitrary amplitude compressive and rarefactive solitons in a certain region of parameter space. Furthermore, numerical results reveal that the nonthermal-Tsallis distribution of electrons may affect the spatial profiles as well as the nature of the electrostatic nonlinear structures.
Bistable states of TM polarized non-linear waves guided by symmetric layered structures
International Nuclear Information System (INIS)
Mihalache, D.
1985-04-01
Dispersion relations for TM polarized non-linear waves propagating in a symmetric single film optical waveguide are derived. The system consists of a layer of thickness d with dielectric constant epsilon 1 bounded at two sides by a non-linear medium characterized by the diagonal dielectric tensor epsilon 11 =epsilon 22 =epsilon 0 , epsilon 33 =epsilon 0 +α|E 3 | 2 , where E 3 is the normal electric field component. For sufficiently large d/lambda (lambda is the wavelength) we predict bistable states of both symmetric and antisymmetric modes provided that the power flow is the control parameter. (author)
Nonlinear fiber-optic strain sensor based on four-wave mixing in microstructured optical fiber
DEFF Research Database (Denmark)
Gu, Bobo; Yuan, Scott Wu; Frosz, Michael H.
2012-01-01
We demonstrate a nonlinear fiber-optic strain sensor, which uses the shifts of four-wave mixing Stokes and anti-Stokes peaks caused by the strain-induced changes in the structure and refractive index of a microstructured optical fiber. The sensor thus uses the inherent nonlinearity of the fiber...... and does not require any advanced post-processing of the fiber. Strain sensitivity of -0.23 pm/mu epsilon is achieved experimentally and numerical simulations reveal that for the present fiber the sensitivity can be increased to -4.46 pm/mu epsilon by optimizing the pump wavelength and power....
Three dimensional full-wave nonlinear acoustic simulations: Applications to ultrasound imaging
Energy Technology Data Exchange (ETDEWEB)
Pinton, Gianmarco [Joint Department of Biomedical Engineering, University of North Carolina - North Carolina State University, 348 Taylor Hall, Chapel Hill, NC 27599, USA gfp@unc.edu (United States)
2015-10-28
Characterization of acoustic waves that propagate nonlinearly in an inhomogeneous medium has significant applications to diagnostic and therapeutic ultrasound. The generation of an ultrasound image of human tissue is based on the complex physics of acoustic wave propagation: diffraction, reflection, scattering, frequency dependent attenuation, and nonlinearity. The nonlinearity of wave propagation is used to the advantage of diagnostic scanners that use the harmonic components of the ultrasonic signal to improve the resolution and penetration of clinical scanners. One approach to simulating ultrasound images is to make approximations that can reduce the physics to systems that have a low computational cost. Here a maximalist approach is taken and the full three dimensional wave physics is simulated with finite differences. This paper demonstrates how finite difference simulations for the nonlinear acoustic wave equation can be used to generate physically realistic two and three dimensional ultrasound images anywhere in the body. A specific intercostal liver imaging scenario for two cases: with the ribs in place, and with the ribs removed. This configuration provides an imaging scenario that cannot be performed in vivo but that can test the influence of the ribs on image quality. Several imaging properties are studied, in particular the beamplots, the spatial coherence at the transducer surface, the distributed phase aberration, and the lesion detectability for imaging at the fundamental and harmonic frequencies. The results indicate, counterintuitively, that at the fundamental frequency the beamplot improves due to the apodization effect of the ribs but at the same time there is more degradation from reverberation clutter. At the harmonic frequency there is significantly less improvement in the beamplot and also significantly less degradation from reverberation. It is shown that even though simulating the full propagation physics is computationally challenging it
Combined effects of traveling seismic waves and soil nonlinearity on nuclear power plant response
International Nuclear Information System (INIS)
Lee, T.H.; Charman, C.M.
1981-01-01
The effects of ground motion nonuniformity on the seismic input have been actively studied in recent years by considering the passage of traveling seismic waves. These studies gave rise to a new class of soil-structure interaction problems in which the seismic input is modified as a result of the spatial variations of ground motion. The phenomena were usually studied by using the elastic half-space simulation or discrete spring-models for modeling the soil medium. Finite element methods were also used recently on a limited scope. Results obtained from these investigations are often manifested by an attenuation of translational excitation along with an addition of rotational ground motion input. The decrease in structural response resulting from the input loss in the translational component was often insignificant since the response reduction tends to be offset by the effects from rotational input. The traveling wave effects have, so far, been investigated within the framework of linear theory with soil nonlinearity ignored. Conversely, the incorporation of soil nonlinearity in soil-structure interaction analyses has been done without including wave effect. Seismic analyses considering the hysteretic behavior of soil have been performed using highly idealized models for steady-state solution. More elaborate nonlinear seismic models deal with only the strain-dependent soil modulus rather than the transient unloading-reloading type of hysteretic characteristics of soil under a time-function input of earthquake trace. Apparently, the traveling wave effect and soil nonlinearity have been separately treated in the past. The purpose of this paper is to demonstrate that these two major effects can be combined in one model such that the influence of wave passage is reflected through the hysteretic behavior of soil particles, and thereby achieving significant reduction in seismic loads. (orig./RW)
Observations on the robustness of internal wave attractors to perturbations
Hazewinkel, Jeroen; Tsimitri, Chrysanthi; Maas, Leo R. M.; Dalziel, Stuart B.
2010-10-01
Previously, internal wave attractors have been studied in the laboratory in idealized situations. Here, we present a series of experiments in which these conditions are modified. Modifications are made by varying the forcing frequency, by using a nonuniform stratification, by introducing finite amplitude perturbations to the trapezoidal domain, and by using a parabolic domain. All these new experiments reveal the persistence of internal wave attractors that remain reasonably well predictable by means of ray tracing. We conclude that the occurrence of wave attractors is likely to be more general than has previously been thought. The fundamental response of the confined, continuously stratified fluids studied in this paper to a sustained forcing has to be described in terms of internal wave attractors.
Chaos induced by breakup of waves in a spatial epidemic model with nonlinear incidence rate
International Nuclear Information System (INIS)
Sun, Gui-Quan; Jin, Zhen; Liu, Quan-Xing; Li, Li
2008-01-01
Spatial epidemiology is the study of spatial variation in disease risk or incidence, including the spatial patterns of the population. The spread of diseases in human populations can exhibit large scale patterns, underlining the need for spatially explicit approaches. In this paper, the spatiotemporal complexity of a spatial epidemic model with nonlinear incidence rate, which includes the behavioral changes and crowding effect of the infective individuals, is investigated. Based on both theoretical analysis and computer simulations, we find out when, under the parameters which can guarantee a stable limit cycle in the non-spatial model, spiral and target waves can emerge. Moreover, two different kinds of breakup of waves are shown. Specifically, the breakup of spiral waves is from the core and the breakup of target waves is from the far-field, and both kinds of waves become irregular patterns at last. Our results reveal that the spatiotemporal chaos is induced by the breakup of waves. The results obtained confirm that diffusion can form spiral waves, target waves or spatial chaos of high population density, which enrich the findings of spatiotemporal dynamics in the epidemic model
Numerical simulation of nonlinear wave force on a quasi-ellipse caisson
Wang, Yongxue; Ren, Xiaozhong; Wang, Guoyu
2011-09-01
A three dimensional numerical model of nonlinear wave action on a quasi-ellipse caisson in a time domain was developed in this paper. Navier-Stokes equations were solved by the finite difference method, and the volume of fluid (VOF) method was employed to trace the free surface. The partial cell method was used to deal with the irregular boundary typical of this type of problem during first-time wave interaction with the structure, and a satisfactory result was obtained. The numerical model was verified and used to investigate the effects of the relative wave height H/d, relative caisson width kD, and relative length-width ratio B/D on the wave forces of the quasi-ellipse caisson. It was shown that the relative wave height H/d has a significant effect on the wave forces of the caisson. Compared with the non-dimensional inline wave force, the relative length-width ratio B/D was shown to have significant influence on the non-dimensional transverse wave force.
Propagation of 3D internal gravity wave beams in a slowly varying stratification
Fan, Boyu; Akylas, T. R.
2017-11-01
The time-mean flows induced by internal gravity wave beams (IGWB) with 3D variations have been shown to have dramatic implications for long-term IGWB dynamics. While uniform stratifications are convenient both theoretically and in the laboratory, stratifications in the ocean can vary by more than an order of magnitude over the ocean depth. Here, in view of this fact, we study the propagation of a 3D IGWB in a slowly varying stratification. We assume that the stratification varies slowly relative to the local variations in the wave profile. In the 2D case, the IGWB bends in response to the changing stratification, but nonlinear effects are minor even in the finite amplitude regime. For a 3D IGWB, in addition to bending, we find that nonlinearity results in the transfer of energy from waves to a large-scale time-mean flow associated with the mean potential vorticity, similar to IGWB behavior in a uniform stratification. In a weakly nonlinear setting, we derive coupled evolution equations that govern this process. We also use these equations to determine the stability properties of 2D IGWB to 3D perturbations. These findings indicate that 3D effects may be relevant and possibly fundamental to IGWB dynamics in nature. Supported by NSF Grant DMS-1512925.
Dynamical criteria for rogue waves in nonlinear Schrödinger models
International Nuclear Information System (INIS)
Calini, Annalisa; Schober, Constance M
2012-01-01
We investigate rogue waves in deep water in the framework of the nonlinear Schrödinger (NLS) and Dysthe equations. Amongst the homoclinic orbits of unstable NLS Stokes waves, we seek good candidates to model actual rogue waves. In this paper we propose two selection criteria: stability under perturbations of initial data, and persistence under perturbations of the NLS model. We find that requiring stability selects homoclinic orbits of maximal dimension. Persistence under (a particular) perturbation selects a homoclinic orbit of maximal dimension all of whose spatial modes are coalesced. These results suggest that more realistic sea states, described by JONSWAP power spectra, may be analyzed in terms of proximity to NLS homoclinic data. In fact, using the NLS spectral theory, we find that rogue wave events in random oceanic sea states are well predicted by proximity to homoclinic data of the NLS equation. (invited article)
Self-similarity of asymmetric sand-ripple profiles formed under nonlinear shoaling waves
Testik, F. Y.; Voropayev, S. I.; Balasubramanian, S.; Fernando, H. J. S.
2006-10-01
We report the results of laboratory experiments conducted to study equilibrium profiles of asymmetric sand ripples that form under nonlinear shoaling waves. Waves were generated in a large wave tank with a sandy slope that mimics the oceanic coastal zone. The measurements revealed that, to the first approximation, the equilibrium asymmetric sand ripples profiles can be considered as self-similar. In the experimental parameter range considered (wave asymmetry A =1.3-5; mobility parameter Ψ =8-70; shoaling coefficient S =1.03-1.6), the ripple profiles can be described by a simple similarity profile of "sawtooth" shape with "universal" onshore θ1 (≈34°) and offshore θ2 (≈18°) ripple slope angles. The results may be useful in parameterization of coastal bed roughness, in underwater acoustics and sediment transport applications.
El-Labany, S. K.; Sabry, R.; El-Shamy, E. F.; Khedr, D. M.; Khedr
2013-10-01
Investigation of arbitrary amplitude nonlinear ion-acoustic solitary waves which accompany collisionless positive-negative ion plasmas with high-energy electrons (represented by kappa distribution) is presented. Arbitrary amplitude solitary waves are investigated by deriving an energy-integral equation involving a Sagdeev-like pseudopotential. The existence regions of solitary pulses are, defined precisely, modified by the superthermality of energetic electrons. Furthermore, numerical calculations reveal that both compressive and rarefactive pulses may exist for negative ion mass groups in Titan's atmosphere. The superthermality of energetic electrons are found to modify the existence domains of large amplitude ion-acoustic waves in Titan's atmosphere. The dependence of solitary excitation characteristics on the superthermal parameter, the negative ion concentration, the positive-to-negative ions mass ratio, and the Mach number have been investigated. The present study might be helpful to understand the excitation of fully nonlinear ion-acoustic solitary pulses that may appear in the interplanetary medium and/or in the astrophysical plasmas in general.
On the generation and evolution of internal solitary waves in the southern Red Sea
Guo, Daquan
2015-04-01
Satellite observations recently revealed the existence of trains of internal solitary waves in the southern Red Sea between 16.0°N and 16.5°N, propagating from the centre of the domain toward the continental shelf [Da silva et al., 2012]. Given the relatively weak tidal velocity in this area and their generation in the central of the domain, Da Silva suggested three possible mechanisms behind the generation of the waves, namely Resonance and disintegration of interfacial tides, Generation of interfacial tides by impinging, remotely generated internal tidal beams and for geometrically focused and amplified internal tidal beams. Tide analysis based on tide stations data and barotropic tide model in the Red Sea shows that tide is indeed very weak in the centre part of the Red Sea, but it is relatively strong in the northern and southern parts (reaching up to 66 cm/s). Together with extreme steep slopes along the deep trench, it provides favourable conditions for the generation of internal solitary in the southern Red Sea. To investigate the generation mechanisms and study the evolution of the internal waves in the off-shelf region of the southern Red Sea we have implemented a 2-D, high-resolution and non-hydrostatic configuration of the MIT general circulation model (MITgcm). Our simulations reproduce well that the generation process of the internal solitary waves. Analysis of the model\\'s output suggests that the interaction between the topography and tidal flow with the nonlinear effect is the main mechanism behind the generation of the internal solitary waves. Sensitivity experiments suggest that neither tidal beam nor the resonance effect of the topography is important factor in this process.
Directory of Open Access Journals (Sweden)
Weiguo Rui
2014-01-01
Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.
Solar Internal Rotation and Dynamo Waves: A Two Dimensional ...
Indian Academy of Sciences (India)
tribpo
Solar Internal Rotation and Dynamo Waves: A Two Dimensional. Asymptotic Solution in the Convection Zone ... We calculate here a spatial 2 D structure of the mean magnetic field, adopting real profiles of the solar internal ... of the asymptotic solution in low (middle) and high (right panel) latitudes. field is shifted towards the ...
Non-linear Alfvén waves in spin-1/2 quantum plasma
Jan, Qasim; Mushtaq, A.; Ikram, M.
2018-02-01
Nonlinear circularly polarized Alfvén waves are studied in Fermionic spin-1/2 quantum plasmas. Using the basic equations for Hall magnetohydrodynamics including quantum corrections, the set of Zakharov-like equations are obtained for circularly polarized nonlinear Alfvén waves. In order to investigate the properties of the Alfvén solitary structure in the presence of spin magnetization and quantum plasma beta, the Sagdeev potential approach is employed. For the case of right-handed circularly polarized Alfvén waves, the amplitude of the Sagdeev potential and the associated solitary profile is observed to enhance with the increase of quantum plasma beta and magnetization energy due to electron spin-1/2 effects. However, it is found that the amplitude of the Sagdeev potential and the related solitary profile decrease with the increasing values of quantum plasma beta and magnetization energy for the case of left-handed circularly polarized Alfvén waves. An increase in the width of the solitary structure is also observed with the increase in the value of magnetization energy for the case of the left-handed circularly polarized wave. An investigation of the modulational instability is also inspected with the effects of spin magnetization and quantum plasma beta.
Directory of Open Access Journals (Sweden)
Lijun Zhang
2014-01-01
Full Text Available An integral-differential model equation arising from neuronal networks with very general kernel functions is considered in this paper. The kernel functions we study here include pure excitations, lateral inhibition, lateral excitations, and more general synaptic couplings (e.g., oscillating kernel functions. The main goal of this paper is to prove the existence and uniqueness of the traveling wave front solutions. The main idea we apply here is to reduce the nonlinear integral-differential equation into a solvable differential equation and test whether the solution we get is really a wave front solution of the model equation.
Nonlinear whistler wave model for lion roars in the Earth’s magnetosheath
DEFF Research Database (Denmark)
Dwivedi, N. K.; Singh, S.
2017-01-01
In the present study, we construct a nonlinear whistler wave model to explain the magnetic field spectra observed for lion roars in the Earth’s magnetosheath region. We use two-fluid theory and semi-analytical approach to derive the dynamical equation of whistler wave propagating along the ambient...... spectrum with a spectral slope of −4.5 superimposed with a narrow band peak. The broadband fluctuations appear due to the energy cascades attributed by low-frequency magnetohydrodynamic modes, whereas, a narrow band peak is observed due to the short period lion roars bursts. The energy spectrum predicted...
The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations
Directory of Open Access Journals (Sweden)
Yusuf Pandir
2018-02-01
Full Text Available In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.
Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations
Novruzov, Emil
2017-11-01
This paper is concerned with blow-up phenomena for the nonlinear dispersive wave equation on the real line, ut -uxxt +[ f (u) ] x -[ f (u) ] xxx +[ g (u) + f″/(u) 2 ux2 ] x = 0 that includes the Camassa-Holm equation as well as the hyperelastic-rod wave equation (f (u) = ku2 / 2 and g (u) = (3 - k) u2 / 2) as special cases. We establish some a local-in-space blow-up criterion (i.e., a criterion involving only the properties of the data u0 in a neighborhood of a single point) simplifying and precising earlier blow-up criteria for this equation.
Nonlinear dispersion of resonance extraordinary wave in a plasma with strong magnetic field
International Nuclear Information System (INIS)
Krasovitskiy, V. B.; Turikov, V. A.; Sotnikov, V. I.
2007-01-01
In this paper, the efficiency of electron acceleration by a short, powerful laser pulse propagating across an external magnetic field is investigated. Conditions for the decay of a laser pulse with frequency close to the upper hybrid resonance frequency are analyzed. It is also shown that a laser pulse propagating as an extraordinary wave in cold, magnetized, low-density plasma takes the form of a nonlinear wave with the modulated amplitude (envelope soliton). Finally, simulation results on the interaction of an electromagnetic pulse with a semi-infinite plasma, obtained with the help of an electromagnetic relativistic PIC code, are discussed and a comparison with the obtained theoretical results is presented
International Nuclear Information System (INIS)
Dai Chaoqing; Wang Yueyue; Tian Qing; Zhang Jiefang
2012-01-01
We present, analytically, self-similar rogue wave solutions (rational solutions) of the inhomogeneous nonlinear Schrödinger equation (NLSE) via a similarity transformation connected with the standard NLSE. Then we discuss the propagation behaviors of controllable rogue waves under dispersion and nonlinearity management. In an exponentially dispersion-decreasing fiber, the postponement, annihilation and sustainment of self-similar rogue waves are modulated by the exponential parameter σ. Finally, we investigate the nonlinear tunneling effect for self-similar rogue waves. Results show that rogue waves can tunnel through the nonlinear barrier or well with increasing, unchanged or decreasing amplitudes via the modulation of the ratio of the amplitudes of rogue waves to the barrier or well height. - Highlights: ► Self-similar rogue wave solutions of the inhomogeneous NLSE are obtained.► Postponement, annihilation and sustainment of self-similar rogue waves are discussed. ► Nonlinear tunneling effects for self-similar rogue waves are investigated.
Detailed characterization of CW- and pulsed-pump four-wave mixing in highly nonlinear fibers
DEFF Research Database (Denmark)
Lillieholm, Mads; Galili, Michael; Grüner-Nielsen, L.
2016-01-01
We present a quantitative comparison of continuouswave- (CW) and pulsed-pump four-wave mixing (FWM) in commercially available highly nonlinear fibers (HNLFs), and suggest properties for which the CW and pulsed FWM bandwidths are limited in practice. The CWand pulsed-pump parametric gain is charac......We present a quantitative comparison of continuouswave- (CW) and pulsed-pump four-wave mixing (FWM) in commercially available highly nonlinear fibers (HNLFs), and suggest properties for which the CW and pulsed FWM bandwidths are limited in practice. The CWand pulsed-pump parametric gain...... bandwidth. However, an inverse scaling of the TOD with the dispersion fluctuations, leads to different CW-optimized fibers, which depend only on the even dispersion-orders....
Efficient Hybrid-Spectral Model for Fully Nonlinear Numerical Wave Tank
DEFF Research Database (Denmark)
Christiansen, Torben; Bingham, Harry B.; Engsig-Karup, Allan Peter
2013-01-01
A new hybrid-spectral solution strategy is proposed for the simulation of the fully nonlinear free surface equations based on potential flow theory. A Fourier collocation method is adopted horisontally for the discretization of the free surface equations. This is combined with a modal Chebyshev Tau...... method in the vertical for the discretization of the Laplace equation in the fluid domain, which yields a sparse and spectrally accurate Dirichletto-Neumann operator. The Laplace problem is solved with an efficient Defect Correction method preconditioned with a spectral discretization of the linearised...... wave problem, ensuring fast convergence and optimal scaling with the problem size. Preliminary results for very nonlinear waves show expected convergence rates and a clear advantage of using spectral schemes....
On the new soliton and optical wave structures to some nonlinear evolution equations
Bulut, Hasan; Sulaiman, Tukur Abdulkadir; Baskonus, Haci Mehmet
2017-11-01
In this study, with the aid of the Wolfram Mathematica software, the powerful sine-Gordon expansion method is utilized to search for the solutions to some important nonlinear mathematical models arising in nonlinear sciences, namely, the (2 + 1) -dimensional Zakharov-Kuznetsov modified equal width equation, the cubic Boussinesq equation and the modified regularized long wave equation. We successfully obtain some new soliton, singular soliton, singular periodic waves and kink-type solutions with complex hyperbolic structures to these equations. We also present the two- and three-dimensional shapes of all the solutions obtained in this study. We further give the physical meaning of all the obtained solutions. We compare our results with the existing results in the literature.
A stabilised nodal spectral element method for fully nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, C.; Bigoni, Daniele
2016-01-01
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although...... the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions...... can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively...
International Nuclear Information System (INIS)
Mirzade, F. Kh.
2006-01-01
A system of equations is formulated to describe the self-consistent behavior of elastic displacement fields and the concentration field of point defects in irradiated crystals with a symmetry center (germanium, silicon). In accordance with the values of the defect relaxation times, the model evolution equations are derived, describing the steady-state nonlinear longitudinal waves, with regard to the flexoelectric effect. The effect is due to the dielectric polarization induced by nonuniform elastic deformations of the lattice. For a particular relationship between the coefficients of these equations, i.e., between the parameters of the subsystem of defects and those of the nonlinear elastic medium, the exact solutions are obtained, which describe the generation of solitons and low-intensity shock waves. The contributions of the strain-defect interaction and the flexoelectric effect to the linear velocity of sound and the dispersion properties of the medium are estimated
Solitary waves under the competition of linear and nonlinear periodic potentials
International Nuclear Information System (INIS)
Rapti, Z; Kevrekidis, P G; Konotop, V V; Jones, C K R T
2007-01-01
In this paper, we study the competition of the linear and nonlinear lattices and its effects on the stability and dynamics of bright solitary waves. We consider both lattices in a perturbative framework, whereby the technique of Hamiltonian perturbation theory can be used to obtain information about the existence of solutions, and the same approach, as well as eigenvalue count considerations, can be used to obtain detailed conditions about their linear stability. We find that the analytical results are in very good agreement with our numerical findings and can also be used to predict features of the dynamical evolution of such solutions. A particularly interesting result of these considerations is the existence of a tunable cancellation effect between the linear and nonlinear lattices that allows for increased mobility of the solitary wave
Energy Technology Data Exchange (ETDEWEB)
El-Taibany, W. F., E-mail: eltaibany@du.edu.eg, E-mail: eltaibany@hotmail.com; Selim, M. M.; Al-Abbasy, O. M. [Department of Physics, Faculty of Science, Damietta University, New Damietta P. O. 34517 (Egypt); El-Bedwehy, N. A., E-mail: nab-elbedwehy@yahoo.com [Department of Mathematics, Faculty of Science, Damietta University, New Damietta P. O. 34517 (Egypt)
2014-07-15
The propagation of both linear and nonlinear dust acoustic waves (DAWs) in an inhomogeneous magnetized collisional and warm dusty plasma (DP) consisting of Boltzmann ions, nonextensive electrons, and inertial dust particles is investigated. The number density gradients of all DP components besides the inhomogeneities of electrostatic potential and the initial dust fluid velocity are taken into account. The linear dispersion relation and a nonlinear modified Zakharov-Kusnetsov (MZK) equation governing the propagation of the three-dimensional DAWs are derived. The analytical solution of the MZK reveals the creation of both compressive and rarefactive DAW solitons in the proposed model. It is found that the inhomogeneity dimension parameter and the electron nonextensive parameter affect significantly the nonlinear DAW's amplitude, width, and Mach number. The relations of our findings with some astrophysical situations have been given.
Variational methods in nonlinear field equations solitary waves, hylomorphic solitons and vortices
Benci, Vieri
2014-01-01
The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.
General decay of solutions of a nonlinear system of viscoelastic wave equations
Said-Houari, Belkacem
2011-04-16
This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.
Nonlinear dynamic effects in a two-wave CO2 laser
International Nuclear Information System (INIS)
Gorobets, V A; Kozlov, K V; Kuntsevich, B F; Petukhov, V O
1999-01-01
Theoretical and experimental investigations were made of nonlinear dynamic regimes of the operation of a two-wave CO 2 laser with cw excitation in an electric discharge and loss modulation in one of the channels. Nonlinear amplitude - frequency characteristics of each of the laser channels have two low-frequency resonance spikes, associated with forced linear oscillations of two coupled oscillators, and high-frequency spikes, corresponding to doubling of the period of the output radiation oscillations. At low loss-modulation frequencies the intensity oscillations of the output radiation in the coupled channels are in antiphase, whereas at high modulation frequencies the dynamics is cophasal. Nonlinear dynamic effects, such as doubling of the period and of the repetition frequency of the pulses and chaotic oscillations of the output radiation intensity, are observed for certain system parameters. (control of laser radiation parameters)
Directory of Open Access Journals (Sweden)
Kurt L. Polzin
2017-06-01
Full Text Available There is no theoretical underpinning that successfully explains how turbulent mixing is fed by wave breaking associated with nonlinear wave-wave interactions in the background oceanic internal wavefield. We address this conundrum using one-dimensional ray tracing simulations to investigate interactions between high frequency internal waves and inertial oscillations in the extreme scale separated limit known as “Induced Diffusion”. Here, estimates of phase locking are used to define a resonant process (a resonant well and a non-resonant process that results in stochastic jumps. The small amplitude limit consists of jumps that are small compared to the scale of the resonant well. The ray tracing simulations are used to estimate the first and second moments of a wave packet’s vertical wavenumber as it evolves from an initial condition. These moments are compared with predictions obtained from the diffusive approximation to a self-consistent kinetic equation derived in the ‘Direct Interaction Approximation’. Results indicate that the first and second moments of the two systems evolve in a nearly identical manner when the inertial field has amplitudes an order of magnitude smaller than oceanic values. At realistic (oceanic amplitudes, though, the second moment estimated from the ray tracing simulations is inhibited. The transition is explained by the stochastic jumps obtaining the characteristic size of the resonant well. We interpret this transition as an adiabatic ‘saturation’ process which changes the nominal background wavefield from supporting no mixing to the point where that background wavefield defines the normalization for oceanic mixing models.
Czech Academy of Sciences Publication Activity Database
Dos Santos, S.; Vejvodová, Šárka; Převorovský, Zdeněk
2009-01-01
Roč. 19, č. 2 (2009), s. 14-14 ISSN 1213-3825. [NDT in PROGRESS. 12.11.2009-14.11.2009, Praha] R&D Projects: GA ČR GA106/07/1393; GA MPO(CZ) FR-TI1/274 Institutional research plan: CEZ:AV0Z20760514 Keywords : nonlinear elastic wave spectroscopy (NEWS) * ESAM * time reversal (TR) * TR-NEWS imaging * tomography * DORT Subject RIV: BI - Acoustics
DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Hesthaven, Jan; Bingham, Harry B.
2008-01-01
equations in complex and curvilinear geometries which amends the application range of previous numerical models that have been based on structured Cartesian grids. The Boussinesq method provides the basis for the accurate description of fully nonlinear and dispersive water waves in both shallow and deep...... and absorbed in the interior of the computational domain using a flexible relaxation technique applied on the free surface variables....
Method and analysis for determining yielding of titanium alloy with nonlinear Rayleigh surface waves
Energy Technology Data Exchange (ETDEWEB)
Guo, Shifeng; Zhang, Lei; Mirshekarloo, Meysam Sharifzadeh; Chen, Shuting; Chen, Yi Fan; Wong, Zheng Zheng; Shen, Zhiyuan; Liu, Huajun; Yao, Kui, E-mail: k-yao@imre.a-star.edu.sg
2016-07-04
Methods for determining yielding of titanium (Ti) alloy material with second harmonic Rayleigh ultrasonic wave are investigated. Both piezoelectric angle beam transducers and high frequency laser scanning vibrometer (LSV) are used to detect ultrasonic signals in the Ti alloy specimens with different plastic strain levels. Technical features and outcomes with use of piezoelectric transducers and LSV are compared. The method using piezoelectric transducers, with much higher signal-to-noise ratio than LSV, has been further improved by deploying two transducers with central frequencies corresponding to the fundamental and second order harmonic signals respectively to improve the testing reliability and accuracy. Both the techniques using piezoelectric transducer and LSV demonstrate consistently that the acoustic nonlinearity increases with plastic strain, and the second harmonic Rayleigh ultrasonic wave can be utilized for effective determination of yielding in Ti alloy. Our experiments further show that the acoustic nonlinearity increases gradually with plastic strain at small plastic strain level, and there is a more significant increase of acoustic nonlinearity when the plastic strain reaches a higher level. Microscopic investigations using scanning electron microscopy (SEM) and high resolution transmission electron microscopy (HRTEM) are conducted for clarifying the relationship between the observed acoustic nonlinearity and micro-structural changes.