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)
Nonlinear instability and chaos in plasma wave-wave interactions
International Nuclear Information System (INIS)
Kueny, C.S.
1993-01-01
Conventional linear stability analysis may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes. Instability may then occur either via dissipation of the negative energy modes. Instability may then occur either via dissipitation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, which leads to explosive growth. In the dissipationaless case, it is conjectured that intrinsic chaotic behavior may allow initially non-resonant systems to reach resonance by diffusion in phase space. This is illustrated for a simple equilibrium involving cold counter-streaming ions. The system is described in the fluid approximation by a Hamilitonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamilitonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, which occur generically for long enough wavelengths. Three-wave interactions which occur in isolated, but numerous, regions of parameter space can drive either decay instability or explosive instability. When the resonance for explosive growth is detuned, a stable region exists around the equilibrium point in phase space, while explosive growth occurs outside of a separatrix. These interactions may be described exactly if only one resonance is considered, while multiple nonlinear terms make the Hamiltonian nonintegradable. Simple Hamiltonians of two and three degrees of freedom are studied numerically using symplectic integration algorithms, including an explicit algorithm derived using Lie algebraic methods
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
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.)
Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves
Tobita, Miwa; Omura, Yoshiharu
2018-03-01
We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.
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 wave particle interaction in the Earth's foreshock
Mazelle, C.; LeQueau, D.; Meziane, K.; Lin, R. P.; Parks, G.; Reme, H.; Sanderson, T.; Lepping, R. P.
1997-01-01
The possibility that ion beams could provide a free energy source for driving an ion/ion instability responsible for the ULF wave occurrence is investigated. For this, the wave dispersion relation with the observed parameters is solved. Secondly, it is shown that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered around a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions with the observations are compared.
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...
On the interaction of small-scale linear waves with nonlinear solitary waves
Xu, Chengzhu; Stastna, Marek
2017-04-01
In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow
Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao
2018-04-01
We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.
Asymptotic approach for the nonlinear equatorial long wave interactions
International Nuclear Information System (INIS)
Ramirez Gutierrez, Enver; Silva Dias, Pedro L; Raupp, Carlos
2011-01-01
In the present work we use an asymptotic approach to obtain the long wave equations. The shallow water equation is put as a function of an external parameter that is a measure of both the spatial scales anisotropy and the fast to slow time ratio. The values given to the external parameters are consistent with those computed using typical values of the perturbations in tropical dynamics. Asymptotically, the model converge toward the long wave model. Thus, it is possible to go toward the long wave approximation through intermediate realizable states. With this approach, the resonant nonlinear wave interactions are studied. To simplify, the reduced dynamics of a single resonant triad is used for some selected equatorial trios. It was verified by both theoretical and numerical results that the nonlinear energy exchange period increases smoothly as we move toward the long wave approach. The magnitude of the energy exchanges is also modified, but in this case depends on the particular triad used and also on the initial energy partition among the triad components. Some implications of the results for the tropical dynamics are discussed. In particular, we discuss the implications of the results for El Nino and the Madden-Julian in connection with other scales of time and spatial variability.
Nonlinear interaction and wave breaking with a submerged porous structure
Hsieh, Chih-Min; Sau, Amalendu; Hwang, Robert R.; Yang, W. C.
2016-12-01
Numerical simulations are performed to investigate interactive velocity, streamline, turbulent kinetic energy, and vorticity perturbations in the near-field of a submerged offshore porous triangular structure, as Stokes waves of different heights pass through. The wave-structure interaction and free-surface breaking for the investigated flow situations are established based on solutions of 2D Reynolds Averaged Navier-Stokes equations in a Cartesian grid in combination with K-ɛ turbulent closure and the volume of fluid methodology. The accuracy and stability of the adopted model are ascertained by extensive comparisons of computed data with the existing experimental and theoretical findings and through efficient predictions of the internal physical kinetics. Simulations unfold "clockwise" and "anticlockwise" rotation of fluid below the trough and the crest of the viscous waves, and the penetrated wave energy creates systematic flow perturbation in the porous body. The interfacial growths of the turbulent kinetic energy and the vorticity appear phenomenal, around the apex of the immersed structure, and enhanced significantly following wave breaking. Different values of porosity parameter and two non-porous cases have been examined in combination with varied incident wave height to reveal/analyze the nonlinear flow behavior in regard to local spectral amplification and phase-plane signatures. The evolution of leading harmonics of the undulating free-surface and the vertical velocity exhibits dominating roles of the first and the second modes in inducing the nonlinearity in the post-breaking near-field that penetrates well below the surface layer. The study further suggests the existence of a critical porosity that can substantially enhance the wave-shoaling and interface breaking.
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
Ulysses Observations of Nonlinear Wave-wave Interactions in the ...
Indian Academy of Sciences (India)
tribpo
The Ulysses Unified Radio and Plasma Wave Experiment. (URAP) has observed Langmuir, ... gesting that strong turbulence processes, such as modulational instability and soliton formation, often coexist ... Solar and interplanetary type III radio bursts, which occur at the fundamental and the second harmonic of the electron ...
Lagrangian analysis of nonlinear wave-wave interactions in bounded plasmas
International Nuclear Information System (INIS)
Carr, A.R.
1979-01-01
In a weakly turbulent nonlinear wave-supporting medium, one of the important nonlinear processes which may occur is resonant three-wave interaction. Whitham's averaged Lagrangian method provides a general formulation of wave evolution laws which is easily adapted to nonlinear dispersive media. In this thesis, the strength of nonlinear interactions between three coherent, axisymmetric, low frequency, magnetohydrodynamic (Alfven) waves propagating in resonance along a cold cylindrical magnetized plasma column is calculated. Both a uniform and a parabolic density distribution have been considered. To account for a non-zero plasma temperature, pressure effects have been included. Distinctive features of the work are the use of cylindrical geometry, the presence of a finite rather than an infinite axial magnetic field, the treatment of a parabolic density distribution, and the inclusion of both ion and electron contributions in all expressions. Two astrophysical applications of the presented theory have been considered. In the first, the possibility of resonant three-wave coupling between geomagnetic micropulsations, which propagate as Alfven or magnetosonic waves along the Earth's magnetic field lines, has been investigated. The second case is the theory of energy transport through the solar chromosphere by upward propagating magnetohydrodynamic waves, which may then couple to heavily damped waves in the corona, causing the observed excess heating in that region
Experimental investigation of gravity wave turbulence and of non-linear four wave interactions..
Berhanu, Michael
2017-04-01
Using the large basins of the Ecole Centrale de Nantes (France), non-linear interactions of gravity surface waves are experimentally investigated. In a first part we study statistical properties of a random wave field regarding the insights from the Wave Turbulence Theory. In particular freely decaying gravity wave turbulence is generated in a closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonl-inear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, non-linear and dissipative time scales to test the time scale separation. By estimation of the mean energy flux from the initial decay of wave energy, the Kolmogorov-Zakharov constant of the weak turbulence theory is evaluated. In a second part, resonant interactions of oblique surface gravity waves in a large basin are studied. We generate two oblique waves crossing at an acute angle. These mother waves mutually interact and give birth to a resonant wave whose properties (growth rate, resonant response curve and phase locking) are fully characterized. All our experimental results are found in good quantitative agreement with four-wave interaction theory. L. Deike, B. Miquel, P. Gutiérrez, T. Jamin, B. Semin, M. Berhanu, E. Falcon and F. Bonnefoy, Role of the basin boundary conditions in gravity wave turbulence, Journal of Fluid Mechanics 781, 196 (2015) F. Bonnefoy, F. Haudin, G. Michel, B. Semin, T. Humbert, S. Aumaître, M. Berhanu and E. Falcon, Observation of resonant interactions among surface gravity waves, Journal of Fluid Mechanics (Rapids) 805, R3 (2016)
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
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.
Nonlinear instability and chaos in plasma wave-wave interactions, I., Introduction
International Nuclear Information System (INIS)
Kueny, C.S.; Morrison, P.J.
1994-11-01
Conventional linear stability analyses may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper [submitted to Physics of Plasmas], this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various (integrable) systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper
Nonlinear instability and chaos in plasma wave--wave interactions. I. Introduction
International Nuclear Information System (INIS)
Kueny, C.S.; Morrison, P.J.
1995-01-01
Conventional linear stability analyses may fail for fluid systems with an indefinite free-energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave--wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper (submitted to Phys. Plasmas), this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various integrable systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper. copyright 1995 American Institute of Physics
Beach steepness effects on nonlinear infragravity-wave interactions : A numerical study
De Bakker, A. T M; Tissier, M.F.S.; Ruessink, B. G.
2016-01-01
The numerical model SWASH is used to investigate nonlinear energy transfers between waves for a diverse set of beach profiles and wave conditions, with a specific focus on infragravity waves. We use bispectral analysis to study the nonlinear triad interactions, and estimate energy transfers to
Beach steepness effects on nonlinear infragravity-wave interactions : A numerical study
de Bakker, A. T M; Tissier, M. F S; Ruessink, B. G.
2016-01-01
The numerical model SWASH is used to investigate nonlinear energy transfers between waves for a diverse set of beach profiles and wave conditions, with a specific focus on infragravity waves. We use bispectral analysis to study the nonlinear triad interactions, and estimate energy transfers to
Robust Numerical Methods for Nonlinear Wave-Structure Interaction in a Moving Frame of Reference
DEFF Research Database (Denmark)
Kontos, Stavros; Lindberg, Ole
This project is focused on improving the state of the art for predicting the interaction between nonlinear ocean waves and marine structures. To achieve this goal, a flexible order finite difference potential flow solver has been extended to calculate for fully nonlinear wave-structure interaction...
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)
International Nuclear Information System (INIS)
Amein, W.H.; El-Siragy, N.M.; Nagy, O.Z.; Sayed, Y.A.
1981-01-01
Nonlinear interaction of S-Polarized surface waves at the boundary of a semibounded magnetized plasma is investigated. The expressions of the amplitudes of the generated waves are found. It is shown that, the generated waves with combined frequencies are equally radiated from the transient layer into plasma and vacuum
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 O...
Energy Technology Data Exchange (ETDEWEB)
Huang, K.M. [Wuhan Univ. (China). School of Electronic Information; Chinese Academey of Sciences, Hefei (China). Key Lab. of Geospace Environment; Embry Riddle Aeronautical Univ., Daytona Beach, FL (United States). Dept. of Physical Science; Ministry of Education, Wuhan (China). Key Lab. of Geospace Environment and Geodesy; State Observatory for Atmospheric Remote Sensing, Wuhan (China); Liu, A.Z.; Li, Z. [Embry Riddle Aeronautical Univ., Daytona Beach, FL (United States). Dept. of Physical Science; Zhang, S.D.; Yi, F. [Wuhan Univ. (China). School of Electronic Information; Ministry of Education, Wuhan (China). Key Lab. of Geospace Environment and Geodesy; State Observatory for Atmospheric Remote Sensing, Wuhan (China)
2012-07-01
Nonlinear interactions of gravity waves are studied with a two-dimensional, fully nonlinear model. The energy exchanges among resonant and near-resonant triads are examined in order to understand the spectral energy transfer through interactions. The results show that in both resonant and near-resonant interactions, the energy exchange between two high frequency waves is strong, but the energy transfer from large to small vertical scale waves is rather weak. This suggests that the energy cascade toward large vertical wavenumbers through nonlinear interaction is inefficient, which is different from the rapid turbulence cascade. Because of considerable energy exchange, nonlinear interactions can effectively spread high frequency spectrum, and play a significant role in limiting wave amplitude growth and transferring energy into higher altitudes. In resonant interaction, the interacting waves obey the resonant matching conditions, and resonant excitation is reversible, while near-resonant excitation is not so. Although near-resonant interaction shows the complexity of match relation, numerical experiments show an interesting result that when sum and difference near-resonant interactions occur between high and low frequency waves, the wave vectors tend to approximately match in horizontal direction, and the frequency of the excited waves is also close to the matching value. (orig.)
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 ...
Nonlinear infragravity–wave interactions on a gently sloping laboratory beach
De Bakker, A.T.M.; Herbers, T.H.C.; Smit, P.B.; Tissier, M.F.S.; Ruessink, B.G.
2015-01-01
A high-resolution dataset of three irregular wave conditions collected on a gently sloping laboratory beach is analyzed to study nonlinear energy transfers involving infragravity frequencies. This study uses bispectral analysis to identify the dominant, nonlinear interactions and estimate energy
Nonlinear infragravity-wave interactions on a gently sloping laboratory beach
de Bakker, A. T M; Herbers, T. H C; Smit, P. B.; Tissier, M. F S; Ruessink, B. G.
2015-01-01
A high-resolution dataset of three irregular wave conditions collected on a gently sloping laboratory beach is analyzed to study nonlinear energy transfers involving infragravity frequencies. This study uses bispectral analysis to identify the dominant, nonlinear interactions and estimate energy
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)
Nonlinear theory of surface-wave--particle interactions in a cylindrical plasma
International Nuclear Information System (INIS)
Dengra, A.; Palop, J.I.F.
1994-01-01
This work is an application of the specular reflection hypothesis to the study of the nonlinear surface-wave--particle interactions in a cylindrical plasma. The model is based on nonlinear resolution of the Vlasov equation by the method of characteristics. The expression obtained for the rate of increase of kinetic energy per electron has permitted us to investigate the temporal behavior of nonlinear collisionless damping for different situations as a function of the critical parameters
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich
2011-01-01
A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves the Hami...... is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance equation. © 2010 Springer Science+Business Media B.V.......A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves...... the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity potential. Numerical studies of the evolution of a number of arbitrary initial conditions...
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]....
Zhao, J. S.; Voitenko, Y.; De Keyser, J.; Wu, D. J.
2018-04-01
We study the decay of Alfvén waves in the solar wind, accounting for the joint operation of two-dimensional (2D) scalar and three-dimensional (3D) vector nonlinear interactions between Alfvén and slow waves. These interactions have previously been studied separately in long- and short-wavelength limits where they lead to 2D scalar and 3D vector decays, correspondingly. The joined action of the scalar and vector interactions shifts the transition between 2D and 3D decays to significantly smaller wavenumbers than was predicted by Zhao et al. who compared separate scalar and vector decays. In application to the broadband Alfvén waves in the solar wind, this means that the vector nonlinear coupling dominates in the extended wavenumber range 5 × 10‑4 ≲ ρ i k 0⊥ ≲ 1, where the decay is essentially 3D and nonlocal, generating product Alfvén and slow waves around the ion gyroscale. Here ρ i is the ion gyroradius, and k 0⊥ is the pump Alfvén wavenumber. It appears that, except for the smallest wavenumbers at and below {ρ }i{k}0\\perp ∼ {10}-4 in Channel I, the nonlinear decay of magnetohydrodynamic Alfvén waves propagating from the Sun is nonlocal and cannot generate counter-propagating Alfvén waves with similar scales needed for the turbulent cascade. Evaluation of the nonlinear frequency shift shows that product Alfvén waves can still be approximately described as normal Alfvénic eigenmodes. On the contrary, nonlinearly driven slow waves deviate considerably from normal modes and are therefore difficult to identify on the basis of their phase velocities and/or polarization.
Nonlinear interaction of fast particles with Alfven waves in toroidal plasmas
International Nuclear Information System (INIS)
Candy, J.; Borba, D.; Huysmans, G.T.A.; Kerner, W.; Berk, H.L.
1996-01-01
A numerical algorithm to study the nonlinear, resonant interaction of fast particles with Alfven waves in tokamak geometry has been developed. The scope of the formalism is wide enough to describe the nonlinear evolution of fishbone modes, toroidicity-induced Alfven eigenmodes and ellipticity-induced Alfven eigenmodes, driven by both passing and trapped fast ions. When the instability is sufficiently weak, it is known that the wave-particle trapping nonlinearity will lead to mode saturation before wave-wave nonlinearities are appreciable. The spectrum of linear modes can thus be calculated using a magnetohydrodynamic normal-mode code, then nonlinearly evolved in time in an efficient way according to a two-time-scale Lagrangian dynamical wave model. The fast particle kinetic equation, including the effect of orbit nonlinearity arising from the mode perturbation, is simultaneously solved of the deviation, δf = f - f 0 , from an initial analytic distribution f 0 . High statistical resolution allows linear growth rates, frequency shifts, resonance broadening effects, and nonlinear saturation to be calculated quickly and precisely. The results have been applied to an ITER instability scenario. Results show that weakly-damped core-localized modes alone cause negligible alpha transport in ITER-like plasmas--even with growth rates one order of magnitude higher than expected values. However, the possibility of significant transport in reactor-type plasmas due to weakly unstable global modes remains an open question
International Nuclear Information System (INIS)
Wang Lei; Zhu Yujie; Wang Ziqi; Xu Tao; Qi Fenghua; Xue Yushan
2016-01-01
We study the nonlinear localized waves on constant backgrounds of the Hirota–Maxwell–Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons. (author)
Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan
2016-02-01
We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.
Nonlinear surface Alfven waves
International Nuclear Information System (INIS)
Cramer, N.F.
1991-01-01
The problem of nonlinear surface Alfven waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schroedinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field. (author)
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
Nonlinear Interaction of Waves in Rotating Spherical Layers
Zhilenko, D.; Krivonosova, O.; Gritsevich, M.
2018-01-01
Flows of a viscous incompressible fluid in a spherical layer that are due to rotational oscillations of its inner boundary at two frequencies with respect to the state of rest are numerically studied. It is found that an increase in the amplitude of oscillations of the boundary at the higher frequency can result in a significant enhancement of the low-frequency mode in a flow near the outer boundary. The direction of propagation of the low-frequency wave changes from radial to meridional, whereas the high-frequency wave propagates in the radial direction in a limited inner region of the spherical layer. The role of the meridional circulation in the energy exchange between spaced waves is demonstrated.
Effect of nonlinear wave-particle interaction on electron-cyclotron absorption
Energy Technology Data Exchange (ETDEWEB)
Tsironis, C; Vlahos, L [Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki (Greece)
2006-09-15
We perform a self-consistent analysis of the nonlinear interaction of magnetized plasmas with electron-cyclotron (EC) waves. A closed set of equations is derived, which consists of the relativistic equations of motion under the wave field and the wave equation for the vector potential. The plasma is described in terms of ensembles of electrons which collectively determine the evolution of the wave amplitude and frequency through the current response. This description allows for effects of the electron motions on the efficiency of the wave absorption, for example, the asynchrony between the wave phase and the gyroperiod. As an application, we study the absorption of an EC wave beam in a simplified tokamak geometry, for plasma parameters relevant to current and future fusion experiments. We conclude that, within the limits of our model, there are cases where the linear theory for the absorption of EC waves, used widely in the current literature, may overestimate the energy deposition. In such cases, nonlinear effects are essential for the accurate estimation of the plasma-wave coupling and their inclusion should be considered, especially when the wave power is dramatically increased as in the case of ITER.
Effect of nonlinear wave-particle interaction on electron-cyclotron absorption
International Nuclear Information System (INIS)
Tsironis, C; Vlahos, L
2006-01-01
We perform a self-consistent analysis of the nonlinear interaction of magnetized plasmas with electron-cyclotron (EC) waves. A closed set of equations is derived, which consists of the relativistic equations of motion under the wave field and the wave equation for the vector potential. The plasma is described in terms of ensembles of electrons which collectively determine the evolution of the wave amplitude and frequency through the current response. This description allows for effects of the electron motions on the efficiency of the wave absorption, for example, the asynchrony between the wave phase and the gyroperiod. As an application, we study the absorption of an EC wave beam in a simplified tokamak geometry, for plasma parameters relevant to current and future fusion experiments. We conclude that, within the limits of our model, there are cases where the linear theory for the absorption of EC waves, used widely in the current literature, may overestimate the energy deposition. In such cases, nonlinear effects are essential for the accurate estimation of the plasma-wave coupling and their inclusion should be considered, especially when the wave power is dramatically increased as in the case of ITER
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...... waters within the breaking limit. To demonstrate the current applicability of the model both linear and mildly nonlinear test cases are considered in two horizontal dimensions where the water waves interact with bottom-mounted fully reflecting structures. It is established that, by simple symmetry...... considerations combined with a mirror principle, it is possible to impose weak slip boundary conditions for both structured and general curvilinear wall boundaries while maintaining the accuracy of the scheme. As is standard for current high-order Boussinesq-type models, arbitrary waves can be generated...
Nonlinear interaction of an intense radio wave with ionospheric D/E layer plasma
Sodha, Mahendra Singh; Agarwal, Sujeet Kumar
2018-05-01
This paper considers the nonlinear interaction of an intense electromagnetic wave with the D/E layer plasma in the ionosphere. A simultaneous solution of the electromagnetic wave equation and the equations describing the kinetics of D/E layer plasma is obtained; the phenomenon of ohmic heating of electrons by the electric field of the wave causes enhanced collision frequency and ionization of neutral species. Electron temperature dependent recombination of electrons with ions, electron attachment to O 2 molecules, and detachment of electrons from O2 - ions has also been taken into account. The dependence of the plasma parameters on the square of the electric vector of the wave E0 2 has been evaluated for three ionospheric heights (viz., 90, 100, and 110 km) corresponding to the mid-latitude mid-day ionosphere and discussed; these results are used to investigate the horizontal propagation of an intense radio wave at these heights.
Romanelli, N.; Mazelle, C.; Meziane, K.
2018-02-01
Seen from the solar wind (SW) reference frame, the presence of newborn planetary protons upstream from the Martian and Venusian bow shocks and SW protons reflected from each of them constitutes two sources of nonthermal proton populations. In both cases, the resulting proton velocity distribution function is highly unstable and capable of giving rise to ultralow frequency quasi-monochromatic electromagnetic plasma waves. When these instabilities take place, the resulting nonlinear waves are convected by the SW and interact with nonthermal protons located downstream from the wave generation region (upstream from the bow shock), playing a predominant role in their dynamics. To improve our understanding of these phenomena, we study the interaction between a charged particle and a large-amplitude monochromatic circularly polarized electromagnetic wave propagating parallel to a background magnetic field, from first principles. We determine the number of fix points in velocity space, their stability, and their dependence on different wave-particle parameters. Particularly, we determine the temporal evolution of a charged particle in the pitch angle-gyrophase velocity plane under nominal conditions expected for backstreaming protons in planetary foreshocks and for newborn planetary protons in the upstream regions of Venus and Mars. In addition, the inclusion of wave ellipticity effects provides an explanation for pitch angle distributions of suprathermal protons observed at the Earth's foreshock, reported in previous studies. These analyses constitute a mean to evaluate if nonthermal proton velocity distribution functions observed at these plasma environments present signatures that can be understood in terms of nonlinear wave-particle processes.
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.
Nonlinear interaction of energetic ring current protons with magnetospheric hydromagnetic waves
International Nuclear Information System (INIS)
Chan, A.A.; Chen, L.; White, R.B.
1989-01-01
In order to study nonlinear wave-particle interactions in the Earth's magnetosphere we have derived Hamiltonian equations for the gyrophase-averaged nonrelativistic motion of charged particles in a perturbed dipole magnetic field. We assume low frequency (less than the proton gyrofrequency) fully electromagnetic perturbations, and we retain finite Larmor radius effects. Analytic and numerical results for the stochastic threshold of energetic protons (approx-gt 100 keV) in compressional geomagnetic pulsations in the Pc 5 range of frequencies 150--600 seconds are presented. These protons undergo a drift-bounce resonance with the Pc 5 waves which breaks the second (longitudinal) and third (flux) adiabatic invariants, while the first invariant (the magnetic moment) and the proton energy are approximately conserved. The proton motion in the observed spectrum of waves is found to be strongly diffusive, due to the overlap of neighboring primary resonances. copyright American Geophysical Union 1989
Nonlinear interaction of energetic ring current protons with magnetospheric hydromagnetic waves
International Nuclear Information System (INIS)
Chan, A.A.; Chen, Liu; White, R.B.
1989-09-01
In order to study nonlinear wave-particle interactions in the earth's magnetosphere we have derived Hamiltonian equations for the gyrophase-averaged nonrealistic motion of charged particles in a perturbed dipole magnetic field. We assume low frequency (less than the proton gyrofrequency) fully electromagnetic perturbations, and we retain finite Larmor radius effects. Analytic and numerical results for the stochastic threshold of energetic protons (approx gt 100 keV) in compressional geomagnetic pulsations in the Pc 5 range of frequencies (150--600 seconds) are presented. These protons undergo a drift-bounce resonance with the Pc 5 waves which breaks the second (longitudinal) and third (flux) adiabatic invariants, while the first invariant (the magnetic moment) and the proton energy are approximately conserved. The proton motion in the observed spectrum of waves is found to be strongly diffusive, due to the overlap of neighboring primary resonances. 17 refs., 2 figs
Nonlinear plasma wave models in 3D fluid simulations of laser-plasma interaction
Chapman, Thomas; Berger, Richard; Arrighi, Bill; Langer, Steve; Banks, Jeffrey; Brunner, Stephan
2017-10-01
Simulations of laser-plasma interaction (LPI) in inertial confinement fusion (ICF) conditions require multi-mm spatial scales due to the typical laser beam size and durations of order 100 ps in order for numerical laser reflectivities to converge. To be computationally achievable, these scales necessitate a fluid-like treatment of light and plasma waves with a spatial grid size on the order of the light wave length. Plasma waves experience many nonlinear phenomena not naturally described by a fluid treatment, such as frequency shifts induced by trapping, a nonlinear (typically suppressed) Landau damping, and mode couplings leading to instabilities that can cause the plasma wave to decay rapidly. These processes affect the onset and saturation of stimulated Raman and Brillouin scattering, and are of direct interest to the modeling and prediction of deleterious LPI in ICF. It is not currently computationally feasible to simulate these Debye length-scale phenomena in 3D across experimental scales. Analytically-derived and/or numerically benchmarked models of processes occurring at scales finer than the fluid simulation grid offer a path forward. We demonstrate the impact of a range of kinetic processes on plasma reflectivity via models included in the LPI simulation code pF3D. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Nonlinear wave-particle interaction upstream from the Earth's bow shock
Directory of Open Access Journals (Sweden)
C. Mazelle
2000-01-01
Full Text Available Well-defined ring-like backstreaming ion distributions have been recently reported from observations made by the 3DP/PESA-High analyzer onboard the WIND spacecraft in the Earth's foreshock at large distances from the bow shock, which suggests a local production mechanism. The maximum phase space density for these distributions remains localized at a nearly constant pitch-angle value for a large number of gyroperiods while the shape of the distribution remains very steady. These distributions are also observed in association with quasi-monochromatic low frequency (~ 50 mHz waves with substantial amplitude (δB/B>0.2. The analysis of the magnetic field data has shown that the waves are propagating parallel to the background field in the right-hand mode. Parallel ion beams are also often observed in the same region before the observation of both the ring-like distributions and the waves. The waves appear in cyclotron resonance with the ion parallel beams. We investigate first the possibility that the ion beams could provide the free energy source for driving an ion/ion instability responsible for the ULF wave occurrence. For that, we solve the wave dispersion relation with the observed parameters. Second, we show that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered on a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions are in good quantitative agreement with the observations
Ulku, Huseyin Arda
2014-07-06
Effects of material nonlinearities on electromagnetic field interactions become dominant as field amplitudes increase. A typical example is observed in plasmonics, where highly localized fields “activate” Kerr nonlinearities. Naturally, time domain solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation easier and the material nonlinearity can be easily accounted for using an auxiliary differential equation (J.H. Green and A. Taflove, Opt. Express, 14(18), 8305-8310, 2006). On the other hand, explicit marching on-in-time (MOT)-based time domain integral equation (TDIE) solvers have never been used for the same purpose even though they offer several advantages over FDTD (E. Michielssen, et al., ECCOMAS CFD, The Netherlands, Sep. 5-8, 2006). This is because explicit MOT solvers have never been stabilized until not so long ago. Recently an explicit but stable MOT scheme has been proposed for solving the time domain surface magnetic field integral equation (H.A. Ulku, et al., IEEE Trans. Antennas Propag., 61(8), 4120-4131, 2013) and later it has been extended for the time domain volume electric field integral equation (TDVEFIE) (S. B. Sayed, et al., Pr. Electromagn. Res. S., 378, Stockholm, 2013). This explicit MOT scheme uses predictor-corrector updates together with successive over relaxation during time marching to stabilize the solution even when time step is as large as in the implicit counterpart. In this work, an explicit MOT-TDVEFIE solver is proposed for analyzing electromagnetic wave interactions on scatterers exhibiting Kerr nonlinearity. Nonlinearity is accounted for using the constitutive relation between the electric field intensity and flux density. Then, this relation and the TDVEFIE are discretized together by expanding the intensity and flux - sing half
Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.
2018-04-01
Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.
Non-linear interactions of multi-level atoms with a near-resonant standing wave
International Nuclear Information System (INIS)
O'Kane, T.J.; Scholten, R.E.; Walkiewicz, M.R.; Farrell, P.M.
1998-01-01
Using a semiclassical density matrix formalism we have calculated the behavior of multi-level atoms interacting with a standing wave field, and show how complex non-linear phenomena, including multi-photon effects, combine to produce saturation spectra as observed in experiments. We consider both 20-level sodium and 24-level rubidium models, contrasting these with a simple 2-level case. The influence of parameters such as atomic trajectory and the time the atom remains in the beam are shown to have a critical effect on the lineshape of these resonances and the emission/absorption processes. Stable oscillations in the excited state populations for both the two-level and multi-level cases are shown to be limit cycles. These limit cycles undergo period doubling as the system evolves into chaos. Finally, using a Monte Carlo treatment, these processes average to produce saturated absorption spectra complete with power and Doppler broadening effects consistent with experiment. (authors)
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.
Nonlinear interaction of infrared waves on a VO2 surface at a semiconductor-metal phase transition
Berger, N. K.; Zhukov, E. A.; Novokhatskii, V. V.
1984-04-01
Nonlinear interactions (including wavefront reversal) of light from CW or pulsed 10.6-micron CO2 lasers at the semiconductor-metal phase transition in a VO2 film are investigated experimentally. The results are presented in graphs and characterized in detail. The intensity reflection coefficients of the three-wave interactions are found to be 0.5 percent for a CW reference wave of intensity 900 mW/sq cm and 42 percent for a pulsed reference wave of threshold density 600-800 microjoule/sq cm.
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...
Wave modulation in a nonlinear dispersive medium
International Nuclear Information System (INIS)
Kim, Y.C.; Khadra, L.; Powers, E.J.
1980-01-01
A model describing the simultaneous amplitude and phase modulation of a carrier wave propagating in a nonlinear dispersive medium is developed in terms of nonlinear wave-wave interactions between the sidebands and a low frequency wave. It is also shown that the asymmetric distribution of sidebands is determined by the wavenumber dependence of the coupling coefficient. Digital complex demodulation techniques are used to study modulated waves in a weakly ionized plasma and the experimental results support the analytical model
Interpretation of nonlinearity in wind generated ocean surface waves
Digital Repository Service at National Institute of Oceanography (India)
Varkey, M.J.
of sinusoidal component waves; a consequent idea arising out of Fourier analysis. It is hypothesised that a sea state which is always nonlinear to various degrees is a result of interaction, both linear and nonlinear, between nonlinear component waves...
Rogue waves in nonlinear science
International Nuclear Information System (INIS)
Yan Zhenya
2012-01-01
Rogue waves, as a special type of solitary waves, play an important role in nonlinear optics, Bose-Einstein condensates, ocean, atmosphere, and even finance. In this report, we mainly review on the history of the rogue wave phenomenon and recent development of rogue wave solutions in some nonlinear physical models arising in the fields of nonlinear science.
Berger, N. K.; Zhukov, E. A.; Novokhatskiĭ, V. V.
1984-04-01
The use of a semiconductor-metal phase transition for wavefront reversal of laser radiation was proposed. An investigation was made of nonlinear reflection of CO2 laser radiation at a phase transition in VO2. A three-wave interaction on a VO2 surface was achieved using low-power cw and pulsed CO2 lasers. In the first case, the intensity reflection coefficient was 0.5% for a reference wave intensity of 0.9 W/cm2 and in the second case, it was 42% for a threshold reference wave energy density of 0.6-0.8 mJ/cm2.
Nonlinear internal gravity waves and their interaction with the mean wind
International Nuclear Information System (INIS)
Grimshaw, R.
1975-01-01
The interaction of a wave packet of internal gravity waves with the mean wind is investigated, for the case when there is a region of wind shear and hence a critical level. The principal equations are the Doppler-shifted dispersion relation, the equation for conservation of wave action and the mean momentum equation, in which the mean wind is accelerated by a 'radiation stress' tensor, due to the waves. These equations are integrated numerically to study the behaviour of a wave packet approaching a critical level, where the horizontal phase speed matches the mean wind. The results demonstrate the exchange of energy from the waves to the mean wind in the vicinity of the critical level. The interaction between the waves and the mean wind is also studied in the absence of any initial wind shear. (author)
Directory of Open Access Journals (Sweden)
Xiaozhong Ren
2015-01-01
Full Text Available A three-dimensional numerical flume is developed to study cnoidal wave interaction with multiple arranged perforated quasi-ellipse caissons. The continuity equation and the Navier-Stokes equations are used as the governing equation, and the VOF method is adopted to capture the free surface elevation. The equations are discretized on staggered cells and then solved using a finite difference method. The generation and propagation of cnoidal waves in the numerical flume are tested first. And the ability of the present model to simulate interactions between waves and structures is verified by known experimental results. Then cnoidal waves with varying incident wave height and period are generated and interact with multiple quasi-ellipse caissons with and without perforation. It is found that the perforation plays an effective role in reducing wave runup/rundown and wave forces on the caissons. The wave forces on caissons reduce with the decreasing incident wave period. The influence of the transverse distance of multiple caissons on wave forces is also investigated. A closer transverse distance between caissons can produce larger wave forces. But when relative adjacent distance L/D (L is the transverse distance and D is the width of the quasi-ellipse caisson is larger than 3, the effect of adjacent distance is limited.
International Nuclear Information System (INIS)
Vladimirov, S.V.; Nambu, Mitsuhiro
1995-01-01
From investigations of resonant interactions of particles and waves in turbulent plasmas it is well known that not only resonant particles contribute to expressions for the wave energy and momentum providing conservation of these quantities for closed systems. In particular, it was demonstrated that contribution of the nonresonant particles is very important for the energy conservation in the quasilinear theory: although the nonresonant terms do not appear in the diffusion equation, they contribute to the wave energy (and, in general, wave momentum) ensuring the conservation of total energy (and momentum) in the system. We note that the real part of the dielectric permittivity ε ωk as well as the wave frequency ω k of the resonant waves do not depend on time in the quasilinear approximation since only nonresonant particles (which distribution is constant) contribute to them. The resonant wave amplitude, however, is the function on time, and changing of the wave energy is completely balanced by the corresponding change of the resonant particle energy. If in the system there are only nonresonant waves, and it is closed (i.e., there is no energy exchange with some external sources or sinks), the system is stationary and the nonresonant wave as well as particle energy are not changing
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...
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 betwe...... nonlinearity. The balance between dispersion and nonlinearity in the equation is investigated.......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...... the solitary waves numerically. It is demonstrated that the waves behave almost like solitons in agreement with the fact that the improved Boussinesq equations are nearly integrable. Thus three conservation theorems can be derived from the equations. A new subsonic quasibreather is found in the case of a cubic...
Nonlinear interaction between a pair of oblique modes in a supersonic mixing layer: Long-wave limit
Balsa, Thomas F.; Gartside, James
1995-01-01
The nonlinear interaction between a pair of symmetric, oblique, and spatial instability modes is studied in the long-wave limit using asymptotic methods. The base flow is taken to be a supersonic mixing layer whose Mach number is such that the corresponding vortex sheet is marginally stable according to Miles' criterion. It is shown that the amplitude of the mode obeys a nonlinear integro-differential equation. Numerical solutions of this equation show that, when the obliqueness angle is less than pi/4, the effect of the nonlinearity is to enhance the growth rate of the instability. The solution terminates in a singularity at a finite streamwise location. This result is reminiscent of that obtained in the vicinity of the neutral point by other authors in several different types of flows. On the other hand, when the obliqueness angle is more than pi/4, the streamwise development of the amplitude is characterized by a series of modulations. This arises from the fact that the nonlinear term in the amplitude equation may be either stabilizing or destabilizing, depending on the value of the streamwise coordinate. However, even in this case the amplitude of the disturbance increases, though not as rapidly as in the case for which the angle is less than pi/4. Quite generally then, the nonlinear interaction between two oblique modes in a supersonic mixing layer enhances the growth of the disturbance.
NONLINEAR WAVE INTERACTIONS AS EMISSION PROCESS OF TYPE II RADIO BURSTS
Energy Technology Data Exchange (ETDEWEB)
Ganse, Urs; Kilian, Patrick; Spanier, Felix [Lehrstuhl fuer Astronomie, Universitaet Wuerzburg, Wuerzburg (Germany); Vainio, Rami, E-mail: uganse@astro.uni-wuerzburg.de [Department of Physics, University of Helsinki, Helsinki (Finland)
2012-06-01
The emission of fundamental and harmonic frequency radio waves of type II radio bursts are assumed to be products of three-wave interaction processes of beam-excited Langmuir waves. Using a particle-in-cell code, we have performed simulations of the assumed emission region, a coronal mass ejection foreshock with two counterstreaming electron beams. Analysis of wavemodes within the simulation shows self-consistent excitation of beam-driven modes, which yield interaction products at both fundamental and harmonic emission frequencies. Through variation of the beam strength, we have investigated the dependence of energy transfer into electrostatic and electromagnetic modes, confirming the quadratic dependence of electromagnetic emission on electron beam strength.
NONLINEAR WAVE INTERACTIONS AS EMISSION PROCESS OF TYPE II RADIO BURSTS
International Nuclear Information System (INIS)
Ganse, Urs; Kilian, Patrick; Spanier, Felix; Vainio, Rami
2012-01-01
The emission of fundamental and harmonic frequency radio waves of type II radio bursts are assumed to be products of three-wave interaction processes of beam-excited Langmuir waves. Using a particle-in-cell code, we have performed simulations of the assumed emission region, a coronal mass ejection foreshock with two counterstreaming electron beams. Analysis of wavemodes within the simulation shows self-consistent excitation of beam-driven modes, which yield interaction products at both fundamental and harmonic emission frequencies. Through variation of the beam strength, we have investigated the dependence of energy transfer into electrostatic and electromagnetic modes, confirming the quadratic dependence of electromagnetic emission on electron beam strength.
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...
International Nuclear Information System (INIS)
Das, K.P.; Sihi, S.
1979-01-01
Assuming amplitudes as slowly varying functions of space and time and using perturbation method three coupled nonlinear partial differential equations are obtained for the nonlinear evolution of a three dimensional longitudinal plasma wave packet in a hot plasma including the effect of its interaction with a long wavelength ion-acoustic wave. These three equations are used to derive the instability conditions of a uniform longitudinal plasma wave train including the effect of its interaction both at resonance and nonresonance, with a long wavelength ion-acoustic wave. (author)
Hamilton, Mark F.
1990-12-01
This report discusses five projects all of which involve basic theoretical research in nonlinear acoustics: (1) pulsed finite amplitude sound beams are studied with a recently developed time domain computer algorithm that solves the KZK nonlinear parabolic wave equation; (2) nonlinear acoustic wave propagation in a liquid layer is a study of harmonic generation and acoustic soliton information in a liquid between a rigid and a free surface; (3) nonlinear effects in asymmetric cylindrical sound beams is a study of source asymmetries and scattering of sound by sound at high intensity; (4) effects of absorption on the interaction of sound beams is a completed study of the role of absorption in second harmonic generation and scattering of sound by sound; and (5) parametric receiving arrays is a completed study of parametric reception in a reverberant environment.
Nonlinear coupled Alfven and gravitational waves
International Nuclear Information System (INIS)
Kaellberg, Andreas; Brodin, Gert; Bradley, Michael
2004-01-01
In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field and the coupling to compressional Alfven waves. The gravitational waves are considered in the high-frequency limit and the plasma is modeled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and electromagnetic wave modes. A WKB-approximation is then applied and as a result we obtain the nonlinear Schroedinger equation for the slowly varying wave amplitudes. The analysis is extended to 3D wave pulses, and we discuss the applications to radiation generated from pulsar binary mergers. It turns out that the electromagnetic radiation from a binary merger should experience a focusing effect, that in principle could be detected
Nonlinear wave collapse and strong turbulence
International Nuclear Information System (INIS)
Robinson, P.A.
1997-01-01
The theory and applications of wave self-focusing, collapse, and strongly nonlinear wave turbulence are reviewed. In the last decade, the theory of these phenomena and experimental realizations have progressed rapidly. Various nonlinear wave systems are discussed, but the simplest case of collapse and strong turbulence of Langmuir waves in an unmagnetized plasma is primarily used in explaining the theory and illustrating the main ideas. First, an overview of the basic physics of linear waves and nonlinear wave-wave interactions is given from an introductory perspective. Wave-wave processes are then considered in more detail. Next, an introductory overview of the physics of wave collapse and strong turbulence is provided, followed by a more detailed theoretical treatment. Later sections cover numerical simulations of Langmuir collapse and strong turbulence and experimental applications to space, ionospheric, and laboratory plasmas, including laser-plasma and beam-plasma interactions. Generalizations to self-focusing, collapse, and strong turbulence of waves in other systems are also discussed, including nonlinear optics, solid-state systems, magnetized auroral and astrophysical plasmas, and deep-water waves. The review ends with a summary of the main ideas of wave collapse and strong-turbulence theory, a collection of open questions in the field, and a brief discussion of possible future research directions. copyright 1997 The American Physical Society
Said-Houari, Belkacem
2012-09-01
The goal of this work is to study a model of the viscoelastic wave equation with nonlinear boundary/interior sources and a nonlinear interior damping. First, applying the Faedo-Galerkin approximations combined with the compactness method to obtain existence of regular global solutions to an auxiliary problem with globally Lipschitz source terms and with initial data in the potential well. It is important to emphasize that it is not possible to consider density arguments to pass from regular to weak solutions if one considers regular solutions of our problem where the source terms are locally Lipschitz functions. To overcome this difficulty, we use an approximation method involving truncated sources and adapting the ideas in [13] to show that the existence of weak solutions can still be obtained for our problem. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term, then the solution ceases to exist and blows up in finite time provided that the initial data are large enough.
Said-Houari, Belkacem; Nascimento, Flá vio A Falcã o
2012-01-01
The goal of this work is to study a model of the viscoelastic wave equation with nonlinear boundary/interior sources and a nonlinear interior damping. First, applying the Faedo-Galerkin approximations combined with the compactness method to obtain existence of regular global solutions to an auxiliary problem with globally Lipschitz source terms and with initial data in the potential well. It is important to emphasize that it is not possible to consider density arguments to pass from regular to weak solutions if one considers regular solutions of our problem where the source terms are locally Lipschitz functions. To overcome this difficulty, we use an approximation method involving truncated sources and adapting the ideas in [13] to show that the existence of weak solutions can still be obtained for our problem. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term, then the solution ceases to exist and blows up in finite time provided that the initial data are large enough.
Nonlinear interaction of instability waves and vortex-pairing noise in axisymmetric subsonic jets
Energy Technology Data Exchange (ETDEWEB)
Yang, Hai-Hua; Zhang, Xing-Chen; Wan, Zhen-Hua; Sun, De-Jun [Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027 (China); Zhou, Lin, E-mail: wanzh@ustc.edu.cn [Institute of Structural Mechanics, Chinese Academy of Engineering Physics, Mianyang 623100 (China)
2016-10-15
A direct simulation with selected inflow forcing is performed for an accurate description of the jet flow field and far-field noise. The effects of the Mach number and heating on the acoustic field are studied in detail. The beam patterns and acoustic intensities are both varied as the change of the Mach number and temperature. The decomposition of the source terms of the Lilley–Goldstein (L–G) equation shows that the momentum and thermodynamic components lead to distinctly different beam patterns. Significant cancellation is found between the momentum and thermodynamic components at low polar angles for the isothermal jet and large polar angles for the hot jet. The cancellation leads to the minimum values of the far-field sound. Based on linear parabolized stability equation solutions, the nonlinear interaction model for sound prediction is built in combination with the L–G equation. The dominant beam patterns and their original locations predicted by the nonlinear model are in good agreement with the direct simulation results, and the predictions of sound pressure level (SPL) by the nonlinear model are relatively reasonable. (paper)
Nonlinear interaction of instability waves and vortex-pairing noise in axisymmetric subsonic jets
Yang, Hai-Hua; Zhou, Lin; Zhang, Xing-Chen; Wan, Zhen-Hua; Sun, De-Jun
2016-10-01
A direct simulation with selected inflow forcing is performed for an accurate description of the jet flow field and far-field noise. The effects of the Mach number and heating on the acoustic field are studied in detail. The beam patterns and acoustic intensities are both varied as the change of the Mach number and temperature. The decomposition of the source terms of the Lilley-Goldstein (L-G) equation shows that the momentum and thermodynamic components lead to distinctly different beam patterns. Significant cancellation is found between the momentum and thermodynamic components at low polar angles for the isothermal jet and large polar angles for the hot jet. The cancellation leads to the minimum values of the far-field sound. Based on linear parabolized stability equation solutions, the nonlinear interaction model for sound prediction is built in combination with the L-G equation. The dominant beam patterns and their original locations predicted by the nonlinear model are in good agreement with the direct simulation results, and the predictions of sound pressure level (SPL) by the nonlinear model are relatively reasonable.
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.
Collapse of nonlinear Langmuir waves
International Nuclear Information System (INIS)
Malkin, V.M.
1986-01-01
The dispersion of sufficiently intensive Langmuir waves is determined by intrinsic (electron) nonlinearity. During Langmuir collapse the wave energy density required for the appearance of electron nonlinearity is attained, generally speaking, prior to the development of dissipative processes. Up to now, the effect of electron nonlinearity on the collapse dynamics and spectrum of strong Langmuir turbulence ( which may be very appreciable ) has not been studied extensively because of the difficulty of describing nonlinear Langmuir waves. In the present paper the positive determinacy of the electron nonlinear hamiltonian is proven, the increment of modulation instability of a nonlinear Langmuir wave cluster localized in a cavity is calculated, and the universal law of their collapse is found
Nonlinear modulation of ionization waves
International Nuclear Information System (INIS)
Bekki, Naoaki
1981-01-01
In order to investigate the nonlinear characteristics of ionization waves (moving-striations) in the positive column of glow discharge, a nonlinear modulation of ionization waves in the region of the Pupp critical current is analysed by means of the reductive perturbation method. The modulation of ionization waves is described by a nonlinear Schroedinger type equation. The coefficients of the equation are evaluated using the data of the low pressure Argon-discharge, and the simple solutions (plane wave and envelope soliton type solutions) are presented. Under a certain condition an envelope soliton is propagated through the positive column. (author)
Radiation from nonlinear coupling of plasma waves
International Nuclear Information System (INIS)
Fung, S.F.
1986-01-01
The author examines the generation of electromagnetic radiation by nonlinear resonant interactions of plasma waves in a cold, uniformly magnetized plasma. In particular, he considers the up-conversion of two electrostatic wave packets colliding to produce high frequency electromagnetic radiation. Efficient conversion of electrostatic to electromagnetic wave energy occurs when the pump amplitudes approach and exceed the pump depletion threshold. Results from the inverse scattering transform analysis of the three-wave interaction equations are applied. When the wave packets are initially separated, the fully nonlinear set of coupling equations, which describe the evolution of the wave packets, can be reduced to three separate eigenvalue problems; each can be considered as a scattering problem, analogous to eh Schroedinger equation. In the scattering space, the wave packet profiles act as the scattering potentials. When the wavepacket areas approach (or exceed) π/2, the wave functions are localized (bound states) and the scattering potentials are said to contain solitons. Exchange of solitons occurs during the interaction. The transfer of solitons from the pump waves to the electromagnetic wave leads to pump depletion and the production of strong radiation. The emission of radio waves is considered by the coupling of two upper-hybrid branch wave packets, and an upper-hybrid and a lower hybrid branch wave packet
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...
Wave transmission in nonlinear lattices
International Nuclear Information System (INIS)
Hennig, D.; Tsironis, G.P.
1999-01-01
The interplay of nonlinearity with lattice discreteness leads to phenomena and propagation properties quite distinct from those appearing in continuous nonlinear systems. For a large variety of condensed matter and optics applications the continuous wave approximation is not appropriate. In the present review we discuss wave transmission properties in one dimensional nonlinear lattices. Our paradigmatic equations are discrete nonlinear Schroedinger equations and their study is done through a dynamical systems approach. We focus on stationary wave properties and utilize well known results from the theory of dynamical systems to investigate various aspects of wave transmission and wave localization. We analyze in detail the more general dynamical system corresponding to the equation that interpolates between the non-integrable discrete nonlinear Schroedinger equation and the integrable Albowitz-Ladik equation. We utilize this analysis in a nonlinear Kronig-Penney model and investigate transmission and band modification properties. We discuss the modifications that are effected through an electric field and the nonlinear Wannier-Stark localization effects that are induced. Several applications are described, such as polarons in one dimensional lattices, semiconductor superlattices and one dimensional nonlinear photonic band gap systems. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Nonlinear hyperbolic waves in multidimensions
Prasad, Phoolan
2001-01-01
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...
On nonlinear periodic drift waves
International Nuclear Information System (INIS)
Kauschke, U.; Schlueter, H.
1990-09-01
Nonlinear periodic drift waves are investigated on the basis of a simple perturbation scheme for both the amplitude and inverse frequency. The coefficients for the generation of the forced harmonics are derived, a nonlinear dispersion relation is suggested and a criterion for the onset of the modulational instability is obtained. The results are compared with the ones obtained with the help of a standard KBM-treatment. Moreover cnoidal drift waves are suggested and compared to an experimental observation. (orig.)
Ulku, Huseyin Arda; Sayed, Sadeed Bin; Bagci, Hakan
2014-01-01
solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation
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
Bell, T. F.
1984-01-01
A theory is presented of the nonlinear gyroresonance interaction that takes place in the magnetosphere between energetic electrons and coherent VLF waves propagating in the whistler mode at an arbitrary angle psi with respect to the earth's magnetic field B-sub-0. Particularly examined is the phase trapping (PT) mechanism believed to be responsible for the generation of VLF emissions. It is concluded that near the magnetic equatorial plane gradients of psi may play a very important part in the PT process for nonducted waves. Predictions of a higher threshold value for PT for nonducted waves generally agree with experimental data concerning VLF emission triggering by nonducted waves.
2015-05-07
associated with the lattice background; the nonlinearity is derived from the inclusion of cubic nonlinearity. Often the background potential is periodic...dispersion branch we can find discrete evolution equations for the envelope associated with the lattice NLS equation (1) by looking for solutions of...spatial operator in the above NLS equation can be elliptic, hyperbolic or parabolic . We remark that further reduction is possible by going into a moving
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.
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 resona......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...... 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....
Continuum contribution to excitonic four-wave mixing due to interaction-induced nonlinearities
DEFF Research Database (Denmark)
Birkedal, Dan; Vadim, Lyssenko; Hvam, Jørn Märcher
1996-01-01
We present an experimental and theoretical investigation of ultrafast transient four-wave mixing of GaAs/AlxGa1-xAs quantum wells for coherent excitation of exciton and continuum states. The signal appears at the exciton resonance and is shown to consist of two contributions: an intense spectrall...
El Sayed, K.; Birkedal, D.; Lyssenko, V. G.; Hvam, J. M.
1997-01-01
We present a theoretical investigation of ultrafast transient four-wave mixing (FWM) of GaAs quantum wells for coherent excitation of excitons and a large number of continuum states. It is shown that in this case the line shape of the FWM signal is drastically altered due to an interaction-induced coupling of the exciton to all the excited continuum states. The signal is dominantly emitted at the spectral position of the exciton and decays, as a function of delay, on a time scale set by the duration of the laser pulse rather than by the intrinsic dephasing time. Nevertheless, the spectral width of the exciton line in the FWM spectrum and in the decay of the time-resolved FWM signal in real time are governed by the intrinsic excitonic dephasing rate. It is shown that for pulse durations of ~ 100 fs (for GaAs quantum wells) this behavior can be explained as the influence of the Coulomb exchange interaction, while for even shorter pulses this behavior is dominantly caused by nonlinear polarization decay.
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 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
Nonlinear laser-plasma interactions
Kaw, P. K.
2017-12-01
Soon after lasers were invented, there was tremendous curiosity on the nonlinear phenomena which would result in their interaction with a fully ionized plasma. Apart from the basic interest, it was realized that it could be used for the achievement of nuclear fusion in the laboratory. This led us to a paper on the propagation of a laser beam into an inhomogeneous fusion plasma, where it was first demonstrated that light would go up to the critical layer (where the frequency matches the plasma frequency) and get reflected from there with a reflection coefficient of order unity. The reflection coefficient was determined by collisional effects. Since the wave was expected to slow down to near zero group speed at the reflection point, the dominant collision frequency determining the reflection coefficient was the collision frequency at the reflection point. It turned out that the absorption of light was rather small for fusion temperatures. This placed a premium on investigation of nonlinear phenomena which might contribute to the absorption and penetration of the light into high-density plasma. An early investigation showed that electron jitter with respect to ions would be responsible for the excitation of decay instabilities which convert light waves into electrostatic plasma waves and ion waves near the critical frequency. These electrostatic waves would then get absorbed into the plasma even in the collisionless case and lead to plasma heating which is nonlinear. Detailed estimates of this heating were made. Similar nonlinear processes which could lead to stimulated scattering of light in the underdense region (ω >ω _p) were investigated together with a number of other workers. All these nonlinear processes need a critical threshold power for excitation. Another important process which was discovered around the same time had to do with filamentation and trapping of light when certain thresholds were exceeded. All of this work has been extensively verified in
Wave Interactions and Fluid Flows
Craik, Alex D. D.
1988-07-01
This up-to-date and comprehensive account of theory and experiment on wave-interaction phenomena covers fluids both at rest and in their shear flows. It includes, on the one hand, water waves, internal waves, and their evolution, interaction, and associated wave-driven means flow and, on the other hand, phenomena on nonlinear hydrodynamic stability, especially those leading to the onset of turbulence. This study provide a particularly valuable bridge between these two similar, yet different, classes of phenomena. It will be of value to oceanographers, meteorologists, and those working in fluid mechanics, atmospheric and planetary physics, plasma physics, aeronautics, and geophysical and astrophysical fluid dynamics.
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.
DEFF Research Database (Denmark)
Sayed, Karim El; Birkedal, Dan; Vadim, Lyssenko
1997-01-01
We present a theoretical investigation of ultrafast transient four-wave mixing (FWM) of GaAs quantum wells for coherent excitation of excitons and a large number of continuum states. It is shown that in this case the line shape of the FWM signal is drastically altered due to an interaction-induce...
Soil-structure interaction including nonlinear soil
Gicev, Vlado
2008-01-01
There are two types of models of soil-structure system depending upon the rigidity of foundation: models with rigid and models with flexible foundation. Main features of the soil-structure interaction phenomenon: -wave scattering, -radiation damping, -reduction of the system frequencies. In this presentation, the influence of interaction on the development of nonlinear zones in the soil is studied.
Some remarks on coherent nonlinear coupling of waves in plasmas
International Nuclear Information System (INIS)
Wilhelmsson, H.
1976-01-01
The analysis of nonlinear processes in plasma physics has given rise to a basic set of coupled equations. These equations describe the coherent nonlinear evolution of plasma waves. In this paper various possibilities of analysing these equations are discussed and inherent difficulties in the description of nonlinear interactions between different types of waves are pointed out. Specific examples of stimulated excitation of waves are considered. These are the parametric excitation of hybrid resonances in hot magnetized multi-ion component plasma and laser-plasma interactions. (B.D.)
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 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 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 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.
Interacting electromagnetic waves in general relativity
International Nuclear Information System (INIS)
Griffiths, J.B.
1976-01-01
The problem is considered of finding exact solutions of the Einstein-Maxwell equations which describe the physical situation of two colliding and subsequently interacting electromagnetic waves. The general theory of relativity predicts a nonlinear interaction between electromagnetic waves. The situation is described using an approximate geometrical method, and a new exact solution describing two interacting electromagnetic waves is given. This describes waves emitted from two sources mutually focusing each other on the opposite source. (author)
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...... dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed....
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
Consecutive opposed interactions of light waves
International Nuclear Information System (INIS)
Volkov, V V; Chirkin, Anatolii S
1999-01-01
The conditions were determined for the occurrence of the opposed interaction of waves having multiple frequencies in two consecutive three-frequency processes in periodically inhomogeneous nonlinear optical crystals. The necessary nonlinear susceptibility modulation period was calculated for an MgO:LiNbO 3 crystal. The characteristic features of the energy exchange between counterpropagating waves with parametric amplification in a low-frequency pump field were investigated. (nonlinear optical phenomena)
Statistical properties of nonlinear one-dimensional wave fields
Directory of Open Access Journals (Sweden)
D. Chalikov
2005-01-01
Full Text Available A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.
Statistical properties of nonlinear one-dimensional wave fields
Chalikov, D.
2005-06-01
A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.
International Nuclear Information System (INIS)
Lu, LingFeng
2016-01-01
Ion Cyclotron Resonant Heating (ICRH) by waves in 30-80 MHz range is currently used in magnetic fusion plasmas. Excited by phased arrays of current straps at the plasma periphery, these waves exist under two polarizations. The Fast Wave tunnels through the tenuous plasma edge and propagates to its center where it is absorbed. The parasitically emitted Slow Wave only exists close to the launchers. How much power can be coupled to the center with 1 A current on the straps? How do the emitted radiofrequency (RF) near and far fields interact parasitically with the edge plasma via RF sheath rectification at plasma-wall interfaces? To address these two issues simultaneously, in realistic geometry over the size of ICRH antennas, this thesis upgraded and tested the Self-consistent Sheaths and Waves for ICH (SSWICH) code. SSWICH couples self-consistently RF wave propagation and Direct Current (DC) plasma biasing via non-linear RF and DC sheath boundary conditions (SBCs) at plasma/wall interfaces. Its upgrade is full wave and was implemented in two dimensions (toroidal/radial). New SBCs coupling the two polarizations were derived and implemented along shaped walls tilted with respect to the confinement magnetic field. Using this new tool in the absence of SBCs, we studied the impact of a density decaying continuously inside the antenna box and across the Lower Hybrid (LH) resonance. Up to the memory limits of our workstation, the RF fields below the LH resonance changed with the grid size. However the coupled power spectrum hardly evolved and was only weakly affected by the density inside the box. In presence of SBCs, SSWICH-FW simulations have identified the role of the fast wave on RF sheath excitation and reproduced some key experimental observations. SSWICH-FW was finally adapted to conduct the first electromagnetic and RF-sheath 2D simulations of the cylindrical magnetized plasma device ALINE. (author) [fr
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.
The Interaction of Ocean Waves and Wind
Janssen, Peter
2004-10-01
Describing in detail the two-way interaction between wind and ocean waves, this book discusses ocean wave evolution in accordance with the energy balance equation. An extensive overview of nonlinear transfer is given, and the role of four-wave interactions in the generation of extreme events as well as the effects on ocean circulation is included. The volume will interest ocean wave modellers, physicists, applied mathematicians, and engineers.
Nonlinear waves in plasma with negative ion
International Nuclear Information System (INIS)
Saito, Maki; Watanabe, Shinsuke; Tanaca, Hiroshi.
1984-01-01
The propagation of nonlinear ion wave is investigated theoretically in a plasma with electron, positive ion and negative ion. The ion wave of long wavelength is described by a modified K-dV equation instead of a K-dV equation when the nonlinear coefficient of the K-dV equation vanishes at the critical density of negative ion. In the vicinity of the critical density, the ion wave is described by a coupled K-dV and modified K-dV equation. The transition from a compressional soliton to a rarefactive soliton and vice versa are examined by the coupled equation as a function of the negative ion density. The ion wave of short wavelength is described by a nonlinear Schroedinger equation. In the plasma with a negative ion, the nonlinear coefficient of the nonlinear Schroedinger equation changes the sign and the ion wave becomes modulationally unstable. (author)
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.
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
Qualitative aspects of nonlinear wave motion: Complexity and simplicity
International Nuclear Information System (INIS)
Engelbrecht, J.
1993-01-01
The nonlinear wave processes possess many qualitative properties which cannot be described by linear theories. In this presentation, an attempt is made to systematize the main aspects of this fascinating area. The sources of nonlinearities are analyzed in order to understand why and how the nonlinear mathematical models are formulated. The technique of evolution equations is discussed then as a main mathematical tool to separate multiwave processes into single waves. The evolution equations give concise but in many cases sufficient description of wave processes in solids permitting to analyze spectral changes, phase changes and velocities, coupling of waves, and interaction of nonlinearities with other physical effects of the same order. Several new problems are listed. Knowing the reasons, the seemingly complex problems can be effectively analyzed. 61 refs
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....
Modulated Langmuir waves and nonlinear Landau damping
International Nuclear Information System (INIS)
Yajima, Nobuo; Oikawa, Masayuki; Satsuma, Junkichi; Namba, Chusei.
1975-01-01
The nonlinear Schroedinger euqation with an integral term, iusub(t)+P/2.usub(xx)+Q/u/ 2 u+RP∫sub(-infinity)sup(infinity)[/u(x',t)/ 2 /(x-x')]dx'u=0, which describes modulated Langmuir waves with the nonlinear Landau damping effect, is solved by numerical calculations. Especially, the effects of nonlinear Landau damping on solitary wave solutions are studied. For both cases, PQ>0 and PQ<0, the results show that the solitary waves deform in an asymmetric way changing its velocity. (auth.)
Three-wave interactions in a warm plasma
International Nuclear Information System (INIS)
Shivamoggi, B.K.
1983-01-01
The nonlinear resonance interactions between a Langmuir wave and two transverse electromagnetic waves (T-T-L) as well as between an ion-acoustic wave and two transverse electromagnetic waves (T-T-S) in a warm plasma are studied. It is shown that an incident transverse electromagnetic wave decays into another transverse electromagnetic wave and a Langmuir wave in a T-T-L wave-wave interaction as well as into another transverse electromagnetic wave and an ion-acoustic wave in a T-T-S wave-wave interaction. The growth rates of the daughter waves in the T-T-L wave-wave interaction are shown to be smaller than those of the daughter waves in the T-T-S wave-wave interaction. (M.F.W.)
Nonlinear plasma waves excited near resonance
International Nuclear Information System (INIS)
Cohen, B.I.; Kaufman, A.N.
1977-01-01
The nonlinear resonant response of a uniform plasma to an external plane-wave field is formulated in terms of the mismatch Δ/sub n l/ between the driving frequency and the time-dependent, complex, nonlinear normal mode frequency at the driving wavenumber. This formalism is applied to computer simulations of this process, yielding a deduced nonlinear frequency shift. The time dependence of the nonlinear phenomena, at frequency Δ/sub n l/ and at the bounce frequency of the resonant particles, is analyzed. The interdependence of the nonlinear features is described by means of energy and momentum relations
Evolution Of Nonlinear Waves in Compressing Plasma
International Nuclear Information System (INIS)
Schmit, P.F.; Dodin, I.Y.; Fisch, N.J.
2011-01-01
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 Δ during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches Δ. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
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.
Directional nonlinear guided wave mixing: Case study of counter-propagating shear horizontal waves
Hasanian, Mostafa; Lissenden, Cliff J.
2018-04-01
While much nonlinear ultrasonics research has been conducted on higher harmonic generation, wave mixing provides the potential for sensitive measurements of incipient damage unencumbered by instrumentation nonlinearity. Studies of nonlinear ultrasonic wave mixing, both collinear and noncollinear, for bulk waves have shown the robust capability of wave mixing for early damage detection. One merit of bulk wave mixing lies in their non-dispersive nature, but guided waves enable inspection of otherwise inaccessible material and a variety of mixing options. Co-directional guided wave mixing was studied previously, but arbitrary direction guided wave mixing has not been addressed until recently. Wave vector analysis is applied to study variable mixing angles to find wave mode triplets (two primary waves and a secondary wave) resulting in the phase matching condition. As a case study, counter-propagating Shear Horizontal (SH) guided wave mixing is analyzed. SH wave interactions generate a secondary Lamb wave mode that is readily receivable. Reception of the secondary Lamb wave mode is compared for an angle beam transducer, an air coupled transducer, and a laser Doppler vibrometer (LDV). Results from the angle beam and air coupled transducers are quite consistent, while the LDV measurement is plagued by variability issues.
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....
Solitons and Weakly Nonlinear Waves in Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans
1985-01-01
Theoretical descriptions of solitons and weakly nonlinear waves propagating in plasma media are reviewed, with particular attention to the Korteweg-de Vries (KDV) equation and the Nonlinear Schrödinger equation (NLS). The modifications of these basic equations due to the effects of resonant...
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.
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.
Modelization of highly nonlinear waves in coastal regions
Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre
2015-04-01
The proposed work deals with the development of a highly non-linear model for water wave propagation in coastal regions. The accurate modelization of surface gravity waves is of major interest in ocean engineering, especially in the field of marine renewable energy. These marine structures are intended to be settled in coastal regions where the effect of variable bathymetry may be significant on local wave conditions. This study presents a numerical model for the wave propagation with complex bathymetry. It is based on High-Order Spectral (HOS) method, initially limited to the propagation of non-linear wave fields over flat bottom. Such a model has been developed and validated at the LHEEA Lab. (Ecole Centrale Nantes) over the past few years and the current developments will enlarge its application range. This new numerical model will keep the interesting numerical properties of the original pseudo-spectral approach (convergence, efficiency with the use of FFTs, …) and enable the possibility to propagate highly non-linear wave fields over long time and large distance. Different validations will be provided in addition to the presentation of the method. At first, Bragg reflection will be studied with the proposed approach. If the Bragg condition is satisfied, the reflected wave generated by a sinusoidal bottom patch should be amplified as a result of resonant quadratic interactions between incident wave and bottom. Comparisons will be provided with experiments and reference solutions. Then, the method will be used to consider the transformation of a non-linear monochromatic wave as it propagates up and over a submerged bar. As the waves travel up the front slope of the bar, it steepens and high harmonics are generated due to non-linear interactions. Comparisons with experimental data will be provided. The different test cases will assess the accuracy and efficiency of the method proposed.
Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.
Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G
2016-12-02
We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.
Nonlinear theory of localized standing waves
Denardo, Bruce; Larraza, Andrés; Putterman, Seth; Roberts, Paul
1992-01-01
An investigation of the nonlinear dispersive equations of continuum mechanics reveals localized standing-wave solutions that are domain walls between regions of different wave number. These states can appear even when the dispersion law is a single-valued function of the wave number. In addition, we calculate solutions for kinks in cutoff and noncutoff modes, as well as cutoff breather solitons. Division of Engineering and Geophysics of the Office of Basic Energy Science of U.S. DOE for su...
Nonlinear extraordinary wave in dense plasma
Energy Technology Data Exchange (ETDEWEB)
Krasovitskiy, V. B., E-mail: krasovit@mail.ru [Russian Academy of Sciences, Keldysh Institute of Applied Mathematics (Russian Federation); Turikov, V. A. [Russian University of Peoples’ Friendship (Russian Federation)
2013-10-15
Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. The possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.
Barashkov, M. S.; Iskanderov, N. A.
1987-08-01
An analysis is made of the reduction of the fluctuations introduced in the intensity of the phase conjugate wave and of the reduction in the time for establishment of quasisteady conjugation conditions and in the relaxation time of the intensity of the conjugate wave after switching on of the pump fields in the case of stochastic excitation of a transition. It is shown that, in principle, it is possible to generate a narrow-band pump-induced component of the conjugate wave spectrum.
Nonlinear ultrasonic imaging with X wave
Du, Hongwei; Lu, Wei; Feng, Huanqing
2009-10-01
X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.
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
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
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)
2014-04-15
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.
Nonlinear interactions in magnetised piezoelectric semiconductor plasmas
International Nuclear Information System (INIS)
Sharma, Giriraj; Ghosh, S.
2000-01-01
Based on hydrodynamics model of plasmas an analytical investigation of frequency modulational interaction between copropagating high frequency pump and acoustic mode and consequent amplification (steady-state and transient) of the modulated waves is carried out in a magnetised piezoelectric semiconductor medium. The phenomenon of modulation amplification is treated as four wave interaction process involving cubic nonlinearity of the medium. Gain constants, threshold-pump intensities and optimum-pulse duration for the onset of modulational instabilities are estimated. The analysis has been performed in non-dispersive regime of the acoustic mode, which is one of the preconditions for achieving an appreciable initial steady-state growth of the modulated signal wave. It is found that the transient gain diminishes very rapidly if one chooses the pump pulse duration beyond the maximum gain point. Moreover, the desired value of the gain can be obtained by adjusting intensity and pulse duration of the pump and doping concentration of the medium concerned. (author)
Solitons and nonlinear waves in space plasmas
International Nuclear Information System (INIS)
Stasiewicz, K.
2005-01-01
Recent measurements made on the ESA/NASA Cluster mission to the Earth's magnetosphere have provided first detailed measurements of magnetosonic solitons in space. The solitons represent localized enhancements of the magnetic field by a factor of 2-10, or depressions down to 10% of the ambient field. The magnetic field signatures are associated with density depressions/enhancements A two-fluid model of nonlinear electron and ion inertial waves in anisotropic plasmas explains the main properties of these structures. It is shown that warm plasmas support four types of nonlinear waves, which correspond to four linear modes: Alfvenic, magnetosonic, sound, and electron inertial waves. Each of these nonlinear modes has slow and fast versions. It is shown by direct integration that the exponential growth rate of nonlinear modes is balanced by the ion and electron dispersion leading to solutions in the form of trains of solitons or cnoidal waves. By using a novel technique of phase portraits it is shown how the dispersive properties of electron and ion inertial waves change at the transition between warm and hot plasmas, and how trains of solitons ('' mirror modes '') are produced in a hot, anisotropic plasma. The applicability of the model is illustrated with data from Cluster spacecraft. (author)
New exact travelling wave solutions of nonlinear physical models
International Nuclear Information System (INIS)
Bekir, Ahmet; Cevikel, Adem C.
2009-01-01
In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The ((G ' )/G )-expansion method presents a wider applicability for handling nonlinear wave equations.
Nonlinear response and bistability of driven ion acoustic waves
Akbari-Moghanjoughi, M.
2017-08-01
The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.
Interactive Nonlinear Multiobjective Optimization Methods
Miettinen, Kaisa; Hakanen, Jussi; Podkopaev, Dmitry
2016-01-01
An overview of interactive methods for solving nonlinear multiobjective optimization problems is given. In interactive methods, the decision maker progressively provides preference information so that the most satisfactory Pareto optimal solution can be found for her or his. The basic features of several methods are introduced and some theoretical results are provided. In addition, references to modifications and applications as well as to other methods are indicated. As the...
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
Nonlinear waves: some biomedical applications
International Nuclear Information System (INIS)
Rudenko, Oleg V
2007-01-01
The field of nonlinear physics, item No. 11 on Ginzburg's list of 'the most important and interesting problems', is reviewed. An example at the intersection of applied physics, medicine, and instrument engineering is discussed to illustrate the range and scope of the field and how deep the ideas and approaches it involves are incorporated in modern natural science and engineering. Results of relevant research and development, which has attracted much recent interest and financial support, are briefly examined. (oral issue of the journal 'uspekhi fizicheskikh nauk')
Closed form solutions of two time fractional nonlinear wave equations
Directory of Open Access Journals (Sweden)
M. Ali Akbar
2018-06-01
Full Text Available In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G′/G-expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics. Keywords: Traveling wave solution, Soliton, Generalized (G′/G-expansion method, Time fractional Duffing equation, Time fractional Riccati equation
Topics in nonlinear wave theory with applications
International Nuclear Information System (INIS)
Tracy, E.R.
1984-01-01
Selected topics in nonlinear wave theory are discussed, and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasi-periodic solutions to several nonlinear wave equations, which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schroedinger equation, an equation with general applicability in one-dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in the numerical studies, and the numerical work of other authors. The method of solution (related to the inverse scattering method) is then analyzed within the context of Hamiltonian dynamics where it is shown that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation, which appears here and in the work of other authors, is shown to be a special form of Liouville's transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's inversion problem, is surveyed briefly
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 ar...... are compared with predictions of conservation theorems for energy and momentum....
Four Wave Mixing using Intermodal Nonlinearities
DEFF Research Database (Denmark)
Rishøj, Lars Søgaard
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...
Nonlinear wavenumber of an electron plasma wave
International Nuclear Information System (INIS)
Vidmar, P.J.; Malmberg, J.H.; Starke, T.P.
1976-01-01
The wavenumber of a large-amplitude electron plasma wave propagating on a collisionless plasma column is measured. The wavenumber is shifted from that of a small-amplitude wave of the same frequency. This nonlinear wavenumber shift, deltak/subr/, depends on position, frequency, and initial wave amplitude, Phi. The observed spatial oscillations of deltak/subr/ agree qualitatively with recent theories. Experimentally deltak/subr/proportionalk/subi/S (Phi) rootPhi where k/subi/ is the linear Landau damping coefficient, S (Phi) equivalentk/subi/(Phi)/k/subi/, and k/subi/(Phi) is the initial damping coefficient which depends on Phi
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
Nonlinear MHD Waves in a Prominence Foot
Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.
2015-11-01
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ˜ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5-11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5-14 G. For the typical prominence density the corresponding fast magnetosonic speed is ˜20 km s-1, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
NONLINEAR 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.
Quantum X waves with orbital angular momentum in nonlinear dispersive media
Ornigotti, Marco; Conti, Claudio; Szameit, Alexander
2018-06-01
We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.
Closed form solutions of two time fractional nonlinear wave equations
Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan
2018-06-01
In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.
Nonlinear damping of oblique whistler mode waves through Landau resonance
Hsieh, Y.; Omura, Y.
2017-12-01
Nonlinear trapping of electrons through Landau resonance is a characteristic dynamics in oblique whistler-mode wave particle interactions. The resonance velocity of the Landau resonance at quasi-parallel propagation becomes very close to the parallel group velocity of whistler-mode wave at frequency around 0.5 Ωe, causing a long distance of resonant interaction and strong acceleration of resonant electrons [1]. We demonstrate these effective accelerations for electrons with high equatorial pitch angle ( > 60°) by test particle simulations with parameters for the Earth's inner magnetosphere at L=5. In the simulations, we focus on slightly oblique whistler mode waves with wave normal angle 10.1002/2016JA023255.
Nonlinear Wave Mixing Technique for Nondestructive Assessment of Infrastructure Materials
Ju, Taeho
To operate safely, structures and components need to be inspected or monitored either periodically or in real time for potential failure. For this purpose, ultrasonic nondestructive evaluation (NDE) techniques have been used extensively. Most of these ultrasonic NDE techniques utilize only the linear behavior of the ultrasound. These linear techniques are effective in detecting discontinuities in materials such as cracks, voids, interfaces, inclusions, etc. However, in many engineering materials, it is the accumulation of microdamage that leads to degradation and eventual failure of a component. Unfortunately, it is difficult for linear ultrasonic NDE techniques to characterize or quantify such damage. On the other hand, the acoustic nonlinearity parameter (ANLP) of a material is often positively correlated with such damage in a material. Thus, nonlinear ultrasonic NDE methods have been used in recently years to characterize cumulative damage such as fatigue in metallic materials, aging in polymeric materials, and degradation of cement-based materials due to chemical reactions. In this thesis, we focus on developing a suit of novel nonlinear ultrasonic NDE techniques based on the interactions of nonlinear ultrasonic waves, namely wave mixing. First, a noncollinear wave mixing technique is developed to detect localized damage in a homogeneous material by using a pair of noncollinear a longitudinal wave (L-wave) and a shear wave (S-wave). This pair of incident waves make it possible to conduct NDE from a single side of the component, a condition that is often encountered in practical applications. The proposed noncollinear wave mixing technique is verified experimentally by carrying out measurements on aluminum alloy (AA 6061) samples. Numerical simulations using the Finite Element Method (FEM) are also conducted to further demonstrate the potential of the proposed technique to detect localized damage in structural components. Second, the aforementioned nonlinear
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.
Symmetry, phase modulation and nonlinear waves
Bridges, Thomas J
2017-01-01
Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.
Fatigue crack localization using laser nonlinear wave modulation spectroscopy (LNWMS)
Energy Technology Data Exchange (ETDEWEB)
Liu, Peipei; Sohn, Hoon [Dept. of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Kundu, Tribikram [Dept. of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson (United States)
2014-12-15
Nonlinear features of ultrasonic waves are more sensitive to the presence of a fatigue crack than their linear counterparts are. For this reason, the use of nonlinear ultrasonic techniques to detect a fatigue crack at its early stage has been widely investigated. Of the different proposed techniques, laser nonlinear wave modulation spectroscopy (LNWMS) is unique because a pulse laser is used to exert a single broadband input and a noncontact measurement can be performed. Broadband excitation causes a nonlinear source to exhibit modulation at multiple spectral peaks owing to interactions among various input frequency components. A feature called maximum sideband peak count difference (MSPCD), which is extracted from the spectral plot, measures the degree of crack-induced material nonlinearity. First, the ratios of spectral peaks whose amplitudes are above a moving threshold to the total number of peaks are computed for spectral signals obtained from the pristine and the current state of a target structure. Then, the difference of these ratios are computed as a function of the moving threshold. Finally, the MSPCD is defined as the maximum difference between these ratios. The basic premise is that the MSPCD will increase as the nonlinearity of the material increases. This technique has been used successfully for localizing fatigue cracks in metallic plates.
Observations of linear and nonlinear processes in the foreshock wave evolution
Directory of Open Access Journals (Sweden)
Y. Narita
2007-07-01
Full Text Available Waves in the foreshock region are studied on the basis of a hypothesis that the linear process first excites the waves and further wave-wave nonlinearities distribute scatter the energy of the primary waves into a number of daughter waves. To examine this wave evolution scenario, the dispersion relations, the wave number spectra of the magnetic field energy, and the dimensionless cross helicity are determined from the observations made by the four Cluster spacecraft. The results confirm that the linear process is the ion/ion right-hand resonant instability, but the wave-wave interactions are not clearly identified. We discuss various reasons why the test for the wave-wave nonlinearities fails, and conclude that the higher order statistics would provide a direct evidence for the wave coupling phenomena.
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 low-frequency wave aspect of foreshock density holes
Directory of Open Access Journals (Sweden)
N. Lin
2008-11-01
Full Text Available Recent observations have uncovered short-duration density holes in the Earth's foreshock region. There is evidence that the formation of density holes involves non-linear growth of fluctuations in the magnetic field and plasma density, which results in shock-like boundaries followed by a decrease in both density and magnetic field. In this study we examine in detail a few such events focusing on their low frequency wave characteristics. The propagation properties of the waves are studied using Cluster's four point observations. We found that while these density hole-structures were convected with the solar wind, in the plasma rest frame they propagated obliquely and mostly sunward. The wave amplitude grows non-linearly in the process, and the waves are circularly or elliptically polarized in the left hand sense. The phase velocities calculated from four spacecraft timing analysis are compared with the velocity estimated from δE/δB. Their agreement justifies the plane electromagnetic wave nature of the structures. Plasma conditions are found to favor firehose instabilities. Oblique Alfvén firehose instability is suggested as a possible energy source for the wave growth. Resonant interaction between ions at certain energy and the waves could reduce the ion temperature anisotropy and thus the free energy, thereby playing a stabilizing role.
Nonlinear low-frequency wave aspect of foreshock density holes
Directory of Open Access Journals (Sweden)
N. Lin
2008-11-01
Full Text Available Recent observations have uncovered short-duration density holes in the Earth's foreshock region. There is evidence that the formation of density holes involves non-linear growth of fluctuations in the magnetic field and plasma density, which results in shock-like boundaries followed by a decrease in both density and magnetic field. In this study we examine in detail a few such events focusing on their low frequency wave characteristics. The propagation properties of the waves are studied using Cluster's four point observations. We found that while these density hole-structures were convected with the solar wind, in the plasma rest frame they propagated obliquely and mostly sunward. The wave amplitude grows non-linearly in the process, and the waves are circularly or elliptically polarized in the left hand sense. The phase velocities calculated from four spacecraft timing analysis are compared with the velocity estimated from δE/δB. Their agreement justifies the plane electromagnetic wave nature of the structures. Plasma conditions are found to favor firehose instabilities. Oblique Alfvén firehose instability is suggested as a possible energy source for the wave growth. Resonant interaction between ions at certain energy and the waves could reduce the ion temperature anisotropy and thus the free energy, thereby playing a stabilizing role.
Nonlinear propagation of Alfven waves in cometary plasmas
International Nuclear Information System (INIS)
Lakhina, G.S.; Shukla, P.K.
1987-07-01
Large amplitude Alfven waves propagating along the guide magnetic field in a three-component plasma are shown to be modulationally unstable due to their nonlinear interaction with nonresonant electrostatic density fluctuations. A new class of subsonic Alfven soliton solutions are found to exist in the three-component plasma. The Alfven solitons can be relevant in explaining the properties of hydromagnetic turbulence near the comets. (author). 15 refs
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.
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....
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.
Wave propagation in non-linear media
Broer, L.J.F.
1965-01-01
The problem of the propagation of electromagnetic waves through solids is essentially one of interaction between light quanta and matter. The most fundamental and general treatment of this subject is therefore undoubtedly based on the quantummechanical theory of this interaction. Nevertheless, a
Qin, Yan-Hong; Zhao, Li-Chen; Yang, Zhan-Ying; Yang, Wen-Li
2018-01-01
We investigate linear interference effects between a nonlinear plane wave and bright solitons, which are admitted by a pair-transition coupled two-component Bose-Einstein condensate. We demonstrate that the interference effects can induce several localized waves possessing distinctive wave structures, mainly including anti-dark solitons, W-shaped solitons, multi-peak solitons, Kuznetsov-Ma like breathers, and multi-peak breathers. Specifically, the explicit conditions for them are clarified by a phase diagram based on the linear interference properties. Furthermore, the interactions between these localized waves are discussed. The detailed analysis indicates that the soliton-soliton interaction induced phase shift brings the collision between these localized waves which can be inelastic for solitons involving collision and can be elastic for breathers. These characters come from the fact that the profile of solitons depends on the relative phase between bright solitons and a plane wave, and the profile of breathers does not depend on the relative phase. These results would motivate more discussions on linear interference between other nonlinear waves. Specifically, the solitons or breathers obtained here are not related to modulational instability. The underlying reasons are discussed in detail. In addition, possibilities to observe these localized waves are discussed in a two species Bose-Einstein condensate.
Nonlinear magnetoacoustic wave propagation with chemical reactions
Margulies, Timothy Scott
2002-11-01
The magnetoacoustic problem with an application to sound wave propagation through electrically conducting fluids such as the ocean in the Earth's magnetic field, liquid metals, or plasmas has been addressed taking into account several simultaneous chemical reactions. Using continuum balance equations for the total mass, linear momentum, energy; as well as Maxwell's electrodynamic equations, a nonlinear beam equation has been developed to generalize the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a fluid with linear viscosity but nonlinear and diffraction effects. Thermodynamic parameters are used and not tailored to only an adiabatic fluid case. The chemical kinetic equations build on a relaxing media approach presented, for example, by K. Naugolnukh and L. Ostrovsky [Nonlinear Wave Processes in Acoustics (Cambridge Univ. Press, Cambridge, 1998)] for a linearized single reaction and thermodynamic pressure equation of state. Approximations for large and small relaxation times and for magnetohydrodynamic parameters [Korsunskii, Sov. Phys. Acoust. 36 (1990)] are examined. Additionally, Cattaneo's equation for heat conduction and its generalization for a memory process rather than a Fourier's law are taken into account. It was introduced for the heat flux depends on the temperature gradient at an earlier time to generate heat pulses of finite speed.
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.
Nonlinear diffuse scattering of the random-phased wave
International Nuclear Information System (INIS)
Kato, Yoshiaki; Arinaga, Shinji; Mima, Kunioki.
1983-01-01
First experimental observation of the nonlinear diffuse scattering is reported. This new effect was observed in the propagation of the random-phased wave through a nonlinear dielectric medium. This effect is ascribed to the diffusion of the wavevector of the electro-magnetic wave to the lateral direction due to the randomly distributed nonlinear increase in the refractive index. (author)
Nonlinear effects on mode-converted lower-hybrid waves
International Nuclear Information System (INIS)
Kuehl, H.H.
1976-01-01
Nonlinear ponderomotive force effects on mode-converted lower-hybrid waves are considered. The nonlinear distortion of these waves is shown to be governed by the cubic nonlinear Schroedinger equation. The threshold condition for self-focusing and filamentation is derived
Optimization of nonlinear wave function parameters
International Nuclear Information System (INIS)
Shepard, R.; Minkoff, M.; Chemistry
2006-01-01
An energy-based optimization method is presented for our recently developed nonlinear wave function expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions, using the graphical unitary group approach (GUGA). The wave function is expanded in a basis of product functions, allowing application to closed-shell and open-shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational function that depends on a relatively small number of nonlinear parameters called arc factors. The energy-based optimization is formulated in terms of analytic arc factor gradients and orbital-level Hamiltonian matrices that correspond to a specific kind of uncontraction of each of the product basis functions. These orbital-level Hamiltonian matrices give an intuitive representation of the energy in terms of disjoint subsets of the arc factors, they provide for an efficient computation of gradients of the energy with respect to the arc factors, and they allow optimal arc factors to be determined in closed form for subspaces of the full variation problem. Timings for energy and arc factor gradient computations involving expansion spaces of > 10 24 configuration state functions are reported. Preliminary convergence studies and molecular dissociation curves are presented for some small molecules
Nonlinear radial propagation of drift wave turbulence
International Nuclear Information System (INIS)
Prakash, M.
1985-01-01
We study the linear and the nonlinear radial propagation of drift wave energy in an inhomogeneous plasma. The drift mode excited in such a plasma is dispersive in nature. The drift wave energy spreads out symmetrically along the direction of inhomogeneity with a finite group velocity. To study the effect of the nonlinear coupling on the propagation of energy in a collision free plasma, we solve the Hasegawa-Mima equation as a mixed initial boundary-value problem. The solutions of the linearized equation are used to check the reliability of our numerical calculations. Additional checks are also performed on the invariants of the system. Our results reveal that a pulse gets distorted as it propagates through the medium. The peak of the pulse propagates with a finite velocity that depends on the amplitude of the initial pulse. The polarity of propagation depends on the initial parameters of the pulse. We have also studied drift wave propagation in a resistive plasma. The Hasegawa-Wakatani equations are used to investigate this problem
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-01-01
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066
Nonlinear interaction model of subsonic jet noise.
Sandham, Neil D; Salgado, Adriana M
2008-08-13
Noise generation in a subsonic round jet is studied by a simplified model, in which nonlinear interactions of spatially evolving instability modes lead to the radiation of sound. The spatial mode evolution is computed using linear parabolized stability equations. Nonlinear interactions are found on a mode-by-mode basis and the sound radiation characteristics are determined by solution of the Lilley-Goldstein equation. Since mode interactions are computed explicitly, it is possible to find their relative importance for sound radiation. The method is applied to a single stream jet for which experimental data are available. The model gives Strouhal numbers of 0.45 for the most amplified waves in the jet and 0.19 for the dominant sound radiation. While in near field axisymmetric and the first azimuthal modes are both important, far-field sound is predominantly axisymmetric. These results are in close correspondence with experiment, suggesting that the simplified model is capturing at least some of the important mechanisms of subsonic jet noise.
Nonlinear bounce resonances between magnetosonic waves and equatorially mirroring electrons
Chen, Lunjin; Maldonado, Armando; Bortnik, Jacob; Thorne, Richard M.; Li, Jinxing; Dai, Lei; Zhan, Xiaoya
2015-08-01
Equatorially mirroring energetic electrons pose an interesting scientific problem, since they generally cannot resonate with any known plasma waves and hence cannot be scattered down to lower pitch angles. Observationally it is well known that the flux of these equatorial particles does not simply continue to build up indefinitely, and so a mechanism must necessarily exist that transports these particles from an equatorial pitch angle of 90° down to lower values. However, this mechanism has not been uniquely identified yet. Here we investigate the mechanism of bounce resonance with equatorial noise (or fast magnetosonic waves). A test particle simulation is used to examine the effects of monochromatic magnetosonic waves on the equatorially mirroring energetic electrons, with a special interest in characterizing the effectiveness of bounce resonances. Our analysis shows that bounce resonances can occur at the first three harmonics of the bounce frequency (nωb, n = 1, 2, and 3) and can effectively reduce the equatorial pitch angle to values where resonant scattering by whistler mode waves becomes possible. We demonstrate that the nature of bounce resonance is nonlinear, and we propose a nonlinear oscillation model for characterizing bounce resonances using two key parameters, effective wave amplitude Ã and normalized wave number k~z. The threshold for higher harmonic resonance is more strict, favoring higher Ã and k~z, and the change in equatorial pitch angle is strongly controlled by k~z. We also investigate the dependence of bounce resonance effects on various physical parameters, including wave amplitude, frequency, wave normal angle and initial phase, plasma density, and electron energy. It is found that the effect of bounce resonance is sensitive to the wave normal angle. We suggest that the bounce resonant interaction might lead to an observed pitch angle distribution with a minimum at 90°.
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...
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...
Periodic and solitary wave solutions of cubic–quintic nonlinear ...
Indian Academy of Sciences (India)
Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.
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...
Numerical Computation of Wave-Plasma Interactions in Multi-Dimensional Systems
International Nuclear Information System (INIS)
D. A. D'Ippolito; J. R. Myra
2005-01-01
This project studied two kinds of nonlinear interactions between ion cyclotron range of frequency waves and fusion plasmas. A wavelet technique was also developed for analyzing the complex wave fields produced by wave propagation codes
Nonlinear drift waves in a dusty plasma with sheared flows
Energy Technology Data Exchange (ETDEWEB)
Vranjes, J. [K.U. Leuven (Belgium). Center for Plasma Astrophysics; Shukla, R.K. [Ruhr-Univ. Bochum (Germany). Inst. fuer Theoretische Physik IV
2002-01-01
Nonlinear properties of dust-modified drift waves and dust-drift waves in a dusty magnetoplasma with equilibrium sheared flows are examined. For this purpose, the relevant nonlinear equations for drift waves are analyzed for various profiles of the perpendicular and parallel plasma flows, and a variety of nonlinear solutions (viz. single and double vortex chains accompanied with zonal flows, tripolar and global vortices), which are driven by nommiform shear flows and nommiform dust density, is presented.
Nonlinear drift waves in a dusty plasma with sheared flows
International Nuclear Information System (INIS)
Vranjes, J.; Shukla, R.K.
2002-01-01
Nonlinear properties of dust-modified drift waves and dust-drift waves in a dusty magnetoplasma with equilibrium sheared flows are examined. For this purpose, the relevant nonlinear equations for drift waves are analyzed for various profiles of the perpendicular and parallel plasma flows, and a variety of nonlinear solutions (viz. single and double vortex chains accompanied with zonal flows, tripolar and global vortices), which are driven by nommiform shear flows and nommiform dust density, is presented
Nonlinear wave beams in a piezo semiconducting layer
International Nuclear Information System (INIS)
Bagdoev, A.G.; Shekoyan, A.V.; Danoyan, Z.N.
1997-01-01
The propagation of quasi-monochromatic nonlinear wave in a piezo semiconducting layer taking into account electron-concentration nonlinearity is considered. For such medium the evolution equations for incoming and reflected waves are derived. Nonlinear Schroedinger equations and solutions for narrow beams are obtained. It is shown that symmetry of incoming and reflected waves does not take place. The focusing of beams is investigated.18 refs
Ma, Li-Yuan; Ji, Jia-Liang; Xu, Zong-Wei; Zhu, Zuo-Nong
2018-03-01
We study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term. Project supported by the National Natural Science Foundation of China (Grant Nos. 11671255 and 11701510), the Ministry of Economy and Competitiveness of Spain (Grant No. MTM2016-80276-P (AEI/FEDER, EU)), and the China Postdoctoral Science Foundation (Grant No. 2017M621964).
Laboratory beam-plasma interactions linear and nonlinear
International Nuclear Information System (INIS)
Christiansen, P.J.; Bond, J.W.; Jain, V.K.
1982-01-01
This chapter attempts to demonstrate that despite unavoidable scaling limitations, laboratory experiments can uncover details of beam plasma interaction processes which could never be revealed through space plasma physics. Topics covered include linear theory, low frequency couplings, indirect effects, nonlinear effects, quasi-linear effects, trapping effects, nonlinear wave-wave interactions, and self modulation and cavitation. Unstable electrostatic waves arising from an exchange of energy with the ''free energy'' beam features are considered as kinetic and as hydrodynamic, or fluid, instabilities. The consequences of such instabilities (e.g. when the waves have grown to a finite level) are examined and some studies are reviewed which have attempted to understand how the free energy originally available in the beam is redistributed to produce a final state of equilibrium turbulence
Laboratory beam-plasma interactions: linear and nonlinear
International Nuclear Information System (INIS)
Christiansen, P.J.; Jain, V.K.; Bond, J.W.
1982-01-01
The present investigation is concerned with the configuration of a cool plasma (often magnetized axially) penetrated by an injected electron beam. The attempt is made to demonstrate that despite unavoidable scaling limitations, laboratory experiments can illuminate, in a controlled fashion, details of beam plasma interaction processes in a way which will never be possible in the space plasma physics. In view of the increasing interest in high frequency instabilities in the auroral zone, the possibilities for interesting cross fertilizations of the two fields appear to be extensive. The linear theory is considered along with low frequency couplings and indirect effects. Attention is given to the evidence for the existence of exponentially growing instabilities in beam plasma interactions. The consequences of such instabilities are also explored and some processes of nonlinear processes are discussed, taking into account quasi-linear effects, trapping effects, nonlinear effects, trapping effects, nonlinear wave-wave interactions, and self-modulation and cavitation. 80 references
Nonlinear propagation of intense electromagnetic waves in weakly-ionized plasmas
International Nuclear Information System (INIS)
Shukla, P.K.
1993-01-01
The nonlinear propagation of intense electromagnetic waves in weakly-ionized plasmas is considered. Stimulated scattering mechanisms involving electromagnetic and acoustic waves in an unmagnetized plasma are investigated. The growth rate and threshold for three-wave decay interactions as well as modulational and filamentation instabilities are presented. Furthermore, the electromagnetic wave modulation theory is generalized for weakly ionized collisional magnetoplasmas. Here, the radiation envelope is generally governed by a nonlinear Schroedinger equation. Accounting for the dependence of the attachment frequency on the radiation intensity, ponderomotive force, as well as the differential Joule heating nonlinearity, the authors derive the equations for the nonthermal electron density and temperature perturbations. The various nonlinear terms in the electron motion are compared. The problems of self-focusing and wave localization are discussed. The relevance of the investigation to ionospheric modification by powerful electromagnetic waves is pointed out
Interaction dynamics of electrostatic solitary waves
Directory of Open Access Journals (Sweden)
V. L. Krasovsky
1999-01-01
Full Text Available Interaction of nonlinear electrostatic pulses associated with electron phase density holes moving in a collisionless plasma is studied. An elementary event of the interaction is analyzed on the basis of the energy balance in the system consisting of two electrostatic solitary waves. It is established that an intrinsic property of the system is a specific irreversibility caused by a nonadiabatic modification of the internal structure of the holes and their effective heating in the process of the interaction. This dynamical irreversibility is closely connected with phase mixing of the trapped electrons comprising the holes and oscillating in the varying self-consistent potential wells. As a consequence of the irreversibility, the "collisions" of the solitary waves should be treated as "inelastic" ones. This explains the general tendency to the merging of the phase density holes frequently observed in numerical simulation and to corresponding coupling of the solitary waves.
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
Computational highlights from a recently developed high-order Boussinesq model are shown. The model is capable of treating fully nonlinear waves (up to the breaking point) out to dimensionless depths of (wavenumber times depth) kh \\approx 25. Cases considered include the study of short......-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...
Modeling the SAR Signature of Nonlinear Internal Waves
National Research Council Canada - National Science Library
Lettvin, Ellen E
2008-01-01
Nonlinear Internal Waves are pervasive globally, particularly in coastal waters. The currents and displacements associated with internal waves influence acoustic propagation and underwater navigation, as well as ocean transport and mixing...
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.
Nonlinear modulation of ion acoustic waves in a magnetized plasma
International Nuclear Information System (INIS)
Bharuthram, R.; Shukla, P.K.
1987-01-01
The quasistatic plasma slow response to coherent ion acoustic waves in a magnetized plasma is considered. A multidimensional cubic nonlinear Schroedinger equation is derived. It is found that the ion acoustic waves remain modulationally stable against oblique perturbations
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.
Nonlinear low frequency (LF) waves - Comets and foreshock phenomena
Tsurutani, Bruce T.
1991-01-01
A review is conducted of LF wave nonlinear properties at comets and in the earth's foreshock, engaging such compelling questions as why there are no cometary cyclotron waves, the physical mechanism responsible for 'dispersive whiskers', and the character of a general description of linear waves. Attention is given to the nonlinear properties of LF waves, whose development is illustrated by examples of waves and their features at different distances from the comet, as well as by computer simulation results. Also discussed is a curious wave mode detected from Comet Giacobini-Zinner, both at and upstream of the bow shock/wave.
Nonlinear Time-Reversal in a Wave Chaotic System
Frazier, Matthew; Taddese, Biniyam; Ott, Edward; Antonsen, Thomas; Anlage, Steven
2012-02-01
Time reversal mirrors are particularly simple to implement in wave chaotic systems and form the basis for a new class of sensors [1-3]. These sensors work by applying the quantum mechanical concepts of Loschmidt echo and fidelity decay to classical waves. The sensors make explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to remotely measure the presence of small perturbations to the system. The underlying ray chaos increases the sensitivity to small perturbations throughout the volume explored by the waves. We extend our time-reversal mirror to include a discrete element with a nonlinear dynamical response. The initially injected pulse interacts with the nonlinear element, generating new frequency components originating at the element. By selectively filtering for and applying the time-reversal mirror to the new frequency components, we focus a pulse only onto the element, without knowledge of its location. Furthermore, we demonstrate transmission of arbitrary patterns of pulses to the element, creating a targeted communication channel to the exclusion of 'eavesdroppers' at other locations in the system. [1] Appl. Phys. Lett. 95, 114103 (2009) [2] J. Appl. Phys. 108, 1 (2010) [3] Acta Physica Polonica A 112, 569 (2007)
International Nuclear Information System (INIS)
Sugaya, R.; Ue, A.; Maehara, T.; Sugawa, M.
1996-01-01
Acceleration and heating of a relativistic electron beam by cascading nonlinear Landau damping involving three or four intense electromagnetic waves in a plasma are studied theoretically based on kinetic wave equations and transport equations derived from relativistic Vlasov endash Maxwell equations. Three or four electromagnetic waves excite successively two or three nonresonant beat-wave-driven relativistic electron plasma waves with a phase velocity near the speed of light [v p =c(1-γ -2 p ) 1/2 , γ p =ω/ω pe ]. Three beat waves interact nonlinearly with the electron beam and accelerate it to a highly relativistic energy γ p m e c 2 more effectively than by the usual nonlinear Landau damping of two electromagnetic waves. It is proved that the electron beam can be accelerated to more highly relativistic energy in the plasma whose electron density decreases temporally with an appropriate rate because of the temporal increase of γ p . copyright 1996 American Institute of Physics
Bispectral analysis of nonlinear compressional waves in a two-dimensional dusty plasma crystal
International Nuclear Information System (INIS)
Nosenko, V.; Goree, J.; Skiff, F.
2006-01-01
Bispectral analysis was used to study the nonlinear interaction of compressional waves in a two-dimensional strongly coupled dusty plasma. A monolayer of highly charged polymer microspheres was suspended in a plasma sheath. The microspheres interacted with a Yukawa potential and formed a triangular lattice. Two sinusoidal pump waves with different frequencies were excited in the lattice by pushing the particles with modulated Ar + laser beams. Coherent nonlinear interaction of the pump waves was shown to be the mechanism of generating waves at the sum, difference, and other combination frequencies. However, coherent nonlinear interaction was ruled out for certain combination frequencies, in particular, for the difference frequency below an excitation-power threshold, as predicted by theory
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
Nonlinear propagation of short wavelength drift-Alfven waves
DEFF Research Database (Denmark)
Shukla, P. K.; Pecseli, H. L.; Juul Rasmussen, Jens
1986-01-01
Making use of a kinetic ion and a hydrodynamic electron description together with the Maxwell equation, the authors derive a set of nonlinear equations which governs the dynamics of short wavelength ion drift-Alfven waves. It is shown that the nonlinear drift-Alfven waves can propagate as two-dim...
Nonlinear self-modulation of ion-acoustic waves
International Nuclear Information System (INIS)
Ikezi, H.; Schwarzenegger, K.; Simons, A.L.; Ohsawa, Y.; Kamimura, T.
1978-01-01
The nonlinear evolution of an ion-acoustic wave packet is studied. Experimentally, it is found that (i) nonlinear phase modulation develops in the wave packet; (ii) the phase modulation, together with the dispersion effect, causes expansion and breaking of the wave packet; (iii) the ions trapped in the troughs of the wave potential introduce self-phase modulation; and (iv) the ion-acoustic wave is stable with respect to the modulational instability. Computer simulations have reproduced the experimental results. The physical picture and the model equation describing the wave evolution are discussed
International Nuclear Information System (INIS)
Kasahara, H.; Seki, T.; Kumazawa, R.; Saito, K.; Mutoh, T.; Kubo, S.; Shimozuma, T.; Igami, H.; Yoshimura, Y.; Takahashi, H.; Yamada, I.; Tokuzawa, T.; Ohdachi, S.; Morita, S.; Nomura, G.; Shimpo, F.; Komori, A.; Motojima, O.; Oosako, T.; Takase, Y.
2008-01-01
A wave detector, a newly designed magnetic probe, is installed in the large helical device (LHD). This wave detector is a 100-turn loop coil with electrostatic shield. Comparing a one-loop coil to this detector, this detector has roughly constant power coupling in the lower frequency range of 40 MHz, and it can easily detect magnetic wave in the frequency of a few megahertz. During high-harmonic fast wave heating, lower frequency waves (<10 MHz) were observed in the LHD for the first time, and for the power density threshold of lower frequency wave excitation (7.5 MHz) the power density of excited pumped wave (38.47 MHz) was approximately -46 dBm/Hz. These lower frequencies are kept constant for electron density and high energy particle distribution, and these lower frequency waves seem to be ion cyclotron waves caused by nonlinear wave-particle interaction, for example, parametric decay instability.
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.
Nonlinear VLF Wave Physics in the Radiation Belts
Crabtree, C. E.; Tejero, E. M.; Ganguli, G.; Mithaiwala, M.; Rudakov, L.; Hospodarsky, G. B.; Kletzing, C.
2014-12-01
Electromagnetic VLF waves, such as whistler mode waves, both control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering and are responsible for the energization of electrons during storms. Traditional approaches to understanding the influence of waves on trapped electrons have assumed that the wave characteristics (frequency spectrum, wave-normal angle distribution, etc.) were both stationary in time and amplitude independent from event to event. In situ data from modern satellite missions, such as the Van Allen probes, are showing that this assumption may not be justified. In addition, recent theoretical results [Crabtree et al. 2012] show that the threshold for nonlinear wave scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear wave scattering (Nonlinear Landau Damping) is an amplitude dependent mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Nonlinear scattering can alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al., 2012]. Such nonlinear wave effects can dramatically reduce electron lifetimes. Nonlinear wave dynamics such as these occur when there are more than one wave present, such a condition necessarily violates the assumption of traditional wave-normal analysis [Santolik et al., 2003] which rely on the plane wave assumption. To investigate nonlinear wave dynamics using modern in situ data we apply the maximum entropy method [Skilling and Bryan, 1984] to solve for the wave distribution function
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
International Nuclear Information System (INIS)
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-01-01
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.
Nonlinear particle-wave kinetics in weakly unstable plasmas
International Nuclear Information System (INIS)
Breizman, B.N.; Berk, H.L.; Pekker, M.S.
1996-01-01
With the motivation to address the behavior of the fusion produced alpha particles in a thermonuclear reactor, a theory is developed for predicting the wave saturation levels and particle transport in weakly unstable systems with a discrete number of modes in the presence of energetic particle sources and sinks. Conditions are established for either steady state or bursting nonlinear scenarios when several modes are excited for cases where there is and there is not resonance overlap. Depending on parameters, the particles can undergo benign relaxation, with only a small fraction of the available free energy released to waves and with no global transport, or the particles can experience rapid global transport caused by a substantial conversion of their free energy into wave energy. When the resonance condition of the particle-wave interaction is varied adiabatically, the particles trapped in a wave are found to form phase space holes or clumps that enhance the particle-wave energy exchange. This mechanism, which has been experimentally observed when there is frequency chirping, causes increased saturation levels of instabilities. If resonance sweeping is imposed externally, the particle free energy can even be tapped in stable systems where background dissipation suppresses linear instability. Externally applied resonance sweeping can be important for alpha particle energy channeling, as well as for understanding fishbone and some Alfven wave instability experiments. Near instability threshold, that is when the destabilizing drive just exceeds the background dissipation, a more sophisticated analysis is developed to predict the correct saturation. To leading order, this problem reduces to an integral equation for the wave amplitude with a temporally non local cubic term. This equation has a self-similar solution that blows-up in a finite time
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.
Interaction of gravitational plane waves
International Nuclear Information System (INIS)
Ferrari, V.
1988-01-01
The mathematical theory of colliding, infinite-fronted, plane gravitational waves is presented. The process of focusing, the creation of singularities and horizons, due to the interaction, and the lens effect due to a beam-like gravitational wave are discussed
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.
Turbulent spectra from three drift-wave interactions
International Nuclear Information System (INIS)
Terry, P.W.; Horton, W.
1982-02-01
Hydrodynamic equations for the drift-wave instability containing the rvec E x rvec B convective nonlinearity are used to show that the three wave interactions lead to temporal chaos with broad-band frequency spectra in the saturated state. 7 refs., 2 figs
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
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...... Alfvén waves. Solutions are found implicitly by deriving a set of integral dispersion relations which link the wave characteristics with the particle distribution functions. A physical discussion is given of the way in which the Alfvén waves can trap particles, and it is shown that the presence...
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Nonlinear Scattering of VLF Waves in the Radiation Belts
Crabtree, Chris; Rudakov, Leonid; Ganguli, Guru; Mithaiwala, Manish
2014-10-01
Electromagnetic VLF waves, such as whistler mode waves, control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering. Since the pitch-angle scattering rate is a strong function of the wave properties, a solid understanding of VLF wave sources and propagation in the magnetosphere is critical to accurately calculate electron lifetimes. Nonlinear scattering (Nonlinear Landau Damping) is a mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation, and has not been accounted for in previous models of radiation belt dynamics. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Recent results show that the threshold for nonlinear scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear scattering can then dramatically alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al. 2012]. By considering these effects, the lifetimes of electrons can be dramatically reduced. This work is supported by the Naval Research Laboratory base program.
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
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.
Nonlinear evolution equations for waves in random media
International Nuclear Information System (INIS)
Pelinovsky, E.; Talipova, T.
1994-01-01
The scope of this paper is to highlight the main ideas of asymptotical methods applying in modern approaches of description of nonlinear wave propagation in random media. We start with the discussion of the classical conception of ''mean field''. Then an exactly solvable model describing nonlinear wave propagation in the medium with fluctuating parameters is considered in order to demonstrate that the ''mean field'' method is not correct. We develop new asymptotic procedures of obtaining the nonlinear evolution equations for the wave fields in random media. (author). 16 refs
Electron non-linearities in Langmuir waves with application to beat-wave experiments
International Nuclear Information System (INIS)
Bell, A.R.; Gibbon, P.
1988-01-01
Non-linear Langmuir waves are examined in the context of the beat-wave accelerator. With a background of immobile ions the waves in one dimension are subject to the relativistic non-linearity of Rosenbluth, M.N. and Liu, C.S., Phys. Rev. Lett., 1972, 29, 701. In two or three dimensions, other electron non-linearities occur which involve electric and magnetic fields. The quasi-linear equations for these non-linearities are developed and solved numerically in a geometry representative of laser-driven beat waves. (author)
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 ...
Effect of Forcing Function on Nonlinear Acoustic Standing Waves
Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce
2003-01-01
Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.
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.
Catastrophes in the interaction of light waves in anisotropic resonator
International Nuclear Information System (INIS)
Mkrtchyan, A.R.; Nersisyan, S.R.; Tabiryan, N.V.
1993-01-01
An origin of jump-like and hysteresical phenomena is predicted theoretically. Those are caused by the ruling of the state of non-linear anisotropic resonator with an orthogonal polarization of light waves. The resonator creates a turned connection as well as causes a complex tying between the waves. The later conditions a whole number of the interacting waves regimes because of a big number of ruling parameters. 5 refs
Interaction of langmuir and ion acoustic waves
International Nuclear Information System (INIS)
Lee, Hee Jae
1991-01-01
Interaction of Langmuir and ion acoustic waves in a plasma is described by Landau-Ginzburg type of equation when the group velocity of the Langmuir wave is equal to the wave velocity of ion acoustic wave. (Author)
NONLINEAR REFLECTION PROCESS OF LINEARLY POLARIZED, BROADBAND ALFVÉN WAVES IN THE FAST SOLAR WIND
Energy Technology Data Exchange (ETDEWEB)
Shoda, M.; Yokoyama, T., E-mail: shoda@eps.s.u-tokyo.ac.jp [Department of Earth and Planetary Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan)
2016-04-01
Using one-dimensional numerical simulations, we study the elementary process of Alfvén wave reflection in a uniform medium, including nonlinear effects. In the linear regime, Alfvén wave reflection is triggered only by the inhomogeneity of the medium, whereas in the nonlinear regime, it can occur via nonlinear wave–wave interactions. Such nonlinear reflection (backscattering) is typified by decay instability. In most studies of decay instabilities, the initial condition has been a circularly polarized Alfvén wave. In this study we consider a linearly polarized Alfvén wave, which drives density fluctuations by its magnetic pressure force. For generality, we also assume a broadband wave with a red-noise spectrum. In the data analysis, we decompose the fluctuations into characteristic variables using local eigenvectors, thus revealing the behaviors of the individual modes. Different from the circular-polarization case, we find that the wave steepening produces a new energy channel from the parent Alfvén wave to the backscattered one. Such nonlinear reflection explains the observed increasing energy ratio of the sunward to the anti-sunward Alfvénic fluctuations in the solar wind with distance against the dynamical alignment effect.
Nonlinear periodic waves in dusty plasma with variable dust charge
International Nuclear Information System (INIS)
Yadav, Lakhan Lal; Bharuthram, R.
2002-01-01
Using the reductive perturbation method, we present a theory of nonlinear periodic waves, viz. the cnoidal waves, in a dusty plasma consisting of electrons, ions, and cold dust grains with charge fluctuations, which in the limiting case reduce to dust acoustic solitons. It is found that the frequency of the dust acoustic cnoidal wave increases with its amplitude. The dust charge fluctuations are found to affect the characteristics of the cnoidal waves
Nonlinear electrostatic solitary waves in electron-positron plasmas
Lazarus, I. J.; Bharuthram, R.; Moolla, S.; Singh, S. V.; Lakhina, G. S.
2016-02-01
The generation of nonlinear electrostatic solitary waves (ESWs) is explored in a magnetized four component two-temperature electron-positron plasma. Fluid theory is used to derive a set of nonlinear equations for the ESWs, which propagate obliquely to an external magnetic field. The electric field structures are examined for various plasma parameters and are shown to yield sinusoidal, sawtooth and bipolar waveforms. It is found that an increase in the densities of the electrons and positrons strengthen the nonlinearity while the periodicity and nonlinearity of the wave increases as the cool-to-hot temperature ratio increases. Our results could be useful in understanding nonlinear propagation of waves in astrophysical environments and related laboratory experiments.
Nonlinear spin wave coupling in adjacent magnonic crystals
Energy Technology Data Exchange (ETDEWEB)
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)
2016-07-25
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Nonlinear spin wave coupling in adjacent magnonic crystals
International Nuclear Information System (INIS)
Sadovnikov, A. V.; Nikitov, S. A.; Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E.
2016-01-01
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
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.
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 traveling wave front as well as the existence and instability of a standing pulse solution if 0 traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.
Nonlinear surface waves at ferrite-metamaterial waveguide structure
Hissi, Nour El Houda; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Shabat, Mohammed Musa; Atangana, Jacques
2016-09-01
A new ferrite slab made of a metamaterial (MTM), surrounded by a nonlinear cover cladding and a ferrite substrate, was shown to support unusual types of electromagnetic surface waves. We impose the boundary conditions to derive the dispersion relation and others necessary to formulate the proposed structure. We analyse the dispersion properties of the nonlinear surface waves and we calculate the associated propagation index and the film-cover interface nonlinearity. In the calculation, several sets of the permeability of the MTM are considered. Results show that the waves behaviour depends on the values of the permeability of the MTM, the thickness of the waveguide and the film-cover interface nonlinearity. It is also shown that the use of the singular solutions to the electric field equation allows to identify several new properties of surface waves which do not exist in conventional waveguide.
Linear interaction of gravitational waves
International Nuclear Information System (INIS)
Ciubotariu, C.D.
1992-01-01
Starting with the linearized Einstein equations written in the same form as Maxwell equations, a damping term is found in the wave equation. The analogy with the propagation of the electromagnetic wave in ohmic media is obvious if we introduce an 'ohmic relation' for gravitational interaction. The possibility of the amplification of gravitational waves by a suitable choice of the velocity field of a dust ('dust with negative viscosity'), for example by the use of the free-electron laser principle, is indicated. (Author)
Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas
Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.
1997-01-01
We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.
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....
On Maximally Dissipative Shock Waves in Nonlinear Elasticity
Knowles, James K.
2010-01-01
Shock waves in nonlinearly elastic solids are, in general, dissipative. We study the following question: among all plane shock waves that can propagate with a given speed in a given one-dimensional nonlinearly elastic bar, which one—if any—maximizes the rate of dissipation? We find that the answer to this question depends strongly on the qualitative nature of the stress-strain relation characteristic of the given material. When maximally dissipative shocks do occur, they propagate according t...
Green function formalism for nonlinear acoustic waves in layered media
International Nuclear Information System (INIS)
Lobo, A.; Tsoy, E.; De Sterke, C.M.
2000-01-01
Full text: The applications of acoustic waves in identifying defects in adhesive bonds between metallic plates have received little attention at high intensities where the media respond nonlinearly. However, the effects of reduced bond strength are more distinct in the nonlinear response of the structure. Here we assume a weak nonlinearity acting as a small perturbation, thereby reducing the problem to a linear one. This enables us to develop a specialized Green function formalism for calculating acoustic fields in layered media
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)
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 ...
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 ...
Stability of nonlinear waves and patterns and related topics
Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn
2018-04-01
Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.
Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates
International Nuclear Information System (INIS)
Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young
2010-01-01
Since the acoustic nonlinearity is sensitive to the minute variation of material properties, the nonlinear ultrasonic technique(NUT) has been considered as a promising method to evaluate the material degradation or fatigue. However, there are certain limitations to apply the conventional NUT using the bulk wave to thin plates. In case of plates, the use of Lamb wave can be considered, however, the propagation characteristics of Lamb wave are completely different with the bulk wave, and thus the separate study for the nonlinearity of Lamb wave is required. For this work, this paper analyzed first the conditions of mode pair suitable for the practical application as well as for the cumulative propagation of quadratic harmonic frequency and summarized the result in for conditions: phase matching, non-zero power flux, group velocity matching, and non-zero out-of-plane displacement. Experimental results in aluminum plates showed that the amplitude of the secondary Lamb wave and nonlinear parameter grew up with increasing propagation distance at the mode pair satisfying the above all conditions and that the ration of nonlinear parameters measured in Al6061-T6 and Al1100-H15 was closed to the ratio of the absolute nonlinear parameters
Propagation of nonlinear ion acoustic wave with generation of long-wavelength waves
International Nuclear Information System (INIS)
Ohsawa, Yukiharu; Kamimura, Tetsuo
1978-01-01
The nonlinear propagation of the wave packet of an ion acoustic wave with wavenumber k 0 asymptotically equals k sub(De) (the electron Debye wavenumber) is investigated by computer simulations. From the wave packet of the ion acoustic wave, waves with long wavelengths are observed to be produced within a few periods for the amplitude oscillation of the original wave packet. These waves are generated in the region where the original wave packet exists. Their characteristic wavelength is of the order of the length of the wave packet, and their propagation velocity is almost equal to the ion acoustic speed. The long-wavelength waves thus produced strongly affect the nonlinear evolution of the original wave packet. (auth.)
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.
Nonlinear pattern formation of Faraday waves
Binks, D.J.; Water, van de W.
1997-01-01
A cascade of surface wave patterns with increasing rotational symmetry ranging from simple square to tenfold quasiperiodic is observed for Faraday waves. The experiment concerns the excitation of subharmonic standing surface waves by oscillating vertical acceleration. Our observation agrees with the
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 ...
Computational and theoretical study of the wave-particle interaction of protons and waves
Directory of Open Access Journals (Sweden)
P. S. Moya
2012-09-01
Full Text Available We study the wave-particle interaction and the evolution of electromagnetic waves propagating through a plasma composed of electrons and protons, using two approaches. First, a quasilinear kinetic theory has been developed to study the energy transfer between waves and particles, with the subsequent acceleration and heating of protons. Second, a one-dimensional hybrid numerical simulation has been performed, with and without including an expanding-box model that emulates the spherical expansion of the solar wind, to investigate the fully nonlinear evolution of this wave-particle interaction. Numerical results of both approaches show that there is an anisotropic evolution of proton temperature.
Tunable Resonators for Nonlinear Modal Interactions
Ramini, Abdallah
2016-10-04
Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.
Tunable Resonators for Nonlinear Modal Interactions
Ramini, Abdallah; Hajjaj, Amal Z.; Younis, Mohammad I.
2016-01-01
Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.
Nonlinear frequency shift of finite-amplitude electrostatic surface waves
International Nuclear Information System (INIS)
Stenflo, L.
1989-01-01
The problem concerning the appropriate form for the nonlinear frequency shift arising from slow density modulations of electrostatic surface waves in a semi-infinite unmagnetized plasma is reconsidered. The spatial dependence of the wave amplitude normal to the surface is kept general in order to allow for possible nonlinear attenuation behaviour of the surface waves. It is found that if the frequency shift is expressed as a function of the density and its gradient then the result is identical with that of Zhelyazkov, I. Proceedings International Conference on Plasma Physics, Kiev, 1987, Vol. 2, p. 694, who assumed a linear exponential attenuation behaviour. (author)
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 theory of electroelastic and magnetoelastic interactions
Dorfmann, Luis
2014-01-01
This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.
Agapitov, O.; Drake, J. F.; Vasko, I.; Mozer, F. S.; Artemyev, A.; Krasnoselskikh, V.; Angelopoulos, V.; Wygant, J.; Reeves, G. D.
2018-03-01
Whistler mode chorus waves are particularly important in outer radiation belt dynamics due to their key role in controlling the acceleration and scattering of electrons over a very wide energy range. The efficiency of wave-particle resonant interactions is defined by whistler wave properties which have been described by the approximation of plane linear waves propagating through the cold plasma of the inner magnetosphere. However, recent observations of extremely high-amplitude whistlers suggest the importance of nonlinear wave-particle interactions for the dynamics of the outer radiation belt. Oblique chorus waves observed in the inner magnetosphere often exhibit drastically nonsinusoidal (with significant power in the higher harmonics) waveforms of the parallel electric field, presumably due to the feedback from hot resonant electrons. We have considered the nature and properties of such nonlinear whistler waves observed by the Van Allen Probes and Time History of Events and Macroscale Interactions define during Substorms in the inner magnetosphere, and we show that the significant enhancement of the wave electrostatic component can result from whistler wave coupling with the beam-driven electrostatic mode through the resonant interaction with hot electron beams. Being modulated by a whistler wave, the electron beam generates a driven electrostatic mode significantly enhancing the parallel electric field of the initial whistler wave. We confirm this mechanism using a self-consistent particle-in-cell simulation. The nonlinear electrostatic component manifests properties of the beam-driven electron acoustic mode and can be responsible for effective electron acceleration in the inhomogeneous magnetic field.
Nonlinear dynamics of interacting populations
Bazykin, Alexander D
1998-01-01
This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative the
Interactions of solitary waves and compression/expansion waves in core-annular flows
Maiden, Michelle; Anderson, Dalton; El, Gennady; Franco, Nevil; Hoefer, Mark
2017-11-01
The nonlinear hydrodynamics of an initial step leads to the formation of rarefaction waves and dispersive shock waves in dispersive media. Another hallmark of these media is the soliton, a localized traveling wave whose speed is amplitude dependent. Although compression/expansion waves and solitons have been well-studied individually, there has been no mathematical description of their interaction. In this talk, the interaction of solitons and shock/rarefaction waves for interfacial waves in viscous, miscible core-annular flows are modeled mathematically and explored experimentally. If the interior fluid is continuously injected, a deformable conduit forms whose interfacial dynamics are well-described by a scalar, dispersive nonlinear partial differential equation. The main focus is on interactions of solitons with dispersive shock waves and rarefaction waves. Theory predicts that a soliton can either be transmitted through or trapped by the extended hydrodynamic state. The notion of reciprocity is introduced whereby a soliton interacts with a shock wave in a reciprocal or dual fashion as with the rarefaction. Soliton reciprocity, trapping, and transmission are observed experimentally and are found to agree with the modulation theory and numerical simulations. This work was partially supported by NSF CAREER DMS-1255422 (M.A.H.) and NSF GRFP (M.D.M.).
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.
Theoretical studies of some nonlinear laser-plasma interactions
International Nuclear Information System (INIS)
Cohen, B.I.
1975-01-01
The nonlinear coupling of intense, monochromatic, electromagnetic radiation with plasma is considered in a number of special cases. The first part of the thesis serves as an introduction to three-wave interactions. A general formulation of the stimulated scattering of transverse waves by longitudinal modes in a warm, unmagnetized, uniform plasma is constructed. A general dispersion relation is derived that describes Raman and Brillouin scattering, modulational instability, and induced Thomson scattering. Raman scattering (the scattering of a photon into another photon and an electron plasma wave) is investigated as a possible plasma heating scheme. Analytic theory complemented by computer simulation is presented describing the nonlinear mode coupling of laser light with small and large amplitude, resonantly excited electron plasma waves. The simulated scattering of a coherent electromagnetic wave by low frequency density perturbations in homogeneous plasma is discussed. A composite picture of the linear dispersion relations for filamentation and Brillouin scattering is constructed. The absolute instability of Brillouin weak and strong coupling by analytic and numerical means is described
Alfven wave resonances and flow induced by nonlinear Alfven waves in a stratified atmosphere
International Nuclear Information System (INIS)
Stark, B. A.; Musielak, Z. E.; Suess, S. T.
1996-01-01
A nonlinear, time-dependent, ideal MHD code has been developed and used to compute the flow induced by nonlinear Alfven waves propagating in an isothermal, stratified, plane-parallel atmosphere. The code is based on characteristic equations solved in a Lagrangian frame. Results show that resonance behavior of Alfven waves exists in the presence of a continuous density gradient and that the waves with periods corresponding to resonant peaks exert considerably more force on the medium than off-resonance periods. If only off-peak periods are considered, the relationship between the wave period and induced longitudinal velocity shows that short period WKB waves push more on the background medium than longer period, non-WKB, waves. The results also show the development of the longitudinal waves induced by finite amplitude Alfven waves. Wave energy transferred to the longitudinal mode may provide a source of localized heating
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
Mayr, Hans G.; Mengel, J. G.; Chan, K. L.; Huang, F. T.
2010-01-01
As Lindzen (1981) had shown, small-scale gravity waves (GW) produce the observed reversals of the zonal-mean circulation and temperature variations in the upper mesosphere. The waves also play a major role in modulating and amplifying the diurnal tides (DT) (e.g., Waltersheid, 1981; Fritts and Vincent, 1987; Fritts, 1995a). We summarize here the modeling studies with the mechanistic numerical spectral model (NSM) with Doppler spread parameterization for GW (Hines, 1997a, b), which describes in the middle atmosphere: (a) migrating and non-migrating DT, (b) planetary waves (PW), and (c) global-scale inertio gravity waves. Numerical experiments are discussed that illuminate the influence of GW filtering and nonlinear interactions between DT, PW, and zonal mean variations. Keywords: Theoretical modeling, Middle atmosphere dynamics, Gravity wave interactions, Migrating and non-migrating tides, Planetary waves, Global-scale inertio gravity waves.
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
Dynamical soil-structure interactions: influence of soil behaviour nonlinearities
International Nuclear Information System (INIS)
Gandomzadeh, Ali
2011-01-01
The interaction of the soil with the structure has been largely explored the assumption of material and geometrical linearity of the soil. Nevertheless, for moderate or strong seismic events, the maximum shear strain can easily reach the elastic limit of the soil behavior. Considering soil-structure interaction, the nonlinear effects may change the soil stiffness at the base of the structure and therefore energy dissipation into the soil. Consequently, ignoring the nonlinear characteristics of the dynamic soil-structure interaction (DSSI) this phenomenon could lead to erroneous predictions of structural response. The goal of this work is to implement a fully nonlinear constitutive model for soils into a numerical code in order to investigate the effect of soil nonlinearity on dynamic soil structure interaction. Moreover, different issues are taken into account such as the effect of confining stress on the shear modulus of the soil, initial static condition, contact elements in the soil-structure interface, etc. During this work, a simple absorbing layer method based on a Rayleigh/Caughey damping formulation, which is often already available in existing Finite Element softwares, is also presented. The stability conditions of the wave propagation problems are studied and it is shown that the linear and nonlinear behavior are very different when dealing with numerical dispersion. It is shown that the 10 points per wavelength rule, recommended in the literature for the elastic media is not sufficient for the nonlinear case. The implemented model is first numerically verified by comparing the results with other known numerical codes. Afterward, a parametric study is carried out for different types of structures and various soil profiles to characterize nonlinear effects. Different features of the DSSI are compared to the linear case: modification of the amplitude and frequency content of the waves propagated into the soil, fundamental frequency, energy dissipation in
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.
O Wave Interactions: Explosive Resonant Triads and Critical Layers.
Mahoney, Daniel J.
This thesis considers the phenomenon of explosive resonant triads in weakly nonlinear, dispersive wave systems. These are nearly linear waves with slowly varying amplitudes which become unbounded in finite time. It is shown that such interactions are much stronger than previously thought. These waves can be thought of as a nonlinear instability, in the sense that a weakly nonlinear perturbation to some system grows to such magnitudes that the behavior of the system is governed by strongly nonlinear effects. This may occur for systems which are linearly or neutrally stable. This is contrasted with previous resolutions of this problem, which treated such perturbations as being large amplitude, nearly linear waves. Analytical and numerical evidence is presented to support these claims. These waves represent a potentially important effect in a variety of physical systems, most notably plasma physics. Attention here is turned to their occurrence in fluid mechanics. Here previous work is extended to include flow systems with continuously varying basic velocities and densities. Many of the problems encountered here will be found to be of a singular nature themselves, and the techniques for analyzing these difficulties will be developed. This will involve the concept of a critical layer in a fluid, a level at which a wave phase speed equals the unperturbed fluid velocity in the direction of propagation. Examples of such waves in this context will be presented. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).
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.
Nonlinear wave chaos: statistics of second harmonic fields.
Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M
2017-10-01
Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.
Computer simulations on the nonlinear frequency shift and nonlinear modulation of ion-acoustic waves
International Nuclear Information System (INIS)
Ohsawa, Yukiharu; Kamimura, Tetsuo.
1976-11-01
The nonlinear behavior of ion-acoustic waves with rather short wave-length, k lambda sub(De) asymptotically equals 1, is investigated by computer sumulations. It is observed that the nonlinear frequency shift is negative and is proportional to square root of the initial wave amplitude when the amplitude is not too large. This proportionality breaks down and the frequency shift can become positive (for large Te/Ti), when (n tilde sub(i)/n 0 )sup(1/2)>0.25, where n tilde sub(i) is the ion density perturbation and n 0 the average plasma density. Nonlinear modulation of the wave-packet is clearly seen; however, modulational instability was not observed. The importance of the effects of trapped ions to these phenomena is emphasized. (auth.)
Nonlinear generation of zonal flows by ion-acoustic waves in a uniform magnetoplasma
International Nuclear Information System (INIS)
Shukla, Nitin; Shukla, P.K.
2010-01-01
It is shown that large-scale zonal flows (ZFs) can be excited by Reynolds stress of nonlinearly interacting random phase ion-acoustic waves (EIAWs) in a uniform magnetoplasma. Since ZFs are associated with poloidal sheared flows, they can tear apart short scale EIAW turbulence eddies, and hence contribute to the reduction of the cross-field turbulent transport in a magnetized plasma.
Nonlinear transient waves in coupled phase oscillators with inertia.
Jörg, David J
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
Nonlinear modulation of torsional waves in elastic rod. [Instability
Energy Technology Data Exchange (ETDEWEB)
Hirao, M; Sugimoto, N [Osaka Univ., Toyonaka (Japan). Faculty of Engineering Science
1977-06-01
Nonlinear Schroedinger equation, which describes the nonlinear modulation of dispersive torsional waves in an elastic rod of circular cross-section, is derived by the derivative expansion method. It is found, for the lowest dispersive mode, that the modulational instability occurs except in the range of the carrier wavenumber, 2.799
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...
On the Stochastic Wave Equation with Nonlinear Damping
International Nuclear Information System (INIS)
Kim, Jong Uhn
2008-01-01
We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping
Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment
Energy Technology Data Exchange (ETDEWEB)
Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.; Obayashi, T.
1986-01-01
A rocket-borne experiment called MINIX was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction Experiment and was carried out on August 29, 1983. The objectives of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere such as the Ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no Ohmic heating effects were detected. 4 figures.
Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment
Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.
A rocket-borne experiment called 'MINIX' was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction eXperiment and was carried out on August 29, 1983. The objective of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere, such as the ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no ohmic heating effects were detected.
Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment
International Nuclear Information System (INIS)
Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.; Obayashi, T.
1986-01-01
A rocket-borne experiment called MINIX was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction Experiment and was carried out on August 29, 1983. The objectives of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere such as the Ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no Ohmic heating effects were detected. 4 figures
Ganguli, G.; Crabtree, C. E.; Rudakov, L.; Mithaiwala, M.
2014-12-01
Velocity ring instabilities are a common naturally occuring magnetospheric phenomenon that can also be generated by man made ionospheric experiments. These instabilities are known to generate lower-hybrid waves, which generally cannot propagte out of the source region. However, nonlinear wave physics can convert these linearly driven electrostatic lower-hybrid waves into electromagnetic waves that can escape the source region. These nonlinearly generated waves can be an important source of VLF turbulence that controls the trapped electron lifetime in the radiation belts. We develop numerical solutions to the wave-kinetic equation in a periodic box including the effects of nonlinear (NL) scattering (nonlinear Landau damping) of Lower-hybrid waves giving the evolution of the wave-spectra in wavenumber space. Simultaneously we solve the particle diffusion equation of both the background plasma particles and the ring ions, due to both linear and nonlinear Landau resonances. At initial times for cold ring ions, an electrostatic beam mode is excited, while the kinetic mode is stable. As the instability progresses the ring ions heat, the beam mode is stabilized, and the kinetic mode destabilizes. When the amplitude of the waves becomes sufficient the lower-hybrid waves are scattered (by either nearly unmagnetized ions or magnetized electrons) into electromagnetic magnetosonic waves [Ganguli et al 2010]. The effect of NL scattering is to limit the amplitude of the waves, slowing down the quasilinear relaxation time and ultimately allowing more energy from the ring to be liberated into waves [Mithaiwala et al. 2011]. The effects of convection out of the instability region are modeled, additionally limiting the amplitude of the waves, allowing further energy to be liberated from the ring [Scales et al., 2012]. Results are compared to recent 3D PIC simulations [Winske and Duaghton 2012].
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.
Propagation of Quasi-plane Nonlinear Waves in Tubes
Directory of Open Access Journals (Sweden)
P. Koníček
2002-01-01
Full Text Available This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicability of the KZK equation and the GBE equation for describing nonlinear waves in tubes are discussed.
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.
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).
Nonlinear steady-state coupling of LH waves
International Nuclear Information System (INIS)
Ko, K.; Krapchev, V.B.
1981-02-01
The coupling of lower hybrid waves at the plasma edge by a two waveguide array with self-consistent density modulation is solved numerically. For a linear density profile, the governing nonlinear Klein-Gordon equation for the electric field can be written as a system of nonlinearly modified Airy equations in Fourier k/sub z/-space. Numerical solutions to the nonlinear system satisfying radiation condition are obtained. Spectra broadening and modifications to resonance cone trajectories are observed with increase of incident power
Nonlinear reflection of shock shear waves in soft elastic media.
Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël
2010-02-01
For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.
Nonlinear wave equations, formation of singularities
John, Fritz
1990-01-01
This is the second volume in the University Lecture Series, designed to make more widely available some of the outstanding lectures presented in various institutions around the country. Each year at Lehigh University, a distinguished mathematical scientist presents the Pitcher Lectures in the Mathematical Sciences. This volume contains the Pitcher lectures presented by Fritz John in April 1989. The lectures deal with existence in the large of solutions of initial value problems for nonlinear hyperbolic partial differential equations. As is typical with nonlinear problems, there are many results and few general conclusions in this extensive subject, so the author restricts himself to a small portion of the field, in which it is possible to discern some general patterns. Presenting an exposition of recent research in this area, the author examines the way in which solutions can, even with small and very smooth initial data, "blow up" after a finite time. For various types of quasi-linear equations, this time de...
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 e...
Experimental observation of azimuthal shock waves on nonlinear acoustical vortices
International Nuclear Information System (INIS)
Brunet, Thomas; Thomas, Jean-Louis; Marchiano, Regis; Coulouvrat, Francois
2009-01-01
Thanks to a new focused array of piezoelectric transducers, experimental results are reported here to evidence helical acoustical shock waves resulting from the nonlinear propagation of acoustical vortices (AVs). These shock waves have a three-dimensional spiral shape, from which both the longitudinal and azimuthal components are studied. The inverse filter technique used to synthesize AVs allows various parameters to be varied, especially the topological charge which is the key parameter describing screw dislocations. Firstly, an analysis of the longitudinal modes in the frequency domain reveals a wide cascade of harmonics (up to the 60th order) leading to the formation of the shock waves. Then, an original measurement in the transverse plane exhibits azimuthal behaviour which has never been observed until now for acoustical shock waves. Finally, these new experimental results suggest interesting potential applications of nonlinear effects in terms of acoustics spanners in order to manipulate small objects.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Numerical assessment of factors affecting nonlinear internal waves in the South China Sea
Li, Qiang
2014-02-01
Nonlinear internal waves in the South China Sea exhibit diverse characteristics, which are associated with the complex conditions in Luzon Strait, such as the double ridge topography, the Earth’s rotation, variations in stratification and the background current induced by the Kuroshio. These effects are individually assessed using the MITgcm. The performance of the model is first validated through comparison with field observations. Because of in-phased ray interaction, the western ridge in Luzon Strait intensifies the semidiurnal internal tides generated from the eastern ridge, thus reinforcing the formation of nonlinear internal waves. However, the ray interaction for K1 forcing becomes anti-phased so that the K1 internal tide generation is reduced by the western ridge. Not only does the rotational dispersion suppress internal tide generation, it also inhibits nonlinear steepening and consequent internal solitary wave formation. As a joint effect, the double ridges and the rotational dispersion result in a paradoxical phenomenon: diurnal barotropic tidal forcing is dominant in Luzon Strait, but semidiurnal internal tides prevail in the deep basin of the South China Sea. The seasonal variation of the Kuroshio is consistent with the seasonal appearance of nonlinear internal waves in the South China Sea. The model results show that the westward inflow due to the Kuroshio intrusion reduces the amplitude of internal tides in the South China Sea, causing the weakening or absence of internal solitary waves. Winter stratification cannot account for the significant reduction of nonlinear internal waves, because the amplitude growth of internal tides due to increased thermocline tilting counteracts the reduced nonlinearity caused by thermocline deepening.
Hossen, Md. Belal; Roshid, Harun-Or; Ali, M. Zulfikar
2018-05-01
Under inquisition in this paper is a (2 + 1)-dimensional Breaking Soliton equation, which can describe various nonlinear scenarios in fluid dynamics. Using the Bell polynomials, some proficient auxiliary functions are offered to apparently construct its bilinear form and corresponding soliton solutions which are different from the previous literatures. Moreover, a direct method is used to construct its rogue wave and solitary wave solutions using particular auxiliary function with the assist of bilinear formalism. Finally, the interactions between solitary waves and rogue waves are offered with a complete derivation. These results enhance the variety of the dynamics of higher dimensional nonlinear wave fields related to mathematical physics and engineering.
International Nuclear Information System (INIS)
Shang Yadong
2005-01-01
In this paper, the evolution equations with strong nonlinear term describing the resonance interaction between the long wave and the short wave are studied. Firstly, based on the qualitative theory and bifurcation theory of planar dynamical systems, all of the explicit and exact solutions of solitary waves are obtained by qualitative seeking the homoclinic and heteroclinic orbits for a class of Lienard equations. Then the singular travelling wave solutions, periodic travelling wave solutions of triangle functions type are also obtained on the basis of the relationships between the hyperbolic functions and that between the hyperbolic functions with the triangle functions. The varieties of structure of exact solutions of the generalized long-short wave equation with strong nonlinear term are illustrated. The methods presented here also suitable for obtaining exact solutions of nonlinear wave equations in multidimensions
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.
To the complete integrability of long-wave short-wave interaction equations
International Nuclear Information System (INIS)
Roy Chowdhury, A.; Chanda, P.K.
1984-10-01
We show that the non-linear partial differential equations governing the interaction of long and short waves are completely integrable. The methodology we use is that of Ablowitz et al. though in the last section of our paper we have discussed the problem also in the light of the procedure due to Weiss et al. and have obtained a Baecklund transformation. (author)
Non-Linear Dynamics and Fundamental Interactions
Khanna, Faqir
2006-01-01
The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.
Non-linear soil-structure interaction
International Nuclear Information System (INIS)
Wolf, J.P.
1984-01-01
The basic equation of motion to analyse the interaction of a non-linear structure and an irregular soil with the linear unbounded soil is formulated in the time domain. The contribution of the unbounded soil involves convolution integrals of the dynamic-stiffness coefficients in the time domain and the corresponding motions. As another possibility, a flexibility formulation fot the contribution of the unbounded soil using the dynamic-flexibility coefficients in the time domain, together with the direct-stiffness method for the structure and the irregular soil can be applied. As an example of a non-linear soil-structure-interaction analysis, the partial uplift of the basemat of a structure is examined. (Author) [pt
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)
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.
Periodic solutions for one dimensional wave equation with bounded nonlinearity
Ji, Shuguan
2018-05-01
This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient u (x) satisfies ess infηu (x) > 0 with ηu (x) = 1/2 u″/u - 1/4 (u‧/u)2, which actually excludes the classical constant coefficient model. For the case ηu (x) = 0, it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form T = 2p-1/q (p , q are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition ess infηu (x) > 0.
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
Optical rogue waves generation in a nonlinear metamaterial
Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin
2014-11-01
We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.
Nonlinear Bloch waves in metallic photonic band-gap filaments
International Nuclear Information System (INIS)
Kaso, Artan; John, Sajeev
2007-01-01
We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10-50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell's equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament
Nonlinear Bloch waves in metallic photonic band-gap filaments
Kaso, Artan; John, Sajeev
2007-11-01
We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10 50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell’s equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament.
Simulations of nonlinear continuous wave pressure fields in FOCUS
Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.
2017-03-01
The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.
Nonlinear wave mechanics from classical dynamics and scale covariance
International Nuclear Information System (INIS)
Hammad, F.
2007-01-01
Nonlinear Schroedinger equations proposed by Kostin and by Doebner and Goldin are rederived from Nottale's prescription for obtaining quantum mechanics from classical mechanics in nondifferentiable spaces; i.e., from hydrodynamical concepts and scale covariance. Some soliton and plane wave solutions are discussed
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 ...
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.
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.
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...
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
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...
Controlling nonlinear waves in excitable media
International Nuclear Information System (INIS)
Puebla, Hector; Martin, Roland; Alvarez-Ramirez, Jose; Aguilar-Lopez, Ricardo
2009-01-01
A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system's slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.
Controlling nonlinear waves in excitable media
Energy Technology Data Exchange (ETDEWEB)
Puebla, Hector [Departamento de Energia, Universidad Autonoma Metropolitana, Av. San Pablo No. 180, Reynosa-Tamaulipas, Azcapotzalco 02200, DF, Mexico (Mexico)], E-mail: hpuebla@correo.azc.uam.mx; Martin, Roland [Laboratoire de Modelisation et d' Imagerie en Geosciences, CNRS UMR and INRIA Futurs Magique-3D, Universite de Pau (France); Alvarez-Ramirez, Jose [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa (Mexico); Aguilar-Lopez, Ricardo [Departamento de Biotecnologia y Bioingenieria, CINVESTAV-IPN (Mexico)
2009-01-30
A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system's slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.
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 acoustic/seismic waves in earthquake processes
International Nuclear Information System (INIS)
Johnson, Paul A.
2012-01-01
Nonlinear dynamics induced by seismic sources and seismic waves are common in Earth. Observations range from seismic strong ground motion (the most damaging aspect of earthquakes), intense near-source effects, and distant nonlinear effects from the source that have important consequences. The distant effects include dynamic earthquake triggering—one of the most fascinating topics in seismology today—which may be elastically nonlinearly driven. Dynamic earthquake triggering is the phenomenon whereby seismic waves generated from one earthquake trigger slip events on a nearby or distant fault. Dynamic triggering may take place at distances thousands of kilometers from the triggering earthquake, and includes triggering of the entire spectrum of slip behaviors currently identified. These include triggered earthquakes and triggered slow, silent-slip during which little seismic energy is radiated. It appears that the elasticity of the fault gouge—the granular material located between the fault blocks—is key to the triggering phenomenon.
Typology of nonlinear activity waves in a layered neural continuum.
Koch, Paul; Leisman, Gerry
2006-04-01
Neural tissue, a medium containing electro-chemical energy, can amplify small increments in cellular activity. The growing disturbance, measured as the fraction of active cells, manifests as propagating waves. In a layered geometry with a time delay in synaptic signals between the layers, the delay is instrumental in determining the amplified wavelengths. The growth of the waves is limited by the finite number of neural cells in a given region of the continuum. As wave growth saturates, the resulting activity patterns in space and time show a variety of forms, ranging from regular monochromatic waves to highly irregular mixtures of different spatial frequencies. The type of wave configuration is determined by a number of parameters, including alertness and synaptic conditioning as well as delay. For all cases studied, using numerical solution of the nonlinear Wilson-Cowan (1973) equations, there is an interval in delay in which the wave mixing occurs. As delay increases through this interval, during a series of consecutive waves propagating through a continuum region, the activity within that region changes from a single-frequency to a multiple-frequency pattern and back again. The diverse spatio-temporal patterns give a more concrete form to several metaphors advanced over the years to attempt an explanation of cognitive phenomena: Activity waves embody the "holographic memory" (Pribram, 1991); wave mixing provides a plausible cause of the competition called "neural Darwinism" (Edelman, 1988); finally the consecutive generation of growing neural waves can explain the discontinuousness of "psychological time" (Stroud, 1955).
Linear and nonlinear waves with orbital angular momentum in magnetized plasma
Ali, Shahid; Kant Shukla, Padma; Tito Mendonca, José.
2009-11-01
Here we discuss the concept of orbital angular momentum (OAM) for electromagnetic waves in a magnetized plasma. Nonlinear effects of photons with spin and OAM will be considered. In particular, we examine the case of parametric interactions between circularly polarized electromagnetic waves and Langmuir and ion acoustic waves, including the ponderomotive force of light with OAM in magnetized plasma (Shukla & Stenflo, PRA). This will be a generalization of recent results published in PRL by J.T. Mendonca and B. Thide. We also examine the influence of OAM on the magnetic field generation by the inverse Faraday effect.
Acoustic nonlinear periodic waves in pair-ion plasmas
Mahmood, Shahzad; Kaladze, Tamaz; Ur-Rehman, Hafeez
2013-09-01
Electrostatic acoustic nonlinear periodic (cnoidal) waves and solitons are investigated in unmagnetized pair-ion plasmas consisting of same mass and oppositely charged ion species with different temperatures. Using reductive perturbation method and appropriate boundary conditions, the Korteweg-de Vries (KdV) equation is derived. The analytical solutions of both cnoidal wave and soliton solutions are discussed in detail. The phase plane plots of cnoidal and soliton structures are shown. It is found that both compressive and rarefactive cnoidal wave and soliton structures are formed depending on the temperature ratio of positive and negative ions in pair-ion plasmas. In the special case, it is revealed that the amplitude of soliton may become larger than it is allowed by the nonlinear stationary wave theory which is equal to the quantum tunneling by particle through a potential barrier effect. The serious flaws in the earlier published results by Yadav et al., [PRE 52, 3045 (1995)] and Chawla and Misra [Phys. Plasmas 17, 102315 (2010)] of studying ion acoustic nonlinear periodic waves are also pointed out.
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.
A nonlinear analysis of the terahertz serpentine waveguide traveling-wave amplifier
International Nuclear Information System (INIS)
Li, Ke; Cao, Miaomiao; Liu, Wenxin; Wang, Yong
2015-01-01
A nonlinear model for the numerical simulation of terahertz serpentine waveguide traveling-wave tube (SW-TWT) is described. In this model, the electromagnetic wave transmission in the SW is represented as an infinite set of space harmonics to interact with an electron beam. Analytical expressions for axial electric fields in axisymmetric interaction gaps of SW-TWTs are derived and compared with the results from CST simulation. The continuous beam is treated as discrete macro-particles with different initial phases. The beam-tunnel field equations, space-charge field equations, and motion equations are combined to solve the beam-wave interaction. The influence of backward wave and relativistic effect is also considered in the series of equations. The nonlinear model is used to design a 340 GHz SW-TWT. Several favorable comparisons of model predictions with results from a 3-D Particle-in-cell simulation code CHIPIC are presented, in which the output power versus beam voltage and interaction periods are illustrated. The relative error of the predicted output power is less than 15% in the 3 dB bandwidth and the relative error of the saturated length is less than 8%.The results show that the 1-D nonlinear analysis model is appropriate to solve the terahertz SW-TWT operation characteristics
Causal properties of nonlinear gravitational waves in modified gravity
Suvorov, Arthur George; Melatos, Andrew
2017-09-01
Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial f (R ) gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial f (R ) gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient a2 of the Taylor expansion of f (R ) is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of a2. Anisotropic solutions are found, whose wave fronts trace out time- or spacelike hypersurfaces with complicated geometric properties. We show that the solutions exist in f (R ) theories that are consistent with Solar System and pulsar timing experiments.
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.
Wave-particle interaction and Hamiltonian dynamics investigated in a traveling wave tube
International Nuclear Information System (INIS)
Doveil, Fabrice; Macor, Alessandro
2006-01-01
For wave-particle interaction studies, the one-dimensional (1-D) beam-plasma system can be advantageously replaced by a Traveling Wave Tube (TWT). This led us to a detailed experimental analysis of the self-consistent interaction between unstable waves and a small either cold or warm beam. More recently, a test electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s). The velocity distribution function of the electron beam is investigated with a trochoidal energy analyzer that records the beam energy distribution at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The nonlinear synchronization of particles by a single wave responsible for Landau damping is observed. The resonant velocity domain associated to a single wave is also observed, as well as the transition to large-scale chaos when the resonant domains of two waves and their secondary resonances overlap leading to a typical 'devil's staircase' behavior. A new strategy for the control of chaos is tested
Interaction between electromagnetic waves and plasma waves in motional plasma
International Nuclear Information System (INIS)
Chen, S. Y.; Gao, M.; Tang, C. J.; Peng, X. D.
2009-01-01
The electromagnetic wave (EM wave) behavior and the electromagnetic instability caused by the interaction between an EM wave and a plasma wave in motional plasma are studied. The dispersion relation of EM waves and the dielectric tensor of motional plasma are derived by magnetohydrodynamics, and the wave phenomenon in motional plasma is displayed. As a result, the electromagnetic instability, which is excited by the interaction between the EM waves and the plasma waves, is revealed. The mechanism of the instability is the coupling between high frequency electromagnetic field and the transverse electron oscillation derived from the deflection of longitudinal electron oscillation due to self-magnetic field. The present research is useful with regard to the new type of plasma radiation source, ion-focusing accelerator, and plasma diagnostic technique.
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
A new type of surface acoustic waves in solids due to nonlinear elasticity
International Nuclear Information System (INIS)
Mozhaev, V.G.
1988-12-01
It is shown that in nonlinear elastic semi-infinite medium possessing a property of self focusing of shear waves, besides bulk non-linear shear waves, new surface acoustic waves exist, localization of which near the boundary is entirely due to nonlinear effects. (author). 8 refs
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.
Nonlinear interaction of powerful short electromagnetic pulses with an electron plasma
International Nuclear Information System (INIS)
Rao, N.N.; Yu, M.Y.; Shukla, P.K.
1990-01-01
The nonlinear interaction of powerful short electromagnetic pulses with a plasma consisting of two groups of electrons and immobile ions has been studied. It is shown that the interaction is governed by a nonlinear equation for the electromagnetic wave envelope and a driven nonlinear equation for the low-frequency electron fluctuations. The driver for the latter depends explicitly on the spatio-temporal evolution of the electromagnetic wave flux. It is found that, depending on the cold-to-hot electron density ratio, the localized pulse can propagate with sub- as well as supersonic velocities accompanied by compressional or rarefactional density perturbations. The conditions of existence for the different types of solitary pulses are obtained. The present investigation may be relevant to the study of wave-plasma interaction devices such as inertial fusion confinement as well as to ionospheric modification experiments. (author)
Two-tone nonlinear electrostatic waves in the quantum electron–hole plasma of semiconductors
Energy Technology Data Exchange (ETDEWEB)
Dubinov, A. E., E-mail: dubinov-ae@yandex.ru; Kitayev, I. N. [Russian Federal Nuclear Center–All-Russia Scientific and Research Institute of Experimental Physics (RFNC–VNIIEF) (Russian Federation)
2017-01-15
Longitudinal electrostatic waves in the quantum electron–hole plasma of semiconductors are considered taking into account the degeneracy of electrons and holes and the exchange interaction. It is found in the framework of linear theory that the dispersion curve of longitudinal waves has two branches: plasmon and acoustic. An expression for the critical cutoff frequency for plasma oscillations and an expression for the speed of sound for acoustic vibrations are derived. It is shown that the plasma wave always exists in the form of a superposition of two components, characterized by different periods and wavelengths. Two nonlinear solutions are obtained within nonlinear theory: one in the form of a simple superposition of two tones and the other in the form of beats.
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
Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves
International Nuclear Information System (INIS)
Webb, G. M.; Brio, M.; Zank, G. P.
1996-01-01
A formulation of Hamiltonian and Lagrangian variational principles, Lie point symmetries and conservation laws for the triple degenerate DNLS equations describing the propagation of weakly nonlinear dispersive MHD waves along the ambient magnetic field, in β∼1 plasmas is given. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic point, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a g 2 =V A 2 where a g is the gas sound speed and V A is the Alfven speed. A discussion is given of the travelling wave similarity solutions of the equations, which include solitary wave and periodic traveling waves. Strongly compressible solutions indicate the necessity for the insertion of shocks in the flow, whereas weakly compressible, near Alfvenic solutions resemble similar, shock free travelling wave solutions of the DNLS equation
A nonlinear wave equation in nonadiabatic flame propagation
International Nuclear Information System (INIS)
Booty, M.R.; Matalon, M.; Matkowsky, B.J.
1988-01-01
The authors derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time
Nonlinear dynamics and chaotic behaviour of spin wave instabilities
Energy Technology Data Exchange (ETDEWEB)
Rezende, S M; Aguiar, F.M. de.
1986-09-01
Recent experiments revealed that spin wave instabilities driven by microwave fields, either parallel or transverse to the static magnetic field, display chaotic dynamics similar to other physical systems. A theory based on the coupled nonlinear equations of motion for two spin wave modes is presented which explains most features of the experimental observations. The model predicts subharmonic routes to chaos that depend on the parameter values. For certain parameters the system exhibits a Feigenbaum scenario characteristic of one-dimensional maps. Other parameters lead to different subharmonic routes indicative of multidimensional behavior, as observed in some experiments.
Nonlinear electrostatic wave equations for magnetized plasmas - II
DEFF Research Database (Denmark)
Dysthe, K. B.; Mjølhus, E.; Pécseli, H. L.
1985-01-01
For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent (electrosta......For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent...... (electrostatic) cut-off implies that various cases must be considered separately, leading to equations with rather different properties. Various equations encountered previously in the literature are recovered as limiting cases....
Hidden regularity for a strongly nonlinear wave equation
International Nuclear Information System (INIS)
Rivera, J.E.M.
1988-08-01
The nonlinear wave equation u''-Δu+f(u)=v in Q=Ωx]0,T[;u(0)=u 0 ,u'(0)=u 1 in Ω; u(x,t)=0 on Σ= Γx]0,T[ where f is a continuous function satisfying, lim |s| sup →+∞ f(s)/s>-∞, and Ω is a bounded domain of R n with smooth boundary Γ, is analysed. It is shown that there exist a solution for the presented nonlinear wave equation that satisfies the regularity condition: |∂u/∂ η|ε L 2 (Σ). Moreover, it is shown that there exist a constant C>0 such that, |∂u/∂ η|≤c{ E(0)+|v| 2 Q }. (author) [pt
Propagation of Quasi-plane Nonlinear Waves in Tubes
P. Koníček; M. Bednařík; M. Červenka
2002-01-01
This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicabi...
Porous models for wave-seabed interactions
Energy Technology Data Exchange (ETDEWEB)
Jeng, Dong-Sheng [Shanghai Jiaotong Univ., SH (China)
2013-02-01
Detailed discussion about the phenomenon of wave-seabed interactions. Novel models for wave-induced seabed response. Intensive theoretical derivations for wave-seabed interactions. Practical examples for engineering applications. ''Porous Models for Wave-seabed Interactions'' discusses the Phenomenon of wave-seabed interactions, which is a vital issue for coastal and geotechnical engineers involved in the design of foundations for marine structures such as pipelines, breakwaters, platforms, etc. The most important sections of this book will be the fully detailed theoretical models of wave-seabed interaction problem, which are particularly useful for postgraduate students and junior researchers entering the discipline of marine geotechnics and offshore engineering. This book also converts the research outcomes of theoretical studies to engineering applications that will provide front-line engineers with practical and effective tools in the assessment of seabed instability in engineering design.
Nonlinear interactions of focused resonance cone fields with plasmas
International Nuclear Information System (INIS)
Stenzel, R.L.; Gekelman, W.
1977-01-01
A simple yet novel rf exciter structure has been developed for generating remotely intense rf fields in a magnetoplasma. It is a circular line source of radius R in a plane perpendicularB 0 driven with an rf signal at ω 0 E/sub rf/ 2 /nkT/sub e/>0.2, a strong density depression in the focal region (deltan/n>40%) is observed. The density perturbation modifies the cone angle and field distribution. This nonlinear interaction leads to a rapid growth of ion acoustic wave turbulence and a corresponding random rf field distribution in a broadened focal region. The development of the interaction is mapped in space and time
Nonlinear effects in Pulsations of Compact Stars and Gravitational Waves
International Nuclear Information System (INIS)
Passamonti, A
2007-01-01
Nonlinear stellar oscillations can be studied by using a multiparameter perturbative approach, which is appropriate for investigating the low and mild nonlinear dynamical regimes. We present the main properties of our perturbative framework for describing, in the time domain, the nonlinear coupling between the radial and nonradial perturbations of spherically symmetric and perfect fluid compact stars. This particular coupling can be described by gauge invariant quantities that obeys a system of partial differential equations with source terms, which are made up of product of first order radial and nonradial perturbations. We report the results of numerical simulations for both the axial and polar coupling perturbations, that exhibit in the stellar dynamics and in the associated gravitational wave signal some interesting nonlinear effects, such as combination harmonics and resonances. In particular, we concentrate on the axial case, where the linear axial perturbations describe a harmonic component of a differentially rotating neutron star. The gravitational wave signal of this stellar configuration mirrors at second perturbative order the spectral features of the linear radial normal modes. In addition, a signal amplification appears when one of the radial frequencies is close to the axial w-mode frequencies of the star
Nonlinear ultrasonic wave modulation for online fatigue crack detection
Sohn, Hoon; Lim, Hyung Jin; DeSimio, Martin P.; Brown, Kevin; Derriso, Mark
2014-02-01
This study presents a fatigue crack detection technique using nonlinear ultrasonic wave modulation. Ultrasonic waves at two distinctive driving frequencies are generated and corresponding ultrasonic responses are measured using permanently installed lead zirconate titanate (PZT) transducers with a potential for continuous monitoring. Here, the input signal at the lower driving frequency is often referred to as a 'pumping' signal, and the higher frequency input is referred to as a 'probing' signal. The presence of a system nonlinearity, such as a crack formation, can provide a mechanism for nonlinear wave modulation, and create spectral sidebands around the frequency of the probing signal. A signal processing technique combining linear response subtraction (LRS) and synchronous demodulation (SD) is developed specifically to extract the crack-induced spectral sidebands. The proposed crack detection method is successfully applied to identify actual fatigue cracks grown in metallic plate and complex fitting-lug specimens. Finally, the effect of pumping and probing frequencies on the amplitude of the first spectral sideband is investigated using the first sideband spectrogram (FSS) obtained by sweeping both pumping and probing signals over specified frequency ranges.
Quantum corrections to nonlinear ion acoustic wave with Landau damping
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, Abhik; Janaki, M. S. [Saha Institute of Nuclear Physics, Calcutta (India); Bose, Anirban [Serampore College, West Bengal (India)
2014-07-15
Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.
Energy Technology Data Exchange (ETDEWEB)
Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg [School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Zhou, Yu [Advanced Remanufacturing and Technology Center (ARTC), 3 Clean Tech Loop, CleanTech Two, Singapore 637143 (Singapore)
2016-07-15
Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonant frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.
Vorotnikov, K.; Starosvetsky, Y.
2018-01-01
The present study concerns two-dimensional nonlinear mechanisms of bidirectional and unidirectional channeling of longitudinal and shear waves emerging in the locally resonant acoustic structure. The system under consideration comprises an oscillatory chain of the axially coupled masses. Each mass of the chain is subject to the local linear potential along the lateral direction and incorporates the lightweight internal rotator. In the present work, we demonstrate the emergence of special resonant regimes of complete bi- and unidirectional transitions between the longitudinal and the shear waves of the locally resonant chain. These regimes are manifested by the two-dimensional energy channeling between the longitudinal and the shear traveling waves in the recurrent as well as the irreversible fashion. We show that the spatial control of the two dimensional energy flow between the longitudinal and the shear waves is solely governed by the motion of the internal rotators. Nonlinear analysis of the regimes of a bidirectional wave channeling unveils their global bifurcation structure and predicts the zones of their spontaneous transitions from a complete bi-directional wave channeling to the one-directional entrapment. An additional regime of a complete irreversible resonant transformation of the longitudinal wave into a shear wave is analyzed in the study. The intrinsic mechanism governing the unidirectional wave reorientation is described analytically. The results of the analysis of both mechanisms are substantiated by the numerical simulations of the full model and are found to be in a good agreement.
Kinematics of Nonlinearly Interacting MHD Instabilities in a Plasma
International Nuclear Information System (INIS)
Hansen, Alexander K.
2000-01-01
Plasmas play host to a wide variety of instabilities. For example, tearing instabilities use finite plasma resistivity to exploit the free energy provided by plasma currents parallel to the magnetic field to alter the magnetic topology of the plasma through a process known as reconnection. These instabilities frequently make themselves known in magnetic confinement experiments such as tokamaks and reversed field pinches (RFPs). In RFP plasmas, in fact, several tearing instabilities (modes) are simultaneously active, and are of large amplitude. Theory predicts that in addition to interacting linearly with magnetic perturbations from outside the plasma, such as field errors or as resistive wall, the modes in the RFP can interact nonlinearly with each other through a three-wave interaction. In the current work investigations of both the linear (external) and nonlinear contributions to the kinematics of the tearing modes in the Madison Symmetric Torus (MST) RFP are reported Theory predicts that tearing modes will respond only to magnetic perturbations that are spatially resonant with them, and was supported by experimental work done on tokamak devices. The results in this work verified that the theory is still applicable to the RFP, in spite of its more complicated magnetic mode structure, involving perturbations of a single poloidal mode number
Nonlinear ion-acoustic waves and solitons in a magnetized plasma
International Nuclear Information System (INIS)
Lee, L.C.; Kan, J.R.
1981-01-01
A unified formulation is presented to study the nonlinear low-frequency electrostatic waves in a magnetized low-β plasma. It is found that there exist three types of nonlinear waves; (1) nonlinear ion-cyclotron periodic waves with a wave speed V/sub p/ > C/sub s/ (ion-acoustic velocity); (2) nonlinear ion-acoustic periodic waves with V/sub p/ < C/sub s/ costheta; and (3) ion-acoustic solitons with C/sub s/ costheta < V/sub p/ < C/sub s/, where theta is the angle between the wave vector and the magnetic field
Waves reflected by solid wall and wave interaction in vapour bubbly liquids
International Nuclear Information System (INIS)
Duong, N.H.; Nguyen, V.T.
2004-01-01
The vapour bubbly liquids are met in many natural and industrial processes, including in energy equipment. In the nuclear power plants this kind of medium appears in reactor cores (PWR, BWR and etc.), in turbine generators and in heat transfer loops. Due to some circumstances (for example, a hit caused by detonations or strong collisions) the pressure waves can appear in the bubbly liquid medium contained in those facilities. These waves propagate in the mixtures and interact with themselves and with structures. It is important that what will occur during mentioned above processes. The knowledge of this kind processes will be useful for analysing the different sorts of the processes occurred in the energy facilities where the vapor bubbly liquids are used as working or heat transfer medium, like nuclear power plants, and also useful in finding the measures for prevention of unfavourable phenomena (for example, during wave interactions maybe appear too high pressures, which could lead into damages of facilities and etc.) and safety operating the equipment. From the physical point of view, the waves in this kind of medium are interesting that owing to non-linear, dispersion and dissipation effects the wave patterns in them may be diverse and easy altered. In the paper the investigation results of the waves reflected by solid wall or structure of the moderate intensity shock waves, and the behaviour of pressure in the process of wave interaction in some mixtures of liquid with vapour bubbles (of radium ∼1 mm) are presented. (author)
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
International Nuclear Information System (INIS)
Kong, Ling-Bao; Wang, Hong-Yu; Hou, Zhi-Ling; Jin, Hai-Bo; Du, Chao-Hai
2013-01-01
The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained
Energy Technology Data Exchange (ETDEWEB)
Kong, Ling-Bao, E-mail: konglingbao@gmail.com [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 (China); Wang, Hong-Yu [School of Physics, Anshan Normal University, Anshan 114005 (China); Hou, Zhi-Ling, E-mail: houzl@mail.buct.edu.cn [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 (China); Jin, Hai-Bo [School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081 (China); Du, Chao-Hai [Institute of Electronics, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained.
International Nuclear Information System (INIS)
Wang, Xin; Chen, Yong; Cao, Jianli
2015-01-01
In this paper, we utilize generalized Darboux transformation to study higher-order rogue wave solutions of the three-wave resonant interaction equation, which describes the propagation and mixing of waves with different frequencies in weakly nonlinear dispersive media. A general Nth-order rogue wave solution with two characteristic velocities structural parameters and 3N independent parameters under a determined plane-wave background and a specific parameter condition is derived. As an application, we show that four fundamental rogue waves with fundamental, two kinds of line and quadrilateral patterns, or six fundamental rogue waves with fundamental, triangular, two kinds of quadrilateral and circular patterns can emerge in the second-order rogue waves. Moreover, several important wave characteristics including the maximum values, the corresponding coordinate positions of the humps, and the stability problem for some special higher-order rogue wave solutions such as the fundamental and quadrilateral cases are discussed. (paper)
Energy Technology Data Exchange (ETDEWEB)
Raphaldini, Breno; Raupp, Carlos F. M., E-mail: brenorfs@gmail.com, E-mail: carlos.raupp@iag.usp.br [Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Departamento de Geofísica, Rua do Matão, 1226-Cidade Universitária São Paulo-SP 05508-090 (Brazil)
2015-01-20
The solar dynamo is known to be associated with several periodicities, with the nearly 11/22 yr cycle being the most pronounced one. Even though these quasiperiodic variations of solar activity have been attributed to the underlying dynamo action in the Sun's interior, a fundamental theoretical description of these cycles is still elusive. Here, we present a new possible direction in understanding the Sun's cycles based on resonant nonlinear interactions among magnetohydrodynamic (MHD) Rossby waves. The WKB theory for dispersive waves is applied to magnetohydrodynamic shallow-water equations describing the dynamics of the solar tachocline, and the reduced dynamics of a resonant triad composed of MHD Rossby waves embedded in constant toroidal magnetic field is analyzed. In the conservative case, the wave amplitudes evolve periodically in time, with periods on the order of the dominant solar activity timescale (∼11 yr). In addition, the presence of linear forcings representative of either convection or instabilities of meridionally varying background states appears to be crucial in balancing dissipation and thus sustaining the periodic oscillations of wave amplitudes associated with resonant triad interactions. Examination of the linear theory of MHD Rossby waves embedded in a latitudinally varying mean flow demonstrates that MHD Rossby waves propagate toward the equator in a waveguide from –35° to 35° in latitude, showing a remarkable resemblance to the structure of the butterfly diagram of the solar activity. Therefore, we argue that resonant nonlinear magnetohydrodynamic Rossby wave interactions might significantly contribute to the observed cycles of magnetic solar activity.
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
Identification and determination of solitary wave structures in nonlinear wave propagation
International Nuclear Information System (INIS)
Newman, W.I.; Campbell, D.K.; Hyman, J.M.
1991-01-01
Nonlinear wave phenomena are characterized by the appearance of ''solitary wave coherent structures'' traveling at speeds determined by their amplitudes and morphologies. Assuming that these structures are briefly noninteracting, we propose a method for the identification of the number of independent features and their respective speeds. Using data generated from an exact two-soliton solution to the Korteweg-de-Vries equation, we test the method and discuss its strengths and limitations. 41 refs., 2 figs
Nonlinear time-dependent simulation of helix traveling wave tubes
International Nuclear Information System (INIS)
Peng Wei-Feng; Yang Zhong-Hai; Hu Yu-Lu; Li Jian-Qing; Lu Qi-Ru; Li Bin
2011-01-01
A one-dimensional nonlinear time-dependent theory for helix traveling wave tubes is studied. A generalized electromagnetic field is applied to the expression of the radio frequency field. To simulate the variations of the high frequency structure, such as the pitch taper and the effect of harmonics, the spatial average over a wavelength is substituted by a time average over a wave period in the equation of the radio frequency field. Under this assumption, the space charge field of the electron beam can be treated by a space charge wave model along with the space charge coefficient. The effects of the radio frequency and the space charge fields on the electrons are presented by the equations of the electron energy and the electron phase. The time-dependent simulation is compared with the frequency-domain simulation for a helix TWT, which validates the availability of this theory. (interdisciplinary physics and related areas of science and technology)
Dynamics of nonlinear waves in the tubes filled with aerosol
Directory of Open Access Journals (Sweden)
Gubaidullin Damir
2018-01-01
Full Text Available The results of experimental investigations of nonlinear oscillations of finely dispersed aerosol in the tube with various geometry on the end in the shock-wave, the shock-free wave modes and in the mode of transition to shock waves near the resonance frequency are presented. The time dependences of the numerical concentration of the oscillating aerosol droplets are presented. The effect of the frequency and amplitude of the piston displacement and the influence of the diaphragm internal diameter on the time coagulation and sedimentation of aerosol were studied. An increase in the amplitude of the piston displacement in all modes results in acceleration of the process of coagulation and sedimentation of aerosol. The dependence of time of coagulation and sedimentation of aerosol on the excitation frequency was found to be of a nonmonotonic character with the minimum value upon the resonance frequency.
Nonlinear electromagnetic waves in a degenerate electron-positron plasma
Energy Technology Data Exchange (ETDEWEB)
El-Labany, S.K., E-mail: skellabany@hotmail.com [Department of Physics, Faculty of Science, Damietta University, New Damietta (Egypt); El-Taibany, W.F., E-mail: eltaibany@hotmail.com [Department of Physics, College of Science for Girls in Abha, King Khalid University, Abha (Saudi Arabia); El-Samahy, A.E.; Hafez, A.M.; Atteya, A., E-mail: ahmedsamahy@yahoo.com, E-mail: am.hafez@sci.alex.edu.eg, E-mail: ahmed_ateya2002@yahoo.com [Department of Physics, Faculty of Science, Alexandria University, Alexandria (Egypt)
2015-08-15
Using the reductive perturbation technique (RPT), the nonlinear propagation of magnetosonic solitary waves in an ultracold, degenerate (extremely dense) electron-positron (EP) plasma (containing ultracold, degenerate electron, and positron fluids) is investigated. The set of basic equations is reduced to a Korteweg-de Vries (KdV) equation for the lowest-order perturbed magnetic field and to a KdV type equation for the higher-order perturbed magnetic field. The solutions of these evolution equations are obtained. For better accuracy and searching on new features, the new solutions are analyzed numerically based on compact objects (white dwarf) parameters. It is found that including the higher-order corrections results as a reduction (increment) of the fast (slow) electromagnetic wave amplitude but the wave width is increased in both cases. The ranges where the RPT can describe adequately the total magnetic field including different conditions are discussed. (author)
Nonlinear acoustic waves in partially ionized collisional plasmas
International Nuclear Information System (INIS)
Rao, N.N.; Kaup, D.J.; Shukla, P.K.
1991-01-01
Nonlinear propagation of acoustic-type waves in a partially ionized three-component collisional plasma consisting of electrons, ions and neutral particles is investigated. For bidirectional propagation, it is shown that the small- but finite-amplitude waves are governed by the Boussinesq equation, which for unidirectional propagation near the acoustic speed reduces to the usual Korteweg-de Vries equation. For large-amplitude waves, it is demonstrated that the relevant fluid equations are integrable in a stationary frame, and the parameter values for the existence of finite-amplitude solutions are explicitly obtained. In both cases, the different temperatures of the individual species, are taken into account. The relevance of the results to the earth's ionospheric plasma in the lower altitude ranges is pointed out. (author)
Current structure of strongly nonlinear interfacial solitary waves
Semin, Sergey; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim; Churaev, Egor
2015-04-01
The characteristics of highly nonlinear solitary internal waves (solitons) in two-layer flow are computed within the fully nonlinear Navier-Stokes equations with use of numerical model of the Massachusetts Institute of Technology (MITgcm). The verification and adaptation of the model is based on the data from laboratory experiments [Carr & Davies, 2006]. The present paper also compares the results of our calculations with the computations performed in the framework of the fully nonlinear Bergen Ocean Model [Thiem et al, 2011]. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the interface and near the bottom are computed. The results demonstrated completely different trajectories at different depths of the model area. Thus, in the surface layer is observed the largest displacement of Lagrangian particles, which can be more than two and a half times larger than the characteristic width of the soliton. Located at the initial moment along the middle pycnocline fluid particles move along the elongated vertical loop at a distance of not more than one third of the width of the solitary wave. In the bottom layer of the fluid moves in the opposite direction of propagation of the internal wave, but under the influence of the reverse flow, when the bulk of the velocity field of the soliton ceases to influence the trajectory, it moves in the opposite direction. The magnitude of displacement of fluid particles in the bottom layer is not more than the half-width of the solitary wave. 1. Carr, M., and Davies, P.A. The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Phys. Fluids, 2006, vol. 18, No. 1, 1 - 10. 2. Thiem, O., Carr
Study on concentration nonlinearity of interacting acoustic flows in cadmium sulfide and tellurium
International Nuclear Information System (INIS)
Ilisavskij, Yu.V.; Kulakova, L.A.; Yakhkind, Eh.Z.
1976-01-01
The ratio of an one-mode (self-action of an external monochromatic sound wave) and a many-mode (interaction of an external wave with crystal thermal phonons) concentration nonlinearity has been experimentally investigated on sound amplification in cadmium sulphide and tellurium. It has been shown that in a strong piezoelectric the main part in the nonlinear limitation of the sound amplification in a drift field is played by the wave interaction, i.e., the transfer of the sound wave energy into the crystal sound modes starts before the nonlinear self-action of a wave. In Te characterized by a large value of the electromechanical coupling constant value at the sound frequency of about 250 MHz the threshold of many-mode nonlinearity is achieved in fields much below the critical one, and corresponds to the sound intensity as low as 10 -7 W/cm 2 , as compared with 10 -2 W/cm 2 -the threshold of the one-mode nonlinearity
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)
Propagation of nonlinear waves over submerged step: wave separation and subharmonic generation
Monsalve, Eduardo; Maurel, Agnes; Pagneux, Vincent; Petitjeans, Philippe
2015-11-01
Water waves can be described in simplified cases by the Helmholtz equation. However, even in these cases, they present a high complexity, among which their dispersive character and their nonlinearities are the subject of the present study. Using Fourier Transform Profilometry, we study experimentally the propagation of waves passing over a submerged step. Because of the small water depth after the step, the wave enters in a nonlinear regime. In the shallow water region, the second harmonic leads to two types of waves: bound waves which are slaves of the fundamental frequency with wavenumber 2 k (ω) , and free waves which propagate according to the usual dispersion relation with wavenumber k (2 ω) . Because of the presence of these two waves, beats are produced at the second harmonic with characteristic beat length. In this work, for the first time we extended this analysis to the third and higher harmonics. Next, the region after the step is limited to a finite size L with a reflecting wall. For certain frequencies and L- values, the spectral component becomes involved, with the appearance of sub harmonics. This regime is analyzed in more details, suggesting a transition to a chaotic and quasi-periodic wave behavior.
Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface
Energy Technology Data Exchange (ETDEWEB)
Kim, No Hyu; Yang, Seung Yong [Korea University of Technology and Education, Cheonan (Korea, Republic of)
2007-12-15
Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness
Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface
International Nuclear Information System (INIS)
Kim, No Hyu; Yang, Seung Yong
2007-01-01
Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness
Wave-particle Interactions in Space and Laboratory Plasmas
An, Xin
are trapped by the large amplitude Langmuir wave and are accelerated to the beam energy level in the parallel direction. The excitation of whistler waves through Landau resonance is limited by the saturation of Langmuir waves, due to a faster depletion rate of the beam free energy from ∂fb/∂v ∥> 0 by the latter compare to the former. The second part of the thesis considers the interaction between electromagnetic ion cyclotron (EMIC) waves and relativistic electrons. Nonlinear interactions between them are investigated in a two-wave oscillator model. Three interaction regimes are identified depending on the separation of the two wave numbers. Both the decoupled and degenerate regimes are characterized by phase bunching, in which the resonant electrons are scattered preferentially to one direction rather than diffusively. In the coupled regime, resonant electrons experience alternate trapping and de-trapping near the separatrix, from which stochastic motion of electrons arises. For a continuous spectrum of EMIC waves, test particle simulations are compared against quasi-linear diffusion theory (QLT) description of the wave-particle interactions. QLT gives similar results as test particle simulations for the small amplitude and broadband waves, whereas it fails for large amplitude and narrowband waves. By varying the wave spectral width and wave intensity systematically, a regime map is constructed to indicate the applicability of QLT in the wave parameter space.
Barashkov, M. S.; Bel'Diugin, I. M.; Zolotarev, M. V.; Kruzhilin, Iu. I.; Krymskii, M. I.
1989-04-01
A four-wave mirror with thermal nonlinearity has been experimentally realized with the interaction of corunning waves under parametric feedback with a nonreciprocal element. The effective reflection of a sequence of pulses with duration of about 300 ns from a neodymium-glass laser with maximal reflection coefficients greater than 30 has been demonstrated. The quality of the radiation reflected from the mirror is studied. A significant reduction in the steady-state lasing threshold has been shown with thermal nonlinearity at small angles of the interacting beam convergence, compared to the case of counterrunning convergence.
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.
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.
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.
Relativistic harmonic content of nonlinear electromagnetic waves in underdense plasmas
International Nuclear Information System (INIS)
Mori, W.B.; Decker, C.D.; Leemans, W.P.
1993-01-01
The relativistic harmonic content of large amplitude electromagnetic waves propagating in underdense plasmas is investigated. The steady state harmonic content of nonlinear linearly polarized waves is calculated for both the very underdense (w p /w o ) much-lt 1 and critical density (w p /w o ) ≅ 1 limits. For weak nonlinearities, eE o /mcw o p /w o . Arguments are given for extending these results for arbitrary wave amplitudes. The authors also show that the use of the variable x-ct and the quasi-static approximation leads to errors in both magnitude and sign when calculating the third harmonic. In the absence of damping or density gradients the third harmonic's amplitude is found to oscillate between zero and twice the steady state value. Preliminary PIC simulation results are presented. The simulation results are in basic agreement with the uniform plasma predictions for the third harmonic amplitude. However, the higher harmonics are orders of magnitude larger than expected and the presence of density ramps significantly modifies the results
Phase velocity of nonlinear plasma waves in the laser beat-wave accelerator
International Nuclear Information System (INIS)
Spence, W.L.
1985-01-01
The suggested plasma-laser accelerator is an attempt to achieve a very high energy gradient by resonantly exciting a longitudinal wave traveling at close to the speed of light in cold plasma by means of the beat-wave generated by the transverse fields in two laser beams. Previous calculations to all orders in v/sub z/ have been done essentially from the laboratory frame point of view and have treated the plasma wave as having sharply defined phase velocity equal to the speed of light. However a high energy particle beam undergoing acceleration sees the plasma wave from a nearly light-like frame of reference and hence is very sensitive to small deviations in its phase velocity. Here the authors introduce a calculational scheme that includes all orders in v/sub z/ and in the plasma density, and additionally takes into account the influence of plasma nonlinearities on the wave's phase velocity. The main assumption is that the laser frequencies are very large compared to the plasma frequency - under which they are able to in essence formally sum up all orders of forward Raman scattering. They find that the nonlinear plasma wave does not have simply a single phase velocity - it is really a superposition of many - but that the beat-wave which drives it is usefully described by a non-local effective phase velocity function
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 Electron Acoustic Waves in Dissipative Plasma with Superthermal Electrons
El-Hanbaly, A. M.; El-Shewy, E. K.; Kassem, A. I.; Darweesh, H. F.
2016-01-01
The nonlinear properties of small amplitude electron-acoustic ( EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and superthermal hot electrons obeying superthermal distribution, and stationary ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili-Burgers (KP-Brugers) equation. Some solutions of physical interest are obtained. These solutions are related to soliton, monotonic and oscillatory shock waves and their behaviour are shown graphically. The formation of these solutions depends crucially on the value of the Burgers term and the plasma parameters as well. By using the tangent hyperbolic (tanh) method, another interesting type of solution which is a combination between shock and soliton waves is obtained. The topology of phase portrait and potential diagram of the KP-Brugers equation is investigated.The advantage of using this method is that one can predict different classes of the travelling wave solutions according to different phase orbits. The obtained results may be helpful in better understanding of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.
Nonlinear wave-mixing processes in the extreme ultraviolet
International Nuclear Information System (INIS)
Misoguti, L.; Christov, I. P.; Backus, S.; Murnane, M. M.; Kapteyn, H. C.
2005-01-01
We present data from two-color high-order harmonic generation in a hollow waveguide, that suggest the presence of a nonlinear-optical frequency conversion process driven by extreme ultraviolet light. By combining the fundamental and second harmonic of an 800 nm laser in a hollow-core fiber, with varying relative polarizations, and by observing the pressure and power scaling of the various harmonic orders, we show that the data are consistent with a picture where we drive the process of high-harmonic generation, which in turn drives four-wave frequency mixing processes in the extreme EUV. This work promises a method for extending nonlinear optics into the extreme ultraviolet region of the spectrum using an approach that has not previously been considered, and has compelling implications for generating tunable light at short wavelengths
Nonlinear attenuation of S-waves and Love waves within ambient rock
Sleep, Norman H.; Erickson, Brittany A.
2014-04-01
obtain scaling relationships for nonlinear attenuation of S-waves and Love waves within sedimentary basins to assist numerical modeling. These relationships constrain the past peak ground velocity (PGV) of strong 3-4 s Love waves from San Andreas events within Greater Los Angeles, as well as the maximum PGV of future waves that can propagate without strong nonlinear attenuation. During each event, the shaking episode cracks the stiff, shallow rock. Over multiple events, this repeated damage in the upper few hundred meters leads to self-organization of the shear modulus. Dynamic strain is PGV divided by phase velocity, and dynamic stress is strain times the shear modulus. The frictional yield stress is proportional to depth times the effective coefficient of friction. At the eventual quasi-steady self-organized state, the shear modulus increases linearly with depth allowing inference of past typical PGV where rock over the damaged depth range barely reaches frictional failure. Still greater future PGV would cause frictional failure throughout the damaged zone, nonlinearly attenuating the wave. Assuming self-organization has taken place, estimated maximum past PGV within Greater Los Angeles Basins is 0.4-2.6 m s-1. The upper part of this range includes regions of accumulating sediments with low S-wave velocity that may have not yet compacted, rather than having been damaged by strong shaking. Published numerical models indicate that strong Love waves from the San Andreas Fault pass through Whittier Narrows. Within this corridor, deep drawdown of the water table from its currently shallow and preindustrial levels would nearly double PGV of Love waves reaching Downtown Los Angeles.
Interaction-induced effects in the nonlinear coherent response of quantum-well excitons
DEFF Research Database (Denmark)
Wagner, Hans Peter; Schätz, A.; Langbein, Wolfgang Werner
1999-01-01
Interaction-induced processes are studied using the third-order nonlinear polarization created in polarization-dependent four-wave-mixing experiments (FWM) on a ZnSe single quantum well. We discuss their influence by a comparison of the experimental FWM with calculations based on extended optical...
Khushaini, Muhammad Asif A.; Ibrahim, Abdel-Baset M. A.; Choudhury, P. K.
2018-05-01
In this paper, we provide a complete mathematical model of the phenomenon of optical bistability (OB) resulting from the degenerate two-wave mixing (TWM) process of laser beams interacting with a single nonlinear layer of ferroelectric material. Starting with the electromagnetic wave equation for optical wave propagating in nonlinear media, a nonlinear coupled wave (CW) system with both self-phase modulation (SPM) and cross-phase modulation (XPM) sources of nonlinearity are derived. The complete CW system with full nonlinearity is solved numerically and a comparison between both the cases of with and without SPM at various combinations of design parameters is given. Furthermore, to provide a reliable theoretical model for the OB via TWM process, the results obtained theoretically are compared with the available experimental data. We found that the nonlinear system without SPM fails to predict the bistable response at lower combinations of the input parameters. However, at relatively higher values, the solution without SPM shows a reduction in the switching contrast and period in the OB response. A comparison with the experimental results shows better agreement with the system with full nonlinearity.
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.
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)
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
The Impact of Dam-Reservoir-Foundation Interaction on Nonlinear Response of Concrete Gravity Dams
International Nuclear Information System (INIS)
Amini, Ali Reza; Motamedi, Mohammad Hossein; Ghaemian, Mohsen
2008-01-01
To study the impact of dam-reservoir-foundation interaction on nonlinear response of concrete gravity dams, a two-dimensional finite element model of a concrete gravity dam including the dam body, a part of its foundation and a part of the reservoir was made. In addition, the proper boundary conditions were used in both reservoir and foundation in order to absorb the energy of outgoing waves at the far end boundaries. Using the finite element method and smeared crack approach, some different seismic nonlinear analyses were done and finally, we came to a conclusion that the consideration of dam-reservoir-foundation interaction in nonlinear analysis of concrete dams is of great importance, because from the performance point of view, this interaction significantly improves the nonlinear response of concrete dams
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.
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 propagation in discrete and continuous systems
Rothos, V. M.
2016-09-01
In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.
Nonlinear optical interactions in silicon waveguides
Directory of Open Access Journals (Sweden)
Kuyken B.
2017-03-01
Full Text Available The strong nonlinear response of silicon photonic nanowire waveguides allows for the integration of nonlinear optical functions on a chip. However, the detrimental nonlinear optical absorption in silicon at telecom wavelengths limits the efficiency of many such experiments. In this review, several approaches are proposed and demonstrated to overcome this fundamental issue. By using the proposed methods, we demonstrate amongst others supercontinuum generation, frequency comb generation, a parametric optical amplifier, and a parametric optical oscillator.
Conservative numerical methods for solitary wave interactions
Energy Technology Data Exchange (ETDEWEB)
Duran, A; Lopez-Marcos, M A [Departamento de Matematica Aplicada y Computacion, Facultad de Ciencias, Universidad de Valladolid, Paseo del Prado de la Magdalena s/n, 47005 Valladolid (Spain)
2003-07-18
The purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation. It is shown that the so-called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision.
International Nuclear Information System (INIS)
Omura, Yoshiharu; Matsumoto, Hiroshi.
1989-01-01
Past theoretical and numerical studies of the nonlinear evolution of electromagnetic cyclotron waves are reviewed. Such waves are commonly observed in space plasmas such as Alfven waves in the solar wind or VLF whistler mode waves in the magnetosphere. The use of an electromagnetic full-particle code to study an electron cyclotron wave and of an electromagnetic hybrid code to study an ion cyclotron wave is demonstrated. Recent achievements in the simulations of nonlinear revolution of electromagnetic cyclotron waves are discussed. The inverse cascading processes of finite-amplitude whistler and Alfven waves is interpreted in terms of physical elementary processes. 65 refs
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.
Multi-fluid Approach to High-frequency Waves in Plasmas. III. Nonlinear Regime and Plasma Heating
Martínez-Gómez, David; Soler, Roberto; Terradas, Jaume
2018-03-01
The multi-fluid modeling of high-frequency waves in partially ionized plasmas has shown that the behavior of magnetohydrodynamic waves in the linear regime is heavily influenced by the collisional interaction between the different species that form the plasma. Here, we go beyond linear theory and study large-amplitude waves in partially ionized plasmas using a nonlinear multi-fluid code. It is known that in fully ionized plasmas, nonlinear Alfvén waves generate density and pressure perturbations. Those nonlinear effects are more pronounced for standing oscillations than for propagating waves. By means of numerical simulations and analytical approximations, we examine how the collisional interaction between ions and neutrals affects the nonlinear evolution. The friction due to collisions dissipates a fraction of the wave energy, which is transformed into heat and consequently raises the temperature of the plasma. As an application, we investigate frictional heating in a plasma with physical conditions akin to those in a quiescent solar prominence.
Nonlinear interaction of photons and phonons in electron-positron plasmas
International Nuclear Information System (INIS)
Tajima, T.; Taniuti, T.
1990-03-01
Nonlinear interaction of electromagnetic waves and acoustic modes in an electron-positron plasma is investigated. The plasma of electrons and positrons is quite plastic so that the imposition of electromagnetic (EM) waves causes depression of the plasma and other structural imprints on it through either the nonresonant or resonant interaction. Our theory shows that the nonresonant interaction can lead to the coalescence of photons and collapse of plasma cavity in higher (≥ 2) dimensions. The resonant interaction, in which the group velocity of EM waves is equal to the phase velocity of acoustic waves, is analyzed and a set of basic equations of the system is derived via the reductive perturbation theory. We find new solutions of solitary types: bright solitons, kink solitons, and dark solitons as the solutions to these equations. Our computation hints their stability. An impact of the present theory on astrophysical plasma settings is expected, including the cosmological relativistically hot electron-positron plasma. 20 refs., 9 figs
Wave propagation in a strongly nonlinear locally resonant granular crystal
Vorotnikov, K.; Starosvetsky, Y.; Theocharis, G.; Kevrekidis, P. G.
2018-02-01
In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degradation of the well-known traveling pulse of the standard Hertzian chain of elastic beads. Nevertheless, the present system is richer, in that as the primary pulse decays, secondary ones emerge and eventually interfere with it creating modulated wavetrains. Remarkably, upon suitable choices of parameters, this interference "distills" a weakly nonlocal solitary wave (a "nanopteron"). This motivates the consideration of such nonlinear structures through a separate Fourier space technique, whose results suggest the existence of such entities not only with a single-side tail, but also with periodic tails on both ends. These tails are found to oscillate with the intrinsic oscillation frequency of the out-of-phase motion between the outer hollow bead and its internal linear attachment.
Shen, Yanfeng; Cesnik, Carlos E. S.
2016-04-01
This paper presents a parallelized modeling technique for the efficient simulation of nonlinear ultrasonics introduced by the wave interaction with fatigue cracks. The elastodynamic wave equations with contact effects are formulated using an explicit Local Interaction Simulation Approach (LISA). The LISA formulation is extended to capture the contact-impact phenomena during the wave damage interaction based on the penalty method. A Coulomb friction model is integrated into the computation procedure to capture the stick-slip contact shear motion. The LISA procedure is coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized supercomputing on powerful graphic cards. Both the explicit contact formulation and the parallel feature facilitates LISA's superb computational efficiency over the conventional finite element method (FEM). The theoretical formulations based on the penalty method is introduced and a guideline for the proper choice of the contact stiffness is given. The convergence behavior of the solution under various contact stiffness values is examined. A numerical benchmark problem is used to investigate the new LISA formulation and results are compared with a conventional contact finite element solution. Various nonlinear ultrasonic phenomena are successfully captured using this contact LISA formulation, including the generation of nonlinear higher harmonic responses. Nonlinear mode conversion of guided waves at fatigue cracks is also studied.
Resonant interaction of photons with gravitational waves
International Nuclear Information System (INIS)
Mendonca, J.T.; Drury, L. O'C.
2002-01-01
The interaction of photons with a low-amplitude gravitational wave propagating in a flat space-time is studied by using an exact model of photon dynamics. The existence of nearly resonant interactions between the photons and the gravitational waves, which can take place over large distances, can lead to a strong photon acceleration. Such a resonant mechanism can eventually be useful to build consistent new models of gamma-ray emitters
Computational study of nonlinear plasma waves. I. Simulation model and monochromatic wave propagtion
International Nuclear Information System (INIS)
Matda, Y.; Crawford, F.W.
1974-12-01
An economical low noise plasma simulation model is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation, to establish the low noise features and to verify the theoretical linear dispersion relation at wave energy levels as low as 0.000,001 of the plasma thermal energy. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories. The additional phenomena of sideband instability and satellite growth, stimulated by large amplitude wave propagation and the resulting particle trapping, are described. (auth)
Shock wave interaction with turbulence: Pseudospectral simulations
International Nuclear Information System (INIS)
Buckingham, A.C.
1986-01-01
Shock waves amplify pre-existing turbulence. Shock tube and shock wave boundary layer interaction experiments provide qualitative confirmation. However, shock pressure, temperature, and rapid transit complicate direct measurement. Computational simulations supplement the experimental data base and help isolate the mechanisms responsible. Simulations and experiments, particularly under reflected shock wave conditions, significantly influence material mixing. In these pseudospectral Navier-Stokes simulations the shock wave is treated as either a moving (tracked or fitted) domain boundary. The simulations assist development of code mix models. Shock Mach number and pre-existing turbulence intensity initially emerge as key parameters. 20 refs., 8 figs
Acoustic multipath arrivals in the horizontal plane due to approaching nonlinear internal waves.
Badiey, Mohsen; Katsnelson, Boris G; Lin, Ying-Tsong; Lynch, James F
2011-04-01
Simultaneous measurements of acoustic wave transmissions and a nonlinear internal wave packet approaching an along-shelf acoustic path during the Shallow Water 2006 experiment are reported. The incoming internal wave packet acts as a moving frontal layer reflecting (or refracting) sound in the horizontal plane. Received acoustic signals are filtered into acoustic normal mode arrivals. It is shown that a horizontal multipath interference is produced. This has previously been called a horizontal Lloyd's mirror. The interference between the direct path and the refracted path depends on the mode number and frequency of the acoustic signal. A mechanism for the multipath interference is shown. Preliminary modeling results of this dynamic interaction using vertical modes and horizontal parabolic equation models are in good agreement with the observed data.
Wave propagation in a bounded plasma with striction nonlinearity taken into account
International Nuclear Information System (INIS)
Brazhnik, V.A.; Grishaev, V.I.; Demchenko, V.V.; Pavlov, S.S.; Panchenko, V.I.; AN Ukrainskoj SSR, Kharkov. Fiziko-Tekhnicheskij Inst. Nizkikh Temperatur)
1981-01-01
Electromagnetic wave propagation in plasma is analyzed with striction nonlinearity taken into account. The reflection of a circularly polarized wave falling on a layer of homogeneous magnetoactive plasma is analytically investigated under conditions of linear skinning. The large amplitude TE-type wave propagation along the layer of isotropic plasma is numerically determined. It is shown that the distribution of the electric field amplitude essentially differs from the one predicted from the linear theory. Some periodic distributions across the layer become possible, in particular numerical modelling makes it possible to study the evolution of solitons generated by a monochromatic pump field in an inhomogeneous plasma layer bounded by ideally conducting surfaces. It is shown that generated solitons interact with those reflected from the boundary without any change of their form [ru
Nonlinear saturation of wave packets excited by low-energy electron horseshoe distributions.
Krafft, C; Volokitin, A
2013-05-01
Horseshoe distributions are shell-like particle distributions that can arise in space and laboratory plasmas when particle beams propagate into increasing magnetic fields. The present paper studies the stability and the dynamics of wave packets interacting resonantly with electrons presenting low-energy horseshoe or shell-type velocity distributions in a magnetized plasma. The linear instability growth rates are determined as a function of the ratio of the plasma to the cyclotron frequencies, of the velocity and the opening angle of the horseshoe, and of the relative thickness of the shell. The nonlinear stage of the instability is investigated numerically using a symplectic code based on a three-dimensional Hamiltonian model. Simulation results show that the dynamics of the system is mainly governed by wave-particle interactions at Landau and normal cyclotron resonances and that the high-order normal cyclotron resonances play an essential role. Specific features of the dynamics of particles interacting simultaneously with two or more waves at resonances of different natures and orders are discussed, showing that such complex processes determine the main characteristics of the wave spectrum's evolution. Simulations with wave packets presenting quasicontinuous spectra provide a full picture of the relaxation of the horseshoe distribution, revealing two main phases of the evolution: an initial stage of wave energy growth, characterized by a fast filling of the shell, and a second phase of slow damping of the wave energy, accompanied by final adjustments of the electron distribution. The influence of the density inhomogeneity along the horseshoe on the wave-particle dynamics is also discussed.
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.
Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order
International Nuclear Information System (INIS)
Feng Qing-Hua; Zhang Yao-Ming; Meng Fan-Wei
2011-01-01
In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin—Bona—Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method. (general)
Raju, Thokala Soloman; Pal, Ritu
2018-05-01
We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.
Wave-current interaction in Willapa Bay
Olabarrieta, Maitane; Warner, John C.; Kumar, Nirnimesh
2011-01-01
This paper describes the importance of wave-current interaction in an inlet-estuary system. The three-dimensional, fully coupled, Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) modeling system was applied in Willapa Bay (Washington State) from 22 to 29 October 1998 that included a large storm event. To represent the interaction between waves and currents, the vortex-force method was used. Model results were compared with water elevations, currents, and wave measurements obtained by the U.S. Army Corp of Engineers. In general, a good agreement between field data and computed results was achieved, although some discrepancies were also observed in regard to wave peak directions in the most upstream station. Several numerical experiments that considered different forcing terms were run in order to identify the effects of each wind, tide, and wave-current interaction process. Comparison of the horizontal momentum balances results identified that wave-breaking-induced acceleration is one of the leading terms in the inlet area. The enhancement of the apparent bed roughness caused by waves also affected the values and distribution of the bottom shear stress. The pressure gradient showed significant changes with respect to the pure tidal case. During storm conditions the momentum balance in the inlet shares the characteristics of tidal-dominated and wave-dominated surf zone environments. The changes in the momentum balance caused by waves were manifested both in water level and current variations. The most relevant effect on hydrodynamics was a wave-induced setup in the inner part of the estuary.
Ulku, Huseyin Arda
2015-02-01
An explicit marching on-in-time (MOT) based time domain electric field volume integral equation (TDVIE) solver for characterizing electromagnetic wave interactions on scatterers with nonlinear material properties is proposed. Discretization of the unknown electric field intensity and flux density is carried out by half and full Schaubert-Wilton-Glisson basis functions, respectively. Coupled system of spatially discretized TDVIE and the nonlinear constitutive relation between the field intensity and the flux density is integrated in time to compute the samples of the unknowns. An explicit PE(CE)m scheme is used for this purpose. Explicitness allows for \\'easy\\' incorporation of the nonlinearity as a function only to be evaluated on the right hand side of the coupled system of equations. A numerical example that demonstrates the applicability of the proposed MOT scheme to analyzing electromagnetic interactions on Kerr-nonlinear scatterers is presented. © 2015 IEEE.
Cnoidal waves as solutions of the nonlinear liquid drop model
International Nuclear Information System (INIS)
Ludu, Andrei; Sandulescu, Aureliu; Greiner Walter
1997-01-01
By introducing in the hydrodynamic model, i.e. in the hydrodynamic equation and the corresponding boundary conditions, the higher order terms in the deviation of the shape, we obtain in the second order the Korteweg de Vries equations (KdV). The same equation is obtained by introducing in the liquid drop model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms in the second order. The KdV equation has the cnoidal waves as steady-state solutions. These waves could describe the small anharmonic vibrations of spherical nuclei up to the solitary waves. The solitons could describe the preformation of clusters on the nuclear surface. We apply this nonlinear liquid drop model to the alpha formation in heavy nuclei. We find an additional minimum in the total energy of such systems, corresponding to the solitons as clusters on the nuclear surface. By introducing the shell effects we choose this minimum to be degenerated with the ground state. The spectroscopic factor is given by ratio of the square amplitudes in the two minima. (authors)
Directory of Open Access Journals (Sweden)
Y. Nariyuki
2006-01-01
Full Text Available Nonlinear relations among frequencies and phases in modulational instability of circularly polarized Alfvén waves are discussed, within the context of one dimensional, dissipation-less, unforced fluid system. We show that generation of phase coherence is a natural consequence of the modulational instability of Alfvén waves. Furthermore, we quantitatively evaluate intensity of wave-wave interaction by using bi-coherence, and also by computing energy flow among wave modes, and demonstrate that the energy flow is directly related to the phase coherence generation. We first discuss the modulational instability within the derivative nonlinear Schrödinger (DNLS equation, which is a subset of the Hall-MHD system including the right- and left-hand polarized, nearly degenerate quasi-parallel Alfvén waves. The dominant nonlinear process within this model is the four wave interaction, in which a quartet of waves in resonance can exchange energy. By numerically time integrating the DNLS equation with periodic boundary conditions, and by evaluating relative phase among the quartet of waves, we show that the phase coherence is generated when the waves exchange energy among the quartet of waves. As a result, coherent structures (solitons appear in the real space, while in the phase space of the wave frequency and the wave number, the wave power is seen to be distributed around a straight line. The slope of the line corresponds to the propagation speed of the coherent structures. Numerical time integration of the Hall-MHD system with periodic boundary conditions reveals that, wave power of transverse modes and that of longitudinal modes are aligned with a single straight line in the dispersion relation phase space, suggesting that efficient exchange of energy among transverse and longitudinal wave modes is realized in the Hall-MHD. Generation of the longitudinal wave modes violates the assumptions employed in deriving the DNLS such as the quasi
Low-order models of wave interactions in the transition to baroclinic chaos
Directory of Open Access Journals (Sweden)
W.-G. Früh
1996-01-01
Full Text Available A hierarchy of low-order models, based on the quasi-geostrophic two-layer model, is used to investigate complex multi-mode flows. The different models were used to study distinct types of nonlinear interactions, namely wave- wave interactions through resonant triads, and zonal flow-wave interactions. The coupling strength of individual triads is estimated using a phase locking probability density function. The flow of primary interest is a strongly modulated amplitude vacillation, whose modulation is coupled to intermittent bursts of weaker wave modes. This flow was found to emerge in a discontinuous bifurcation directly from a steady wave solution. Two mechanism were found to result in this flow, one involving resonant triads, and the other involving zonal flow-wave interactions together with a strong β-effect. The results will be compared with recent laboratory experiments of multi-mode baroclinic waves in a rotating annulus of fluid subjected to a horizontal temperature gradient.
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
Interaction of High Intensity Electromagnetic Waves with Plasmas: Final Report
International Nuclear Information System (INIS)
Shvets, G.
2008-01-01
The focus of our work during the duration of this grant was on the following areas: (a) the fundamental plasma physics of intense laser-plasma interactions, including the nonlinear excitation of plasma waves for accelerator applications, as well as the recently discovered by us phenomenon of the relativistic bi-stability of relativistic plasma waves driven by a laser beatwave; (b) interaction of high power microwave beams with magnetized plasma, including some of the recently discovered by us phenomena such as the Undulator Induced Transparency (UIT) as well as the new approaches to dynamic manipulation of microwave pulses; (c) investigations of the multi-color laser pulse interactions in the plasma, including the recently discovered by us phenomenon of Electromagnetic Cascading (EC) and the effect of the EC of three-dimensional dynamics of laser pulses (enhanced/suppressed selffocusing etc.); (d) interaction of high-current electron beams with the ambient plasma in the context of Fast Ignitor (FI) physics, with the emphasis on the nonlinear dynamics of the Weibel instability and beam filamentation.
Theory for stationary nonlinear wave propagation in complex magnetic geometry
International Nuclear Information System (INIS)
Watanabe, T.; Hojo, H.; Nishikawa, Kyoji.
1977-08-01
We present our recent efforts to derive a systematic calculation scheme for nonlinear wave propagation in the self-consistent plasma profile in complex magnetic-field geometry. Basic assumptions and/or approximations are i) use of the collisionless two-fluid model with an equation of state; ii) restriction to a steady state propagation and iii) existence of modified magnetic surface, modification due to Coriolis' force. We discuss four situations: i) weak-field propagation without static flow, ii) arbitrary field strength with flow in axisymmetric system, iii) weak field limit of case ii) and iv) arbitrary field strength in nonaxisymmetric torus. Except for case iii), we derive a simple variation principle, similar to that of Seligar and Whitham, by introducing appropriate coordinates. In cases i) and iii), we derive explicit results for quasilinear profile modification. (auth.)
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.
International Nuclear Information System (INIS)
Matsuda, Y.; Crawford, F.W.
1975-01-01
An economical low-noise plasma simulation model originated by Denavit is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation. These tests serve to establish the low-noise features of the model, and to verify the theoretical linear dispersion relation at wave energy levels as low as 10 -6 of the plasma thermal energy: Better quantitative results are obtained, for comparable computing time, than can be obtained by conventional particle simulation models, or direct solution of the Vlasov equation. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories
Nonlinear mechanisms for drift wave saturation and induced particle transport
International Nuclear Information System (INIS)
Dimits, A.M.; Lee, W.W.
1989-12-01
A detailed theoretical study of the nonlinear dynamics of gyrokinetic particle simulations of electrostatic collisionless and weakly collisional drift waves is presented. In previous studies it was shown that, in the nonlinearly saturated phase of the evolution, the saturation levels and especially the particle fluxes have an unexpected dependence on collisionality. In this paper, the explanations for these collisionality dependences are found to be as follows: The saturation level is determined by a balance between the electron and ion fluxes. The ion flux is small for levels of the potential below an E x B-trapping threshold and increases sharply once this threshold is crossed. Due to the presence of resonant electrons, the electron flux has a much smoother dependence on the potential. In the 2-1/2-dimensional (''pseudo-3D'') geometry, the electrons are accelerated away from the resonance as they diffuse spatially, resulting in an inhibition of their diffusion. Collisions and three-dimensional effects can repopulate the resonance thereby increasing the value of the particle flux. 30 refs., 32 figs., 2 tabs
Effect of bottom slope on the nonlinear triad interactions in shallow water
Chen, Hongzhou; Tang, Xiaocheng; Zhang, Ri; Gao, Junliang
2018-05-01
This paper aims at investigating the effect of bottom slope to the nonlinear triad interactions for irregular waves propagating in shallow water. The physical experiments are conducted in a wave flume with respect to the transformation of waves propagating on three bottom slopes ( β = 1/15, 1/30, and 1/45). Irregular waves with different type of breaking that are mechanically generated based on JONSWAP spectra are used for the test. The obviously different variations of spectra measured on each bottom reveal a crucial role of slope effect in the energy transfer between harmonics. The wavelet-based bispectrum were used to examine the bottom slope effect on the nonlinear triad interactions. Results show that the different bottom slopes which waves are propagated on will cause a significant discrepancy of triad interactions. Then, the discussions on the summed bicoherence which denote the distribution of phase coupling on each frequency further clarify the effect of bottom slope. Furthermore, the summed of the real and imaginary parts of bispectrum which could reflect the intensity of frequency components participating in the wave skewness and asymmetry were also investigated. Results indicate that the value of these parameters will increase as the bottom slope gets steeper.
Anomalous transport of magnetized electrons interacting with EC waves
Energy Technology Data Exchange (ETDEWEB)
Tsironis, C; Vlahos, L [Section of Astrophysics, Astronomy and Mechanics, Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki (Greece)
2005-01-01
We consider the nonlinear interaction of magnetized electrons with an oblique narrow-band electromagnetic wave-packet. The interaction is analysed over and near the local threshold to chaos. The statistical character of the forcing that controls the trajectories of the particles is also studied. We focus our analysis on issues related to energy and spatial diffusion across the magnetic field by following the evolution of the ensemble mean squares (({gamma} - {gamma}{sub 0}){sup 2}) and ((r{sub perpendicular}-r{sub perpendicular0}){sup 2}) for various values of the wave amplitude and angle of wave propagation. We study, in particular, the interaction of magnetized electrons with waves having strong and moderate amplitudes, near the transition to chaos, where the dynamics is complex and a mixture of periodic and stochastic orbits coexist. The electron diffusions in real and energy spaces are found to obey simple power laws in time, and the scaling exponents are indicative of sub-diffusion. This is a direct consequence of the effect of the resonant phase-space islands in the particle motion.
The interaction of katabatic winds and mountain waves
Energy Technology Data Exchange (ETDEWEB)
Poulos, Gregory Steve [Colorado State Univ., Fort Collins, CO (United States)
1997-01-01
The variation in the oft-observed, thermally-forced, nocturnal katabatic winds along the east side of the Rocky Mountains can be explained by either internal variability or interactions with various other forcings. Though generally katabatic flows have been studied as an entity protected from external forcing by strong thermal stratification, this work investigates how drainage winds along the Colorado Front Range interact with, in particular, topographically forced mountain waves. Previous work has shown, based on measurements taken during the Atmospheric Studies in Complex Terrain 1993 field program, that the actual dispersion in katabatic flows is often greater than reflected in models of dispersion. The interaction of these phenomena is complicated and non-linear since the amplitude, wavelength and vertical structure of mountain waves developed by flow over the Rocky Mountain barrier are themselves partly determined by the evolving atmospheric stability in which the drainage flows develop. Perturbations to katabatic flow by mountain waves, relative to their more steady form in quiescent conditions, are found to be caused by both turbulence and dynamic pressure effects. The effect of turbulent interaction is to create changes to katabatic now depth, katabatic flow speed, katabatic jet height and, vertical thermal stratification. The pressure effect is found to primarily influence the variability of a given katabatic now through the evolution of integrated column wave forcing on surface pressure. Variability is found to occur on two scales, on the mesoscale due to meso-gamma scale mountain wave evolution, and on the microscale, due to wave breaking. Since existing parameterizations for the statically stable case are predominantly based on nearly flat terrain atmospheric measurements under idealized or nearly quiescent conditions, it is no surprise that these parameterizations often contribute to errors in prediction, particularly in complex terrain.
WAVE: Interactive Wave-based Sound Propagation for Virtual Environments.
Mehra, Ravish; Rungta, Atul; Golas, Abhinav; Ming Lin; Manocha, Dinesh
2015-04-01
We present an interactive wave-based sound propagation system that generates accurate, realistic sound in virtual environments for dynamic (moving) sources and listeners. We propose a novel algorithm to accurately solve the wave equation for dynamic sources and listeners using a combination of precomputation techniques and GPU-based runtime evaluation. Our system can handle large environments typically used in VR applications, compute spatial sound corresponding to listener's motion (including head tracking) and handle both omnidirectional and directional sources, all at interactive rates. As compared to prior wave-based techniques applied to large scenes with moving sources, we observe significant improvement in runtime memory. The overall sound-propagation and rendering system has been integrated with the Half-Life 2 game engine, Oculus-Rift head-mounted display, and the Xbox game controller to enable users to experience high-quality acoustic effects (e.g., amplification, diffraction low-passing, high-order scattering) and spatial audio, based on their interactions in the VR application. We provide the results of preliminary user evaluations, conducted to study the impact of wave-based acoustic effects and spatial audio on users' navigation performance in virtual environments.
An efficient flexible-order model for 3D nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bingham, Harry B.; Lindberg, Ole
2009-01-01
The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal......, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental...
Wave-particle interactions in rotating mirrorsa)
Fetterman, Abraham J.; Fisch, Nathaniel J.
2011-05-01
Wave-particle interactions in E ×B rotating plasmas feature an unusual effect: particles are diffused by waves in both potential energy and kinetic energy. This wave-particle interaction generalizes the alpha channeling effect, in which radio frequency waves are used to remove alpha particles collisionlessly at low energy. In rotating plasmas, the alpha particles may be removed at low energy through the loss cone, and the energy lost may be transferred to the radial electric field. This eliminates the need for electrodes in the mirror throat, which have presented serious technical issues in past rotating plasma devices. A particularly simple way to achieve this effect is to use a high azimuthal mode number perturbation on the magnetic field. Rotation can also be sustained by waves in plasmas without a kinetic energy source. This type of wave has been considered for plasma centrifuges used for isotope separation. Energy may also be transferred from the electric field to particles or waves, which may be useful for ion heating and energy generation.
Wave-particle Interactions In Rotating Mirrors
Energy Technology Data Exchange (ETDEWEB)
Abraham J. Fetterman and Nathaniel J. Fisch
2011-01-11
Wave-particle interactions in E×B rotating plasmas feature an unusual effect: particles are diffused by waves in both potential energy and kinetic energy. This wave-particle interaction generalizes the alpha channeling effect, in which radio frequency waves are used to remove alpha particles collisionlessly at low energy. In rotating plasmas, the alpha particles may be removed at low energy through the loss cone, and the energy lost may be transferred to the radial electric field. This eliminates the need for electrodes in the mirror throat, which have presented serious technical issues in past rotating plasma devices. A particularly simple way to achieve this effect is to use a high azimuthal mode number perturbation on the magnetic field. Rotation can also be sustained by waves in plasmas without a kinetic energy source. This type of wave has been considered for plasma centrifuges used for isotope separation. Energy may also be transferred from the electric field to particles or waves, which may be useful for ion heating and energy generation.
Wave-particle interactions in rotating mirrors
International Nuclear Information System (INIS)
Fetterman, Abraham J.; Fisch, Nathaniel J.
2011-01-01
Wave-particle interactions in ExB rotating plasmas feature an unusual effect: particles are diffused by waves in both potential energy and kinetic energy. This wave-particle interaction generalizes the alpha channeling effect, in which radio frequency waves are used to remove alpha particles collisionlessly at low energy. In rotating plasmas, the alpha particles may be removed at low energy through the loss cone, and the energy lost may be transferred to the radial electric field. This eliminates the need for electrodes in the mirror throat, which have presented serious technical issues in past rotating plasma devices. A particularly simple way to achieve this effect is to use a high azimuthal mode number perturbation on the magnetic field. Rotation can also be sustained by waves in plasmas without a kinetic energy source. This type of wave has been considered for plasma centrifuges used for isotope separation. Energy may also be transferred from the electric field to particles or waves, which may be useful for ion heating and energy generation.
Wave-particle Interactions In Rotating Mirrors
International Nuclear Information System (INIS)
Fetterman, Abraham J.; Fisch, Nathaniel J.
2011-01-01
Wave-particle interactions in E-B rotating plasmas feature an unusual effect: particles are diffused by waves in both potential energy and kinetic energy. This wave-particle interaction generalizes the alpha channeling effect, in which radio frequency waves are used to remove alpha particles collisionlessly at low energy. In rotating plasmas, the alpha particles may be removed at low energy through the loss cone, and the energy lost may be transferred to the radial electric field. This eliminates the need for electrodes in the mirror throat, which have presented serious technical issues in past rotating plasma devices. A particularly simple way to achieve this effect is to use a high azimuthal mode number perturbation on the magnetic field. Rotation can also be sustained by waves in plasmas without a kinetic energy source. This type of wave has been considered for plasma centrifuges used for isotope separation. Energy may also be transferred from the electric field to particles or waves, which may be useful for ion heating and energy generation.
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
Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei
2016-07-01
Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.
Excitation of nonlinear wave patterns in flowing complex plasmas
Jaiswal, S.; Bandyopadhyay, P.; Sen, A.
2018-01-01
We describe experimental observations of nonlinear wave structures excited by a supersonic mass flow of dust particles over an electrostatic potential hill in a dusty plasma medium. The experiments have been carried out in a Π- shaped experimental (DPEx) device in which micron sized Kaolin particles are embedded in a DC glow discharge Argon plasma. An equilibrium dust cloud is formed by maintaining the pumping speed and gas flow rate and the dust flow is induced either by suddenly reducing the height of a potential hill or by suddenly reducing the gas flow rate. For a supersonic flow of the dust fluid precursor solitons are seen to propagate in the upstream direction while wake structures propagate in the downstream direction. For flow speeds with a Mach number greater than 2 the dust particles flowing over the potential hill give rise to dispersive dust acoustic shock waves. The experimental results compare favorably with model theories based on forced K-dV and K-dV Burger's equations.
Workshop on wave-ice interaction
Wadhams, Peter; Squire, Vernon; Rottier, Philip; Liu, Antony; Dugan, John; Czipott, Peter; Shen, Hayley
The subject of wave-ice interaction has been advanced in recent years by small groups of researchers working on a similar range of topics in widely separated geographic locations. Their recent studies inspired a workshop on wave-ice interaction held at the Scott Polar Research Institute, University of Cambridge, England, December 16-18, 1991, where theories in all aspects of the physics of wave-ice interaction were compared.Conveners of the workshop hoped that plans for future observational and theoretical work dealing with outstanding issues in a collaborative way would emerge. The workshop, organized by the Commission on Sea Ice of the International Association for Physical Sciences of the Ocean (IAPSO), was co-chaired by Vernon Squire, professor of mathematics and statistics at the University of Otago, New Zealand, and Peter Wadhams, director of the Scott Polar Research Institute. Participants attended from Britain, Finland, New Zealand, Norway, and the United States.
One-dimensional nonlinear theory for rectangular helix traveling-wave tube
Energy Technology Data Exchange (ETDEWEB)
Fu, Chengfang, E-mail: fchffchf@126.com; Zhao, Bo; Yang, Yudong; Ju, Yongfeng [Faculty of Electronic Information Engineering, Huaiyin Institute of Technology, Huai' an 223003 (China); Wei, Yanyu [School of Physical Electronics, University of Electronic and Technology of China, Chengdu 610054 (China)
2016-08-15
A 1-D nonlinear theory of a rectangular helix traveling-wave tube (TWT) interacting with a ribbon beam is presented in this paper. The RF field is modeled by a transmission line equivalent circuit, the ribbon beam is divided into a sequence of thin rectangular electron discs with the same cross section as the beam, and the charges are assumed to be uniformly distributed over these discs. Then a method of computing the space-charge field by solving Green's Function in the Cartesian Coordinate-system is fully described. Nonlinear partial differential equations for field amplitudes and Lorentz force equations for particles are solved numerically using the fourth-order Runge-Kutta technique. The tube's gain, output power, and efficiency of the above TWT are computed. The results show that increasing the cross section of the ribbon beam will improve a rectangular helix TWT's efficiency and reduce the saturated length.
Achieving nonlinear optical modulation via four-wave mixing in a four-level atomic system
Li, Hai-Chao; Ge, Guo-Qin; Zubairy, M. Suhail
2018-05-01
We propose an accessible scheme for implementing tunable nonlinear optical amplification and attenuation via a synergetic mechanism of four-wave mixing (FWM) and optical interference in a four-level ladder-type atomic system. By constructing a cyclic atom-field interaction, we show that two reverse FWM processes can coexist via optical transitions in different branches. In the suitable input-field conditions, strong interference effects between the input fields and the generated FWM fields can be induced and result in large amplification and deep attenuation of the output fields. Moreover, such an optical modulation from enhancement to suppression can be controlled by tuning the relative phase. The quantum system can be served as a switchable optical modulator with potential applications in quantum nonlinear optics.
Controllable behaviours of rogue wave triplets in the nonautonomous nonlinear and dispersive system
International Nuclear Information System (INIS)
Dai Chaoqing; Tian Qing; Zhu Shiqun
2012-01-01
A similarity transformation connecting the variable coefficient nonlinear Schrödinger equation with the standard nonlinear Schrödinger equation is constructed. The self-similar rogue wave triplet solutions (rational solutions) are analytically obtained for the nonautonomous nonlinear and dispersive system. The controllable behaviours of rogue wave triplets in two typical soliton management systems are discussed. In the exponential dispersion decreasing fibre, three kinds of rogue wave triplets with controllable behaviours are analysed. In the periodic distributed system, the rogue wave triplets recur periodically in the form of a cluster. (paper)
Energy Technology Data Exchange (ETDEWEB)
Ruderman, M S
1988-08-01
Nonlinear Alfven surface wave propagation at a magnetic interface in a compressible fluid is considered. It is supposed that the magnetic field directions at both sides of the interface and the direction of wave propagation coincide. The equation governing time-evolution of nonlinear small-amplitude waves is derived by the method of multiscale expansions. This equation is similar to the equation for nonlinear Alfven surface waves in an incompressible fluid derived previously. The numerical solution of the equation shows that a sinusoidal disturbance overturns, i.e. infinite gradients arise.
International Nuclear Information System (INIS)
Coffey, M.W.
1996-01-01
Due to their short coherence lengths and relatively large energy gaps, the high-transition temperature superconductors are very likely candidates as ultraclean materials at low temperature. This class of materials features significantly modified vortex dynamics, with very little dissipation at low temperature. The motion is then dominated by wave propagation, being in general nonlinear. Here two-dimensional vortex motion is investigated in the ultraclean regime for a superconductor described in cylindrical geometry. The small-amplitude limit is assumed, and the focus is on the long-wavelength limit. Results for both zero and nonzero Hall force are presented, with the effects of nonlocal vortex interaction and vortex inertia being included within London theory. Linear and nonlinear problems are studied, with a predisposition toward the more analytically tractable situations. For a nonlinear problem in 2+1 dimensions, the cylindrical Kadomtsev-Petviashvili equation is derived. Hall angle measurements on high-T c superconductors indicate the need to investigate the properties of such a completely integrable wave equation. copyright 1996 The American Physical Society
On the interaction of deep water waves and exponential shear currents
Cheng, Jun; Cang, Jie; Liao, Shi-Jun
2009-05-01
A train of periodic deep-water waves propagating on a steady shear current with a vertical distribution of vorticity is investigated by an analytic method, namely the homotopy analysis method (HAM). The magnitude of the vorticity varies exponentially with the magnitude of the stream function, while remaining constant on a particular streamline. The so-called Dubreil-Jacotin transformation is used to transfer the original exponentially nonlinear boundary-value problem in an unknown domain into an algebraically nonlinear boundary-value problem in a known domain. Convergent series solutions are obtained not only for small amplitude water waves on a weak current but also for large amplitude waves on a strong current. The nonlinear wave-current interaction is studied in detail. It is found that an aiding shear current tends to enlarge the wave phase speed, sharpen the wave crest, but shorten the maximum wave height, while an opposing shear current has the opposite effect. Besides, the amplitude of waves and fluid velocity decay over the depth more quickly on an aiding shear current but more slowly on an opposing shear current than that of waves on still water. Furthermore, it is found that Stokes criteria of wave breaking is still valid for waves on a shear current: a train of propagating waves on a shear current breaks as the fiuid velocity at crest equals the wave phase speed. Especially, it is found that the highest waves on an opposing shear current are even higher and steeper than that of waves on still water. Mathematically, this analytic method is rather general in principle and can be employed to solve many types of nonlinear partial differential equations with variable coefficients in science, finance and engineering.
Interactions between finite amplitude small and medium-scale waves in the MLT region.
Heale, C. J.; Snively, J. B.
2016-12-01
Small-scale gravity waves can propagate high into the thermosphere and deposit significant momentum and energy into the background flow [e.g., Yamada et al., 2001, Fritts et al., 2014]. However, their propagation, dissipation, and spectral evolution can be significantly altered by other waves and dynamics and the nature of these complex interactions are not yet well understood. While many ray-tracing and time-dependent modeling studies have been performed to investigate interactions between waves of varying scales [e.g., Eckermann and Marks .1996, Sartelet. 2003, Liu et al. 2008, Vanderhoff et al., 2008, Senf and Achatz., 2011, Heale et al., 2015], the majority of these have considered waves of larger (tidal) scales, or have simplified one of the waves to be an imposed "background" and discount (or limit) the nonlinear feedback mechanisms between the two waves. In reality, both waves will influence each other, especially at finite amplitudes when nonlinear effects become important or dominant. We present a study of fully nonlinear interactions between small-scale 10s km, 10 min period) and medium-scale wave packets at finite amplitudes, which include feedback between the two waves and the ambient atmosphere. Time-dependence of the larger-scale wave has been identified as an important factor in reducing reflection [Heale et al., 2015] and critical level effects [Sartelet, 2003, Senf and Achatz, 2011], we choose medium-scale waves of different periods, and thus vertical scales, to investigate how this influences the propagation, filtering, and momentum and energy deposition of the small-scale waves, and in turn how these impacts affect the medium-scale waves. We also consider the observable features of these interactions in the mesosphere and lower thermosphere.
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 role of nonlinear self-interaction in the dynamics of planetary-scale atmospheric fluctuations
International Nuclear Information System (INIS)
Saffioti, C; Malguzzi, P; Speranza, A
2016-01-01
A central role in the general circulation of the atmosphere is played by planetary-scale inertial fluctuations with zonal wavenumber in the range k = 1–4. Geopotential variance in this range is markedly non-gaussian and a great fraction of it is non-propagating, in contrast with the normal distribution of amplitudes and the basically propagating character of fluctuations in the baroclinic range (3 < k < 15). While a wave dispersion relationship can be identified in the baroclinic range, no clear relationship between time and space scales emerges in the ultra-long regime ( k < 5, period >10 days). We investigate the hypothesis that nonlinear self-interaction of planetary waves influences the mobility (and, therefore, the dispersion) of ultra-long planetary fluctuations. By means of a perturbation expansion of the barotropic vorticity equation we derive a minimal analytic description of the impact of self-nonlinearity on mobility and we show that this is responsible for a correction term to phase speed, with the prevalent effect of slowing down the propagation of waves. The intensity of nonlinear self-interaction is shown to increase with the complexity of the flow, depending on both its zonal and meridional modulations. Reanalysis data of geopotential height and zonal wind are analysed in order to test the effect of self-nonlinearity on observed planetary flows. (paper)
Wallen, Samuel P.
Granular media are one of the most common, yet least understood forms of matter on earth. The difficulties in understanding the physics of granular media stem from the fact that they are typically heterogeneous and highly disordered, and the grains interact via nonlinear contact forces. Historically, one approach to reducing these complexities and gaining new insight has been the study of granular crystals, which are ordered arrays of similarly-shaped particles (typically spheres) in Hertzian contact. Using this setting, past works explored the rich nonlinear dynamics stemming from contact forces, and proposed avenues where such granular crystals could form designer, dynamically responsive materials, which yield beneficial functionality in dynamic regimes. In recent years, the combination of self-assembly fabrication methods and laser ultrasonic experimental characterization have enabled the study of granular crystals at microscale. While our intuition may suggest that these microscale granular crystals are simply scaled-down versions of their macroscale counterparts, in fact, the relevant physics change drastically; for example, short-range adhesive forces between particles, which are negligible at macroscale, are several orders of magnitude stronger than gravity at microscale. In this thesis, we present recent advances in analytical and computational modeling of microscale granular crystals, in particular concerning the interplay of nonlinearity, shear interactions, and particle rotations, which have previously been either absent, or included separately at macroscale. Drawing inspiration from past works on phononic crystals and nonlinear lattices, we explore problems involving locally-resonant metamaterials, nonlinear localized modes, amplitude-dependent energy partition, and other rich dynamical phenomena. This work enhances our understanding of microscale granular media, which may find applicability in fields such as ultrasonic wave tailoring, signal processing
Experimental investigation of shock wave - bubble interaction
Energy Technology Data Exchange (ETDEWEB)
Alizadeh, Mohsen
2010-04-09
In this work, the dynamics of laser-generated single cavitation bubbles exposed to lithotripter shock waves has been investigated experimentally. The energy of the impinging shock wave is varied in several steps. High-speed photography and pressure field measurements simultaneously with image acquisition provide the possibility of capturing the fast bubble dynamics under the effect of the shock wave impact. The pressure measurement is performed using a fiber optic probe hydrophone (FOPH) which operates based on optical diagnostics of the shock wave propagating medium. After a short introduction in chapter 1 an overview of the previous studies in chapter 2 is presented. The reported literatures include theoretical and experimental investigations of several configurations of physical problems in the field of bubble dynamics. In chapter 3 a theoretical description of propagation of a shock wave in a liquid like water has been discussed. Different kinds of reflection of a shock wave at an interface are taken into account. Undisturbed bubble dynamics as well as interaction between a planar shock wave and an initially spherical bubble are explored theoretically. Some physical parameters which are important in this issue such as the velocity of the shock-induced liquid jet, Kelvin impulse and kinetic energy are explained. The shock waves are generated in a water filled container by a focusing piezoelectric generator. The shock wave profile has a positive part with pulse duration of ∼1 μs followed by a longer tension tail (i.e. ∼3 μs). In chapter 4 high-speed images depict the propagation of a shock wave in the water filled tank. The maximum pressure is also derived for different intensity levels of the shock wave generator. The measurement is performed in the free field (i.e. in the absence of laser-generated single bubbles). In chapter 5 the interaction between lithotripter shock waves and laserinduced single cavitation bubbles is investigated experimentally. An
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.
Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Sun Chengfeng; Gao Hongjun
2009-01-01
The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.
Effect of weak nonlinearities on the plane waves in a plasma stream
International Nuclear Information System (INIS)
Seshadri, S.R.
1976-01-01
The effect of weak nonlinearities on the monochromatic plane waves in a cold infinite plasma stream is investigated for the case in which the waves are progressing parallel to the drift velocity. The fast and the slow space-charge waves undergo amplitude-dependent frequency and wave number shifts. There is a long time slow modulation of the amplitude of the electromagnetic mode which becomes unstable to this nonlinear wave modulation. The importance of using the relativistically correct equation of motion for predicting correctly the modulational stability of the electromagnetic mode is pointed out. (author)
Creep Damage Evaluation of Titanium Alloy Using Nonlinear Ultrasonic Lamb Waves
International Nuclear Information System (INIS)
Xiang Yan-Xun; Xuan Fu-Zhen; Deng Ming-Xi; Chen Hu; Chen Ding-Yue
2012-01-01
The creep damage in high temperature resistant titanium alloys Ti60 is measured using the nonlinear effect of an ultrasonic Lamb wave. The results show that the normalised acoustic nonlinearity of a Lamb wave exhibits a variation of the 'increase-decrease' tendency as a function of the creep damage. The influence of microstructure evolution on the nonlinear Lamb wave propagation has been analyzed based on metallographic studies, which reveal that the normalised acoustic nonlinearity increases due to a rising of the precipitation volume fraction and the dislocation density in the early stage, and it decreases as a combined result of dislocation change and micro-void initiation in the material. The nonlinear Lamb wave exhibits the potential for the assessment of the remaining creep life in metals
The propagation of nonlinear rayleigh waves in layered elastic half-space
International Nuclear Information System (INIS)
Ahmetolan, S.
2004-01-01
In this work, the propagation of small but finite amplitude generalized Rayleigh waves in an elastic half-space covered by a different elastic layer of uniform and finite thickness is considered. The constituent materials are assumed to be homogeneous, isotropic, compressible hyperelastic. Excluding the harmonic resonance phenomena, it is shown that the nonlinear self modulation of generalized Rayleigh waves is governed asymptotically by a nonlinear Schrodinger (NLS) equation. The stability of the solutions and the existence of solitary wave-type solutions a NLS are strongly depend on the sign of the product of the coefficients of the nonlinear and dipersion terms of the equation.Therefore the analysis continues with the examination of dependence of these coefficients on the nonlinear material parameters. Three different models have been considered which are nonlinear layer-nonlinear half space, linear layer-nonlinear half space and nonlinear layer-linear half space. The behavior of the coefficients of the NLS equation was also analyzed the limit as h(thickness of the layer) goes to zero and k(the wave number) is constant. Then conclusions are drawn about the effect of nonlinear material parameters on the wave modulation. In the numerical investigations both hypothetical and real material models are used
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...
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.
Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma.
El-Shamy, E F
2015-03-01
The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.
Relativistic effects on large amplitude nonlinear Langmuir waves in a two-fluid plasma
International Nuclear Information System (INIS)
Nejoh, Yasunori
1994-07-01
Large amplitude relativistic nonlinear Langmuir waves are analyzed by the pseudo-potential method. The existence conditions for nonlinear Langmuir waves are confirmed by considering relativistic high-speed electrons in a two-fluid plasma. The significant feature of this investigation is that the propagation of nonlinear Langmuir waves depends on the ratio of the electron streaming velocity to the velocity of light, the normalized potential and the ion mass to electron mass ratio. The constant energy is determined by the specific range of the relativistic effect. In the non-relativistic limit, large amplitude relativistic Langmuir waves do not exist. The present investigation predicts new findings of large amplitude nonlinear Langmuir waves in space plasma phenomena in which relativistic electrons are important. (author)
Physical dynamics of quasi-particles in nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Christov, Ivan [Department of Mathematics, Texas A and M University, College Station, TX 77843-3368 (United States)], E-mail: christov@alum.mit.edu; Christov, C.I. [Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010 (United States)], E-mail: christov@louisiana.edu
2008-02-04
By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field.
Physical dynamics of quasi-particles in nonlinear wave equations
International Nuclear Information System (INIS)
Christov, Ivan; Christov, C.I.
2008-01-01
By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field
International Nuclear Information System (INIS)
Benisti, D.
2011-01-01
This manuscript provides a theoretical description, sometimes illustrated by experimental results, of several examples of field-matter interaction in various domains of physics, showing how the same basic concepts and theoretical methods may be used in very different physics situations. The issues addressed here are nonlinear field-matter interaction in plasma physics within the framework of classical mechanics (with a particular emphasis on wave-particle interaction), the linear analysis of beam-plasma instabilities in the relativistic regime, and the quantum description of laser-atom interaction, including quantum electrodynamics. Novel methods are systematically introduced in order to solve some very old problems, like the nonlinear counterpart of the Landau damping rate in plasma physics, for example. Moreover, our results directly apply to inertial confinement fusion, laser propagation in an atomic vapor, ion acceleration in a magnetized plasma and the physics of the Reversed Field Pinch for magnetic fusion. (author)
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.
Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction
Smelyanskiy, V. N.; Luchinsky, D. G.; Stefanovska, A.; McClintock, P. V.
2005-03-01
We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.
Nonlinear PCA: characterizing interactions between modes of brain activity.
Friston, K; Phillips, J; Chawla, D; Büchel, C
2000-01-01
This paper presents a nonlinear principal component analysis (PCA) that identifies underlying sources causing the expression of spatial modes or patterns of activity in neuroimaging time-series. The critical aspect of this technique is that, in relation to conventional PCA, the sources can interact to produce (second-order) spatial modes that represent the modulation of one (first-order) spatial mode by another. This nonlinear PCA uses a simple neural network architecture that embodies a spec...
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.
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
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.
Shock wave interactions with detonable clouds
International Nuclear Information System (INIS)
Ripley, R.C.; Josey, T.; Donahue, L.; Whitehouse, D.R.
2004-01-01
This paper presents results from the numerical simulation of compressible multi-species gases in an unstructured mesh CFD code called Chinook. Multiple species gases are significant to a wide range of CFD applications that involve chemical reactions, in particular detonation. The purpose of this paper is to investigate the interaction of shock waves with localized regions of reactive and non-reactive gas species. Test cases are chosen to highlight shock reflection and acceleration through combustion products resulting from the detonation of an explosive charge, and detonation wave propagation through a fuel-air cloud. Computations are performed in a 2D axi-symmetric framework. (author)
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.
Nonlinear wave coupling in a warm plasma in the fluid
International Nuclear Information System (INIS)
Malara, F.; Veltri, P.
1984-01-01
The general expression for nonlinear coupling between plasma modes is obtained. The nonlinear conductivity tensor is then calculated by means of the two-fluid plasma description taking into account the thermal pressure effects
Cumulative Second Harmonic Generation in Lamb Waves for the Detection of Material Nonlinearities
International Nuclear Information System (INIS)
Bermes, Christian; Jacobs, Laurence J.; Kim, Jin-Yeon; Qu, Jianmin
2007-01-01
An understanding of the generation of higher harmonics in Lamb waves is of critical importance for applications such as remaining life prediction of plate-like structural components. The objective of this work is to use nonlinear Lamb waves to experimentally investigate inherent material nonlinearities in aluminum plates. These nonlinearities, e.g. lattice anharmonicities, precipitates or vacancies, cause higher harmonics to form in propagating Lamb waves. The amplitudes of the higher harmonics increase with increasing propagation distance due to the accumulation of nonlinearity while the Lamb wave travels along its path. Special focus is laid on the second harmonic, and a relative nonlinearity parameter is defined as a function of the fundamental and second harmonic amplitude. The experimental setup uses an ultrasonic transducer and a wedge for the Lamb wave generation, and laser interferometry for detection. The experimentally measured Lamb wave signals are processed with a short-time Fourier transformation (STFT), which yields the amplitudes at different frequencies as functions of time, allowing the observation of the nonlinear behavior of the material. The increase of the relative nonlinearity parameter with propagation distance as an indicator of cumulative second harmonic generation is shown in the results for the alloy aluminum 1100-H14
Solitary Wave Interactions in Granular Media
Institute of Scientific and Technical Information of China (English)
WEN Zhen-Ying; WANG Shun-Jin; ZHANG Xiu-Ming; LI Lei
2007-01-01
We numerically study the interactions of solitary waves in granular media, by considering a chain of beads, which repel upon contact via the Hertz-type potential, V ∝δn, with 5/2 ≤n≤3 and δ≥0,δbeing the bead-bead overlap. There are two collision types of solitary waves, overtaking collision and head-on collision, in the chain of beads. Our quantitative results show that after collision the large solitary wave gains energy and the small one loses energy for overtaking type while the large one loses energy, and the small one gains energy for head-on type. The scattering effects decrease with n for overtaking collision whereas increase with n for head-on collision.
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.
Nonlinear coherent structures of Alfvén wave in a collisional plasma
International Nuclear Information System (INIS)
Jana, Sayanee; Chakrabarti, Nikhil; Ghosh, Samiran
2016-01-01
The Alfvén wave dynamics is investigated in the framework of two-fluid approach in a compressible collisional magnetized plasma. In the finite amplitude limit, the dynamics of the nonlinear Alfvén wave is found to be governed by a modified Korteweg-de Vries Burgers equation (mKdVB). In this mKdVB equation, the electron inertia is found to act as a source of dispersion, and the electron-ion collision serves as a dissipation. The collisional dissipation is eventually responsible for the Burgers term in mKdVB equation. In the long wavelength limit, this weakly nonlinear Alfvén wave is shown to be governed by a damped nonlinear Schrödinger equation. Furthermore, these nonlinear equations are analyzed by means of analytical calculation and numerical simulation to elucidate the various aspects of the phase-space dynamics of the nonlinear wave. Results reveal that nonlinear Alfvén wave exhibits the dissipation mediated shock, envelope, and breather like structures. Numerical simulations also predict the formation of dissipative Alfvénic rogue wave, giant breathers, and rogue wave holes. These results are discussed in the context of the space plasma.
Nonlinear coherent structures of Alfvén wave in a collisional plasma
Energy Technology Data Exchange (ETDEWEB)
Jana, Sayanee; Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India); Ghosh, Samiran [Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata 700 009 (India)
2016-07-15
The Alfvén wave dynamics is investigated in the framework of two-fluid approach in a compressible collisional magnetized plasma. In the finite amplitude limit, the dynamics of the nonlinear Alfvén wave is found to be governed by a modified Korteweg-de Vries Burgers equation (mKdVB). In this mKdVB equation, the electron inertia is found to act as a source of dispersion, and the electron-ion collision serves as a dissipation. The collisional dissipation is eventually responsible for the Burgers term in mKdVB equation. In the long wavelength limit, this weakly nonlinear Alfvén wave is shown to be governed by a damped nonlinear Schrödinger equation. Furthermore, these nonlinear equations are analyzed by means of analytical calculation and numerical simulation to elucidate the various aspects of the phase-space dynamics of the nonlinear wave. Results reveal that nonlinear Alfvén wave exhibits the dissipation mediated shock, envelope, and breather like structures. Numerical simulations also predict the formation of dissipative Alfvénic rogue wave, giant breathers, and rogue wave holes. These results are discussed in the context of the space plasma.
International Nuclear Information System (INIS)
Bhattacharyya, B.; Chakraborty, B.
1979-01-01
Nonlinear corrections of a left and a right circularly polarized electromagnetic wave of the same frequency, propagating in the direction of a static and uniform magnetic field in a cold and collisionally damped two-component plasma, have been evaluated. The nonlinearly correct dispersion relation, self-generating nonlinear precessional rotation of the polarization ellipse of the wave and the shift in a wave parameter depend on linear combinations of products of the amplitude components taken two at a time and hence on the energies of the waves. Both in the low frequency resonance (that is when the ion cyclotron frequency equals the wave frequency) and in the high frequency resonance (that is when the electron cyclotron frequency equals the wave frequency), the self-precessional rate and wavenumber shift are found to be large and so have the possibility of detection in laboratory experiments. Moreover, for the limit leading to Alfven waves, these nonlinear effects have been found to have some interesting and significant properties. (Auth.)
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
Interactions of disparate scales in drift-wave turbulence
International Nuclear Information System (INIS)
Krommes, John A.; Kim, Chang-Bae
2000-01-01
Renormalized statistical theory is used to calculate the interactions between short scales (wave vector k) and long scales (wave vector q parallel =0 fluctuations). The calculations include the zonal-flow growth rate as a special case, but also describe long-wavelength fluctuations with q oriented at an arbitrary angle to the background gradient. The results are fully renormalized. They are subtly different from those of previous authors, in both mathematical form and physical interpretation. A term arising in previous treatments that is related to the propagation of short-scale wave packets is shown to be a higher-order effect that must consistently be neglected to lowest order in a systematic expansion in q/k. Rigorous functional methods are used to show that the long-wavelength growth rate γ q is related to second-order functional variations of the short-wavelength energy and to derive a heuristic algorithm. The principal results are recovered from simple estimates involving the first-order wave-number distension rate tilde γ k (1) dot eqdot kdeltilde Omega k /k 2 , where tilde Ω k is a nonlinear random advection frequency. Fokker-Planck analysis involving tilde γ k (1) is used to heuristically recover the evolution equation for the small scales, and a random-walk flux argument that relates tilde γ k (1) to an effective autocorrelation time is used to give an independent calculation of γ q . Both the rigorous and heuristic derivations demonstrate that the results do not depend on, and cannot be derived from, properties of linear normal modes; they are intrinsically nonlinear. The importance of random-Galilean-invariant renormalization is stressed
Non-linear electromagnetic interactions in thermal QED
International Nuclear Information System (INIS)
Brandt, F.T.; Frenkel, J.
1994-08-01
The behavior of the non-linear interactions between electromagnetic fields at high temperature is examined. It is shown that, in general, the log(T) dependence on the temperature of the Green functions is simply related to their UV behavior at zero-temperature. It is argued that the effective action describing the nonlinear thermal electromagnetic interactions has a finite limit as T -> ∞. This thermal action approaches, in the long wavelength limit, the negative of the corresponding zero-temperature action. (author). 12 refs, 1 fig
Nonlinear waves in reaction-diffusion systems: The effect of transport memory
International Nuclear Information System (INIS)
Manne, K. K.; Hurd, A. J.; Kenkre, V. M.
2000-01-01
Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity. (c) 2000 The American Physical Society
Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse
Energy Technology Data Exchange (ETDEWEB)
Grishkov, V. E.; Uryupin, S. A., E-mail: uryupin@sci.lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)
2017-03-15
Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse is analyzed within the kinetic approach. It is shown that the most efficient source of plasma waves is the nonlinear current arising due to the gradient of the energy density of the high-frequency field. Generation of plasma waves by the drag current is usually less efficient but not negligibly small at relatively high frequencies of electron–ion collisions. The influence of electron collisions on the excitation of plasma waves by pulses of different duration is described quantitatively.
Basic principles approach for studying nonlinear Alfven wave-alpha particle dynamics
International Nuclear Information System (INIS)
Berk, H.L.; Breizman, B.N.; Pekker, M.
1994-01-01
An analytical model and a numerical procedure are presented which give a kinetic nonlinear description of the Alfven-wave instabilities driven by the source of energetic particles in a plasma. The steady-state and bursting nonlinear scenarios predicted by the analytical theory are verified in the test numerical simulation of the bump-on-tail instability. A mathematical similarity between the bump-on-tail problem for plasma waves and the Alfven wave problem gives a guideline for the interpretation of the bursts in the wave energy and fast particle losses observed in the tokamak experiments with neutral beam injection
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
Collisionless damping of nonlinear dust ion acoustic wave due to dust charge fluctuation
International Nuclear Information System (INIS)
Ghosh, Samiran; Chaudhuri, Tushar K.; Sarkar, Susmita; Khan, Manoranjan; Gupta, M.R.
2002-01-01
A dissipation mechanism for the damping of the nonlinear dust ion acoustic wave in a collisionless dusty plasma consisting of nonthermal electrons, ions, and variable charge dust grains has been investigated. It is shown that the collisionless damping due to dust charge fluctuation causes the nonlinear dust ion acoustic wave propagation to be described by the damped Korteweg-de Vries equation. Due to the presence of nonthermal electrons, the dust ion acoustic wave admits both positive and negative potential and it suffers less damping than the dust acoustic wave, which admits only negative potential
Nonlinear waves in reaction-diffusion systems: The effect of transport memory
Manne, K. K.; Hurd, A. J.; Kenkre, V. M.
2000-04-01
Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.
Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation
Energy Technology Data Exchange (ETDEWEB)
Zhaqilao,, E-mail: zhaqilao@imnu.edu.cn
2013-12-06
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.
Energy Technology Data Exchange (ETDEWEB)
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.
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 inertial Alfven waves in plasmas with sheared magnetic field and flow
International Nuclear Information System (INIS)
Chen Yinhua; Wang Ge; Tan Liwei
2004-01-01
Nonlinear equations describing inertial Alfven waves in plasmas with sheared magnetic field and flow are derived. For some specific parameters chosen, authors have found a new type of electromagnetic coherent structures in the tripolar vortex-like form
Wave instabilities in nonlinear Schrödinger systems with non vanishing background
Trillo, Stefano; Gongora, J. S. Totero; Fratalocchi, Andrea
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 gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria
International Nuclear Information System (INIS)
Frieman, E.A.; Chen, L.
1981-10-01
A nonlinear gyrokinetic formalism for low-frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed. The nonlinear equations thus derived are valid in the strong-turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magentic field geometries. The specific case of axisymmetric tokamaks is then considered, and a model nonlinear equation is derived for electrostatic drift waves. Also, applying the formalism to the shear Alfven wave heating sceme, it is found that nonlinear ion Landau damping of kinetic shear-Alfven waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects. In particular, wave energy is found to cascade in wavenumber instead of frequency
Dynamic nonlinear interaction of elastic plates on discrete supports
International Nuclear Information System (INIS)
Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.
1984-01-01
A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt
Three-wave interaction during electron cyclotron resonance heating and current drive
DEFF Research Database (Denmark)
Nielsen, Stefan Kragh; Jacobsen, Asger Schou; Hansen, Søren Kjer
2016-01-01
Non-linear wave-wave interactions in fusion plasmas, such as the parametric decay instability (PDI) of gyrotron radiation, can potentially hamper the use of microwave diagnostics. Here we report on anomalous scattering in the ASDEX Upgrade tokamak during electron cyclotron resonance heating...... experiments. The observations can be linked to parametric decay of the gyrotron radiation at the second harmonic upper hybrid resonance layer....
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.
International Nuclear Information System (INIS)
Tian Lixin; Yin Jiuli
2004-01-01
In this paper, we introduce the fully nonlinear generalized Camassa-Holm equation C(m,n,p) and by using four direct ansatzs, we obtain abundant solutions: compactons (solutions with the absence of infinite wings), solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions and obtain kink compacton solutions and nonsymmetry compacton solutions. We also study other forms of fully nonlinear generalized Camassa-Holm equation, and their compacton solutions are governed by linear equations
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.
Nonlinear Waves in a Cigar-Shaped Bose-Einstein Condensate with Dissipation
International Nuclear Information System (INIS)
Yang Xiaoxian; Shi Yuren; Duan Wenshan
2008-01-01
We discuss the possible nonlinear waves of atomic matter waves in a cigar-shaped Bose-Einstein condensate with dissipation. The waves can be described by a KdV-type equation. The KdV-type equation has a solitary wave solution. The amplitude, speed, and width of the wave vary exponentially with time t. The dissipative term of γ plays an important role for the wave amplitude, speed, and width. Comparisons have been given between the analytical solutions and the numerical results. It is shown that both are in good agreement.
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...
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 a...
Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
International Nuclear Information System (INIS)
Kartashov, Yaroslav V; Egorov, Alexey A; Vysloukh, Victor A; Torner, Lluis
2004-01-01
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
Chaotic saddles in nonlinear modulational interactions in a plasma
International Nuclear Information System (INIS)
Miranda, Rodrigo A.; Rempel, Erico L.; Chian, Abraham C.-L.
2012-01-01
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.
Chaotic saddles in nonlinear modulational interactions in a plasma
Energy Technology Data Exchange (ETDEWEB)
Miranda, Rodrigo A. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); University of Brasilia (UnB), Gama Campus, and Plasma Physics Laboratory, Institute of Physics, Brasilia, DF 70910-900 (Brazil); Rempel, Erico L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Chian, Abraham C.-L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Observatoire de Paris, LESIA, CNRS, 92195 Meudon (France)
2012-11-15
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.
Self-focusing of nonlinear waves in a relativistic plasma with positive and negative ions
International Nuclear Information System (INIS)
Mukherjee, Joydeep; Chowdhury, A.R.
1994-01-01
The phenomenon of self-focusing of nonlinear waves was analysed in a relativistic plasma consisting of both positive and negative ions, which are assumed to be hot. The effect of the inertia of the relativistic electron is also considered by treating it dynamically. A modified form of reductive perturbation is used to deduce a nonlinear Schroedinger equation describing the purely spatial variation of the nonlinear wave. Self-focusing of the wave can be ascertained by analysing the transversal stability of the solitary wave. It is shown that the zones of stability of the wave may become wider due to the mutual influence of various factors present in the plasma, thus favouring the process of self-focusing. 10 refs., 2 figs
Thermal Aging Evaluation of Mod. 9Cr-1Mo Steel using Nonlinear Rayleigh Waves
Energy Technology Data Exchange (ETDEWEB)
Joo, Young-Sang; Kim, Hoe-Woong; Kim, Jong-Bum [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Marino, Daniel; Kim, Jin-Yeon; Jacobs, L.J [Georgia Institute of Technology, Atlanta (United States); Ruiz, Alberto [UMSNH, Morelia (Mexico)
2014-10-15
Thermal aging can pose a high risk to decreases in the mechanical properties such as strength or creep resistance. This can lead to an unexpected failure during long term operation. Nonlinear NDE techniques are preferred over conventional NDE techniques (linear ultrasonic measurements) because nonlinear ultrasonic techniques have shown their capability to detect a microstructural damage in the structures undergoing fatigue and creep. These nonlinear ultrasonic techniques make use of the fact that the dislocation density increases, which will create a nonlinear distortion of an ultrasonic wave; this damage causes the generation of measurable higher harmonic components in an initially mono-chromatic ultrasonic signal. This study investigates the recently developed non-contact nonlinear ultrasonic technique to detect the microstructural damage of mod. 9Cr-1Mo steel based on nonlinear Rayleigh wave with varying propagation distances. Nonlinear Rayleigh surface wave measurements using a non-contact, air-coupled ultrasonic transducer have been applied for the thermal aging evaluation of modified 9Cr-1Mo ferritic-martensitic steel. Thermal aging for various heat treatment times of mod.. 9Cr-1Mo steel specimens is performed to obtain the nucleation and growth of precipitated particles in specimens. The amplitudes of the first and second harmonics are measured along the propagation distance and the relative nonlinearity parameter is obtained from these amplitudes. The relative nonlinearity parameter shows a similar trend with the Rockwell C hardness.
Musammil, N. M.; Porsezian, K.; Nithyanandan, K.; Subha, P. A.; Tchofo Dinda, P.
2017-09-01
We present the study of the dark soliton dynamics in an inhomogeneous fiber by means of a variable coefficient modified nonlinear Schrödinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and linear gain/loss. The ultrashort dark soliton pulse evolution and interaction is studied by using the Hirota bilinear (HB) method. In particular, we give much insight into the effect of self-steepening (SS) on the dark soliton dynamics. The study reveals a shock wave formation, as a major effect of SS. Numerically, we study the dark soliton propagation in the continuous wave background, and the stability of the soliton solution is tested in the presence of photon noise. The elastic collision behaviors of the dark solitons are discussed by the asymptotic analysis. On the other hand, considering the nonlinear tunneling of dark soliton through barrier/well, we find that the tunneling of the dark soliton depends on the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or valley and retains its shape after the tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well.