Adiabatic nonlinear waves with trapped particles. III. Wave dynamics
Dodin, I. Y.; Fisch, N. J.
2012-01-15
The evolution of adiabatic waves with autoresonant trapped particles is described within the Lagrangian model developed in Paper I, under the assumption that the action distribution of these particles is conserved, and, in particular, that their number within each wavelength is a fixed independent parameter of the problem. One-dimensional nonlinear Langmuir waves with deeply trapped electrons are addressed as a paradigmatic example. For a stationary wave, tunneling into overcritical plasma is explained from the standpoint of the action conservation theorem. For a nonstationary wave, qualitatively different regimes are realized depending on the initial parameter S, which is the ratio of the energy flux carried by trapped particles to that carried by passing particles. At S < 1/2, a wave is stable and exhibits group velocity splitting. At S > 1/2, the trapped-particle modulational instability (TPMI) develops, in contrast with the existing theories of the TPMI yet in agreement with the general sideband instability theory. Remarkably, these effects are not captured by the nonlinear Schroedinger equation, which is traditionally considered as a universal model of wave self-action but misses the trapped-particle oscillation-center inertia.
Makarov, V A; Petnikova, V M; Rudenko, K V; Shuvalov, V V
2015-01-31
The adiabatic approximation is used to obtain an analytical solution to a nonintegrable problem of propagation of a plane elliptically polarised light wave with zero mean amplitudes of orthogonal circularly polarised field components through an isotropic gyrotropic medium with local and nonlocal components of Kerr nonlinearity and second-order group velocity dispersion. We describe the aperiodic evolution of bound (attributable to the medium nonlinearity) paired states, which are responsible for the propagation of two orthogonal polarisation components – cnoidal waves with significantly different periods. (nonlinear optical phenomena)
On a Nonlinear Model in Adiabatic Evolutions
NASA Astrophysics Data System (ADS)
Sun, Jie; Lu, Song-Feng
2016-08-01
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using. Supported by the National Natural Science Foundation of China under Grant Nos. 61402188 and 61173050. The first author also gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2014M552041
Adiabatic theory of solitons fed by dispersive waves
NASA Astrophysics Data System (ADS)
Pickartz, Sabrina; Bandelow, Uwe; Amiranashvili, Shalva
2016-09-01
We consider scattering of low-amplitude dispersive waves at an intense optical soliton which constitutes a nonlinear perturbation of the refractive index. Specifically, we consider a single-mode optical fiber and a group velocity matched pair: an optical soliton and a nearly perfectly reflected dispersive wave, a fiber-optical analog of the event horizon. By combining (i) an adiabatic approach that is used in soliton perturbation theory and (ii) scattering theory from quantum mechanics, we give a quantitative account of the evolution of all soliton parameters. In particular, we quantify the increase in the soliton peak power that may result in the spontaneous appearance of an extremely large, so-called champion soliton. The presented adiabatic theory agrees well with the numerical solutions of the pulse propagation equation. Moreover, we predict the full frequency band of the scattered dispersive waves and explain an emerging caustic structure in the space-time domain.
Analytical Nonlinear Adiabatic Theory of the Autophase Microwave Tube
NASA Astrophysics Data System (ADS)
Belyavskiy, Eugene; Khotiaintsev, Sergei
We present an analytical nonlinear adiabatic theory of the microwave electron device that we call the Autophase Microwave Tube (AMT). In contrast to the well-known Traveling Wave Tube (TWT), the AMT exploits a highly efficient non-synchronous beam-wave interaction for the amplification (or generation) of the HF electromagnetic waves, and, differently from klystron and such hybrid devices as twystron, it employs a continuous beam-wave interaction. Because of these distinctive features, the AMT presents a special class of microwave electron devices, which feature very high electronic efficiency (which tends to 100%) and large bandwidth. Here, we develop the theory that allows one to find the profiles of static longitudinal electric or magnetic field (or both) over the device length, which yield negligible de-bunching together with highly efficient amplification (generation) of the HF electromagnetic wave. The analysis of electron motion in the bunch is performed by means of Lyapunov stability theory. The numerical example illustrates the possibility of achieving the electronic efficiency of AMT as high as 92%. We compare different autophase regimes in the AMT and show that the profiling of the longitudinal static magnetic focusing field in the helix AMT with the non-azimuthally symmetric wave has many advantages with respect to other regimes.
Evolution Of Nonlinear Waves in Compressing Plasma
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.
Nonlinear Hysteretic Torsional Waves
NASA Astrophysics Data System (ADS)
Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.
2015-07-01
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity.
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-12
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic XY spin chains from the Toda equations are studied in detail.
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
NASA Astrophysics Data System (ADS)
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-01
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.
The dynamic instability of adiabatic blast waves
NASA Technical Reports Server (NTRS)
Ryu, Dongsu; Vishniac, Ethan T.
1991-01-01
Adiabatic blastwaves, which have a total energy injected from the center E varies as t(sup q) and propagate through a preshock medium with a density rho(sub E) varies as r(sup -omega) are described by a family of similarity solutions. Previous work has shown that adiabatic blastwaves with increasing or constant postshock entropy behind the shock front are susceptible to an oscillatory instability, caused by the difference between the nature of the forces on the two sides of the dense shell behind the shock front. This instability sets in if the dense postshock layer is sufficiently thin. The stability of adiabatic blastwaves with a decreasing postshock entropy is considered. Such blastwaves, if they are decelerating, always have a region behind the shock front which is subject to convection. Some accelerating blastwaves also have such region, depending on the values of q, omega, and gamma where gamma is the adiabatic index. However, since the shock interface stabilizes dynamically induced perturbations, blastwaves become convectively unstable only if the convective zone is localized around the origin or a contact discontinuity far from the shock front. On the other hand, the contact discontinuity of accelerating blastwaves is subject to a strong Rayleigh-Taylor instability. The frequency spectra of the nonradial, normal modes of adiabatic blastwaves have been calculated. The results have been applied to the shocks propagating through supernovae envelopes. It is shown that the metal/He and He/H interfaces are strongly unstable against the Rayleigh-Taylor instability. This instability will induce mixing in supernovae envelopes. In addition the implications of this work for the evolution of planetary nebulae is discussed.
Adiabatic continuity, wave-function overlap, and topological phase transitions
NASA Astrophysics Data System (ADS)
Gu, Jiahua; Sun, Kai
2016-09-01
In this paper, we study the relation between wave-function overlap and adiabatic continuity in gapped quantum systems. We show that for two band insulators, a scalar function can be defined in the momentum space, which characterizes the wave-function overlap between Bloch states in the two insulators. If this overlap is nonzero for all momentum points in the Brillouin zone, these two insulators are adiabatically connected, i.e., we can deform one insulator into the other smoothly without closing the band gap. In addition, we further prove that this adiabatic path preserves all the symmetries of the insulators. The existence of such an adiabatic path implies that two insulators with nonzero wave-function overlap belong to the same topological phase. This relation, between adiabatic continuity and wave-function overlap, can be further generalized to correlated systems. The generalized relation cannot be applied to study generic many-body systems in the thermodynamic limit, because of the orthogonality catastrophe. However, for certain interacting systems (e.g., quantum Hall systems), the quantum wave-function overlap can be utilized to distinguish different quantum states. Experimental implications are also discussed.
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity.
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-12
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic XY spin chains from the Toda equations are studied in detail. PMID:27563938
Relativistic blast waves in two dimensions. I - The adiabatic case
NASA Technical Reports Server (NTRS)
Shapiro, P. R.
1979-01-01
Approximate solutions are presented for the dynamical evolution of strong adiabatic relativistic blast waves which result from a point explosion in an ambient gas in which the density varies both with distance from the explosion center and with polar angle in axisymmetry. Solutions are analytical or quasi-analytical for the extreme relativistic case and numerical for the arbitrarily relativistic case. Some general properties of nonplanar relativistic shocks are also discussed, including the incoherence of spherical ultrarelativistic blast-wave fronts on angular scales greater than the reciprocal of the shock Lorentz factor, as well as the conditions for producing blast-wave acceleration.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.
Goto, Hayato
2016-01-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
Goto, Hayato
2016-01-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
NASA Astrophysics Data System (ADS)
Goto, Hayato
2016-02-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.
Goto, Hayato
2016-02-22
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Some properties of adiabatic blast waves in preexisting cavities
NASA Technical Reports Server (NTRS)
Cox, D. P.; Franco, J.
1981-01-01
Cox and Anderson (1982) have conducted an investigation regarding an adiabatic blast wave in a region of uniform density and finite external pressure. In connection with an application of the results of the investigation to a study of interstellar blast waves in the very hot, low-density matrix, it was found that it would be desirable to examine situations with a positive radial density gradient in the ambient medium. Information concerning such situations is needed to learn about the behavior of blast waves occurring within preexisting, presumably supernova-induced cavities in the interstellar mass distribution. The present investigation is concerned with the first steps of a study conducted to obtain the required information. A review is conducted of Sedov's (1959) similarity solutions for the dynamical structure of any explosion in a medium with negligible pressure and power law density dependence on radius.
Adiabatic corrections to density functional theory energies and wave functions.
Mohallem, José R; Coura, Thiago de O; Diniz, Leonardo G; de Castro, Gustavo; Assafrão, Denise; Heine, Thomas
2008-09-25
The adiabatic finite-nuclear-mass-correction (FNMC) to the electronic energies and wave functions of atoms and molecules is formulated for density-functional theory and implemented in the deMon code. The approach is tested for a series of local and gradient corrected density functionals, using MP2 results and diagonal-Born-Oppenheimer corrections from the literature for comparison. In the evaluation of absolute energy corrections of nonorganic molecules the LDA PZ81 functional works surprisingly better than the others. For organic molecules the GGA BLYP functional has the best performance. FNMC with GGA functionals, mainly BLYP, show a good performance in the evaluation of relative corrections, except for nonorganic molecules containing H atoms. The PW86 functional stands out with the best evaluation of the barrier of linearity of H2O and the isotopic dipole moment of HDO. In general, DFT functionals display an accuracy superior than the common belief and because the corrections are based on a change of the electronic kinetic energy they are here ranked in a new appropriate way. The approach is applied to obtain the adiabatic correction for full atomization of alcanes C(n)H(2n+2), n = 4-10. The barrier of 1 mHartree is approached for adiabatic corrections, justifying its insertion into DFT. PMID:18537228
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
NASA Astrophysics Data System (ADS)
Goto, Hayato
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via its bifurcation with a slowly varying parameter. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing. To distinguish them, we refer to the present approach as bifurcation-based adiabatic quantum computation. Our numerical simulation results suggest that quantum superposition and quantum fluctuation work effectively to find optimal solutions.
Properties of Nonlinear Dynamo Waves
NASA Technical Reports Server (NTRS)
Tobias, S. M.
1997-01-01
Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.
Solitary shock waves and adiabatic phase transition in lipid interfaces and nerves
NASA Astrophysics Data System (ADS)
Shrivastava, Shamit; Kang, Kevin Heeyong; Schneider, Matthias F.
2015-01-01
This study shows that the stability of solitary waves excited in a lipid monolayer near a phase transition requires positive curvature of the adiabats, a known necessary condition in shock compression science. It is further shown that the condition results in a threshold for excitation, saturation of the wave's amplitude, and the splitting of the wave at the phase boundaries. Splitting in particular confirms that a hydrated lipid interface can undergo condensation on adiabatic heating, thus showing retrograde behavior. Finally, using the theoretical insights and state dependence of conduction velocity in nerves, the curvature of the adiabatic state diagram is shown to be closely tied to the thermodynamic blockage of nerve pulse propagation.
Solitary shock waves and adiabatic phase transition in lipid interfaces and nerves.
Shrivastava, Shamit; Kang, Kevin Heeyong; Schneider, Matthias F
2015-01-01
This study shows that the stability of solitary waves excited in a lipid monolayer near a phase transition requires positive curvature of the adiabats, a known necessary condition in shock compression science. It is further shown that the condition results in a threshold for excitation, saturation of the wave's amplitude, and the splitting of the wave at the phase boundaries. Splitting in particular confirms that a hydrated lipid interface can undergo condensation on adiabatic heating, thus showing retrograde behavior. Finally, using the theoretical insights and state dependence of conduction velocity in nerves, the curvature of the adiabatic state diagram is shown to be closely tied to the thermodynamic blockage of nerve pulse propagation.
Reconstruction of nonlinear wave propagation
Fleischer, Jason W; Barsi, Christopher; Wan, Wenjie
2013-04-23
Disclosed are systems and methods for characterizing a nonlinear propagation environment by numerically propagating a measured output waveform resulting from a known input waveform. The numerical propagation reconstructs the input waveform, and in the process, the nonlinear environment is characterized. In certain embodiments, knowledge of the characterized nonlinear environment facilitates determination of an unknown input based on a measured output. Similarly, knowledge of the characterized nonlinear environment also facilitates formation of a desired output based on a configurable input. In both situations, the input thus characterized and the output thus obtained include features that would normally be lost in linear propagations. Such features can include evanescent waves and peripheral waves, such that an image thus obtained are inherently wide-angle, farfield form of microscopy.
Schmidt, Slawa; Engelke, Pascal; Piglosiewicz, Björn; Esmann, Martin; Becker, Simon F; Yoo, Kyungwan; Park, Namkyoo; Lienau, Christoph; Groß, Petra
2013-11-01
We describe and demonstrate the use of an adaptive wave front optimization scheme for enhancing the efficiency of adiabatic nanofocusing of surface plasmon polariton (SPP) waves along an ultrasharp conical gold taper. Adiabatic nanofocusing is an emerging and promising scheme for controlled focusing of far field light into nanometric volumes. It comprises three essential steps: SPP excitation by coupling far field light to an SPP waveguide, SPP propagation along the waveguide and adiabatic SPP nanofocusing towards a geometric singularity. For commonly used complex waveguide geometries, such as, e.g., conical metal tapers, a realistic modeling and efficiency optimization is challenging. Here, we use a deformable mirror to adaptively control the wave front of the incident far field light. We demonstrate an eight-fold enhancement in nanofocusing efficiency and analyze the shape of the resulting optimized wave front. The introduced wave front optimization scheme is of general interest for guiding and controlling light on the nanoscale.
Nonlinear Pressure Wave Analysis by Concentrated Mass Model
NASA Astrophysics Data System (ADS)
Ishikawa, Satoshi; Kondou, Takahiro; Matsuzaki, Kenichiro
A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effect of fluid. Analyzing this phenomenon by the finite difference method requires high computational cost. To lessen the computational cost, a concentrated mass model is proposed. This model consists of masses, connecting nonlinear springs, connecting dampers, and base support dampers. The characteristic of a connecting nonlinear spring is derived from the adiabatic change of fluid, and the equivalent mass and equivalent damping coefficient of the base support damper are derived from the equation of motion of fluid in a cylindrical tube. Pressure waves generated in a hydraulic oil tube, a sound tube and a plane-wave tube are analyzed numerically by the proposed model to confirm the validity of the model. All numerical computational results agree very well with the experimental results carried out by Okamura, Saenger and Kamakura. Especially, the numerical analysis reproduces the phenomena that a pressure wave with large amplitude propagating in a sound tube or in a plane tube changes to a shock wave. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem.
Arbitrary Amplitude DIA and DA Solitary Waves in Adiabatic Dusty Plasmas
Mamun, A. A.; Jahan, N.; Shukla, P. K.
2008-10-15
The dust-ion-acoustic (DIA) as well as the dust-acoustic (DA) solitary waves (SWs) in an adiabatic dusty plasma are investigated by the pseudo-potential approach which is valid for arbitrary amplitude SWs. The role of the adiabaticity of electrons and ions in modifying the basic features (polarity, speed, amplitude and width) of arbitrary amplitude DIA and DA SWs are explicitly examined. It is found that the effects of the adiabaticity of electrons and ions significantly modify the basic features (polarity, speed, amplitude and width) of the DIA and DA SWs. The implications of our results in space and laboratory dusty plasmas are briefly discussed.
Solitons and nonlinear wave equations
Dodd, Roger K.; Eilbeck, J. Chris; Gibbon, John D.; Morris, Hedley C.
1982-01-01
A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory. The subjects addressed include: solitary waves and solitons, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation, and the inverse method for the isospectral Schroedinger equation and the general solution of the solvable nonlinear equations. Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of solitons. 45 references.
Ray invariants, plane wave spectra, and adiabatic modes for tapered dielectric waveguides
NASA Astrophysics Data System (ADS)
Arnold, J. M.; Felsen, L. B.
1984-10-01
In nonseparable problems resulting from the analysis of wave propagation in longitudinally varying waveguides, such as a wedge-shaped taper, singularities appear in both ray and coupled mode treatments at the local normal mode cutoff transition. A uniformization of the local normal (adiabatic) mode is proposed, using plane wave spectra, which effectively resolves this difficulty.
Nonlinear positron acoustic solitary waves
Tribeche, Mouloud; Aoutou, Kamel; Younsi, Smain; Amour, Rabia
2009-07-15
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.
Nonlinear wave dynamics in honeycomb lattices
Bahat-Treidel, Omri; Segev, Mordechai
2011-08-15
We study the nonlinear dynamics of wave packets in honeycomb lattices and show that, in quasi-one-dimensional configurations, the waves propagating in the lattice can be separated into left-moving and right-moving waves, and any wave packet composed of only left (or only right) movers does not change its intensity structure in spite of the nonlinear evolution of its phase. We show that the propagation of a general wave packet can be described, within a good approximation, as a superposition of left- and right-moving self-similar (nonlinear) wave packets. Finally, we find that Klein tunneling is not suppressed by nonlinearity.
Nonlinear Fourier analysis with cnoidal waves
Osborne, A.R.
1996-12-31
Fourier analysis is one of the most useful tools to the ocean engineer. The approach allows one to analyze wave data and thereby to describe a dynamical motion in terms of a linear superposition of ordinary sine waves. Furthermore, the Fourier technique allows one to compute the response function of a fixed or floating structure: each sine wave in the wave or force spectrum yields a sine wave in the response spectrum. The counting of fatigue cycles is another area where the predictable oscillations of sine waves yield procedures for the estimation of the fatigue life of structures. The ocean environment, however, is a source of a number of nonlinear effects which must also be included in structure design. Nonlinearities in ocean waves deform the sinusoidal shapes into other kinds of waves such as the Stokes wave, cnoidal wave or solitary wave. A key question is: Does there exist a generalization of linear Fourier analysis which uses nonlinear basis functions rather than the familiar sine waves? Herein addresses the dynamics of nonlinear wave motion in shallow water where the basis functions are cnoidal waves and discuss nonlinear Fourier analysis in terms of a linear superposition of cnoidal waves plus their mutual nonlinear interactions. He gives a number of simple examples of nonlinear Fourier wave motion and then analyzes an actual surface-wave time series obtained on an offshore platform in the Adriatic Sea. Finally, he briefly discusses application of the cnoidal wave spectral approach to the computation of the frequency response function of a floating vessel. The results given herein will prove useful in future engineering studies for the design of fixed, floating and complaint offshore structures.
NASA Astrophysics Data System (ADS)
Sutin, A. M.; Johnson, P. A.
2005-04-01
This paper presents the second part of the review of Nonlinear Elastic Wave Spectroscopy (NEWS) in NDE, and describe two different methods of nonlinear NDE that provide not only damage detection but location as well. Nonlinear Wave Modulation Spectroscopy is based on the application of an ultrasonic probe signal modulated by a low frequency vibration. Damage location can be obtained by application of Impulse Modulation Techniques that exploit the modulation of a short pulse reflected from a damage feature (e.g. crack) by low frequency vibration. Nonlinear Time Reversed Acoustic methods provide the means to focus acoustic energy to any point in a solid. In combination, we are applying the focusing properties of TRA and the nonlinear properties of cracks to locate them.
Measuring Acoustic Nonlinearity by Collinear Mixing Waves
NASA Astrophysics Data System (ADS)
Liu, M.; Tang, G.; Jacobs, L. J.; Qu, J.
2011-06-01
It is well known that the acoustic nonlinearity parameter β is correlated to fatigue damage in metallic materials. Various methods have been developed to measure β. One of the most often used methods is the harmonic generation technique, in which β is obtained by measuring the magnitude of the second order harmonic waves. An inherent weakness of this method is the difficulty in distinguishing material nonlinearity from the nonlinearity of the measurement system. In this paper, we demonstrate the possibility of using collinear mixing waves to measure β. The wave mixing method is based on the interaction between two incident waves in a nonlinear medium. Under certain conditions, such interactions generate a third wave of different frequency. This generated third wave is also called resonant wave, because its amplitude is unbounded if the medium has no attenuation. Such resonant waves are less sensitive to the nonlinearity of the measurement system, and have the potential to identify the source location of the nonlinearity. In this work, we used a longitudinal wave and a shear wave as the incident waves. The resonant shear wave is measured experimentally on samples made of aluminum and steel, respectively. Numerical simulations of the tests were also performed using a finite difference method.
Shortcut to adiabaticity in full-wave optics for ultra-compact waveguide junctions
NASA Astrophysics Data System (ADS)
Della Valle, Giuseppe; Perozziello, Gerardo; Longhi, Stefano
2016-09-01
We extend the concept of shortcuts to adiabaticity to full-wave optics and provide an application to the design of an ultra-compact waveguide junction. In particular, we introduce a procedure allowing one to synthesize a purely dielectric optical potential that precisely compensates for non-adiabatic losses of the transverse electric fundamental mode in any (sufficiently regular) two-dimensional waveguide junction. Our results are corroborated by finite-element method numerical simulations in a Pöschl–Teller waveguide mode expander.
Nonlinear waves in the solar atmosphere.
Ruderman, Michael S
2006-02-15
In this paper, we give a brief review of the contemporary theory of nonlinear waves in the solar atmosphere. The choice of topics reflects personal interests of the author. Historically the theory of nonlinear waves was first applied to the solar atmosphere to explain the chromospheric and coronal heating. It was assumed that the turbulent motion in the solar convective zone excites sound waves that propagate upwards. Due to nonlinearity these waves steepen and form shocks. The wave energy dissipates in these shocks thus heating the corona. We give a brief description of propagation and damping of nonlinear sound waves in the stratified solar atmosphere, and point out that, at present, the acoustic heating remains the most popular theory of heating the lower chromosphere. Then we extend the analysis to nonlinear slow magnetosonic waves in coronal plumes and loops, and discuss its implications for interpretation of observational results. The next topic of interest is the propagation of nonlinear waves in a magnetically structured atmosphere. Here, we restrict our analysis to slow sausage waves in magnetic tubes and discuss properties of solitary waves described by the Leibovich-Roberts equation. We conclude with the discussion of nonlinear theory of slow resonant layers, and its possible application to helioseismology. PMID:16414893
The adiabatic limit of the exact factorization of the electron-nuclear wave function.
Eich, F G; Agostini, Federica
2016-08-01
We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical nuclear momentum. Its dependence on the mass ratio is tested numerically on a model of proton-coupled electron transfer in different non-adiabatic regimes. PMID:27497542
The adiabatic limit of the exact factorization of the electron-nuclear wave function
NASA Astrophysics Data System (ADS)
Eich, F. G.; Agostini, Federica
2016-08-01
We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical nuclear momentum. Its dependence on the mass ratio is tested numerically on a model of proton-coupled electron transfer in different non-adiabatic regimes.
Strongly Nonlinear Stress Waves in Dissipative Metamaterials
NASA Astrophysics Data System (ADS)
Xu, Yichao; Nesterenko, Vitali
2015-06-01
We present the measurements, numerical simulations, and theoretical analysis of stress wave propagation in a one-dimensional strongly nonlinear dissipative metamaterial composed of steel disks and Nitrile O-rings. A stress wave of bell shape is generated by impactor with different masses. A strongly nonlinear double power-law is used to describe the nonlinear viscoelastic force interaction between the disks due to the compression of rubber O-rings. Numerical modeling including a nonlinear dissipative term is developed to predict the wave shape and propagation speed. The shape of generated stress wave can be dramatically changed by the viscous dissipation, which may prevent the pulse from splitting into trains of solitary waves. This strongly nonlinear dissipative metamaterial has a potential for attenuation of dynamic loading and allows an enhanced tunability of signal speed.
Dislocation nonlinearity and nonlinear wave processes in polycrystals with dislocations
NASA Astrophysics Data System (ADS)
Nazarov, V. E.
2016-09-01
Based on the modification of the linear part of the Granato-Lücke dislocation theory of absorption, the equation of state of polycrystalline solids with dissipative and reactive nonlinearity has been derived. The nonlinear effects of the interaction and self-action of longitudinal elastic waves in such media have been theoretically studied.
Linear superposition solutions to nonlinear wave equations
NASA Astrophysics Data System (ADS)
Liu, Yu
2012-11-01
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.
Adiabatic cooling of atoms by an intense standing wave
NASA Astrophysics Data System (ADS)
Chen, Jian; Story, J. G.; Tollett, J. J.; Hulet, Randall G.
1992-08-01
Lithium atoms channeled in the nodes of an intense standing-wave radiation field are cooled to near the recoil limit by adibatically reducing the radiation intensity. The final momentum distribution has a narrow component with a root-mean-squared momentum of 2ħk in one dimension, where ħk is the momentum of a radiation-field photon. The data are compared with the results of a Monte Carlo simulation using a two-level atom model. This process may be useful for cooling and increasing the phase-space density of atoms confined in a magnetic trap.
Nonlinear, relativistic Langmuir waves in astrophysical magnetospheres
NASA Technical Reports Server (NTRS)
Chian, Abraham C.-L.
1987-01-01
Large amplitude, electrostatic plasma waves are relevant to physical processes occurring in the astrophysical magnetospheres wherein charged particles are accelerated to relativistic energies by strong waves emitted by pulsars, quasars, or radio galaxies. The nonlinear, relativistic theory of traveling Langmuir waves in a cold plasma is reviewed. The cases of streaming electron plasma, electronic plasma, and two-streams are discussed.
Heavy-Ion-Acoustic Solitary and Shock Waves in an Adiabatic Multi-Ion Plasma
NASA Astrophysics Data System (ADS)
Hossen, M. A.; Rahman, M. M.; Hossen, M. R.; Mamun, A. A.
2015-08-01
The standard reductive perturbation method has been employed to derive the Korteweg-deVries (K-dV) and Burgers (BG) equations to investigate the basic properties of heavy-ion-acoustic (HIA) waves in a plasma system which is supposed to be composed of nonthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions. The HIA solitary and shock structures are found to exist with either positive or negative potential. It is found that the effects of adiabaticity of inertial heavy ions, nonthermality of electrons, and number densities of plasma components significantly modify the basic properties of the HIA solitary and shock waves. The implications of our results may be helpful in understanding the electrostatic perturbations in various laboratory and astrophysical plasma environments.
Nonlinear waves in capillary electrophoresis
Ghosal, Sandip; Chen, Zhen
2011-01-01
Electrophoretic separation of a mixture of chemical species is a fundamental technique of great usefulness in biology, health care and forensics. In capillary electrophoresis the sample migrates in a microcapillary in the presence of a background electrolyte. When the ionic concentration of the sample is sufficiently high, the signal is known to exhibit features reminiscent of nonlinear waves including sharp concentration ‘shocks’. In this paper we consider a simplified model consisting of a single sample ion and a background electrolyte consisting of a single co-ion and a counterion in the absence of any processes that might change the ionization states of the constituents. If the ionic diffusivities are assumed to be the same for all constituents the concentration of sample ion is shown to obey a one dimensional advection diffusion equation with a concentration dependent advection velocity. If the analyte concentration is sufficiently low in a suitable non-dimensional sense, Burgers’ equation is recovered, and thus, the time dependent problem is exactly solvable with arbitrary initial conditions. In the case of small diffusivity either a leading edge or trailing edge shock is formed depending on the electrophoretic mobility of the sample ion relative to the background ions. Analytical formulas are presented for the shape, width and migration velocity of the sample peak and it is shown that axial dispersion at long times may be characterized by an effective diffusivity that is exactly calculated. These results are consistent with known observations from physical and numerical simulation experiments. PMID:20238181
Linear and nonlinear heavy ion-acoustic waves in a strongly coupled plasma
Ema, S. A. Mamun, A. A.; Hossen, M. R.
2015-09-15
A theoretical study on the propagation of linear and nonlinear heavy ion-acoustic (HIA) waves in an unmagnetized, collisionless, strongly coupled plasma system has been carried out. The plasma system is assumed to contain adiabatic positively charged inertial heavy ion fluids, nonextensive distributed electrons, and Maxwellian light ions. The normal mode analysis is used to study the linear behaviour. On the other hand, the well-known reductive perturbation technique is used to derive the nonlinear dynamical equations, namely, Burgers equation and Korteweg-de Vries (K-dV) equation. They are also numerically analyzed in order to investigate the basic features of shock and solitary waves. The adiabatic effects on the HIA shock and solitary waves propagating in such a strongly coupled plasma are taken into account. It has been observed that the roles of the adiabatic positively charged heavy ions, nonextensivity of electrons, and other plasma parameters arised in this investigation have significantly modified the basic features (viz., polarity, amplitude, width, etc.) of the HIA solitary/shock waves. The findings of our results obtained from this theoretical investigation may be useful in understanding the linear as well as nonlinear phenomena associated with the HIA waves both in space and laboratory plasmas.
Linear and nonlinear heavy ion-acoustic waves in a strongly coupled plasma
NASA Astrophysics Data System (ADS)
Ema, S. A.; Hossen, M. R.; Mamun, A. A.
2015-09-01
A theoretical study on the propagation of linear and nonlinear heavy ion-acoustic (HIA) waves in an unmagnetized, collisionless, strongly coupled plasma system has been carried out. The plasma system is assumed to contain adiabatic positively charged inertial heavy ion fluids, nonextensive distributed electrons, and Maxwellian light ions. The normal mode analysis is used to study the linear behaviour. On the other hand, the well-known reductive perturbation technique is used to derive the nonlinear dynamical equations, namely, Burgers equation and Korteweg-de Vries (K-dV) equation. They are also numerically analyzed in order to investigate the basic features of shock and solitary waves. The adiabatic effects on the HIA shock and solitary waves propagating in such a strongly coupled plasma are taken into account. It has been observed that the roles of the adiabatic positively charged heavy ions, nonextensivity of electrons, and other plasma parameters arised in this investigation have significantly modified the basic features (viz., polarity, amplitude, width, etc.) of the HIA solitary/shock waves. The findings of our results obtained from this theoretical investigation may be useful in understanding the linear as well as nonlinear phenomena associated with the HIA waves both in space and laboratory plasmas.
Nonlinear density waves in planetary rings
NASA Technical Reports Server (NTRS)
Borderies, Nicole; Goldreich, Peter; Tremaine, Scott
1986-01-01
The steady-state structure of planetary rings in the presence of density waves at the Lindblad resonances of a satellite is indicated. The study is based on the dispersion relation and damping rate for nonlinear density waves, derived by Shu et al. (1985) and by Borderies, Goldreich, and Tremaine (1985). It is shown that strong density waves lead to an enhancement of the background surface density in the wave zone.
Dispersive shock waves with nonlocal nonlinearity.
Barsi, Christopher; Wan, Wenjie; Sun, Can; Fleischer, Jason W
2007-10-15
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Longitudinal nonlinear wave propagation through soft tissue.
Valdez, M; Balachandran, B
2013-04-01
In this paper, wave propagation through soft tissue is investigated. A primary aim of this investigation is to gain a fundamental understanding of the influence of soft tissue nonlinear material properties on the propagation characteristics of stress waves generated by transient loadings. Here, for computational modeling purposes, the soft tissue is modeled as a nonlinear visco-hyperelastic material, the geometry is assumed to be one-dimensional rod geometry, and uniaxial propagation of longitudinal waves is considered. By using the linearized model, a basic understanding of the characteristics of wave propagation is developed through the dispersion relation and in terms of the propagation speed and attenuation. In addition, it is illustrated as to how the linear system can be used to predict brain tissue material parameters through the use of available experimental ultrasonic attenuation curves. Furthermore, frequency thresholds for wave propagation along internal structures, such as axons in the white matter of the brain, are obtained through the linear analysis. With the nonlinear material model, the authors analyze cases in which one of the ends of the rods is fixed and the other end is subjected to a loading. Two variants of the nonlinear model are analyzed and the associated predictions are compared with the predictions of the corresponding linear model. The numerical results illustrate that one of the imprints of the nonlinearity on the wave propagation phenomenon is the steepening of the wave front, leading to jump-like variations in the stress wave profiles. This phenomenon is a consequence of the dependence of the local wave speed on the local deformation of the material. As per the predictions of the nonlinear material model, compressive waves in the structure travel faster than tensile waves. Furthermore, it is found that wave pulses with large amplitudes and small elapsed times are attenuated over shorter spans. This feature is due to the elevated
Interactive Workshop Discusses Nonlinear Waves and Chaos
NASA Astrophysics Data System (ADS)
Tsurutani, Bruce; Morales, George; Passot, Thierry
2010-07-01
Eighth International Nonlinear Wave Workshop; La Jolla, California, 1-5 March 2010; Nonlinear waves and chaos were the focus of a weeklong series of informal and interactive discussions at the Eighth International Nonlinear Wave Workshop (NWW8), held in California. The workshop gathered nonlinear plasma and water wave experts from the United States, France, Czech Republic, Germany, Greece, Holland, India, and Japan. Attendees were from the fields of space, laboratory, and fusion plasma physics, astrophysics, and applied mathematics. Special focus was placed on nonlinear waves and turbulence in the terrestrial environment as well as in the interstellar medium from observational, laboratory, and theoretical perspectives. Discussions covered temperature anisotropies and related instabilities, the properties and origin of the so-called dissipation range, and various coherent structures of electromagnetic as well as electrostatic nature. Reconnection and shocks were also topics of discussion, as were properties of magnetospheric whistler and chorus waves. Examples and analysis techniques for superdiffusion and subdiffusion were identified. On this last topic, a good exchange of ideas and results occurred between a water wave expert and a plasma expert, with the rest of the audience listening intently.
Nonlinear compressional waves in marine sediments
NASA Astrophysics Data System (ADS)
McDonald, B. Edward
2005-09-01
A theory for nonlinear waves in marine sediments must account for the presence of a granular frame filled with water and possibly gas bubbles. When grains are in full contact, the stress-strain relation for the sediment contains a contribution varying as strain to the power 3/2, referred to as the Hertz force. The quadratic nonlinearity parameter derived from the second pressure derivative with respect to density thus diverges in the limit of small strain. We present a simple nonlinear wave equation model (a variant of the NPE) for compressional waves in marine sediments that avoids Taylor expansion and the problem of diverging nonlinearity parameter. An equation of state for partially consolidated sediments is derived from consolidation test results. Pressure is found to increase with overdensity to the power 5/2, indicating an increase in the number of contacts per grain as density increases. Numerical results for nonlinear compressional waves show agreement with analytic self-similar profiles derived from the nonlinear wave equation. [Work supported by the ONR.
Nonlinear Talbot effect of rogue waves.
Zhang, Yiqi; Belić, Milivoj R; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Song, Jianping; Zhang, Yanpeng
2014-03-01
Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.
Compact waves in microscopic nonlinear diffusion.
Hurtado, P I; Krapivsky, P L
2012-06-01
We analyze the spread of a localized peak of energy into vacuum for nonlinear diffusive processes. In contrast with standard diffusion, the nonlinearity results in a compact wave with a sharp front separating the perturbed region from vacuum. In d spatial dimensions, the front advances as t^{1/(2+da)} according to hydrodynamics, with a the nonlinearity exponent. We show that fluctuations in the front position grow as ∼t^{μ}η, where μ<1/2+da is an exponent that we measure and η is a random variable whose distribution we characterize. Fluctuating corrections to hydrodynamic profiles give rise to an excess penetration into vacuum, revealing scaling behaviors and robust features. We also examine the discharge of a nonlinear rarefaction wave into vacuum. Our results suggest the existence of universal scaling behaviors at the fluctuating level in nonlinear diffusion.
Narrow-band nonlinear sea waves
NASA Technical Reports Server (NTRS)
Tayfun, M. A.
1980-01-01
Probabilistic description of nonlinear waves with a narrow-band spectrum is simplified to a form in which each realization of the surface displacement becomes an amplitude-modulated Stokes wave with a mean frequency and random phase. Under appropriate conditions this simplification provides a convenient yet rigorous means of describing nonlinear effects on sea surface properties in a semiclosed or closed form. In particular, it is shown that surface displacements are non-Gaussian and skewed, as was previously predicted by the Gram-Charlier approximation; that wave heights are Rayleigh distributed, just as in the linear case; and that crests are non-Rayleigh.
Nonlinear sharpening during superposition of surface waves
NASA Astrophysics Data System (ADS)
Chalikov, Dmitry; Babanin, Alexander V.
2016-08-01
Two-dimensional direct wave model is used for demonstration of the role of reversible interactions which probably is the main process leading to breaking. One-dimensional model was used for performing of thousands of exact short-term simulations of evolution of two superposed wave trains with different steepness, and wavenumbers were performed to investigate the effect of wave crests merging. Nonlinear sharpening of the merging crests is demonstrated. It is suggested that such effect may be responsible for appearance of the typical sharp crests of surface waves, as well as for wave breaking.
Nonlinear extraordinary wave in dense plasma
Krasovitskiy, V. B.; Turikov, V. A.
2013-10-15
Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. The possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.
Nonlinear Landau damping and Alfven wave dissipation
NASA Technical Reports Server (NTRS)
Vinas, Adolfo F.; Miller, James A.
1995-01-01
Nonlinear Landau damping has been often suggested to be the cause of the dissipation of Alfven waves in the solar wind as well as the mechanism for ion heating and selective preacceleration in solar flares. We discuss the viability of these processes in light of our theoretical and numerical results. We present one-dimensional hybrid plasma simulations of the nonlinear Landau damping of parallel Alfven waves. In this scenario, two Alfven waves nonresonantly combine to create second-order magnetic field pressure gradients, which then drive density fluctuations, which in turn drive a second-order longitudinal electric field. Under certain conditions, this electric field strongly interacts with the ambient ions via the Landau resonance which leads to a rapid dissipation of the Alfven wave energy. While there is a net flux of energy from the waves to the ions, one of the Alfven waves will grow if both have the same polarization. We compare damping and growth rates from plasma simulations with those predicted by Lee and Volk (1973), and also discuss the evolution of the ambient ion distribution. We then consider this nonlinear interaction in the presence of a spectrum of Alfven waves, and discuss the spectrum's influence on the growth or damping of a single wave. We also discuss the implications for wave dissipation and ion heating in the solar wind.
Laboratory investigation of nonlinear whistler wave processes
NASA Astrophysics Data System (ADS)
Amatucci, Bill; Tejero, Erik; Crabtree, Chris; Enloe, Lon; Blackwell, Dave; Ganguli, Guru
2015-11-01
Nonlinear interactions involving whistler wave turbulence result from processes such as wave-particle interactions in the radiation belts and instability generation in sharp magnetospheric boundary layers. Nonlinear scattering of large amplitude waves off thermal electrons substantially changes the wave vector direction and energy flux, while inducing a small frequency shift [Crabtree, Phys. Plasmas 19, 032903 (2012)]. This nonlinear scattering of primarily electrostatic lower hybrid waves into electromagnetic whistler modes is being investigated in the NRL Space Chamber under conditions scaled to match the respective environments. Lower hybrid waves are generated directly by antennas or self-consistently from sheared cross-magnetic field flows with scale length less than an ion gyroradius via the Electron-Ion Hybrid Instability [Ganguli, Phys. Fluids 31, 2753 (1988)), Amatucci, Phys. Plasmas 10, 1963 (2003)]. Sufficiently large amplitude lower hybrid waves have been observed to convert into whistler modes by scattering from thermal electrons. The plasma response as a function of transmitted lower hybrid wave amplitude is monitored with magnetic loop antennas. Details of the observed wave spectra and mode characteristics will be presented. This work supported by the NRL Base Program.
Nonlinear noise waves in soft biological tissues
NASA Astrophysics Data System (ADS)
Rudenko, O. V.; Gurbatov, S. N.; Demin, I. Yu.
2013-09-01
The study of intense waves in soft biological tissues is necessary both for diagnostics and therapeutic aims. Tissue represents an inherited medium with frequency-dependent dissipative properties, in which waves are described by nonlinear integro-differential equations. The equations for such waves are well known. Their group analysis has been performed, and a number of exact solutions have been found. However, statistical problems for nonlinear waves in tissues have hardly been studied. As well, for medical applications, both intense noise waves and waves with fluctuating parameters can be used. In addition, statistical solutions are simpler in structure than regular solutions; they are useful for understanding the physics of processes. Below a general approach is described for solving nonlinear statistical problems applied to the considered mathematical models of biological tissues. We have calculated the dependences of the intensities of the narrowband noise harmonics on distance. For wideband noise, we have calculated the dependence of the spectral integral intensity on distance. In all cases, wave attenuation is determined both by the specific dissipative properties of the tissue and the nonlinearity of the medium.
Boosted X Waves in Nonlinear Optical Systems
Arevalo, Edward
2010-01-15
X waves are spatiotemporal optical waves with intriguing superluminal and subluminal characteristics. Here we theoretically show that for a given initial carrier frequency of the system localized waves with genuine superluminal or subluminal group velocity can emerge from initial X waves in nonlinear optical systems with normal group velocity dispersion. Moreover, we show that this temporal behavior depends on the wave detuning from the carrier frequency of the system and not on the particular X-wave biconical form. A spatial counterpart of this behavior is also found when initial X waves are boosted in the plane transverse to the direction of propagation, so a fully spatiotemporal motion of localized waves can be observed.
Boosted X waves in nonlinear optical systems.
Arévalo, Edward
2010-01-15
X waves are spatiotemporal optical waves with intriguing superluminal and subluminal characteristics. Here we theoretically show that for a given initial carrier frequency of the system localized waves with genuine superluminal or subluminal group velocity can emerge from initial X waves in nonlinear optical systems with normal group velocity dispersion. Moreover, we show that this temporal behavior depends on the wave detuning from the carrier frequency of the system and not on the particular X-wave biconical form. A spatial counterpart of this behavior is also found when initial X waves are boosted in the plane transverse to the direction of propagation, so a fully spatiotemporal motion of localized waves can be observed.
A Numerical Study of Nonlinear Wave Interactions
NASA Astrophysics Data System (ADS)
de Bakker, A.; Tissier, M.; Ruessink, G.
2014-12-01
Nonlinear triad interactions redistribute energy among a wave field, which transforms the shape of the incident short waves (f = 0.05 - 2 Hz) and generates energy at infragravity frequencies (f = 0.005-0.05 Hz). Recently, it has been suggested that infragravity energy may dissipate by energy transfers from infragravity frequencies to either the (former) short-wave spectral peak, or through infragravity-infragravity self-interactions that cause the infragravity waves to steepen and to eventually break. To investigate these infragravity dissipation mechanisms, we use the non-hydrostatic SWASH model. In this study, we first validate the model with the high-resolution GLOBEX laboratory data set and then explore the dependence of the energy transfers, with a focus on infragravity frequencies, on beach slope. Consistent with previous studies we find that SWASH is able to reproduce the transformation and corresponding nonlinear energy transfers of shoreward propagating waves to great detail. Bispectral analysis is used to study the coupling between wave frequencies; nonlinear energy transfers are then quantified using the Boussinesq coupling coefficient. To obtain more detailed insight we divide the nonlinear interactions in four categories based on triads including 1) infragravity frequencies only, 2) two infragravity frequencies and one short-wave frequency, 3) one infragravity frequency and two short-wave frequencies and 4) short-wave frequencies only. Preliminary results suggest that interactions are rather weak on gently beach slopes (1:80) and, in the innermost part of the surf zone, are dominated by infragravity-infragravity interactions. On steeper slopes (1:20), interactions are stronger, but entirely dominated by those involving short-wave frequencies only. The dependence of the transfers on offshore wave conditions and beach shape will be explored too. Funded by NWO.
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming
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 gravity-capillary water waves
NASA Astrophysics Data System (ADS)
Jiang, Lei
1997-11-01
Two-dimensional gravity-capillary water waves are analyzed using a fully-nonlinear Cauchy-integral method with spectral accuracy. Standing waves are generated in experiments by vertical oscillation and measured by a non-intrusive optical system along with a wave probe. Nonlinear resonance of standing waves with non-wetting contact line effects are discussed in detail. Amplitude- dependent wave frequency and damping in a glass rectangular tank suggest a new contact-line model. A new type of sideband resonance due to modulated forcing is discovered and explained by weakly-nonlinear analysis. This analytical solution is verified by our numerical simulations and physical experiments. New standing waveforms with dimpled or sharp crests are observed in experiments and computations. These new waveforms have strong symmetry breaking in time as a result of nonlinear harmonic interaction. With increasing wave steepness, steep standing waves experience period- tripling with three distinct forms: sharp crest, dimpled or flat crest, and round crest. Significant breaking occurs in the sharp-crest mode and the dimpled-crest mode. Using a complex-demodulation technique, I find that these breaking waves are related to the same 1:2 internal resonance (harmonic interaction) that causes the new steep waveforms. Novel approaches are used to estimate the (breaking and non-breaking) wave dissipation in steep and breaking standing waves. The breaking events (spray, air entrainment, and plunging) approximately double the wave dissipation. Weak capillarity significantly affects the limiting wave height and the form of standing waves, as demonstrated by both computations and small-scale Faraday-wave experiments. Capillary ripple generation on traveling waves is shown to be significant even at moderate wave steepness. The ubiquitous horizontal asymmetry of traveling waves is shown to be critical to capillary ripple generation. Two new asymmetric modes are identified and are shown to have an
Kinetic effects on Alfven wave nonlinearity. II - The modified nonlinear wave equation
NASA Technical Reports Server (NTRS)
Spangler, Steven R.
1990-01-01
A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.
Solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity.
Cooper, Fred; Khare, Avinash; Mihaila, Bogdan; Saxena, Avadh
2010-09-01
We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction g{2}/k+1(ΨΨ){k+1} , as well as a vector-vector self interaction g{2}/k+1(Ψγ{μ}ΨΨγ{μ}Ψ){1/2(k+1)} . We find the exact analytic form for solitary waves for arbitrary k and find that they are a generalization of the exact solutions for the nonlinear Schrödinger equation (NLSE) and reduce to these solutions in a well defined nonrelativistic limit. We perform the nonrelativistic reduction and find the 1/2m correction to the NLSE, valid when |ω-m|<2m , where ω is the frequency of the solitary wave in the rest frame. We discuss the stability and blowup of solitary waves assuming the modified NLSE is valid and find that they should be stable for k<2 . PMID:21230200
Nonlinear traveling waves in confined ferrofluids.
Lira, Sérgio A; Miranda, José A
2012-11-01
We study the development of nonlinear traveling waves on the interface separating two viscous fluids flowing in parallel in a vertical Hele-Shaw cell. One of the fluids is a ferrofluid and a uniform magnetic field is applied in the plane of the cell, making an angle with the initially undisturbed interface. We employ a mode-coupling theory that predicts the possibility of controlling the speed of the waves by purely magnetic means. The influence of the tilted magnetic field on the waves shape profile and the establishment of stationary traveling wave structures are investigated. PMID:23214870
Artemyev, A. V. Vasiliev, A. A.; Mourenas, D.; Krasnoselskikh, V. V.
2014-10-15
In this paper, we consider high-energy electron scattering and nonlinear trapping by oblique whistler waves via the Landau resonance. We use recent spacecraft observations in the radiation belts to construct the whistler wave model. The main purpose of the paper is to provide an estimate of the critical wave amplitude for which the nonlinear wave-particle resonant interaction becomes more important than particle scattering. To this aim, we derive an analytical expression describing the particle scattering by large amplitude whistler waves and compare the corresponding effect with the nonlinear particle acceleration due to trapping. The latter is much more rare but the corresponding change of energy is substantially larger than energy jumps due to scattering. We show that for reasonable wave amplitudes ∼10–100 mV/m of strong whistlers, the nonlinear effects are more important than the linear and nonlinear scattering for electrons with energies ∼10–50 keV. We test the dependencies of the critical wave amplitude on system parameters (background plasma density, wave frequency, etc.). We discuss the role of obtained results for the theoretical description of the nonlinear wave amplification in radiation belts.
Nonlinear Interaction of Waves in Geomaterials
NASA Astrophysics Data System (ADS)
Ostrovsky, L. A.
2009-05-01
Progress of 1990s - 2000s in studying vibroacoustic nonlinearities in geomaterials is largely related to experiments in resonance samples of rock and soils. It is now a common knowledge that many such materials are very strongly nonlinear, and they are characterized by hysteresis in the dependence between the stress and strain tensors, as well as by nonlinear relaxation ("slow time"). Elastic wave propagation in such media has many peculiarities; for example, third harmonic amplitude is a quadratic (not cubic as in classical solids) function of the main harmonic amplitude, and average wave velocity is linearly (not quadratically as usual) dependent on amplitude. The mechanisms of these peculiarities are related to complex structure of a material typically consisting of two phases: a hard matrix and relatively soft inclusions such as microcracks and grain contacts. Although most informative experimental results have been obtained in rock in the form of resonant bars, few theoretical models are yet available to describe and calculate waves interacting in such samples. In this presentation, a brief overview of structural vibroacoustic nonlinearities in rock is given first. Then, a simple but rather general approach to the description of wave interaction in solid resonators is developed based on accounting for resonance nonlinear perturbations which are cumulating from period to period. In particular, the similarity and the differences between traveling waves and counter-propagating waves are analyzed for materials with different stress-strain dependences. These data can be used for solving an inverse problem, i.e. characterizing nonlinear properties of a geomaterial by its measured vibroacoustic parameters. References: 1. L. Ostrovsky and P. Johnson, Riv. Nuovo Chimento, v. 24, 1-46, 2007 (a review); 2. L. Ostrovsky, J. Acoust. Soc. Amer., v. 116, 3348-3353, 2004.
Laboratory investigation of nonlinear whistler wave processes
NASA Astrophysics Data System (ADS)
Amatucci, B.; Tejero, E.; Cothran, C.; Ganguli, G.; Crabtree, C.; Mithiawala, M.; Sotnikov, V.
2012-10-01
Nonlinear interactions involving whistler wave turbulence result from processes, including wave-particle interactions and instabilities in sharp boundary layers. Given sufficient whistler energy density, nonlinear scattering off thermal electrons substantially changes the wave vector direction and energy flux, while inducing a small frequency shift.footnotetextCrabtree et al., Phys. Plasmas, 19, Art. No. 032903 (2012). In the magnetosphere, boundary layers often have highly sheared plasma flows and lower hybrid turbulence. Such nonlinear processes are being investigated in the NRL Space Chamber in conditions scaled to match the respective environments. By creating boundary layers with controllable density gradient and transverse electric fields and scale length much smaller than an ion gyroradius, lower hybrid waves consistent with the Electron-Ion Hybrid InstabilityfootnotetextGanguli et al., Phys. Fluids, 31, 2753 (1988). have been observed. Sufficiently large amplitude lower hybrid waves have been observed to scatter into whistler modes by scattering from thermal electrons. The plasma response as a function of transmitted lower hybrid wave amplitude is monitored with magnetic antennas. Details of the observed wave spectra and mode characteristics will be presented.
Nonlinear Internal Waves - Evolution and Energy Dissipation
NASA Astrophysics Data System (ADS)
Orr, M.; Mignerey, P.
2003-04-01
Nonlinear internal waves have been observed propagating up the slope of the South China Sea during the recent ONR Asian Seas International Acoustics Experiment. Energy dissipation rates have been extracted. The location of the initiation of the depression to elevation conversion has been identified. Scaling parameters have been extracted and used to initialize a two-layer evolution equation model simulation. Mode1, 2 linear and nonlinear internal waves and instabilities have been observed near the shelf break of the United States of America New Jersey Shelf. Acoustic flow visualization records will be presented. Work supported by the Office of Naval Research (ONR) Ocean Acoustics Program and ONR's NRL base funding.
Nonlinear excited waves on the interventricular septum
NASA Astrophysics Data System (ADS)
Bekki, Naoaki; Harada, Yoshifumi; Kanai, Hiroshi
2012-11-01
Using a novel ultrasonic noninvasive imaging method, we observe some phase singularities in propagating excited waves on a human cardiac interventricular septum (IVS) for a healthy young male. We present a possible physical model explaining one-dimensional dynamics of phase singularities in nonlinearly excited waves on the IVS. We show that at least one of the observed phase singularities in the excited waves on the IVS can be explained by the Bekki-Nozaki hole solution of the complex Ginzburg-Landau equation without any adjustable parameters. We conclude that the complex Ginzburg-Landau equation is such a suitable model for one-dimensional dynamics of cardiac phase singularities in nonlinearly excited waves on the IVS.
Optics in a nonlinear gravitational plane wave
NASA Astrophysics Data System (ADS)
Harte, Abraham I.
2015-09-01
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. At least for freely falling sources and observers, it is shown that the commonly-used predictions of linear perturbation theory can be generically overshadowed by nonlinear effects; even for very weak gravitational waves, higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected when considering observations of sufficiently distant sources. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.
Nonlinear whistler wave scattering in space plasmas
Yukhimuk, V.; Roussel-Dupre, R.
1997-04-01
In this paper the evolution of nonlinear scattering of whistler mode waves by kinetic Alfven waves (KAW) in time and two spatial dimensions is studied analytically. The authors suggest this nonlinear process as a mechanism of kinetic Alfven wave generation in space plasmas. This mechanism can explain the dependence of Alfven wave generation on whistler waves observed in magnetospheric and ionospheric plasmas. The observational data show a dependence for the generation of long periodic pulsations Pc5 on whistler wave excitation in the auroral and subauroral zone of the magnetosphere. This dependence was first observed by Ondoh T.I. For 79 cases of VLF wave excitation registered by Ondoh at College Observatory (L=64.6 N), 52 of them were followed by Pc5 geomagnetic pulsation generation. Similar results were obtained at the Loparskaia Observatory (L=64 N) for auroral and subauroral zone of the magnetosphere. Thus, in 95% of the cases when VLF wave excitation occurred the generation of long periodic geomagnetic pulsations Pc5 were observed. The observations also show that geomagnetic pulsations Pc5 are excited simultaneously or insignificantly later than VLF waves. In fact these two phenomena are associated genetically: the excitation of VLF waves leads to the generation of geomagnetic pulsations Pc5. The observations show intensive generation of geomagnetic pulsations during thunderstorms. Using an electromagnetic noise monitoring system covering the ULF range (0.01-10 Hz) A.S. Fraser-Smith observed intensive ULF electromagnetic wave during a large thunderstorm near the San-Francisco Bay area on September 23, 1990. According to this data the most significant amplification in ULF wave activity was observed for waves with a frequency of 0.01 Hz and it is entirely possible that stronger enhancements would have been measured at lower frequencies.
Extended adiabatic blast waves and a model of the soft X-ray background. [interstellar matter
NASA Technical Reports Server (NTRS)
Cox, D. P.; Anderson, P. R.
1981-01-01
An analytical approximation is generated which follows the development of an adiabatic spherical blast wave in a homogeneous ambient medium of finite pressure. An analytical approximation is also presented for the electron temperature distribution resulting from coulomb collisional heating. The dynamical, thermal, ionization, and spectral structures are calculated for blast waves of energy E sub 0 = 5 x 10 to the 50th power ergs in a hot low-density interstellar environment. A formula is presented for estimating the luminosity evolution of such explosions. The B and C bands of the soft X-ray background, it is shown, are reproduced by such a model explosion if the ambient density is about .000004 cm, the blast radius is roughly 100 pc, and the solar system is located inside the shocked region. Evolution in a pre-existing cavity with a strong density gradient may, it is suggested, remove both the M band and OVI discrepancies.
Nonlinear interaction of kinetic Alfven wave and whistler: Turbulent spectra and anisotropic scaling
Kumar Dwivedi, Navin; Sharma, R. P.
2013-04-15
In this work, we are presenting the excitation of oblique propagating whistler wave as a consequence of nonlinear interaction between whistler wave and kinetic Alfven wave (KAW) in intermediate beta plasmas. Numerical simulation has been done to study the transient evolution of magnetic field structures of KAW when the nonlinearity arises due to ponderomotive effects by taking the adiabatic response of the background density. Weak oblique propagating whistler signals in these nonlinear plasma density filaments (produced by KAW localization) get amplified. The spectral indices of the power spectrum at different times are calculated with given initial conditions of the simulations. Anisotropic scaling laws for KAW and whistlers are presented. The relevance of the present investigation to solar wind turbulence and its acceleration is also pointed out.
Incompressible magnetohydrodynamic surface waves - Nonlinear aspects
NASA Technical Reports Server (NTRS)
Hollweg, Joseph V.
1987-01-01
The nonlinear properties of MHD surface waves in the solar atmosphere are investigated analytically, assuming that the fluid is incompressible and that the waves are confined to a single surface, with semiinfinite regions on both sides. The governing equations are derived in detail, and qualitative results are presented in a graph. For propagating waves, second-order terms in the wave amplitude are found to lead to wave steepening at leading or trailing edges, the steepening rate becoming very large as the threshold for the linear Kelvin-Helmholtz instability is approached. Second-order effects on standing waves include crest and trough sharpening (increasing with time), a current independent of distance on the surface but decreasing exponentially with distance from the surface, and pressure-field fluctuations of infinite extent. It is suggested that these effects could account for a large fraction of solar-atmosphere heating.
Nonlinear random optical waves: Integrable turbulence, rogue waves and intermittency
NASA Astrophysics Data System (ADS)
Randoux, Stéphane; Walczak, Pierre; Onorato, Miguel; Suret, Pierre
2016-10-01
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we specifically focus on optical fiber systems accurately described by the integrable one-dimensional nonlinear Schrödinger equation. We consider random complex fields having a Gaussian statistics and an infinite extension at initial stage. We use numerical simulations with periodic boundary conditions and optical fiber experiments to investigate spectral and statistical changes experienced by nonlinear waves in focusing and in defocusing propagation regimes. As a result of nonlinear propagation, the power spectrum of the random wave broadens and takes exponential wings both in focusing and in defocusing regimes. Heavy-tailed deviations from Gaussian statistics are observed in focusing regime while low-tailed deviations from Gaussian statistics are observed in defocusing regime. After some transient evolution, the wave system is found to exhibit a statistically stationary state in which neither the probability density function of the wave field nor the spectrum changes with the evolution variable. Separating fluctuations of small scale from fluctuations of large scale both in focusing and defocusing regimes, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian.
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
Nonlinear MHD Waves in a Prominence Foot
NASA Astrophysics Data System (ADS)
Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.
2015-11-01
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ˜ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5-11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5-14 G. For the typical prominence density the corresponding fast magnetosonic speed is ˜20 km s-1, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
Nonlinear analysis of helix traveling wave tubes
Freund, H.P.; Zaidman, E.G.; Mankofsky, A.; Vanderplaats, N.R.; Kodis, M.A.
1995-10-01
A time-dependent nonlinear formulation of the interaction in the helix traveling wave tube is presented for a configuration in which an electron beam propagates through a sheath helix surrounded by a conducting wall. In order to describe both the variation in the wave dispersion and in the transverse inhomogeneity of the electromagnetic field with wave number, the field is represented as a superposition of waves in a vacuum sheath helix. An overall explicit sinusoidal variation of the form exp({ital ikz}{minus}{ital i}{omega}{ital t}) is assumed (where {omega} denotes the angular frequency corresponding to the wave number {ital k} in the vacuum sheath helix), and the polarization and radial variation of each wave is determined by the boundary conditions in a vacuum sheath helix. Thus, while the field is three-dimensional in nature, it is azimuthally symmetric. The propagation of each wave {ital in} {ital vacuo} as well as the interaction of each wave with the electron beam is included by allowing the amplitudes of the waves to vary in {ital z} and {ital t}. A dynamical equation for the field amplitudes is derived analogously to Poynting`s equation, and solved in conjunction with the three-dimensional Lorentz force equations for an ensemble of electrons. Numerical examples are presented corresponding to both single- and multiwave interactions. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Nonlinear guided wave propagation in prestressed plates.
Pau, Annamaria; Lanza di Scalea, Francesco
2015-03-01
The measurement of stress in a structure presents considerable interest in many fields of engineering. In this paper, the diagnostic potential of nonlinear elastic guided waves in a prestressed plate is investigated. To do so, an analytical model is formulated accounting for different aspects involved in the phenomenon. The fact that the initial strains can be finite is considered using the Green Lagrange strain tensor, and initial and final configurations are not merged, as it would be assumed in the infinitesimal strain theory. Moreover, an appropriate third-order expression of the strain energy of the hyperelastic body is adopted to account for the material nonlinearities. The model obtained enables to investigate both the linearized case, which gives the variation of phase and group velocity as a function of the initial stress, and the nonlinear case, involving second-harmonic generation as a function of the initial state of stress. The analysis is limited to Rayleigh-Lamb waves propagating in a plate. Three cases of initial prestress are considered, including prestress in the direction of the wave propagation, prestress orthogonal to the direction of wave propagation, and plane isotropic stress.
Nonlinear guided wave propagation in prestressed plates.
Pau, Annamaria; Lanza di Scalea, Francesco
2015-03-01
The measurement of stress in a structure presents considerable interest in many fields of engineering. In this paper, the diagnostic potential of nonlinear elastic guided waves in a prestressed plate is investigated. To do so, an analytical model is formulated accounting for different aspects involved in the phenomenon. The fact that the initial strains can be finite is considered using the Green Lagrange strain tensor, and initial and final configurations are not merged, as it would be assumed in the infinitesimal strain theory. Moreover, an appropriate third-order expression of the strain energy of the hyperelastic body is adopted to account for the material nonlinearities. The model obtained enables to investigate both the linearized case, which gives the variation of phase and group velocity as a function of the initial stress, and the nonlinear case, involving second-harmonic generation as a function of the initial state of stress. The analysis is limited to Rayleigh-Lamb waves propagating in a plate. Three cases of initial prestress are considered, including prestress in the direction of the wave propagation, prestress orthogonal to the direction of wave propagation, and plane isotropic stress. PMID:25786963
Nonlinear acoustic wave propagation in atmosphere
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1985-01-01
A model problem that simulates an atmospheric acoustic wave propagation situation that is nonlinear is considered. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.
Nonlinear acoustic wave propagation in atmosphere
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1986-01-01
In this paper a model problem is considered that simulates an atmospheric acoustic wave propagation situation that is nonlinear. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well-posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.
Nonlinear plasma wave in magnetized plasmas
NASA Astrophysics Data System (ADS)
Bulanov, Sergei V.; Zh. Esirkepov, Timur; Kando, Masaki; Koga, James K.; Hosokai, Tomonao; Zhidkov, Alexei G.; Kodama, Ryosuke
2013-08-01
Nonlinear axisymmetric cylindrical plasma oscillations in magnetized collisionless plasmas are a model for the electron fluid collapse on the axis behind an ultrashort relativisically intense laser pulse exciting a plasma wake wave. We present an analytical description of the strongly nonlinear oscillations showing that the magnetic field prevents closing of the cavity formed behind the laser pulse. This effect is demonstrated with 3D PIC simulations of the laser-plasma interaction. An analysis of the betatron oscillations of fast electrons in the presence of the magnetic field reveals a characteristic "Four-Ray Star" pattern.
Relationship among shock-wave velocity, particle velocity, and adiabatic exponent for dry air
NASA Astrophysics Data System (ADS)
Kim, In H.; Hong, Sang H.; Jhung, Kyu S.; Oh, Ki-Hwan; Yoon, Yo K.
1991-07-01
Using the results of the detailed numerical calculations, it is shown that the relationship between the shock-wave velocity U sub s and the particle velocity U sub p for shock-compressed dry air can be represented accurately by the linear relation U sub s = a(P0) + b(P0)U sub p in a wide range of U sub p (U sub p = 2 to 9 ) km/s and initial pressure P0 = 10 to the -6th to 1 atm, where a and b are given by the cubic polynomials of log10P0. Based on the linear U sub s - U sub p relation, an analytic expression has been obtained for the adiabatic exponent gamma as a function of particle velocity.
Filtering of matter-wave vibrational states via spatial adiabatic passage
Loiko, Yu.; Ahufinger, V.; Corbalan, R.; Mompart, J.; Birkl, G.
2011-03-15
We discuss the filtering of the vibrational states of a cold atom in an optical trap by chaining this trap with two empty ones and adiabatically controlling the tunneling. Matter-wave filtering is performed by selectively transferring the population of the highest populated vibrational state to the most distant trap while the population of the rest of the states remains in the initial trap. Analytical conditions for two-state filtering are derived and then applied to an arbitrary number of populated bound states. Realistic numerical simulations close to state-of-the-art experimental arrangements are performed by modeling the triple well with time-dependent Poeschl-Teller potentials. In addition to filtering of vibrational states, we discuss applications for quantum tomography of the initial population distribution and engineering of atomic Fock states that, eventually, could be used for tunneling-assisted evaporative cooling.
Extended adiabatic blast waves and a model of the soft X-ray background
NASA Technical Reports Server (NTRS)
Cox, D. P.; Anderson, P. R.
1982-01-01
The suggestion has been made that much of the soft X-ray background observed in X-ray astronomy might arise from being inside a very large supernova blast wave propagating in the hot, low-density component of the interstellar (ISM) medium. An investigation is conducted to study this possibility. An analytic approximation is presented for the nonsimilar time evolution of the dynamic structure of an adiabatic blast wave generated by a point explosion in a homogeneous ambient medium. A scheme is provided for evaluating the electron-temperature distribution for the evolving structure, and a procedure is presented for following the state of a given fluid element through the evolving dynamical and thermal structures. The results of the investigation show that, if the solar system were located within a blast wave, the Wisconsin soft X-ray rocket payload would measure the B and C band count rates that it does measure, provided conditions correspond to the values calculated in the investigation.
Nonlinear wave vacillation in the atmosphere
NASA Technical Reports Server (NTRS)
Antar, Basil N.
1987-01-01
The problem of vacillation in a baroclinically unstable flow field is studied through the time evolution of a single nonlinearly unstable wave. To this end a computer code is being developed to solve numerically for the time evolution of the amplitude of such a wave. The final working code will be the end product resulting from the development of a heirarchy of codes with increasing complexity. The first code in this series was completed and is undergoing several diagnostic analyses to verify its validity. The development of this code is detailed.
Nonlinear Generation of Vorticity by Surface Waves.
Filatov, S V; Parfenyev, V M; Vergeles, S S; Brazhnikov, M Yu; Levchenko, A A; Lebedev, V V
2016-02-01
We demonstrate that waves excited on a fluid surface produce local surface rotation owing to hydrodynamic nonlinearity. We examine theoretically the effect and obtain an explicit formula for the vertical vorticity in terms of the surface elevation. Our theoretical predictions are confirmed by measurements of surface motion in a cell with water where surface waves are excited by vertical and harmonic shaking the cell. The experimental data are in good agreement with the theoretical predictions. We discuss physical consequences of the effect. PMID:26894714
Variational modelling of nonlinear water waves
NASA Astrophysics Data System (ADS)
Kalogirou, Anna; Bokhove, Onno
2015-11-01
Mathematical modelling of water waves is demonstrated by investigating variational methods. A potential flow water wave model is derived using variational techniques and extented to include explicit time-dependence, leading to non-autonomous dynamics. As a first example, we consider the problem of a soliton splash in a long wave channel with a contraction at its end, resulting after a sluice gate is removed at a finite time. The removal of the sluice gate is included in the variational principle through a time-dependent gravitational potential. A second example involving non-autonomous dynamics concerns the motion of a free surface in a vertical Hele-Shaw cell. Explicit time-dependence now enters the model through a linear damping term due to the effect of wall friction and a term representing the motion of an artificially driven wave pump. In both cases, the model is solved numerically using a Galerkin FEM and the numerical results are compared to wave structures observed in experiments. The water wave model is also adapted to accommodate nonlinear ship dynamics. The novelty is this case is the coupling between the water wave dynamics, the ship dynamics and water line dynamics on the ship. For simplicity, we consider a simple ship structure consisting of V-shaped cross-sections.
Nonlinear diffusion-wave equation for a gas in a regenerator subject to temperature gradient
NASA Astrophysics Data System (ADS)
Sugimoto, N.
2015-10-01
This paper derives an approximate equation for propagation of nonlinear thermoacoustic waves in a gas-filled, circular pore subject to temperature gradient. The pore radius is assumed to be much smaller than a thickness of thermoviscous diffusion layer, and the narrow-tube approximation is used in the sense that a typical axial length associated with temperature gradient is much longer than the radius. Introducing three small parameters, one being the ratio of the pore radius to the thickness of thermoviscous diffusion layer, another the ratio of a typical speed of thermoacoustic waves to an adiabatic sound speed and the other the ratio of a typical magnitude of pressure disturbance to a uniform pressure in a quiescent state, a system of fluid dynamical equations for an ideal gas is reduced asymptotically to a nonlinear diffusion-wave equation by using boundary conditions on a pore wall. Discussion on a temporal mean of an excess pressure due to periodic oscillations is included.
Probing Acoustic Nonlinearity by Mixing Surface Acoustic Waves
Hurley, David Howard; Telschow, Kenneth Louis
2000-07-01
Measurement methods aimed at determining material properties through nonlinear wave propagation are sensitive to artifacts caused by background nonlinearities inherent in the ultrasonic generation and detection methods. The focus of this paper is to describe our investigation of nonlinear mixing of surface acoustic waves (SAWs) as a means to decrease sensitivity to background nonlinearity and increase spatial sensitivity to acoustic nonlinearity induced by material microstructure.
Nonlinear waves with negative phase velocity.
Huang, Xiaoqing; Liao, Xuhong; Cui, Xiaohua; Zhang, Hong; Hu, Gang
2009-09-01
Recently, waves propagating with negative phase velocity [simply called antiwaves (AWs)] have attracted great attention in the area of nonlinear oscillatory systems. In the present work we investigate the parameter conditions for AWs. So far AWs have been revealed from systems slightly beyond Hopf bifurcation or some other instabilities, and from some wave sources with certain restricted frequencies. Here we study general oscillatory media (including generalized complex Ginzburg-Landau systems and Brusselator model) and specify the parameter conditions of AWs by certain characteristic behaviors of the dispersion relation of the systems. Moreover, we predict that AWs and NWs (normal waves with positive phase velocity) can be realized at a same intrinsic parameter values but different pacing frequencies in parameter regions where the dispersion relation exhibits a maximum or minimum. All numerical simulations are perfectly consistent with these theoretical predictions where the oscillatory systems are driven by external periodic pacings with 1:1 frequency locking responses. PMID:19905204
Nonlinear waves with negative phase velocity
NASA Astrophysics Data System (ADS)
Huang, Xiaoqing; Liao, Xuhong; Cui, Xiaohua; Zhang, Hong; Hu, Gang
2009-09-01
Recently, waves propagating with negative phase velocity [simply called antiwaves (AWs)] have attracted great attention in the area of nonlinear oscillatory systems. In the present work we investigate the parameter conditions for AWs. So far AWs have been revealed from systems slightly beyond Hopf bifurcation or some other instabilities, and from some wave sources with certain restricted frequencies. Here we study general oscillatory media (including generalized complex Ginzburg-Landau systems and Brusselator model) and specify the parameter conditions of AWs by certain characteristic behaviors of the dispersion relation of the systems. Moreover, we predict that AWs and NWs (normal waves with positive phase velocity) can be realized at a same intrinsic parameter values but different pacing frequencies in parameter regions where the dispersion relation exhibits a maximum or minimum. All numerical simulations are perfectly consistent with these theoretical predictions where the oscillatory systems are driven by external periodic pacings with 1:1 frequency locking responses.
Linear and Nonlinear Electrostatic Waves in Unmagnetized Dusty Plasmas
Mamun, A. A.; Shukla, P. K.
2010-12-14
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.
Detecting plastic strain distribution by a nonlinear wave mixing method
NASA Astrophysics Data System (ADS)
Tang, Guangxin; Liu, Minghe; Jacobs, Laurence J.; Qu, Jianmin
2013-01-01
A nonlinear wave mixing method is used to measure the plastic strain distribution in polycrystalline materials. A pair of collinear longitudinal and shear waves is generated. Under the phase matching condition, a resonant shear wave with a difference frequency is generated and propagates towards the shear wave transducer. The amplitude of this resonant shear wave is proportional to the acoustic nonlinearity parameter β, which is known to be related to plastic deformation. By adjusting the two primary waves so that they mix at different locations, the distribution of β can be obtained. This study demonstrates the feasibility of detecting plastic strain distribution in polycrystalline materials by the nonlinear wave mixing technique.
Nonlinear traveling wave solution for the MJO skeleton model
NASA Astrophysics Data System (ADS)
Chen, S.; Stechmann, S. N.
2014-12-01
Recently, a minimal dynamical model is presented for capturing MJO's fundamental features. The model is a nonlinear oscillator model for the MJO skeleton and it involves interactions between convection, moisture and circulation. I will present the exact nonlinear traveling wave solutions for the model based on its energy conservation. The exact nonlinear solution provides for an explicit comparison of features between linear and nonlinear waves such as dispersion relations and traveling wave speeds. Moreover, the nonlinear solutions, compared with the linear ones, produce a narrow region of active convection and a wider region of suppressed convection. These predictions offer nonlinear MJO features that could potentially be targets of observational investigations.
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.
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 ion acoustic waves scattered by vortexes
NASA Astrophysics Data System (ADS)
Ohno, Yuji; Yoshida, Zensho
2016-09-01
The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.
Nonlinear wave scattering and electron beam relaxation
NASA Technical Reports Server (NTRS)
Muschietti, L.; Dum, C. T.
1991-01-01
The role played by nonlinear scattering during the relaxation of a warm electron beam is investigated through a numerical code based on kinetic equations. The code encompasses the quasi-linear wave-electron interaction and wave-wave scattering off ion clouds. Ions with velocities 2 nu sub i (nu sub i being the ion thermal velocity) are found to be the most efficient for scattering the Langmuir waves off their polarization clouds. The transfer rate of the spectrum out of resonance with the beam is larger by a factor 3 compared to usual estimates. The changes produced in the dispersion relation by the presence of the beam electrons dramatically alter the characteristics of the secondary spectrum. In a late phase the classic condensate K of about 0 is depleted, with the formation of a new condensate in resonance with the flat-topped beam distribution, which follows from the fact that the mere presence of the beam electrons creates a minimum in the frequency-wave-number relation. For strong and slow beams, the predictions of the code are found to be in excellent agreement with the results of the particle simulation if a dispersion relation that includes the beam is used.
Nonlinear scattering of acoustic waves by vibrating obstacles
NASA Astrophysics Data System (ADS)
Piquette, J. C.
1983-06-01
The problem of the generation of sum- and difference-frequency waves produced via the scattering of an acoustic wave by an obstacle whose surface vibrates harmonically was studied both theoretically and experimentally. The theoretical approach involved solving the nonlinear wave equation, subject to appropriate boundary conditions, by the use of a perturbation expansion of the fields and a Green's function method. In addition to ordinary rigid-body scattering, Censor predicted nongrowing waves at frequencies equal to the sum and to the difference of the frequencies of the primary waves. The solution to the nonlinear wave equation also yields scattered waves at the sum and difference frequencies. However, the nonlinearity of the medium causes these waves to grow with increasing distance from the scatter's surface and, after a very small distance, dominate those predicted by Censor. The simple-source formulation of the second-order nonlinear wave equation for a lossless fluid medium has been derived for arbitrary primary wave fields. This equation was used to solve the problem of nonlinear scattering of acoustic waves by a vibrating obstacle for three geometries: (1) a plane-wave scattering by a vibrating plane, (2) cylindrical-wave scattering by a vibrating cylinder, and (3) plane-wave scattering by a vibrating cylinder. Successful experimental validation of the theory was inhibited by previously unexpected levels of nonlinearity in the hydrophones used. Such high levels of hydrophone nonlinearity appeared in hydrophones that, by their geometry of construction, were expected to be fairly linear.
Nonlinear shallow ocean-wave soliton interactions on flat beaches.
Ablowitz, Mark J; Baldwin, Douglas E
2012-09-01
Ocean waves are complex and often turbulent. While most ocean-wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these shallow-water nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. Here we report that such nonlinear interactions occur every day, close to low tide, on two flat beaches that are about 2000 km apart. These interactions are closely related to the analytic, soliton solutions of a widely studied multidimensional nonlinear wave equation. On a much larger scale, tsunami waves can merge in similar ways.
Electromagnetic shock wave in nonlinear vacuum: exact solution.
Kovachev, Lubomir M; Georgieva, Daniela A; Kovachev, Kamen L
2012-10-01
An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. An exact solution with its own angular momentum in the form of a shock wave is obtained.
Nonlinear Dispersion of Magnetostatic Surface Waves on Ferromagnetic Films
NASA Astrophysics Data System (ADS)
A, D. Boardman; Bao, Jiashan; Wang, Qi; Cai, Yingshi; S, A. Nikitov
1991-11-01
The wave equation of nonlinear magnetostatic surface waves (MSSW) on ferromagnetic films is derived and its solution is found. The nonlinear dispersion relation of MSSW is discussed. Our result shows that the wave power has a little effect to the frequency shift of MSSW with lower frequency, but has a considerably larger effect to that with higher frequency within the band.
Group velocity and nonlinear dispersive wave propagation.
NASA Technical Reports Server (NTRS)
Hayes, W. D.
1973-01-01
By the use of a Hamiltonian formulation, a basic group velocity is defined as the derivative of frequency with respect to wavenumber keeping action density constant, and is shown to represent an incremental action velocity in the general nonlinear case. The stability treatment of Whitham and Lighthill is extended to several dimensions. The water-wave analysis of Whitham (1967) is extended to two space dimensions, and is shown to predict oblique-mode instabilities for kh smaller than 1.36. A treatment of Lighthill's (1965) solution in the one-dimensional elliptic case resolves the problem of the energy distribution in the solution past the critical time.
Strongly nonlinear magnetosonic waves and ion acceleration
Rau, B.; Tajima, T.
1997-11-01
The electromagnetic fields associated with a nonlinear compressional Alfven wave propagating perpendicular to an external magnetic field of arbitrary strength are derived. For the strongly magnetized and high phase velocity case relevant for ion acceleration to high energies, we show that the electric field increases proportionally only to the external magnetic field O (B{sub ext}[in T] MV/cm) and the electrostatic potential increases with the square root of the ion-to-electron mass ratio {radical}M{sub i}/m{sub e}.
Nonlinear chorus wave effects on energetic electrons reexamined
NASA Astrophysics Data System (ADS)
Zheng, Q.; Fok, M. H.; Zheng, Y.; Lui, A.
2012-12-01
Electron energy transport due to nonlinear plasma wave particle interactions are carried out by wave and particles resonating with each other. Many nonlinear wave studies conducted in the past have only considered the main resonance between wave and electrons. However, we have found through test particle simulations that although independent, separate contributions from higher order resonances can be small, but they can have a rather significant impact on the main-order contribution hence the total nonlinear wave effects. Contribution from different orders can interfere with each other hence the overall nonlinear wave effect is significantly different from that of just the major resonance. Therefore in the nonlinear wave particle interaction regime, contribution from different resonant orders is inseparable and contributions from higher order wave-particle resonances should be all included. For the same token, banded plasma waves should be used in nonlinear wave studies instead of assumed monochromatic waves. By including all the essential factors mentioned above, the overall electron transport due to the nonlinear plasma wave effects take the form of diffusion-like rather than advection, which was reported in many previous studies. It is also found that chorus wave induced electron transport is one important mechanism for the formation of electron butterfly pitch angle distribution.
Nonlinear ship waves and computational fluid dynamics
MIYATA, Hideaki; ORIHARA, Hideo; SATO, Yohei
2014-01-01
Research works undertaken in the first author’s laboratory at the University of Tokyo over the past 30 years are highlighted. Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design. Based on these findings, a multitude of the Computational Fluid Dynamic (CFD) techniques have been developed over this period, and are highlighted in this paper. The TUMMAC code has been developed for wave problems, based on a rectangular grid system, while the WISDAM code treats both wave and viscous flow problems in the framework of a boundary-fitted grid system. These two techniques are able to cope with almost all fluid dynamical problems relating to ships, including the resistance, ship’s motion and ride-comfort issues. Consequently, the two codes have contributed significantly to the progress in the technology of ship design, and now form an integral part of the ship-designing process. PMID:25311139
Nonlinear ship waves and computational fluid dynamics.
Miyata, Hideaki; Orihara, Hideo; Sato, Yohei
2014-01-01
Research works undertaken in the first author's laboratory at the University of Tokyo over the past 30 years are highlighted. Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design. Based on these findings, a multitude of the Computational Fluid Dynamic (CFD) techniques have been developed over this period, and are highlighted in this paper. The TUMMAC code has been developed for wave problems, based on a rectangular grid system, while the WISDAM code treats both wave and viscous flow problems in the framework of a boundary-fitted grid system. These two techniques are able to cope with almost all fluid dynamical problems relating to ships, including the resistance, ship's motion and ride-comfort issues. Consequently, the two codes have contributed significantly to the progress in the technology of ship design, and now form an integral part of the ship-designing process.
Interaction of Oblique Instability Waves with a Nonlinear Plane Wave
NASA Technical Reports Server (NTRS)
Wundrow, David W.; Hultgren, Lennart S.; Goldstein, M. E.
1994-01-01
This paper is concerned with the downstream evolution of a resonant triad of initially non-interacting linear Instability waves in a boundary layer with a weak adverse pressure gradient. The triad consists of a two-dimensional fundamental mode and a pair of equal-amplitude oblique modes that form a subharmonic standing wave in the spanwise direction. The growth rates are small and there is a well-defined common critical layer for these waves. As in Goldstein & Lee (1992), the wave interaction takes place entirely within this critical layer and is initially of the parametric-resonance type. This enhances the spatial growth rate of the subharmonic but does not affect that of the fundamental. However, in contrast to Goldstein & Lee (1992), the initial subharmonic amplitude is assumed to be small enough so that the fundamental can become nonlinear within its own critical layer before it is affected by the subharmonic. The subharmonic evolution is then dominated by the parametric-resonance effects and occurs on a much shorter streamwise scale than that of the fundamental. The subharmonic amplitude continues to increase during this parametric-resonance stage - even as the growth rate of the fundamental approaches zero - and the subharmonic eventually becomes large enough to influence the fundamental which causes both waves to evolve on the same shorter streamwise scale.
Nonlinear wavenumber shift of large amplitude Langmuir waves
NASA Astrophysics Data System (ADS)
Li, Dehui; Wang, Shaojie
2016-07-01
Nonlinear particle-in-cell simulation is carried out to investigate the nonlinear behavior of the Langmuir wave launched with a fixed frequency in a uniform plasma. It is found that in the strong driving case, the launched wave propagates in a phase velocity larger than that predicted by the linear theory; there appears a nonlinear down-shift of wavenumber. The phase velocity of the nonlinear wave and the down-shift of the wavenumber are demonstrated to be determined by the velocity of nonlinearly accelerated resonant electrons.
Nonlinear wave propagation in constrained solids subjected to thermal loads
NASA Astrophysics Data System (ADS)
Nucera, Claudio; Lanza di Scalea, Francesco
2014-01-01
The classical mathematical treatment governing nonlinear wave propagation in solids relies on finite strain theory. In this scenario, a system of nonlinear partial differential equations can be derived to mathematically describe nonlinear phenomena such as acoustoelasticity (wave speed dependency on quasi-static stress), wave interaction, wave distortion, and higher-harmonic generation. The present work expands the topic of nonlinear wave propagation to the case of a constrained solid subjected to thermal loads. The origin of nonlinear effects in this case is explained on the basis of the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion. Such "residual" energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. Closed-form solutions are given for the longitudinal wave speed and the second-harmonic nonlinear parameter as a function of interatomic potential parameters and temperature increase. The model predicts a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature, as a result of the thermal stresses caused by the prevented thermal expansion of the solid. Experimental measurements of the ultrasonic nonlinear parameter on a steel block under constrained thermal expansion confirm this trend. These results suggest the potential of a nonlinear ultrasonic measurement to quantify thermal stresses from prevented thermal expansion. This knowledge can be extremely useful to prevent thermal buckling of various structures, such as continuous-welded rails in hot weather.
Resonantly driven nonlinear density waves in protostellar disks
NASA Technical Reports Server (NTRS)
Yuan, Chi; Cassen, Pat
1994-01-01
Recent observations of binary, pre-main-sequence, solar-type stars provide evidence that such systems may coexist with circumstellar disks. The binary disk systems, besides being of general interest for the study of star formation, potentially provide useful tests of companion-disk interaction theories prominent in current hypotheses of planet formation. In this paper, we apply an asymptotic analysis of the nonlinear, resonant interaction of a stellar companion with a disk to understand the dependence of such interactions on the properties of the system: the binary mass ratio, the physical properties of the disk, and the effective dissipation (treated herein as viscosity). The method is based on a WKBJ approximation and exploits the conditions that the disk is thin and much less massive than the primary, but does not require that the companion-induced disturbance be small. Both isothermal and adiabatic responses are treated. Only circular orbit resonances are considered in this paper. It is demonstrated that the temperature of the disk as well as the relative mass of the companion affects the degree of nonlinearity, and that nonlinearity promotes high wave compression ratios, long wavelengths, and increased propagation distances. Nevertheless, the total torque exerted between the companion and the disk is well represented by linear theory. The amplitudes of density disturbances are reduced by viscosity and nonisothermality. Because resonant interactions are generally strong and capable of driving rapid evolution, one might expect observations of systems undergoing strong, resonant-driven evolution to be rare. In this connection, it is pointed out that the m = 1 resonance is distinguished by being anomalously weaker than the others and is therefore of observational interest. It is speculated that, in conditions of intrinsically small dissipation, the propagation of resonant-driven density waves is limited by the tendency of their wavelength to diminish with distance
Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru
2015-12-31
We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understand dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.
On tidal variability induced by nonlinear interaction with planetary waves
Teitelbaum, H.; Vial, F. )
1991-08-01
Short-time variability of the atmospheric tides is frequently observed in the meteor region but is not yet fully explained in terms of production mechanisms. This is probably due to the existence of several such mechanisms acting together or separately. In this paper the authors show that many observations can be explained by nonlinear interactions between tides and planetary waves having periods corresponding to those of the observed tidal amplitude modulations. These nonlinear interactions generate two secondary waves whose frequencies are the sum and difference of frequencies of the primary waves. These two waves beat with the tide, modulating its amplitude with the planetary wave period. A numerical model is used to demonstrate that with primary waves of reasonable amplitudes the nonlinear interactions can be quite large. This is because the importance of nonlinearity depends essentially on the amplitude of the induced fluid velocity in the direction of wave propagation compared to the wave propagation velocity. When two waves propagate simultaneously, the fluid velocity can have a large component in the direction of propagation of one of the waves, and advective (nonlinear) terms can be large. This point is further illustrated in the case of two gravity waves interacting together. Finally, some observational campaigns carried out above Garchy (45{degree}N) are analyzed using a nonparametric method. The results indicate that nonlinear interactions between tides and planetary waves really take place in the upper mesosphere and lower thermosphere.
Nonlinear Trivelpiece-Gould Waves: Frequency, Functional Form, and Stability
NASA Astrophysics Data System (ADS)
Dubin, Daniel H. E.
2015-11-01
This poster considers the frequency, spatial form, and stability, of nonlinear Trivelpiece- Gould (TG) waves on a cylindrical plasma column of length L and radius rp, treating both traveling and standing waves, and focussing on the regime of experimental interest in which L/rp >> 1. In this regime TG waves are weakly dispersive, allowing strong mode-coupling between Fourier harmonics. The mode coupling implies that linear theory for such waves is a poor approximation even at fairly small amplitudes, and nonlinear theories that include only a small number of harmonics (such as 3-wave parametric resonance theory) fail to fully capture the stability properties of the system. We find that nonlinear standing waves suffer jumps in their functional form as their amplitude is varied continuously. The jumps are caused by nonlinear resonances between the standing wave and nearly linear waves whose frequencies and wave numbers are harmonics of the standing wave. Also, the standing waves are found to be unstable to a multi-wave version of 3-wave parametric resonance, with an amplitude required for instability onset that is much larger than expected from three wave theory. For traveling wave, linearly stability is found for all amplitudes that could be studied, in contradiction to 3-wave theory. Supported by National Science Foundation Grant PHY-1414570, Department of Energy Grants DE-SC0002451and DE-SC0008693.
Investigation of Nonlinear Whistler Wave Processes in the Laboratory
NASA Astrophysics Data System (ADS)
Tejero, E. M.; Blackwell, D. D.; Amatucci, B.; Crabtree, C. E.; Ganguli, G.; Rudakov, L.
2015-12-01
Nonlinear interactions involving whistler wave turbulence can strongly effect the dynamics of the radiation belts. The building blocks of whistler wave turbulence are currently being studied in the NRL Space Physics Simulation Chamber (SPSC) under scaled magnetospheric conditions. These processes include parametric three-wave decay and a nonlinear wave-particle scattering off of thermal electrons that can substantially change the wave vector direction and energy flux. In the laboratory experiments, both of these processes have been observed and characterized. The results are consistent with theoretical predictions. Results from continuing laboratory experiments demonstrating triggered emissions and chorus-like emissions via nonlinear whistler wave-energetic particle interactions will be discussed. These chirped whistler waves are also observed to exhibit three-wave decay/coalescence and wave-particle scattering.
Compactification of nonlinear patterns and waves.
Rosenau, Philip; Kashdan, Eugene
2008-12-31
We present a nonlinear mechanism(s) which may be an alternative to a missing wave speed: it induces patterns with a compact support and sharp fronts which propagate with a finite speed. Though such mechanism may emerge in a variety of physical contexts, its mathematical characterization is universal, very simple, and given via a sublinear substrate (site) force. Its utility is shown studying a Klein-Gordon -u(tt) + [phi/(u(x)]x = P'(u) equation, where phi'(sigma) = sigma + beta sigma3 and endowed with a subquadratic site potential P(u) approximately /1-u2/(alpha+1), 0 < or = alpha < 1, and the Schrödinger iZt + inverted delta2 Z = G(/Z/)Z equation in a plane with G(A) = gammaA(-delta) - sigmaA2, 0 < delta < or = 1.
NASA Astrophysics Data System (ADS)
Das, Jayasree; Bandyopadhyay, Anup; Das, K. P.; Das
2014-02-01
Schamel's modified Korteweg-de Vries-Zakharov-Kuznetsov (S-ZK) equation, governing the behavior of long wavelength, weak nonlinear ion acoustic waves propagating obliquely to an external uniform static magnetic field in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field, admits solitary wave solutions having a sech 4 profile. The higher order stability of this solitary wave solution of the S-ZK equation has been analyzed with the help of multiple-scale perturbation expansion method of Allen and Rowlands (Allen, M. A. and Rowlands, G. 1993 J. Plasma Phys. 50, 413; 1995 J. Plasma Phys. 53, 63). The growth rate of instability is obtained correct to the order k 2, where k is the wave number of a long wavelength plane wave perturbation. It is found that the lowest order (at the order k) instability condition is strongly sensitive to the angle of propagation (δ) of the solitary wave with the external uniform static magnetic field, whereas at the next order (at the order k 2) the solitary wave solutions of the S-ZK equation are unstable irrespective of δ. It is also found that the growth rate of instability up to the order k 2 for the electrons having Boltzmann distribution is higher than that of the non-thermal electrons having vortex-like distribution for any fixed δ.
Nonlinear wave interactions in shallow water magnetohydrodynamics of astrophysical plasma
NASA Astrophysics Data System (ADS)
Klimachkov, D. A.; Petrosyan, A. S.
2016-05-01
The rotating magnetohydrodynamic flows of a thin layer of astrophysical and space plasmas with a free surface in a vertical external magnetic field are considered in the shallow water approximation. The presence of a vertical external magnetic field changes significantly the dynamics of wave processes in an astrophysical plasma, in contrast to a neutral fluid and a plasma layer in an external toroidal magnetic field. There are three-wave nonlinear interactions in the case under consideration. Using the asymptotic method of multiscale expansions, we have derived nonlinear equations for the interaction of wave packets: three magneto- Poincare waves, three magnetostrophic waves, two magneto-Poincare and one magnetostrophic waves, and two magnetostrophic and one magneto-Poincare waves. The existence of decay instabilities and parametric amplification is predicted. We show that a magneto-Poincare wave decays into two magneto-Poincare waves, a magnetostrophic wave decays into two magnetostrophic waves, a magneto-Poincare wave decays into one magneto-Poincare and one magnetostrophic waves, and a magnetostrophic wave decays into one magnetostrophic and one magneto-Poincare waves. There are the following parametric amplification mechanisms: the parametric amplification of magneto-Poincare waves, the parametric amplification of magnetostrophic waves, the amplification of a magneto-Poincare wave in the field of a magnetostrophic wave, and the amplification of a magnetostrophic wave in the field of a magneto-Poincare wave. The instability growth rates and parametric amplification factors have been found for the corresponding processes.
Solitary and Shock Waves in Strongly Nonlinear Metamaterials
NASA Astrophysics Data System (ADS)
Herbold, E. B.; Nesterenko, V. F.
2007-12-01
Strongly nonlinear laminar metamaterials can be assembled using rigid metal plates interacting through light deformable strongly nonlinear elements placed between them. They may consist of single toroidal polymer o-rings, combinations of o-rings with different stiffness or combinations of hardening and softening nonlinear elements including gaps between them. Solitary waves and shocks are investigated in these metamaterials numerically and experimentally.
Application of nonlinear wave modulation spectroscopy to discern material damage
Johnson, P.A.; Sutin, A.; Abeele, K.E.A. van den
1999-04-01
Materials containing structural damage have a far greater nonlinear elastic response than materials with no structural damage. This is the basis for nonlinear wave diagnostics of damage, methods which are remarkably sensitive to the detection and progression of damage in materials. Here the authors describe one nonlinear method, the application of harmonics and sum and difference frequency to discern damage in materials. The method is termed Nonlinear Wave Modulation Spectroscopy (NWMS). It consists of exciting a sample with continuous waves of two separate frequencies simultaneously, and inspecting the harmonics of the two waves, and their sum and difference frequencies (sidebands). Undamaged materials are essentially linear in their response to the two waves, while the same material, when damaged, becomes highly nonlinear, manifested by harmonics and sideband generation. The authors illustrate the method by experiments on uncracked and cracked plexiglass and sandstone samples, and by applying it to intact and damaged engine components.
Nonlinear analysis of helix traveling wave tubes
Freund, H.P.; Zaidman, E.G.; Vanderplaats, N.R.; Kodis, M.A.
1994-12-31
A nonlinear formulation of the interaction in a helix traveling wave tube (TWT) is presented. The formulation is intended to treat a wide class of helix TWTs including both emission-gated and multi-tone operation. The essential feature of each of these configurations is that multiple waves must be included in the formulation. As a result, a fully time-dependent analysis is required. The numerical procedure for this in a helix TWT is complicated by the fact that the radial profile of the field varies with frequency. This contrasts, for example, with the case of a smooth bore waveguide in which the radial profile for each TE{sub ln} or TM{sub ln} mode is invariant in frequency. Because of this, a complete self-consistent particle-in-cell (PIC) formulation must be three-dimensional. In order to circumvent the computational expense of a 3D PIC formulation, the authors adopt an approach in which the electromagnetic field is represented as a superposition of azimuthally symmetric modes in a vacuum sheath helix. The specific electron distributions are chosen to model either a continuous beam for the multi-tone TWT and a pulsed beam for the emission-gated TWT. Numerical results of the simulation for examples of interest to an emission-gated TWT experiment at NRL will be presented.
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-06-23
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 {beta} when the nonlinearity distribution in the layer is a stochastic process.
Introduction to Wave Propagation in Nonlinear Fluids and Solids
NASA Astrophysics Data System (ADS)
Drumheller, Douglas S.
1998-02-01
Waves occur widely in nature and have innumerable commercial uses. Waves are responsible for the sound of speech, meteors igniting the atmosphere, radio and television broadcasting, medical diagnosis using ultrasound. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models for a variety of gases, liquids, and solids. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Students at an advanced undergraduate/graduate level will find this text a clear and comprehensive introduction to the study of nonlinear wave phenomena, and it will also be valuable as a professional reference in engineering and applied physics.
Nonlinear interference and unidirectional wave mixing in metamaterials.
Rose, Alec; Huang, Da; Smith, David R
2013-02-01
When both electric and magnetic mechanisms contribute to a particular nonlinear optical process, there exists the possibility for nonlinear interference, often characterized by constructive or destructive interference in the radiation pattern of harmonics and mix waves. However, observation of a significant effect from nonlinear interference requires careful balancing of the various contributions. For this purpose, we propose an artificial metamaterial, using the formalism of nonlinear magnetoelectric coupling to simultaneously engineer the nonlinear polarization and magnetization. We confirm our predictions of nonlinear interference with both simulations and experiment, demonstrating unidirectional wave mixing in two microwave metamaterials. Our results point toward an ever wider range of nonlinear properties, in which nonlinear interference is just one of many potential applications.
Acoustic field distribution of sawtooth wave with nonlinear SBE model
Liu, Xiaozhou Zhang, Lue; Wang, Xiangda; Gong, Xiufen
2015-10-28
For precise prediction of the acoustic field distribution of extracorporeal shock wave lithotripsy with an ellipsoid transducer, the nonlinear spheroidal beam equations (SBE) are employed to model acoustic wave propagation in medium. To solve the SBE model with frequency domain algorithm, boundary conditions are obtained for monochromatic and sawtooth waves based on the phase compensation. In numerical analysis, the influence of sinusoidal wave and sawtooth wave on axial pressure distributions are investigated.
Nonlinear physics of shear Alfvén waves
NASA Astrophysics Data System (ADS)
Zonca, Fulvio; Chen, Liu
2014-02-01
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These "nonlinear equilibria" or "phase-space zonal structures" dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
Nonlinear physics of shear Alfvén waves
Zonca, Fulvio; Chen, Liu
2014-02-12
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.
NASA Astrophysics Data System (ADS)
Hofmann, C.; Zimmermann, T.; Zielinski, A.; Landsman, A. S.
2016-04-01
The validity of the adiabatic approximation in strong field ionization under typical experimental conditions has recently become a topic of great interest. Experimental results have been inconclusive, in part, due to the uncertainty in experimental calibration of intensity. Here we turn to the time-dependent Schrödinger equation, where all the laser parameters are known exactly. We find that the centre of the electron momentum distribution (typically used for calibration of elliptically and circularly polarized light) is sensitive to non-adiabatic effects, leading to intensity shifts in experimental data that can significantly affect the interpretation of results. On the other hand, the transverse momentum spread in the plane of polarization is relatively insensitive to such effects, even in the Keldysh parameter regime approaching γ ≈ 3. This suggests the transverse momentum spread in the plane of polarization as a good alternative to the usual calibration method, particularly for experimental investigation of non-adiabatic effects using circularly polarized light.
NASA Astrophysics Data System (ADS)
Ranjbar, Monireh; Bahari, Ali
2016-09-01
Four-wave mixing in propagation of cylindrical waves in a homogeneous nonlinear optical media has been investigated theoretically. An explicit analytical expression which contains all the main nonlinear optical effects, including third harmonic generation, sum and difference frequency generation has been obtained. A comparison between sum frequency efficiency for exact and approximation expression in a homogeneous nonlinear medium has been done. The effect of increasing the nonlinear optical coefficient (χeff(3)) and increasing the frequency difference between two adjacent waves (Δ ω) , on the efficiency of sum frequency generation in homogeneous media has been investigated.
Amplitude-dependent Lamb wave dispersion in nonlinear plates.
Packo, Pawel; Uhl, Tadeusz; Staszewski, Wieslaw J; Leamy, Michael J
2016-08-01
The paper presents a perturbation approach for calculating amplitude-dependent Lamb wave dispersion in nonlinear plates. Nonlinear dispersion relationships are derived in closed form using a hyperelastic stress-strain constitutive relationship, the Green-Lagrange strain measure, and the partial wave technique integrated with a Lindstedt-Poincaré perturbation approach. Solvability conditions are derived using an operator formalism with inner product projections applied against solutions to the adjoint problem. When applied to the first- and second-order problems, these solvability conditions lead to amplitude-dependent, nonlinear dispersion corrections for frequency as a function of wavenumber. Numerical simulations verify the predicted dispersion shifts for an example nonlinear plate. The analysis and identification of amplitude-dependent, nonlinear Lamb wave dispersion complements recent research focusing on higher harmonic generation and internally resonant waves, which require precise dispersion relationships for frequency-wavenumber matching. PMID:27586758
Nonlinear propagation and control of acoustic waves in phononic superlattices
NASA Astrophysics Data System (ADS)
Jiménez, Noé; Mehrem, Ahmed; Picó, Rubén; García-Raffi, Lluís M.; Sánchez-Morcillo, Víctor J.
2016-05-01
The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g., cubic) nonlinearities, or extremely linear media (where distortion can be canceled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime. xml:lang="fr"
Book review: Nonlinear ocean waves and the inverse scattering transform
Geist, Eric L.
2011-01-01
Nonlinear Ocean Waves and the Inverse Scattering Transform is a comprehensive examination of ocean waves built upon the theory of nonlinear Fourier analysis. The renowned author, Alfred R. Osborne, is perhaps best known for the discovery of internal solitons in the Andaman Sea during the 1970s. In this book, he provides an extensive treatment of nonlinear water waves based on a nonlinear spectral theory known as the inverse scattering transform. The writing is exceptional throughout the book, which is particularly useful in explaining some of the more difficult mathematical concepts. Review info: Nonlinear Ocean Waves and the Inverse Scattering Transform. By Alfred R. Osborne, 2010. ISBN: 978-125286299, 917 pp.
Superposed nonlinear waves in coherently coupled Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Babu Mareeswaran, R.; Kanna, T.
2016-09-01
We study the dynamics of superposed nonlinear waves in coherently coupled Gross-Pitaevskii (CCGP) equations with constant (autonomous system) and time varying (non-autonomous system) nonlinearity coefficients. By employing a linear transformation, the autonomous CCGP system is converted into two separate scalar nonlinear Schrödinger equations and we show that linear superposition of different nonlinear wave solutions of these scalar equations results into several kinds of nonlinear coherent structures namely, coexisting rogue wave-Ma breather, Akhmediev-Ma breathers, collision and bound states of Ma breathers and solitons. Next, the non-autonomous CCGP system is converted into an autonomous CCGP system with a similarity transformation. We show an interesting possibility of soliton compression and appearance of creeping solitons for kink-like and periodically modulated nonlinearity coefficient.
NASA Astrophysics Data System (ADS)
Tchinang Tchameu, J. D.; Togueu Motcheyo, A. B.; Tchawoua, C.
2016-09-01
The discrete multi-rogue waves (DMRW) as solution of the discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearities is studied numerically. These biological rogue waves represent the complex probability amplitude of finding an amide-I vibrational quantum at a site. We observe that the growth in the higher order saturable nonlinearity implies the formation of DMRW including an increase in the short-living DMRW and a decrease in amplitude of the long-living DMRW.
Generation of dispersion in nondispersive nonlinear waves in thermal equilibrium
Lee, Wonjung; Kovačič, Gregor; Cai, David
2013-01-01
In this work, we examine the important theoretical question of whether dispersion relations can arise from purely nonlinear interactions among waves that possess no linear dispersive characteristics. Using two prototypical examples of nondispersive waves, we demonstrate how nonlinear interactions can indeed give rise to effective dispersive-wave–like characteristics in thermal equilibrium. Physically, these example systems correspond to the strong nonlinear coupling limit in the theory of wave turbulence. We derive the form of the corresponding dispersion relation, which describes the effective dispersive structures, using the generalized Langevin equations obtained in the Zwanzig–Mori projection framework. We confirm the validity of this effective dispersion relation in our numerical study using the wavenumber–frequency spectral analysis. Our work may provide insight into an important connection between highly nonlinear turbulent wave systems, possibly with no discernible dispersive properties, and the dispersive nature of the corresponding renormalized waves. PMID:23401526
Experimental characterization of nonlinear processes of whistler branch waves
NASA Astrophysics Data System (ADS)
Tejero, E. M.; Crabtree, C.; Blackwell, D. D.; Amatucci, W. E.; Ganguli, G.; Rudakov, L.
2016-05-01
Experiments in the Space Physics Simulation Chamber at the Naval Research Laboratory isolated and characterized important nonlinear wave-wave and wave-particle interactions that can occur in the Earth's Van Allen radiation belts by launching predominantly electrostatic waves in the intermediate frequency range with wave normal angle greater than 85 ° and measuring the nonlinearly generated electromagnetic scattered waves. The scattered waves have a perpendicular wavelength that is nearly an order of magnitude larger than that of the pump wave. Calculations of scattering efficiency from experimental measurements demonstrate that the scattering efficiency is inversely proportional to the damping rate and trends towards unity as the damping rate approaches zero. Signatures of both wave-wave and wave-particle scatterings are also observed in the triggered emission process in which a launched wave resonant with a counter-propagating electron beam generates a large amplitude chirped whistler wave. The possibility of nonlinear scattering or three wave decay as a saturation mechanism for the triggered emission is suggested. The laboratory experiment has inspired the search for scattering signatures in the in situ data of chorus emission in the radiation belts.
Nonlinear time reversal of classical waves: experiment and model.
Frazier, Matthew; Taddese, Biniyam; Xiao, Bo; Antonsen, Thomas; Ott, Edward; Anlage, Steven M
2013-12-01
We consider time reversal of electromagnetic waves in a closed, wave-chaotic system containing a discrete, passive, harmonic-generating nonlinearity. An experimental system is constructed as a time-reversal mirror, in which excitations generated by the nonlinearity are gathered, time-reversed, transmitted, and directed exclusively to the location of the nonlinearity. Here we show that such nonlinear objects can be purely passive (as opposed to the active nonlinearities used in previous work), and we develop a higher data rate exclusive communication system based on nonlinear time reversal. A model of the experimental system is developed, using a star-graph network of transmission lines, with one of the lines terminated by a model diode. The model simulates time reversal of linear and nonlinear signals, demonstrates features seen in the experimental system, and supports our interpretation of the experimental results.
Self-organization in nonlinear wave turbulence
Jordan, Richard; Josserand, Christophe
2000-02-01
We present a statistical equilibrium model of self-organization in a class of focusing, nonintegrable nonlinear Schroedinger (NLS) equations. The theory predicts that the asymptotic-time behavior of the NLS system is characterized by the formation and persistence of a large-scale coherent solitary wave, which minimizes the Hamiltonian given the conserved particle number (L{sup 2}-norm squared), coupled with small-scale random fluctuations, or radiation. The fluctuations account for the difference between the conserved value of the Hamiltonian and the Hamiltonian of the coherent state. The predictions of the statistical theory are tested against the results of direct numerical simulations of NLS, and excellent qualitative and quantitative agreement is demonstrated. In addition, a careful inspection of the numerical simulations reveals interesting features of the transitory dynamics leading up to the long-time statistical equilibrium state starting from a given initial condition. As time increases, the system investigates smaller and smaller scales, and it appears that at a given intermediate time after the coalescense of the soliton structures has ended, the system is nearly in statistical equilibrium over the modes that it has investigated up to that time. (c) 2000 The American Physical Society.
Nonlinear time reversal in a wave chaotic system.
Frazier, Matthew; Taddese, Biniyam; Antonsen, Thomas; Anlage, Steven M
2013-02-01
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems and is embodied in the time-reversal mirror. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We demonstrate that the time-reversed nonlinear excitations reconstruct exclusively upon the source of the nonlinearity. As an example of its utility, we demonstrate a new form of secure communication and point out other applications.
Nonlinear waves in nonplanar and nonuniform dusty plasmas
Xue Jukui; Zhang Liping
2006-02-15
The nonlinear properties of the dust acoustic solitary wave and shock wave in inhomogeneous nonplanar dusty plasmas are considered theoretically and numerically. The effects of nonthermally distributed ions, nonadiabatic dust charge fluctuation, and the inhomogeneity caused by nonuniform equilibrium particle density, nonuniform equilibrium charging, and nonplanar geometry on waves are presented. When {tau}{sub ch}/{tau}{sub d} is small but finite, where {tau}{sub ch} is the charging time scale and {tau}{sub d} is the hydrodynamical time scale, a variable coefficients nonplanar Korteweg-de Vries (KdV) Burgers equation governing the nonlinear waves is derived by the perturbation method. The analytical expressions for the evolution of soliton and shock wave (both oscillatory and monotone shock) are obtained and the theoretical results are confirmed by the numerical solution of the nonlinear wave equation.
Effect of Forcing Function on Nonlinear Acoustic Standing Waves
NASA Technical Reports Server (NTRS)
Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce
2003-01-01
Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.
Signatures of Nonlinear Waves in Coronal Plumes and Holes
NASA Technical Reports Server (NTRS)
Ofman, Leon
1999-01-01
In recent Ultraviolet Coronagraph Spectrometer/Solar and Heliospheric Observatory (UVCS/SOHO) White Light Channel (WLC) observations we found quasi-periodic variations in the polarized brightness (pB) in the polar coronal holes at heliocentric distances of 1.9-2.45 solar radii. The motivation for the observation is the 2.5D Magnetohydrodynamics (MHD) model of solar wind acceleration by nonlinear waves, that predicts compressive fluctuations in coronal holes. To help identify the waves observed with the UVCS/WLC we model the propagation and dissipation of slow magnetosonic waves in polar plumes using 1D MHD code in spherical geometry, We find that the slow waves nonlinearly steepen in the gravitationally stratified plumes. The nonlinear steepening of the waves leads to enhanced dissipation due to compressive viscosity at the wave-fronts.
Nonlinear hyperbolic theory of thermal waves in metals
NASA Technical Reports Server (NTRS)
Wilhelm, H. E.; Choi, S. H.
1975-01-01
A closed-form solution for cylindrical thermal waves in metals is given based on the nonlinear hyperbolic system of energy-conservation and heat-flux relaxation equations. It is shown that heat released from a line source propagates radially outward with finite speed in the form of a thermal wave which exhibits a discontinuous wave front. Unique nonlinear thermal-wave solutions exist up to a critical amount of driving energy, i.e., for larger energy releases, the thermal flow becomes multivalued (occurrence of shock waves). By comparison, it is demonstrated that the parabolic thermal-wave theory gives, in general, a misleading picture of the profile and propagation of thermal waves and leads to physical (infinite speed of heat propagation) and mathematical (divergent energy integrals) difficulties. Attention is drawn to the importance of temporal heat-flux relaxation for the physical understanding of fast transient processes such as thermal waves and more general explosions and implosions.
Forecasting the future: is it possible for adiabatically time-varying nonlinear dynamical systems?
Yang, Rui; Lai, Ying-Cheng; Grebogi, Celso
2012-09-01
Nonlinear dynamical systems in reality are often under environmental influences that are time-dependent. To assess whether such a system can perform as desired or as designed and is sustainable requires forecasting its future states and attractors based solely on time series. We propose a viable solution to this challenging problem by resorting to the compressive-sensing paradigm. In particular, we demonstrate that, for a dynamical system whose equations are unknown, a series expansion in both dynamical and time variables allows the forecasting problem to be formulated and solved in the framework of compressive sensing using only a few measurements. We expect our method to be useful in addressing issues of significant current concern such as the sustainability of various natural and man-made systems.
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time. PMID:26986334
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.
Variational principle for nonlinear wave propagation in dissipative systems
NASA Astrophysics Data System (ADS)
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.
Nonlinear spin wave coupling in adjacent magnonic crystals
NASA Astrophysics Data System (ADS)
Sadovnikov, A. V.; Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E.; Nikitov, S. A.
2016-07-01
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.
Nonlinear Alfven waves in high-speed solar wind streams
NASA Technical Reports Server (NTRS)
Abraham-Shrauner, B.; Feldman, W. C.
1977-01-01
A nonlinear proton distribution function that is an exact stationary solution of the nonlinear Vlasov equation and Maxwell's equations and which supports a single nonlinear transverse Alfven (ion cyclotron) wave that is circularly polarized and nondispersive is proposed for most of the observations during high-speed solar wind streams. This nonlinear distribution removes the strong Alfven wave instability, inconsistent with the persistence of the observed proton distribution functions in high-speed streams, found by the linear stability analysis. Model temperature anisotropies and drift velocities of the two spatially inhomogeneous bi-Maxwellian components are consistent with typical proton velocity distributions measured in high-speed streams at 1 AU. Two derived relations for each of the wave number and the phase velocity of the wave are obeyed within experimental uncertainties by two typical proton measurements. Our model also predicts that the alpha particle bulk flow velocity exceeds the proton particle bulk flow velocity, as is observed.
Late-time attractor for the cubic nonlinear wave equation
Szpak, Nikodem
2010-08-15
We apply our recently developed scaling technique for obtaining late-time asymptotics to the cubic nonlinear wave equation and explain the appearance and approach to the two-parameter attractor found recently by Bizon and Zenginoglu.
Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas
NASA Technical Reports Server (NTRS)
Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.
1997-01-01
We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.
Highly nonlinear Bragg quasisolitons in the dynamics of water waves.
Ruban, V P
2008-05-01
Finite-amplitude gravity water waves in Bragg resonance with a periodic one-dimensional topography are studied numerically using exact equations of motion for ideal potential free-surface flows. Spontaneous formation of highly nonlinear localized structures is observed in the numerical experiments. These coherent structures consisting of several nearly standing extreme waves are similar in many aspects to the Bragg solitons previously known in nonlinear optics. PMID:18643128
Nonlinear dynamics of one-dimensional supersonic Langmuir waves
Jungwirth, K. ); Breizman, B.N. )
1991-08-01
In this review specific features of dynamics of Langmuir waves in the supersonic regime are illustrated with several examples. It is shown that the limit of an adiabatic approximation considerably extends the range of analytically solvable problems. It permits one to formulate and rigorously analyze the modulational instability, as well as to explain many empirical laws deduced from numerical simulations. The formulation describes not only collapsing cavities in two and three dimensions, but predicts also the existence of compound'' solitons in a one-dimensional model. In the same model the transition from weak turbulence to the adiabatic approximation is analyzed, including phenomena of ion-sound emission by autolocalized and self-trapped plasmons. Further, the individual and collective processes of soliton formation, their mutual collisions, and their destruction by ion-sound pulses are discussed.
Simulation of the nonlinear evolution of electron plasma waves
NASA Technical Reports Server (NTRS)
Nishikawa, K.-I.; Cairns, I. H.
1991-01-01
Electrostatic waves driven by an electron beam in an ambient magnetized plasma were studied using a quasi-1D PIC simulation of electron plasma waves (i.e., Langmuir waves). The results disclose the presence of a process for moving wave energy from frequencies and wavenumbers predicted by linear theory to the Langmuir-like frequencies during saturation of the instability. A decay process for producing backward propagating Langmuir-like waves, along with low-frequency waves, is observed. The simulation results, however, indicate that the backscattering process is not the conventional Langmuir wave decay. Electrostatic waves near multiples of the electron plasma frequency are generated by wave-wave coupling during the nonlinear stage of the simulations, confirming the suggestion of Klimas (1983).
Persistent subplasma-frequency kinetic electrostatic electron nonlinear waves
Johnston, T. W.; Tyshetskiy, Y.; Ghizzo, A.; Bertrand, P.
2009-04-15
Driving a one-dimensional collisionless Maxwellian (Vlasov) plasma with a sufficiently strong longitudinal ponderomotive driver for a sufficiently long time results in a self-sustaining nonsinusoidal wave train with well-trapped electrons even for frequencies well below the plasma frequency, i.e., in the plasma wave spectral gap. Typical phase velocities of these waves are somewhat above the electron thermal velocity. This new nonlinear wave is being termed a kinetic electrostatic electron nonlinear (KEEN) wave. The drive duration must exceed the bounce period {tau}{sub B} of the trapped electrons subject to the drive, as calculated from the drive force and the linear plasma response to the drive. For a given wavenumber a wide range of KEEN wave frequencies can be readily excited. The basic KEEN structure is essentially kinetic, with the trapped electron density variation being almost completely shielded by the free electrons, leaving just enough net charge to support the wave.
Nonlinear upper hybrid waves and the induced density irregularities
Kuo, Spencer P.
2015-08-15
Upper hybrid waves are excited parametrically by the O-mode high-frequency heater waves in the ionospheric heating experiments. These waves grow to large amplitudes and self-induced density perturbations provide nonlinear feedback. The lower hybrid resonance modifies the nonlinear feedback driven by the ponderomotive force; the nonlinear equation governing the envelope of the upper hybrid waves is derived. Solutions in symmetric alternating functions, in non-alternating periodic functions, as well as in solitary functions are shown. The impact of lower hybrid resonance on the envelope of the upper hybrid waves is explored; the results show that both the spatial period and amplitude are enlarged. The average fluctuation level of induced density irregularities is also enhanced. In the soliton form, the induced density cavity is widened considerably.
Nonlinear electron acoustic waves in presence of shear magnetic field
Dutta, Manjistha; Khan, Manoranjan; Ghosh, Samiran; Chakrabarti, Nikhil
2013-12-15
Nonlinear electron acoustic waves are studied in a quasineutral plasma in the presence of a variable magnetic field. The fluid model is used to describe the dynamics of two temperature electron species in a stationary positively charged ion background. Linear analysis of the governing equations manifests dispersion relation of electron magneto sonic wave. Whereas, nonlinear wave dynamics is being investigated by introducing Lagrangian variable method in long wavelength limit. It is shown from finite amplitude analysis that the nonlinear wave characteristics are well depicted by KdV equation. The wave dispersion arising in quasineutral plasma is induced by transverse magnetic field component. The results are discussed in the context of plasma of Earth's magnetosphere.
Yu, X.; Hsu, T.-J.; Hanes, D.M.
2010-01-01
Sediment transport under nonlinear waves in a predominately sheet flow condition is investigated using a two-phase model. Specifically, we study the relative importance between the nonlinear waveshape and nonlinear boundary layer streaming on cross-shore sand transport. Terms in the governing equations because of the nonlinear boundary layer process are included in this one-dimensional vertical (1DV) model by simplifying the two-dimensional vertical (2DV) ensemble-averaged two-phase equations with the assumption that waves propagate without changing their form. The model is first driven by measured time series of near-bed flow velocity because of a wave group during the SISTEX99 large wave flume experiment and validated with the measured sand concentration in the sheet flow layer. Additional studies are then carried out by including and excluding the nonlinear boundary layer terms. It is found that for the grain diameter (0.24 mm) and high-velocity skewness wave condition considered here, nonlinear waveshape (e.g., skewness) is the dominant mechanism causing net onshore transport and nonlinear boundary layer streaming effect only causes an additional 36% onshore transport. However, for conditions of relatively low-wave skewness and a stronger offshore directed current, nonlinear boundary layer streaming plays a more critical role in determining the net transport. Numerical experiments further suggest that the nonlinear boundary layer streaming effect becomes increasingly important for finer grain. When the numerical model is driven by measured near-bed flow velocity in a more realistic surf zone setting, model results suggest nonlinear boundary layer processes may nearly double the onshore transport purely because of nonlinear waveshape. Copyright 2010 by the American Geophysical Union.
Optical surface wave in a crystal with diffusion photorefractive nonlinearity
Chetkin, S A; Akhmedzhanov, I M
2011-11-30
We consider a steady-state nonlinear photorefractive surface wave (PR SW) with TE or TM polarisation when the refractive index of the photorefractive crystal (PRC) depends on the strength of the diffusion crystal electric field emerging upon the wave propagation. We have determined the phase trajectory and transverse structure of the PR SW intensity distribution for different values of the diffusion photorefractive nonlinearity. We have investigated a photorefractive diffraction grating, which arises in the surface PRC layer during propagation of the nonlinear PR SW.
Nonlinear volume holography for wave-front engineering.
Hong, Xu-Hao; Yang, Bo; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan
2014-10-17
The concept of volume holography is applied to the design of an optical superlattice for the nonlinear harmonic generation. The generated harmonic wave can be considered as a holographic image caused by the incident fundamental wave. Compared with the conventional quasi-phase-matching method, this new method has significant advantages when applied to complicated nonlinear processes such as the nonlinear generation of special beams. As an example, we experimentally realized a second-harmonic Airy beam, and the results are found to agree well with numerical simulations.
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.
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. PMID:25937493
Exact Nonlinear Internal Equatorial Waves in the f-plane
NASA Astrophysics Data System (ADS)
Hsu, Hung-Chu
2016-07-01
We present an explicit exact solution of the nonlinear governing equations for internal geophysical water waves propagating westward above the thermocline in the f-plane approximation near the equator. Moreover, the mass transport velocity induced by this internal equatorial wave is eastward and a westward current occurs in the transition zone between the great depth where the water is still and the thermocline.
Quantification and prediction of rare events in nonlinear waves
NASA Astrophysics Data System (ADS)
Sapsis, Themistoklis; Cousins, Will; Mohamad, Mustafa
2014-11-01
The scope of this work is the quantification and prediction of rare events characterized by extreme intensity, in nonlinear dispersive models that simulate water waves. In particular we are interested for the understanding and the short-term prediction of rogue waves in the ocean and to this end, we consider 1-dimensional nonlinear models of the NLS type. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A stochastic analysis of the Gabor coefficients reveals i) the low-dimensionality of the intermittent structures, ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as iii) the critical scales (or Gabor coefficients) where a critical energy can trigger the formation of an extreme event. The unstable character of these critical localized modes is analysed directly through the system equation and it is shown that it is defined as the result of the system nonlinearity and the wave dissipation (that mimics wave breaking). These unstable modes are randomly triggered through the dispersive ``heat bath'' of random waves that propagate in the nonlinear medium. Using these properties we formulate low-dimensional functionals of these Gabor coefficients that allow for the prediction of extreme event well before the strongly nonlinear interactions begin to occur. The prediction window is further enhanced by the combination of the developed scheme with traditional filtering schemes.
Nonlinear wave propagation in strongly coupled dusty plasmas
Veeresha, B. M.; Tiwari, S. K.; Sen, A.; Kaw, P. K.; Das, A.
2010-03-15
The nonlinear propagation of low-frequency waves in a strongly coupled dusty plasma medium is studied theoretically in the framework of the phenomenological generalized hydrodynamic (GH) model. A set of simplified model nonlinear equations are derived from the original nonlinear integrodifferential form of the GH model by employing an appropriate physical ansatz. Using standard perturbation techniques characteristic evolution equations for finite small amplitude waves are then obtained in various propagation regimes. The influence of viscoelastic properties arising from dust correlation contributions on the nature of nonlinear solutions is discussed. The modulational stability of dust acoustic waves to parallel perturbation is also examined and it is shown that dust compressibility contributions influenced by the Coulomb coupling effects introduce significant modification in the threshold and range of the instability domain.
Stochastic acceleration of charged particle in nonlinear wave field
NASA Astrophysics Data System (ADS)
He, Kaifen
2003-04-01
Possibility of stochastic acceleration of charged particle by nonlinear waves is investigated. Spatially regular (SR) and spatiotemporal chaotic (STC) wave solutions evolving from saddle steady wave are tested as the fields. In the non-steady SR field the particle is finally trapped by the wave and averagely gains its group velocity, while in the STC field the particle motion displays trapped-free phases with its averaged velocity larger or smaller than the group velocity depending on the charge sign. A simplified model is established to investigate the acceleration mechanism. By analogy with motor protein, it is found that the virtual pattern of saddle steady wave plays a role of asymmetric potential, which and the nonlinear varying perturbation wave are the two sufficient ingredients for the acceleration in our case.
Time-reversed wave mixing in nonlinear optics.
Zheng, Yuanlin; Ren, Huaijin; Wan, Wenjie; Chen, Xianfeng
2013-11-19
Time-reversal symmetry is important to optics. Optical processes can run in a forward or backward direction through time when such symmetry is preserved. In linear optics, a time-reversed process of laser emission can enable total absorption of coherent light fields inside an optical cavity of loss by time-reversing the original gain medium. Nonlinearity, however, can often destroy such symmetry in nonlinear optics, making it difficult to study time-reversal symmetry with nonlinear optical wave mixings. Here we demonstrate time-reversed wave mixings for optical second harmonic generation (SHG) and optical parametric amplification (OPA) by exploring this well-known but underappreciated symmetry in nonlinear optics. This allows us to observe the annihilation of coherent beams. Our study offers new avenues for flexible control in nonlinear optics and has potential applications in efficient wavelength conversion, all-optical computing.
Nonlinear waves in PT -symmetric systems
NASA Astrophysics Data System (ADS)
Konotop, Vladimir V.; Yang, Jianke; Zezyulin, Dmitry A.
2016-07-01
Recent progress on nonlinear properties of parity-time (PT )-symmetric systems is comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying PT symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a PT -symmetric system. The natural inclusion of nonlinearity into these PT systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above PT -symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear PT -symmetric systems arising from various physical disciplines are presented, nonlinear properties of these systems are thoroughly elucidated, and relevant experimental results are described. In addition, emerging applications of PT symmetry are pointed out.
Nonlinear Self-Similar Beams of Electromagnetic Waves in Vacuum
NASA Astrophysics Data System (ADS)
Vlasov, S. N.
2015-12-01
We study nonlinear beams of electromagnetic waves in vacuum. Within the lowest approximation, their structure is determined by the cubic self-focusing nonlinearity, which manifests itself with the maximum intensity in the presence of counterpropagating waves. It is shown that the fields in the beams have no singularities if their power is less than the critical power of the self-focusing. The dependences of the eigenfrequencies of the modes of the quasioptical resonator on the beam power are found. The structure of the fields of these modes corresponds to self-similar wave beams.
Artemyev, A V; Neishtadt, A I; Zelenyi, L M; Vainchtein, D L
2010-12-01
We present an analytical and numerical study of the surfatron acceleration of nonrelativistic charged particles by electromagnetic waves. The acceleration is caused by capture of particles into resonance with one of the waves. We investigate capture for systems with one or two waves and provide conditions under which the obtained results can be applied to systems with more than two waves. In the case of a single wave, the once captured particles never leave the resonance and their velocity grows linearly with time. However, if there are two waves in the system, the upper bound of the energy gain may exist and we find the analytical value of that bound. We discuss several generalizations including the relativistic limit, different wave amplitudes, and a wide range of the waves' wavenumbers. The obtained results are used for qualitative description of some phenomena observed in the Earth's magnetosphere.
Artemyev, A V; Neishtadt, A I; Zelenyi, L M; Vainchtein, D L
2010-12-01
We present an analytical and numerical study of the surfatron acceleration of nonrelativistic charged particles by electromagnetic waves. The acceleration is caused by capture of particles into resonance with one of the waves. We investigate capture for systems with one or two waves and provide conditions under which the obtained results can be applied to systems with more than two waves. In the case of a single wave, the once captured particles never leave the resonance and their velocity grows linearly with time. However, if there are two waves in the system, the upper bound of the energy gain may exist and we find the analytical value of that bound. We discuss several generalizations including the relativistic limit, different wave amplitudes, and a wide range of the waves' wavenumbers. The obtained results are used for qualitative description of some phenomena observed in the Earth's magnetosphere. PMID:21198098
Nonlinear ring waves in a two-layer fluid
NASA Astrophysics Data System (ADS)
Khusnutdinova, Karima R.; Zhang, Xizheng
2016-10-01
Surface and interfacial weakly-nonlinear ring waves in a two-layer fluid are modelled numerically, within the framework of the recently derived 2 + 1-dimensional cKdV-type equation. In a case study, we consider concentric waves from a localised initial condition and waves in a 2D version of the dam-break problem, as well as discussing the effect of a piecewise-constant shear flow. The modelling shows, in particular, the formation of 2D dispersive shock waves and oscillatory wave trains.
Relativistic nonlinear plasma waves in a magnetic field
NASA Technical Reports Server (NTRS)
Kennel, C. F.; Pellat, R.
1976-01-01
An investigation is conducted of five relativistic plane nonlinear waves, taking into account circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. It is found that a large-amplitude superluminous wave determines the average plasma properties, and not vice versa. Attention is given to the implications of the obtained results for the acceleration of cosmic rays in pulsar magnetospheres.
Relativistic nonlinear plasma waves in a magnetic field
NASA Technical Reports Server (NTRS)
Kennel, C. F.; Pellat, R.
1975-01-01
Five relativistic plane nonlinear waves were investigated: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. When the ions are driven relativistic, they behave like electrons, and the assumption of an 'electron-positron' plasma leads to equations which have the form of a one-dimensional potential well. The solutions indicate that a large-amplitude superluminous wave determines the average plasma properties.
Localized Nonlinear Waves in Systems with Time- and Space-Modulated Nonlinearities
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Konotop, Vladimir V.
2008-04-25
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schroedinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.
Exact and explicit solitary wave solutions to some nonlinear equations
Jiefang Zhang
1996-08-01
Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative {Phi}{sup 4}-model equation, the generalized Fisher equation, and the elastic-medium wave equation.
Particle-Wave Micro-Dynamics in Nonlinear Self-Excited Dust Acoustic Waves
Tsai, C.-Y.; Teng, L.-W.; Liao, C.-T.; I Lin
2008-09-07
The large amplitude dust acoustic wave can be self-excited in a low-pressure dusty plasma. In the wave, the nonlinear wave-particle interaction determines particle motion, which in turn determines the waveform and wave propagation. In this work, the above behaviors are investigated by directly tracking particle motion through video-microscopy. A Lagrangian picture for the wave dynamics is constructed. The wave particle interaction associated with the transition from ordered to disordered particle oscillation, the wave crest trapping and wave heating are demonstrated and discussed.
On the adiabatic walking of plasma waves in a pulsar magnetosphere
Melikidze, George I.; Gil, Janusz; Mitra, Dipanjan E-mail: jag@astro.ia.uz.zgora.pl
2014-10-20
The pulsar radio emission is generated in the near magnetosphere of the neutron star, and it must propagate through the rest of it to emerge into the interstellar medium. An important issue is whether this propagation affects the planes of polarization of the generated radiation. Observationally, there is sufficient evidence that the emerging radiation is polarized parallel or perpendicular to the magnetic field line planes that should be associated with the ordinary (O) and extraordinary (X) plasma modes, respectively, excited by some radiative process. This strongly suggests that the excited X and O modes are not affected by the so-called adiabatic walking that causes a slow rotation of polarization vectors. In this paper, we demonstrate that the conditions for adiabatic walking are not fulfilled within the soliton model of pulsar radio emission, in which the coherent curvature radiation occurs at frequencies much lower than the characteristic plasma frequency, The X mode propagates freely and observationally represents the primary polarization mode. The O mode has difficulty escaping from the pulsar plasma; however, it is sporadically observed as a weaker secondary polarization mode. We discuss a possible scenario under which the O mode can also escape from the plasma and reach an observer.
Nonlinear waves in second order conformal hydrodynamics
NASA Astrophysics Data System (ADS)
Fogaça, D. A.; Marrochio, H.; Navarra, F. S.; Noronha, J.
2015-02-01
In this work we study wave propagation in dissipative relativistic fluids described by a simplified set of the 2nd order viscous conformal hydrodynamic equations corresponding to Israel-Stewart theory. Small amplitude waves are studied within the linearization approximation while waves with large amplitude are investigated using the reductive perturbation method, which is generalized to the case of 2nd order relativistic hydrodynamics. Our results indicate the presence of a "soliton-like" wave solution in Israel-Stewart hydrodynamics despite the presence of dissipation and relaxation effects.
Nonlinear dynamics of trapped waves on jet currents and rogue waves.
Shrira, V I; Slunyaev, A V
2014-04-01
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrow band in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonlinear theory based on the modal approach of Shrira and Slunyaev [J. Fluid. Mech. 738, 65 (2014)] leads to the one-dimensional modified nonlinear Schrödinger equation of self-focusing type for a single mode. Its solutions such as envelope solitons and breathers are considered to be prototypes of rogue waves; these solutions, in contrast to waves in the absence of currents, are robust with respect to transverse perturbations, which suggests a potentially higher probability of rogue waves. Robustness of the long-lived analytical solutions describing modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations. PMID:24827178
Nonlinear dynamics of trapped waves on jet currents and rogue waves.
Shrira, V I; Slunyaev, A V
2014-04-01
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrow band in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonlinear theory based on the modal approach of Shrira and Slunyaev [J. Fluid. Mech. 738, 65 (2014)] leads to the one-dimensional modified nonlinear Schrödinger equation of self-focusing type for a single mode. Its solutions such as envelope solitons and breathers are considered to be prototypes of rogue waves; these solutions, in contrast to waves in the absence of currents, are robust with respect to transverse perturbations, which suggests a potentially higher probability of rogue waves. Robustness of the long-lived analytical solutions describing modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations.
Behavior of a Moist Kelvin Wave Packet with Nonlinear Heating.
NASA Astrophysics Data System (ADS)
Wang, Bin; Xue, Yan
1992-04-01
The effects of nonlinear (positive only or conditional) heating on moist Kelvin waves are examined with a simple equatorial zonal-plane model describing the gravest baroclinic mode.The unstable perturbation subject to nonlinear beating emerges as a wave packet. A typical amplifying, eastward-moving wave packet is characterized by an asymmetric structure: 1) the ascending branch (wet region) is much narrower than the two descending ones (dry regions); and 2) the circulation cell to the east of the wet region center is smaller and stronger than its counterpart to the west of the center. The wet-dry asymmetry is primarily caused by the nonlinear beating effect, while the east-west asymmetry is a result of the movement of the wave packet relative to mean flow. The existence of Newtonian cooling and Rayleigh friction enhances the structural asymmetries.The unstable wave packet is characterized by two zonal length scales: the ascending branch length (ABL) and total circulation extent (TCE). For a given basic state, the growth rate of a wave packet increases with decreasing ABL or TCE. However, up to a moderate growth rate (order of day1) the energy spectra of all wave packets are dominated by zonal wavenumber one regardless of ABL size. In particular, the slowly growing (low frequency) wave packets normally exhibit TCEs of planetary scale and ABLs of synoptic scale.Observed equatorial intraseasonal disturbances often display a narrow convection region in between two much broader dry regions and a total circulation of planetary scale. These structure and scale characteristics are caused by the effects of nonlinear heating and the cyclic geometry of the equator. It is argued that the unstable disturbance found in numerical experiments (e.g., Lau and Peng; Hayashi and Sumi) is a manifestation of the nonlinear wave packet.
Shoaling of nonlinear internal waves in Massachusetts Bay
Scotti, A.; Beardsley, R.C.; Butman, B.; Pineda, J.
2008-01-01
The shoaling of the nonlinear internal tide in Massachusetts Bay is studied with a fully nonlinear and nonhydrostatic model. The results are compared with current and temperature observations obtained during the August 1998 Massachusetts Bay Internal Wave Experiment and observations from a shorter experiment which took place in September 2001. The model shows how the approaching nonlinear undular bore interacts strongly with a shoaling bottom, offshore of where KdV theory predicts polarity switching should occur. It is shown that the shoaling process is dominated by nonlinearity, and the model results are interpreted with the aid of a two-layer nonlinear but hydrostatic model. After interacting with the shoaling bottom, the undular bore emerges on the shallow shelf inshore of the 30-m isobath as a nonlinear internal tide with a range of possible shapes, all of which are found in the available observational record. Copyright 2008 by the American Geophysical Union.
Das, Jayasree; Bandyopadhyay, Anup; Das, K. P.
2007-09-15
The purpose of this paper is to present the recent work of Das et al. [J. Plasma Phys. 72, 587 (2006)] on the existence and stability of the alternative solitary wave solution of fixed width of the combined MKdV-KdV-ZK (Modified Korteweg-de Vries-Korteweg-de Vries-Zakharov-Kuznetsov) equation for the ion-acoustic wave in a magnetized nonthermal plasma consisting of warm adiabatic ions in a more generalized form. Here we derive the alternative solitary wave solution of variable width instead of fixed width of the combined MKdV-KdV-ZK equation along with the condition for its existence and find that this solution assumes the sech profile of the MKdV-ZK (Modified Korteweg-de Vries-Zakharov-Kuznetsov) equation, when the coefficient of the nonlinear term of the KdV-ZK (Korteweg-de Vries-Zakharov-Kuznetsov) equation tends to zero. The three-dimensional stability analysis of the alternative solitary wave solution of variable width of the combined MKdV-KdV-ZK equation shows that the instability condition and the first order growth rate of instability are exactly the same as those of the solitary wave solution (the sech profile) of the MKdV-ZK equation, when the coefficient of the nonlinear term of the KdV-ZK equation tends to zero.
The Role of Wave Nonlinearity on Sediment Motion and Transport
NASA Astrophysics Data System (ADS)
Foster, D. L.; Kaihatu, J. M.; Frank, D. P.
2014-12-01
It has long been assumed that higher moments of velocity and acceleration affect the motion and transport of mobile sediment beds. The goal of this effect is to identify the influence of wave shape on sediment motion and mobile layer thickness. Theoretic predictions of neared velocity and horizontal pressure gradient will be approximated with Dean's 1965 stream function theory for representing nonlinear waves. The formulation also allows for the inclusion of mean flow. Wave nonlinearity is characterized with skewness and asymmetry of the wave shape. An incipient motion criterion that resolves the fluid forcing due to both the bed shear stress and the horizontal pressure gradients is applied to a slab of sediment. The resulting formulation provides a measure of sediment transport vulnerability to commonly available wave parameters (wave height, wave period, water depth, skewness, and asymmetry). The formulation is compared with several available data sets with a range of forcing and sediment conditions. Particle image velocimetry observations of velocity and sediment motion and acoustic Doppler observations of the three-dimensional velocity field provide high resolution of the near bed dynamics. The wave shape is characterized with mid water column pressure sensors and wave gages. As the wave nonlinearities increase, the role of the horizontal pressure gradient also increases. The influence of the pressure gradient also is shown to be particularly sensitive to a decrease in the wave period and an increase in the wave asymmetry. The influence of the bed shear is shown to be particularly sensitive to wave skewness. The analysis demonstrates the potential for improving the larger scale predictions of sediment transport in our nearshore and coastal waters.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
Tataronis, J. A.
2004-06-01
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 Alfvkn 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.
A direct Vlasov simulation of nonlinear plasma waves
NASA Astrophysics Data System (ADS)
Hara, Kentaro; Boyd, Iain; Kaganovich, Igor
2013-10-01
A direct Vlasov simulation, which solves the collisionless Vlasov equation directly on a discretized phase space, achieves good resolution of velocity distribution functions in comparison to particle methods. In this presentation, nonlinear electron plasma waves (EPWs) and ion acoustic waves (IAWs) are investigated with a fully-kinetic one-dimensional Vlasov simulation. A parallelized Vlasov simulation is employed since grid resolution of the discretized phase space is required to be fine enough in order to capture the nonlinear waves with higher harmonic modes. The primary goal is benchmarking our simulation with results obtained from another Vlasov code and verification with the nonlinear theories [R. L. Berger et al., Phys. Plasmas 20, 032107 (2013)]. The frequency shift of nonlinear plasma waves is investigated by applying an initial density perturbation or an external driver potential. It has been observed that the plasma frequency decreases for EPWs and increases for IAWs for Te /Ti = 10 , which agrees with Berger's simulation and theories. A further investigation varying the generation of the nonlinear wave such as driver amplitude and duration time will be performed and discussed. Supported by the U.S. Department of Energy Office of Science, Fusion Energy Sciences Program, Grant # DE-SC0001939, and the Air Force Research Laboratory Grant # F9550-09-1-0695.
Self-similar rogue waves and nonlinear tunneling effects in inhomogeneous nonlinear fiber optics
NASA Astrophysics Data System (ADS)
Wang, Lei; Zhu, Yu-Jie; Jiang, Dong-Yang
2016-04-01
Analytical first- and second-order rogue wave solutions of the inhomogeneous modified nonlinear Schrödinger equation are presented by using similarity transformation. Then, by the proper choices of the inhomogeneous coefficients and free parameters, the controllable behaviors of the optical rogue waves are graphically discussed in the nonlinear fiber optics context. It is found that the width of the rogue wave can be tuned by adjusting the parameter ? and the locations of the rogue waves are linearly controlled by the parameter ?. The intensities of the rogue waves are influenced by the inhomogeneous linear gain/loss coefficient ? and parameter ?. The dispersion management function ? has effects on the periods and trajectories of the rogue waves and can induce maintenance (or annihilation) along ? direction. Interestingly, the composite rogue waves are revealed, the location of which is manipulated through changing the dispersion management function ?. Additionally, the nonlinear tunneling of those rogue waves is investigated as they propagate through a dispersion barrier (or well) and nonlinear barrier (or well).
Emergent geometries and nonlinear-wave dynamics in photon fluids.
Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D
2016-03-22
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.
Emergent geometries and nonlinear-wave dynamics in photon fluids
Marino, F.; Maitland, C.; Vocke, D.; Ortolan, A.; Faccio, D.
2016-01-01
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level. PMID:27001128
Emergent geometries and nonlinear-wave dynamics in photon fluids.
Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D
2016-01-01
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level. PMID:27001128
Self-sustained nonlinear waves in traffic flow
NASA Astrophysics Data System (ADS)
Flynn, M. R.; Kasimov, A. R.; Nave, J.-C.; Rosales, R. R.; Seibold, B.
2009-05-01
In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions to the hyperbolic (“inviscid”) continuum traffic equations. Generic existence criteria are examined in the context of the Lax entropy conditions. Our analysis naturally precludes traveling wave solutions for which the shocks travel downstream more rapidly than individual vehicles. Consistent with recent experimental observations from a periodic roadway [Y. Sugiyama , N. J. Phys. 10, 033001 (2008)], our numerical calculations show that nonlinear traveling waves are attracting solutions, with the time evolution of the system converging toward a wave-dominated configuration. Theoretical principles are elucidated by considering examples of traffic flow on open and closed roadways.
Langmuir wave harmonics due to driven nonlinear currents
NASA Astrophysics Data System (ADS)
Malaspina, David M.; Graham, Daniel B.; Ergun, Robert E.; Cairns, Iver H.
2013-11-01
The conversion of Langmuir waves into electromagnetic radiation near the local plasma frequency (fpe) and twice the local plasma frequency (2fpe) occurs in diverse heliospheric environments including along the path of type III radio bursts, at interplanetary shocks, and in planetary foreshocks. This radiation has the potential to act as a probe of remote plasma conditions, provided that the conversion mechanism is well understood. One candidate conversion mechanism is the antenna radiation of localized Langmuir waves. Antenna radiation near 2fpe requires the presence of nonlinear currents at 2fpe. In this work, properties of these currents are predicted from theory and compared with observations of Langmuir wave electric fields made using the WAVES instrument on the STEREO spacecraft. It is found that the observed frequency structure, polarization, and wave number ratio are consistent with nonlinear current predictions, once electric fields near 2fpeconsistent with sheath effects are taken into account.
Ion thermal effects on slow mode solitary waves in plasmas with two adiabatic ion species
Nsengiyumva, F. Hellberg, M. A. Mace, R. L.
2015-09-15
Using both the Sagdeev and Korteweg-de Vries (KdV) methods, ion thermal effects on slow mode ion acoustic solitons and double layers are investigated in a plasma with two adiabatic positive ion species. It is found that reducing the gap between the two ion thermal speeds by increasing the relative temperature of the cool ions increases the typical soliton/double layer speeds for all values of the ion-ion density ratio and reduces the range in the density ratio that supports double layers. The effect of increasing the relative cool ion temperature on the soliton/double layer amplitudes depends on the relative densities. For lower values of the ion density ratio, an increase in cool ion temperature leads to a significant decrease in soliton/double layer amplitude, so one may find that solitons of all permissible speeds lie within the range of KdV theory.
Nonlinear Alfvén wave dynamics in plasmas
NASA Astrophysics Data System (ADS)
Sarkar, Anwesa; Chakrabarti, Nikhil; Schamel, Hans
2015-07-01
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
Nonlinear Alfvén wave dynamics in plasmas
Sarkar, Anwesa; Chakrabarti, Nikhil
2015-07-15
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
On the use of nonlinear solitary waves for energy harvesting
NASA Astrophysics Data System (ADS)
Li, Kaiyuan; Rizzo, Piervincenzo
2015-04-01
In the last decade there has been an increasing attention on the use of highly- and weakly- nonlinear solitary waves in engineering and physics. These waves can form and travel in nonlinear systems such as one-dimensional chains of spherical particles. One engineering application of solitary waves is the fabrication of acoustic lenses, which are employed in a variety of fields ranging from biomedical imaging and surgery to defense systems and damage detection. In this paper we propose to couple an acoustic lens to a wafer-type lead zirconate titanate transducer (PZT) to harvest energy from the vibration of an object tapping the lens. The lens is composed of a circle array made of chains of particles in contact with a polycarbonate material where the nonlinear waves coalesce into linear waves. The PZT located at the designed focal point converts the mechanical energy carried by the stress wave into electricity to power a load resistor. The performance of the designed harvester is compared to a conventional cantilever beam, and the experimental results show that the power generated with the nonlinear lens has the same order of magnitude of the beam.
Torello, David; Kim, Jin-Yeon; Qu, Jianmin; Jacobs, Laurence J.
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.
Nonparaxial elliptic waves and solitary waves in coupled nonlinear Helmholtz equations
NASA Astrophysics Data System (ADS)
Tamilselvan, K.; Kanna, T.; Khare, Avinash
2016-10-01
We obtain a class of elliptic wave solutions of coupled nonlinear Helmholtz (CNLH) equations describing nonparaxial ultra-broad beam propagation in nonlinear Kerr-like media, in terms of the Jacobi elliptic functions and also discuss their limiting forms (hyperbolic solutions). Especially, we show the existence of non-trivial solitary wave profiles in the CNLH system. The effect of nonparaxiality on speed, pulse width and amplitude of the nonlinear waves is analyzed in detail. Particularly, a mechanism for tuning the speed by altering the nonparaxial parameter is proposed. We also identify a novel phase-unlocking behavior due to the presence of nonparaxial parameter.
Numerical modelling of nonlinear full-wave acoustic propagation
Velasco-Segura, Roberto Rendón, Pablo L.
2015-10-28
The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on a GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.
Adiabatically tapered hyperbolic metamaterials for dispersion control of high-k waves.
West, Paul R; Kinsey, Nathaniel; Ferrera, Marcello; Kildishev, Alexander V; Shalaev, Vladimir M; Boltasseva, Alexandra
2015-01-14
Hyperbolic metamaterials (HMMs) have shown great promise in the optical and quantum communities due to their extremely large, broadband photonic density of states. This feature is a direct consequence of supporting photonic modes with unbounded k-vectors. While these materials support such high-k waves, they are intrinsically confined inside the HMM and cannot propagate into the far-field, rendering them impractical for many applications. Here, we demonstrate how the magnitude of k-vectors can be engineered as the propagating radiation passes through media of differing dispersion relations (including type II HMMs and dielectrics) in the in-plane direction. The total outcoupling efficiency of waves in the in-plane direction is shown to be on average 2 orders of magnitude better than standard out-of-plane outcoupling methods. In addition, the outcoupling can be further enhanced using a proposed tapered HMM waveguide that is fabricated using a shadowed glancing angle deposition technique; thereby proving the feasibility of the proposed device. Applications for this technique include converting high-k waves to low-k waves that can be out-coupled into free-space and creating extremely high-k waves that are quickly quenched. Most importantly, this method of in-plane outcoupling acts as a bridge through which waves can cross between the regimes of low-k waves in classical dielectric materials and the high-k waves in HMMs with strongly reduced reflective losses.
Nonlinear transient waves in coupled phase oscillators with inertia
NASA Astrophysics Data System (ADS)
Jörg, David J.
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
Nonlinear wave particle interaction in the Earth's foreshock
NASA Technical Reports Server (NTRS)
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.
Nonlinear absorption of Alfven wave in dissipative plasma
Taiurskii, A. A. Gavrikov, M. B.
2015-10-28
We propose a method for studying absorption of Alfven wave propagation in a homogeneous non-isothermal plasma along a constant magnetic field, and relaxation of electron and ion temperatures in the A-wave. The absorption of a A-wave by the plasma arises due to dissipative effects - magnetic and hydrodynamic viscosities of electrons and ions and their elastic interaction. The method is based on the exact solution of two-fluid electromagnetic hydrodynamics of the plasma, which for A-wave, as shown in the work, are reduced to a nonlinear system of ordinary differential equations.
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 acoustic wave equations with fractional loss operators.
Prieur, Fabrice; Holm, Sverre
2011-09-01
Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations.
Kinetic equation for nonlinear resonant wave-particle interaction
NASA Astrophysics Data System (ADS)
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
Nonlinear waves propagating in the electrical transmission line
NASA Astrophysics Data System (ADS)
Duan, W.-S.
2004-04-01
A coupled Zakharov-Kuznetsov (ZK) equation is derived for a nonlinear transmission line in which the nonlinear capacitance C is of a general form C = C0(1 + k1V + k2V2 + ...). For a solitary-wave solution of the ZK equation, there is an instability region which is given numerically in this paper. It is in agreement with the analytical results for special cases.
FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations
NASA Astrophysics Data System (ADS)
Ibragimov, N. H.; Torrisi, M.; Tracinà, R.
2010-11-01
In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
NASA Astrophysics Data System (ADS)
Alka, W.; Goyal, Amit; Nagaraja Kumar, C.
2011-01-01
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces
NASA Astrophysics Data System (ADS)
Jin, Boyuan; Argyropoulos, Christos
2016-06-01
Plasmonic metasurfaces provide an effective way to increase the efficiency of several nonlinear processes while maintaining nanoscale dimensions. In this work, nonlinear metasurfaces based on film-coupled silver nanostripes loaded with Kerr nonlinear material are proposed to achieve efficient four-wave mixing (FWM). Highly localized plasmon resonances are formed in the nanogap between the metallic film and nanostripes. The local electric field is dramatically enhanced in this subwavelength nanoregion. These properties combined with the relaxed phase matching condition due to the ultrathin area lead to a giant FWM efficiency, which is enhanced by nineteen orders of magnitude compared to a bare silver screen. In addition, efficient visible and low-THz sources can be constructed based on the proposed nonlinear metasurfaces. The FWM generated coherent wave has a directional radiation pattern and its output power is relatively insensitive to the incident angles of the excitation sources. This radiated power can be further enhanced by increasing the excitation power. The dielectric nonlinear material placed in the nanogap is mainly responsible for the ultrastrong FWM response. Compact and efficient wave mixers and optical sources spanning different frequency ranges are envisioned to be designed based on the proposed nonlinear metasurface designs.
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces.
Jin, Boyuan; Argyropoulos, Christos
2016-01-01
Plasmonic metasurfaces provide an effective way to increase the efficiency of several nonlinear processes while maintaining nanoscale dimensions. In this work, nonlinear metasurfaces based on film-coupled silver nanostripes loaded with Kerr nonlinear material are proposed to achieve efficient four-wave mixing (FWM). Highly localized plasmon resonances are formed in the nanogap between the metallic film and nanostripes. The local electric field is dramatically enhanced in this subwavelength nanoregion. These properties combined with the relaxed phase matching condition due to the ultrathin area lead to a giant FWM efficiency, which is enhanced by nineteen orders of magnitude compared to a bare silver screen. In addition, efficient visible and low-THz sources can be constructed based on the proposed nonlinear metasurfaces. The FWM generated coherent wave has a directional radiation pattern and its output power is relatively insensitive to the incident angles of the excitation sources. This radiated power can be further enhanced by increasing the excitation power. The dielectric nonlinear material placed in the nanogap is mainly responsible for the ultrastrong FWM response. Compact and efficient wave mixers and optical sources spanning different frequency ranges are envisioned to be designed based on the proposed nonlinear metasurface designs. PMID:27345755
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces
Jin, Boyuan; Argyropoulos, Christos
2016-01-01
Plasmonic metasurfaces provide an effective way to increase the efficiency of several nonlinear processes while maintaining nanoscale dimensions. In this work, nonlinear metasurfaces based on film-coupled silver nanostripes loaded with Kerr nonlinear material are proposed to achieve efficient four-wave mixing (FWM). Highly localized plasmon resonances are formed in the nanogap between the metallic film and nanostripes. The local electric field is dramatically enhanced in this subwavelength nanoregion. These properties combined with the relaxed phase matching condition due to the ultrathin area lead to a giant FWM efficiency, which is enhanced by nineteen orders of magnitude compared to a bare silver screen. In addition, efficient visible and low-THz sources can be constructed based on the proposed nonlinear metasurfaces. The FWM generated coherent wave has a directional radiation pattern and its output power is relatively insensitive to the incident angles of the excitation sources. This radiated power can be further enhanced by increasing the excitation power. The dielectric nonlinear material placed in the nanogap is mainly responsible for the ultrastrong FWM response. Compact and efficient wave mixers and optical sources spanning different frequency ranges are envisioned to be designed based on the proposed nonlinear metasurface designs. PMID:27345755
Evidence for nonlinear wave-wave interactions in solar type III radio bursts
NASA Technical Reports Server (NTRS)
Lin, R. P.; Levedahl, W. K.; Lotko, W.; Gurnett, D. A.; Scarf, F. L.
1986-01-01
Evidence is presented that nonlinear wave-wave interactions occur in type III solar radio bursts. Intense, spiky Langmuir waves are observed to be driven by electron beams associated with type III solar radio bursts in the interplanetary medium. Bursts of 30-300 Hz (in the spacecraft frame) waves are often observed coincident in time with the most intense spikes of the Langmuir waves. These low-frequency waves appear to be long-wavelength ion acoustic waves, with wavenumber approximately equal to the beam resonant Langmuir wavenumber. Three possible interpretations of these observations are considered: modulational instability, parametric decay of the parent Langmuir waves to daughter ion acoustic and Langmuir waves, and decay to daughter electromagnetic waves and ion acoustic waves.
Nonlinear fast sausage waves in homogeneous magnetic flux tubes
NASA Astrophysics Data System (ADS)
Mikhalyaev, Badma B.; Ruderman, Michael S.
2015-12-01
> We consider fast sausage waves in straight homogeneous magnetic tubes. The plasma motion is described by the ideal magnetohydrodynamic equations in the cold plasma approximation. We derive the nonlinear Schrödinger equation describing the nonlinear evolution of an envelope of a carrier wave. The coefficients of this equation are expressed in terms Bessel and modified Bessel functions. They are calculated numerically for various values of parameters. In particular, we show that the criterion for the onset of the modulational or Benjamin-Fair instability is satisfied. The implication of the obtained results for solar physics is discussed.
Selection rules for the nonlinear interaction of internal gravity waves.
Jiang, Chung-Hsiang; Marcus, Philip S
2009-03-27
Two intersecting beams of internal gravity waves will generically create two wave packets by nonlinear interaction. The frequency of one packet will be the sum and that of the other packet will be the difference of the frequencies of the intersecting beams. In principle, each packet should form an "X" pattern, or "St. Andrew's cross" consisting of four beams outgoing from the point of intersection. Here we derive selection rules and show that most of the expected nonlinear beams are forbidden. These rules can also be applied to the reflection of a beam from a boundary.
Oblique propagation of nonlinear electrostatic waves in dense astrophysical magnetoplasmas
Masood, W.; Siddiq, M.; Rizvi, H.
2011-10-15
Nonlinear quantum ion-acoustic waves in dense dissipative as well as non-dissipative magnetized plasmas are investigated employing the quantum hydrodynamic model. In this regard, Zakharov Kuznetsov Burgers equation is derived in quantum plasmas, for the first time, using the small amplitude perturbation expansion method. The unique features of nonlinear electrostatic structures in pure electron-ion quantum magnetoplasma are highlighted and the parametric domain of the applicability of the model is unequivocally expressed. The present study may be useful to understand the nonlinear propagation characteristics of electrostatic shock and solitary structures in dense astrophysical systems where the quantum effects are expected to dominate.
Oblique propagation of nonlinear electrostatic waves in dense astrophysical magnetoplasmas
NASA Astrophysics Data System (ADS)
Masood, W.; Rizvi, H.; Siddiq, M.
2011-10-01
Nonlinear quantum ion-acoustic waves in dense dissipative as well as non-dissipative magnetized plasmas are investigated employing the quantum hydrodynamic model. In this regard, Zakharov Kuznetsov Burgers equation is derived in quantum plasmas, for the first time, using the small amplitude perturbation expansion method. The unique features of nonlinear electrostatic structures in pure electron-ion quantum magnetoplasma are highlighted and the parametric domain of the applicability of the model is unequivocally expressed. The present study may be useful to understand the nonlinear propagation characteristics of electrostatic shock and solitary structures in dense astrophysical systems where the quantum effects are expected to dominate.
Nonlinear evolution of Alfven waves in a finite beta plasma
Som, B.K. ); Dasgupta, B.; Patel, V.L. ); Gupta, M.R. )
1989-12-01
A general form of the derivative nonlinear Schroedinger (DNLS) equation, describing the nonlinear evolution of Alfven waves propagating parallel to the magnetic field, is derived by using two-fluid equations with electron and ion pressure tensors obtained from Braginskii (in {ital Reviews} {ital of} {ital Plasma Physics} (Consultants Bureau, New York, 1965), Vol. 1, p. 218). This equation is a mixed version of the nonlinear Schroedinger (NLS) equation and the DNLS, as it contains an additional cubic nonlinear term that is of the same order as the derivative of the nonlinear terms, a term containing the product of a quadratic term, and a first-order derivative. It incorporates the effects of finite beta, which is an important characteristic of space and laboratory plasmas.
Nonlinear waves in a fluid-filled thin viscoelastic tube
NASA Astrophysics Data System (ADS)
Zhang, Shan-Yuan; Zhang, Tao
2010-11-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incompressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin—Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the propagation of nonlinear pressure wave in the solid—liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the exponent α of the perturbation parameter in Gardner—Morikawa transformation according to the order of viscous coefficient η, three kinds of evolution equations with soliton solution, i.e. Korteweg—de Vries (KdV)—Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
Time-reversal of nonlinear waves: Applicability and limitations
NASA Astrophysics Data System (ADS)
Ducrozet, G.; Fink, M.; Chabchoub, A.
2016-09-01
Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.
Nonlinear Internal Waves in the South China Sea During ASIAEX
NASA Technical Reports Server (NTRS)
Liu, Antony K.; Tang, David T.; Ramp, Steve R.
2002-01-01
Internal wave distribution maps have been compiled from more than one hundred ERS-1/2, RADARSAT and Space Shuttle SAR images in the South China Sea (SCS) from 1993 to 2000. Based on these distribution maps, most of internal waves in the northeast part of SCS were propagating westward. The wave crest can be as long as 200 km with amplitude of 100 m, due to strong current from the Kuroshio branching out into the SCS. In recent Asian Seas International Acoustics Experiment (ASIAEX), moorings have been deployed in April 2000 and May 2001. Simultaneous RADARSAT ScanSAR images have been collected during the field test to integrate with the model and the in-situ measurements in the SCS. During ASIAEX in May 2001, many large internal waves were observed at the test area and were the major features for acoustic volume interaction. The environmental parameters have been calculated based on extensive CTD castings and mooring data. Nonlinear internal wave models have been applied to simulate the wave evolution on the continental shelf and the results compare reasonably with mooring measurements. The evolution and dissipation of huge internal waves on the shelf break, mode-two waves, elevation waves, and wave-wave interaction are very important issues for acoustic propagation. The implication of internal wave effects on acoustic propagation will also be discussed.
Reverberation clutter induced by nonlinear internal waves in shallow water.
Henyey, Frank S; Tang, Dajun
2013-10-01
Clutter is related to false alarms for active sonar. It is demonstrated that, in shallow water, target-like clutter in reverberation signals can be caused by nonlinear internal waves. A nonlinear internal wave is modeled using measured stratification on the New Jersey shelf. Reverberation in the presence of the internal wave is modeled numerically. Calculations show that acoustic energy propagating near a sound speed minimum is deflected as a high intensity, higher angle beam into the bottom, where it is backscattered along the reciprocal path. The interaction of sound with the internal wave is isolated in space, hence resulting in a target-like clutter, which is found to be greater than 10 dB above the mean reverberation level. PMID:24116532
Nonlinear particle simulation of ion cyclotron waves in toroidal geometry
Kuley, A. Lin, Z.; Bao, J.; Wei, X. S.; Xiao, Y.
2015-12-10
Global particle simulation model has been developed in this work to provide a first-principles tool for studying the nonlinear interactions of radio frequency (RF) waves with plasmas in tokamak. In this model, ions are considered as fully kinetic particles using the Vlasov equation and electrons are treated as guiding centers using the drift kinetic equation with realistic electron-to-ion mass ratio. Boris push scheme for the ion motion has been developed in the toroidal geometry using magnetic coordinates and successfully verified for the ion cyclotron and ion Bernstein waves in global gyrokinetic toroidal code (GTC). The nonlinear simulation capability is applied to study the parametric decay instability of a pump wave into an ion Bernstein wave side band and a low frequency ion cyclotron quasi mode.
Effect of nonlinear instability on gravity-wave momentum transport
NASA Technical Reports Server (NTRS)
Dunkerton, Timothy J.
1987-01-01
This paper investigates the nonlinear instability of internal gravity waves and the effects of their nonlinear interaction on momentum flux, using simple theoretical and numerical models. From the result of an analysis of parametric instability of a two-dimensional internal gravity wave as discussed by Yeh and Liu (1981) and Klostermeyer (1982), a group trajectory length scale for a gravity wave packet was determined, expressed in terms of the dominant vertical wavelenght and the degree of convective saturation. It is shown that this analysis justifies the Eikonal saturation method for relatively transient packets, that are well below the saturation amplitude, propagating in a slowly varying mean flow. Conversely, linear theory fails for persistent disturbances and trasient wave packets near convective saturation.
On the nature of kinetic electrostatic electron nonlinear (KEEN) waves
Dodin, I. Y.; Fisch, N. J.
2014-03-15
An analytical theory is proposed for the kinetic electrostatic electron nonlinear (KEEN) waves originally found in simulations by Afeyan et al. [arXiv:1210.8105]. We suggest that KEEN waves represent saturated states of the negative mass instability (NMI) reported recently by Dodin et al. [Phys. Rev. Lett. 110, 215006 (2013)]. Due to the NMI, trapped electrons form macroparticles that produce field oscillations at harmonics of the bounce frequency. At large enough amplitudes, these harmonics can phase-lock to the main wave and form stable nonlinear dissipationless structures that are nonstationary but otherwise similar to Bernstein-Greene-Kruskal modes. The theory explains why the formation of KEEN modes is sensitive to the excitation scenario and yields estimates that agree with the numerical results of Afeyan et al. A new type of KEEN wave may be possible at even larger amplitudes of the driving field than those used in simulations so far.
Doppler effect of nonlinear waves and superspirals in oscillatory media.
Brusch, Lutz; Torcini, Alessandro; Bär, Markus
2003-09-01
Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example in which waves originate from a source exhibiting a back-and-forth movement in a radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves ("superspiral"). Using direct simulations as well as numerical nonlinear analysis within the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonic growth or decay as well as saturation of these modulations depending on the perturbation frequency. Our findings elucidate recent experimental observations concerning superspirals and their decay to spatiotemporal chaos.
Reverberation clutter induced by nonlinear internal waves in shallow water.
Henyey, Frank S; Tang, Dajun
2013-10-01
Clutter is related to false alarms for active sonar. It is demonstrated that, in shallow water, target-like clutter in reverberation signals can be caused by nonlinear internal waves. A nonlinear internal wave is modeled using measured stratification on the New Jersey shelf. Reverberation in the presence of the internal wave is modeled numerically. Calculations show that acoustic energy propagating near a sound speed minimum is deflected as a high intensity, higher angle beam into the bottom, where it is backscattered along the reciprocal path. The interaction of sound with the internal wave is isolated in space, hence resulting in a target-like clutter, which is found to be greater than 10 dB above the mean reverberation level.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
ERIC Educational Resources Information Center
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Nonlinear reflection of internal gravity wave onto a slope
NASA Astrophysics Data System (ADS)
Raja, Keshav; Sommeria, Joel; Staquet, Chantal; Leclair, Matthieu; Grisouard, Nicolas; Gostiaux, Louis
2016-04-01
The interaction of internal waves on sloping topography is one of the processes that cause mixing and transport in oceans. The mixing caused by internal waves is considered to be an important source of energy that is needed to bring back deep, dense water from the abyss to the surface of the ocean, across constant density surfaces. Apart from the vertical transport of heat (downwards) and mass (upwards), internal waves are also observed to irreversibly induce a mean horizontal flow. Mixing and wave induced mean flow may be considered as the processes that transfer wave induced energy to smaller and larger scales respectively. The process of mixing has been a subject of intense research lately. However, the process of wave induced mean flow and their dynamic impact await thorough study. The present study involves this wave induced mean flow, its generation and energetics. The nonlinear subcritical reflection of internal waves from a sloping boundary is studied using laboratory experiments carried out on the Coriolis Platform at Grenoble and, 2D and 3D numerical simulations done using a non-hydrostatic code. In the experiment, a plane wave is produced using a wave generator and is made to reflect normally on a sloping bottom in a uniformly stratified fluid. We consider both rotating and non-rotating cases. The numerical simulation mimicks the laboratory setup with an initial condition of an analytical plane wave solution in a vertical plane limited by a smooth envelope to simulate the finite wave generator. The interaction of the incident and reflected waves produce, apart from higher harmonics, an irreversible wave induced mean flow which grows in time and is localised in the interacting region. The finite extent of the wave generator allows the mean flow to recirculate in the horizontal plane, resulting in a dipolar potential vorticity field. Moreover, the generation of mean flow and higher harmonics, along with dissipative effects, diminishes the amplitude of
Optical vortex interaction and generation via nonlinear wave mixing
Lenzini, F.; Residori, S.; Bortolozzo, U.; Arecchi, F. T.
2011-12-15
Optical vortex beams are made to interact via degenerate two-wave mixing in a Kerr-like nonlinear medium. Vortex mixing is shown to occur inside the medium, leading to exchange of topological charge and cascaded generation of vortex beams. A mean-field model is developed and is shown to account for the selection rules of the topological charges observed after the wave-mixing process. Fractional charges are demonstrated to follow the same rules as for integer charges.
Nonlinear Guided Wave Mixing for Localized Material State Characterization
NASA Astrophysics Data System (ADS)
Lissenden, Cliff J.; Liu, Yang; Chillara, Vamshi K.; Choi, Gloria; Cho, Hwanjeong
Material state characterization methods sensitive to incipient damage provide new opportunities for managing the life cycle of structures. Finite element simulations of ultrasonic guided waves show the potential of nonlinear wave mixing to detect localized degradation invisible to both linear elastic stress-strain response and the eye. Correlation of material degradation to the generation of higher harmonics or combinational harmonics makes estimation of remaining life possible from material state data early in the service life.
Coda wave interferometry for estimating nonlinear behavior in seismic velocity.
Snieder, Roel; Grêt, Alexandre; Douma, Huub; Scales, John
2002-03-22
In coda wave interferometry, one records multiply scattered waves at a limited number of receivers to infer changes in the medium over time. With this technique, we have determined the nonlinear dependence of the seismic velocity in granite on temperature and the associated acoustic emissions. This technique can be used in warning mode, to detect the presence of temporal changes in the medium, or in diagnostic mode, where the temporal change in the medium is quantified.
Warm wavebreaking of nonlinear plasma waves with arbitrary phasevelocities
Schroeder, C.B.; Esarey, E.; Shadwick, B.A.
2004-11-12
A warm, relativistic fluid theory of a nonequilibrium, collisionless plasma is developed to analyze nonlinear plasma waves excited by intense drive beams. The maximum amplitude and wavelength are calculated for nonrelativistic plasma temperatures and arbitrary plasma wave phase velocities. The maximum amplitude is shown to increase in the presence of a laser field. These results set a limit to the achievable gradient in plasma-based accelerators.
On the pressure field of nonlinear standing water waves
NASA Technical Reports Server (NTRS)
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.
Nonlinear Generalized Hydrodynamic Wave Equations in Strongly Coupled Dusty Plasmas
Veeresha, B. M.; Sen, A.; Kaw, P. K.
2008-09-07
A set of nonlinear equations for the study of low frequency waves in a strongly coupled dusty plasma medium is derived using the phenomenological generalized hydrodynamic (GH) model and is used to study the modulational stability of dust acoustic waves to parallel perturbations. Dust compressibility contributions arising from strong Coulomb coupling effects are found to introduce significant modifications in the threshold and range of the instability domain.
Rayleigh wave nonlinear inversion based on the Firefly algorithm
NASA Astrophysics Data System (ADS)
Zhou, Teng-Fei; Peng, Geng-Xin; Hu, Tian-Yue; Duan, Wen-Sheng; Yao, Feng-Chang; Liu, Yi-Mou
2014-06-01
Rayleigh waves have high amplitude, low frequency, and low velocity, which are treated as strong noise to be attenuated in reflected seismic surveys. This study addresses how to identify useful shear wave velocity profile and stratigraphic information from Rayleigh waves. We choose the Firefly algorithm for inversion of surface waves. The Firefly algorithm, a new type of particle swarm optimization, has the advantages of being robust, highly effective, and allows global searching. This algorithm is feasible and has advantages for use in Rayleigh wave inversion with both synthetic models and field data. The results show that the Firefly algorithm, which is a robust and practical method, can achieve nonlinear inversion of surface waves with high resolution.
Weak nonlinear coupling of Rossby-Haurwitz waves
NASA Astrophysics Data System (ADS)
Becker, G.
1986-11-01
The Rossby-Haurwitz waves as solutions of the linearized free barotropic vorticity equation in a spherical coordinate system are in good agreement with the observed ultralong planetary waves of the troposphere. Within an antisymmetric basic flow, as in the middle atmosphere, the solutions become unstable because of mathematical singularities, called 'critical latitudes'. Therefore the nonlinear advection terms have to be considered in such a case. Analytical solutions of a corresponding spectral truncated model demonstrate the weak interaction between the mean flow and the ultralong waves of zonal wavenumbers one to three. The time structures of the planetary waves change from periodic oscillations via vacillations to turbulent character with increasing initial amplitudes. Finally the spectral model is extended by the waves of wavenumber four. The numerical solutions for the periods of the planetary waves within tropospheric and stratospheric basic flow configurations agree with observations.
Nonlinear interaction of dispersive Alfven waves and magnetosonic waves in space plasma
Sharma, R. P.; Kumar, Sanjay; Singh, H. D.
2009-03-15
This paper presents the model equations governing the nonlinear interaction between dispersive Alfven wave (DAW) and magnetosonic wave in the low-{beta} plasmas ({beta}<
Nonlinear dynamics of Airy-vortex 3D wave packets: emission of vortex light waves.
Driben, Rodislav; Meier, Torsten
2014-10-01
The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Because of the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and nonzero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse.
Corrigendum and addendum. Modeling weakly nonlinear acoustic wave propagation
Christov, Ivan; Christov, C. I.; Jordan, P. M.
2014-12-18
This article presents errors, corrections, and additions to the research outlined in the following citation: Christov, I., Christov, C. I., & Jordan, P. M. (2007). Modeling weakly nonlinear acoustic wave propagation. The Quarterly Journal of Mechanics and Applied Mathematics, 60(4), 473-495.
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.
A k-space method for moderately nonlinear wave propagation.
Jing, Yun; Wang, Tianren; Clement, Greg T
2012-08-01
A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant-Friedrichs-Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation.
A k-Space Method for Moderately Nonlinear Wave Propagation
Jing, Yun; Wang, Tianren; Clement, Greg T.
2013-01-01
A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant–Friedrichs–Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation. PMID:22899114
Non-linear Langmuir waves in a warm quantum plasma
Dubinov, Alexander E. Kitaev, Ilya N.
2014-10-15
A non-linear differential equation describing the Langmuir waves in a warm quantum electron-ion plasma has been derived. Its numerical solutions of the equation show that ordinary electronic oscillations, similar to the classical oscillations, occur along with small-scale quantum Langmuir oscillations induced by the Bohm quantum force.
Nonlinear wave interactions in bubble layers
NASA Astrophysics Data System (ADS)
Karpov, S.; Prosperetti, A.; Ostrovsky, L.
2003-03-01
Due to the large compressibility of gas bubbles, layers of a bubbly liquid surrounded by pure liquid exhibit many resonances that can give rise to a strongly nonlinear behavior even for relatively low-level excitation. In an earlier paper [Druzhinin et al., J. Acoust. Soc. Am. 100, 3570 (1996)] it was pointed out that, by exciting the bubbly layer in correspondence of two resonant modes, so chosen that the difference frequency also corresponds to a resonant mode, it might be possible to achieve an efficient parametric generation of a low-frequency signal. The earlier work made use of a simplified model for the bubbly liquid that ignored the dissipation and dispersion introduced by the bubbles. Here a more realistic description of the bubble behavior is used to study the nonlinear oscillations of a bubble layer under both single- and dual-frequency excitation. It is found that a difference-frequency power of the order of 1% can be generated with incident pressure amplitudes of the order of 50 kPa or so. It appears that similar phenomena would occur in other systems, such as porous waterlike or rubberlike media.
Linear and nonlinear acoustic wave propagation in the atmosphere
NASA Technical Reports Server (NTRS)
Hariharan, S. I.; Yu, Ping
1988-01-01
The investigation of the acoustic wave propagation theory and numerical implementation for the situation of an isothermal atmosphere is described. A one-dimensional model to validate an asymptotic theory and a 3-D situation to relate to a realistic situation are considered. In addition, nonlinear wave propagation and the numerical treatment are included. It is known that the gravitational effects play a crucial role in the low frequency acoustic wave propagation. They propagate large distances and, as such, the numerical treatment of those problems become difficult in terms of posing boundary conditions which are valid for all frequencies.
Nonlinear acoustic/seismic waves in earthquake processes
Johnson, Paul A.
2012-09-04
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.
Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types
NASA Astrophysics Data System (ADS)
Remillieux, Marcel C.; Guyer, Robert A.; Payan, Cédric; Ulrich, T. J.
2016-03-01
In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. This result could lead to further understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.
Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types.
Remillieux, Marcel C; Guyer, Robert A; Payan, Cédric; Ulrich, T J
2016-03-18
In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. This result could lead to further understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials. PMID:27035309
Nonlinear acoustic/seismic waves in earthquake processes
NASA Astrophysics Data System (ADS)
Johnson, Paul A.
2012-09-01
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.
Nonlinear elastic wave tomography for the imaging of corrosion damage.
Ciampa, Francesco; Scarselli, Gennaro; Pickering, Simon; Meo, M
2015-09-01
This paper presents a nonlinear elastic wave tomography method, based on ultrasonic guided waves, for the image of nonlinear signatures in the dynamic response of a damaged isotropic structure. The proposed technique relies on a combination of high order statistics and a radial basis function approach. The bicoherence of ultrasonic waveforms originated by a harmonic excitation was used to characterise the second order nonlinear signature contained in the measured signals due to the presence of surface corrosion. Then, a radial basis function interpolation was employed to achieve an effective visualisation of the damage over the panel using only a limited number of receiver sensors. The robustness of the proposed nonlinear imaging method was experimentally demonstrated on a damaged 2024 aluminium panel, and the nonlinear source location was detected with a high level of accuracy, even with few receiving elements. Compared to five standard ultrasonic imaging methods, this nonlinear tomography technique does not require any baseline with the undamaged structure for the evaluation of the corrosion damage, nor a priori knowledge of the mechanical properties of the specimen. PMID:26044196
Evolution of Nonlinear Internal Waves in China Seas
NASA Technical Reports Server (NTRS)
Liu, Antony K.; Hsu, Ming-K.; Liang, Nai K.
1997-01-01
Synthetic Aperture Radar (SAR) images from ERS-I have been used to study the characteristics of internal waves of Taiwan in the East China Sea, and east of Hainan Island in the South China Sea. Rank-ordered packets of internal solitons propagating shoreward from the edge of the continental shelf were observed in the SAR images. Based on the assumption of a semidiurnal tidal origin, the wave speed can be estimated and is consistent with the internal wave theory. By using the SAR images and hydrographic data, internal waves of elevation have been identified in shallow water due to a thicker mixed layer as compared with the bottom layer on the continental shelf. The generation mechanism includes the influences of the tide and the Kuroshio intrusion across the continental shelf for the formations of elevation internal waves. The effects of water depth on the evolution of solitons and wave packets are modeled by nonlinear Kortweg-deVries (KdV) type equation and linked to satellite image observations. The numerical calculations of internal wave evolution on the continental shelf have been performed and compared with the SAR observations. For a case of depression waves in deep water, the solitons first disintegrate into dispersive wave trains and then evolve to a packet of elevation waves in the shallow water area after they pass through a turning point of approximately equal layer depths has been observed in the SAR image and simulated by numerical model.
Nonlinear dynamic behaviors of a floating structure in focused waves
NASA Astrophysics Data System (ADS)
Cao, Fei-feng; Zhao, Xi-zeng
2015-12-01
Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house CFD code is developed to investigate the accurate prediction of nonlinear dynamic behaviors of a two-dimensional (2-D) box-shaped floating structure in focused waves. Computations are performed by an enhanced Constrained Interpolation Profile (CIP)-based Cartesian grid model, in which a more accurate VOF (Volume of Fluid) method, the THINC/SW scheme (THINC: tangent of hyperbola for interface capturing; SW: Slope Weighting), is used for interface capturing. A focusing wave theory is used for the focused wave generation. The wave component of constant steepness is chosen. Comparisons between predictions and physical measurements show good agreement including body motions and free surface profiles. Although the overall agreement is good, some discrepancies are observed for impact pressure on the superstructure due to water on deck. The effect of grid resolution on the results is checked. With a fine grid, no obvious improvement is seen in the global body motions and impact pressures due to water on deck. It is concluded that highly nonlinear phenomena, such as distorted free surface, large-amplitude body motions, and violent impact flow, have been predicted successfully.
NONLINEAR GRAVITATIONAL-WAVE MEMORY FROM BINARY BLACK HOLE MERGERS
Favata, Marc
2009-05-10
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 {approx}< 2. Detection of the nonlinear memory could serve as an experimental test of the ability of gravity to 'gravitate'.
Negative-mass Instability in Nonlinear Plasma Waves
Dodin, I. Y.; Schmit, P. F.; Rocks, J.; Fisch, N. J.
2013-01-30
The negative-mass instability (NMI), previously found in ion traps, appears as a distinct regime of the sideband instability in nonlinear plasma waves with trapped particles. As the bounce frequency of these particles decreases with the bounce action, bunching can occur if the action distribution is inverted in trapping islands. In contrast to existing theories that also infer instabilities from the anharmonicity of bounce oscillations, spatial periodicity of the islands turns out to be unimportant, and the particle distribution can be unstable even if it is at at the resonance. An analytical model is proposed which describes both single traps and periodic nonlinear waves and concisely generalizes the conventional description of the sideband instability in plasma waves. The theoretical results are supported by particle-in-cell simulations carried out for a regime accentuating the NMI effect.
Viscous Fluid Conduits as a Prototypical Nonlinear Dispersive Wave Platform
NASA Astrophysics Data System (ADS)
Lowman, Nicholas K.
This thesis is devoted to the comprehensive characterization of slowly modulated, nonlinear waves in dispersive media for physically-relevant systems using a threefold approach: analytical, long-time asymptotics, careful numerical simulations, and quantitative laboratory experiments. In particular, we use this interdisciplinary approach to establish a two-fluid, interfacial fluid flow setting known as viscous fluid conduits as an ideal platform for the experimental study of truly one dimensional, unidirectional solitary waves and dispersively regularized shock waves (DSWs). Starting from the full set of fluid equations for mass and linear momentum conservation, we use a multiple-scales, perturbation approach to derive a scalar, nonlinear, dispersive wave equation for the leading order interfacial dynamics of the system. Using a generalized form of the approximate model equation, we use numerical simulations and an analytical, nonlinear wave averaging technique, Whitham-El modulation theory, to derive the key physical features of interacting large amplitude solitary waves and DSWs. We then present the results of quantitative, experimental investigations into large amplitude solitary wave interactions and DSWs. Overtaking interactions of large amplitude solitary waves are shown to exhibit nearly elastic collisions and universal interaction geometries according to the Lax categories for KdV solitons, and to be in excellent agreement with the dynamics described by the approximate asymptotic model. The dispersive shock wave experiments presented here represent the most extensive comparison to date between theory and data of the key wavetrain parameters predicted by modulation theory. We observe strong agreement. Based on the work in this thesis, viscous fluid conduits provide a well-understood, controlled, table-top environment in which to study universal properties of dispersive hydrodynamics. Motivated by the study of wave propagation in the conduit system, we
Nonlinear responses of mesospheric emission layers to wave disturbances
NASA Astrophysics Data System (ADS)
Belyaev, Alexey
2016-09-01
Model-based investigations of the wave-induced responses of O(1S), O2(b,0-0) and OH(8-3) emissions have been performed. A series of digital experiments performed using the one-dimensional simulation model proposed by Liu and Swenson (2003) demonstrated that, in addition to the variable component, the wave disturbance of airglow emissions has a constant component. This component is the enhancement/depletion of the background emission intensity of an emission layer. To interpret its appearance, the simplest analytical model of airglow disturbance due to a gravity wave has been constructed. This model indicates that enhancement/depletion of the background emission intensity is a nonlinear airglow response to a wave disturbance. Its magnitude depends quadratically on the wave amplitude and can reach a few dozen percent relative to the value of the zenith brightness of the unperturbed OH(8-3)/O(1S) emission layer.
Nonlinear Alfvén waves in dissipative MHD plasmas
NASA Astrophysics Data System (ADS)
Zheng, Jugao; Chen, Yinhua; Yu, M. Y.
2016-03-01
Nonlinear Alfvén wave trains in resistive and viscous magnetohydrodynamics plasmas are investigated. In weakly dissipative one-dimensional systems the inclusion of these effects leads to dissipative damping of Alfvén waves and heating of the plasma. It is found that plasma flow along the background magnetic field can reduce/increase the visco-resistive damping when the flow is along/against the Alfvén wave. In strongly dissipative systems, the front of the Alfvén wave train damps slower than the others, and it gradually forms a damping soliton. In two-dimensional systems, Alfvén wave phase mixing induced by inhomogeneity of the background plasma leads to enhancement of the dissipative damping and the corresponding plasma heating.
Spatiotemporal mode structure of nonlinearly coupled drift wave modes
Brandt, Christian; Grulke, Olaf; Klinger, Thomas; Negrete, Jose Jr.; Bousselin, Guillaume; Brochard, Frederic; Bonhomme, Gerard; Oldenbuerger, Stella
2011-11-15
This paper presents full cross-section measurements of drift waves in the linear magnetized plasma of the Mirabelle device. Drift wave modes are studied in regimes of weakly developed turbulence. The drift wave modes develop azimuthal space-time structures of plasma density, plasma potential, and visible light fluctuations. A fast camera diagnostic is used to record visible light fluctuations of the plasma column in an azimuthal cross section with a temporal resolution of 10 {mu}s corresponding approximately to 10% of the typical drift wave period. Mode coupling and drift wave dispersion are studied by spatiotemporal Fourier decomposition of the camera frames. The observed coupling between modes is compared to calculations of nonlinearly coupled oscillators described by the Kuramoto model.
Exact solutions for two nonlinear wave equations with nonlinear terms of any order
NASA Astrophysics Data System (ADS)
Chen, Yong; Li, Biao; Zhang, Hongqing
2005-03-01
In this paper, based on a variable-coefficient balancing-act method, by means of an appropriate transformation and with the help of Mathematica, we obtain some new types of solitary-wave solutions to the generalized Benjamin-Bona-Mahony (BBM) equation and the generalized Burgers-Fisher (BF) equation with nonlinear terms of any order. These solutions fully cover the various solitary waves of BBM equation and BF equation previously reported.
Liu, Chang; Dodin, Ilya Y.
2015-08-15
The nonlinear frequency shift is derived in a transparent asymptotic form for intense Langmuir waves in general collisionless plasma. The formula describes both fluid and kinetic effects simultaneously. The fluid nonlinearity is expressed, for the first time, through the plasma dielectric function, and the kinetic nonlinearity accounts for both smooth distributions and trapped-particle beams. Various known limiting scalings are reproduced as special cases. The calculation avoids differential equations and can be extended straightforwardly to other nonlinear plasma waves.
Generation and propagation of nonlinear internal waves in Massachusetts Bay
Scotti, A.; Beardsley, R.C.; Butman, B.
2007-01-01
During the summer, nonlinear internal waves (NLIWs) are commonly observed propagating in Massachusetts Bay. The topography of the area is unique in the sense that the generation area (over Stellwagen Bank) is only 25 km away from the shoaling area, and thus it represents an excellent natural laboratory to study the life cycle of NLIWs. To assist in the interpretation of the data collected during the 1998 Massachusetts Bay Internal Wave Experiment (MBIWE98), a fully nonlinear and nonhydrostatic model covering the generation/shoaling region was developed, to investigate the response of the system to the range of background and driving conditions observed. Simplified models were also used to elucidate the role of nonlinearity and dispersion in shaping the NLIW field. This paper concentrates on the generation process and the subsequent evolution in the basin. The model was found to reproduce well the range of propagation characteristics observed (arrival time, propagation speed, amplitude), and provided a coherent framework to interpret the observations. Comparison with a fully nonlinear hydrostatic model shows that during the generation and initial evolution of the waves as they move away from Stellwagen Bank, dispersive effects play a negligible role. Thus the problem can be well understood considering the geometry of the characteristics along which the Riemann invariants of the hydrostatic problem propagate. Dispersion plays a role only during the evolution of the undular bore in the middle of Stellwagen Basin. The consequences for modeling NLIWs within hydrostatic models are briefly discussed at the end.
Excitation of nonlinear ion acoustic waves in CH plasmas
NASA Astrophysics Data System (ADS)
Feng, Q. S.; Zheng, C. Y.; Liu, Z. J.; Xiao, C. Z.; Wang, Q.; He, X. T.
2016-08-01
Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number k λ D e increases, the linear Landau damping of the fast mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of T i / T e < 0.2 in which the fast mode is weakly damped mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with k λ D e increasing. When k λ D e is not large, such as k λ D e = 0.1 , 0.3 , 0.5 , the nonlinear IAW can be excited by the driver with the linear frequency of the modes. However, when k λ D e is large, such as k λ D e = 0.7 , the linear frequency cannot be applied to exciting the nonlinear IAW, while the frequency calculated by the dispersion relation with no damping can be applied to exciting the nonlinear IAW.
Nonlinear behavior of acoustic waves in combustion chambers
NASA Technical Reports Server (NTRS)
Culick, F. E. C.
1975-01-01
The nonlinear growth and limiting amplitude of acoustic waves in a combustion chamber are considered. A formal framework is provided within which practical problems can be treated with a minimum of effort and expense. The general conservation equations were expanded in two small parameters, one characterizing the mean flow field and one measuring the amplitude of oscillations, and then combined to yield a nonlinear inhomogeneous wave equation. The unsteady pressure and velocity fields were expressed as syntheses of the normal modes of the chamber, but with unknown time-varying amplitudes. This procedure yielded a representation of a general unsteady field as a system of coupled nonlinear oscillators. The system of nonlinear equations was treated by the method of averaging to produce a set of coupled nonlinear first order differential equations for the amplitudes and phases of the modes. The analysis is applicable to any combustion chamber. The most interesting applications are probably to solid rockets, liquid rockets, or thrust augmentors on jet engines.
Nonlinear aspects of the motion behavior of directional wave buoys
Wang, H.T.; Teng, C.C.
1994-12-31
The possibility of nonlinear behavior in the motions of two classes of widely used directional wave buoys is investigated. One is a spherical buoy with a large underwater drag sting. The other is the National Data Buoy Center (NDBC) 3-meter (10-ft) discuss buoy. The motions of the buoys are calculated by using a time domain model and a frequency domain model which uses an equivalent linearization technique to approximate the nonlinear hydrodynamic drag. The existence of nonlinear behavior is determined by directly examining the output of the equivalent linearization code, and by using Hilbert and spectral analysis techniques on the output of the time domain code. It is found that the motions of the discuss buoy are only weakly nonlinear. In particular, the motion transfer functions show only moderately small variations in different sea states. The spherical buoy pitch motion shows strongly nonlinear behavior in the presence of high sea states. In these cases, the buoy pitch transfer function shows a strong dependence on the wave height which is used.
Xiao, Jianyuan; Liu, Jian; Qin, Hong; Yu, Zhi; Xiang, Nong
2015-09-15
In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. It is illustrated that nonlinear effects significantly modify the physics of the radio-frequency injection in magnetized plasmas. The evolutions of the radio-frequency wave reflectivity and the energy deposition are observed, as well as the self-interaction of the Bernstein waves and mode excitations. Even for waves with small magnitude, nonlinear effects can also become important after continuous wave injections, which are common in the realistic radio-frequency wave heating and current drive experiments.
Nonlinear bounce resonances between magnetosonic waves and equatorially mirroring electrons
NASA Astrophysics Data System (ADS)
Chen, Lunjin; Maldonado, Armando; Bortnik, Jacob; Thorne, Richard M.; Li, Jinxing; Dai, Lei; Zhan, Xiaoya
2015-08-01
Equatorially mirroring energetic electrons pose an interesting scientific problem, since they generally cannot resonate with any known plasma waves and hence cannot be scattered down to lower pitch angles. Observationally it is well known that the flux of these equatorial particles does not simply continue to build up indefinitely, and so a mechanism must necessarily exist that transports these particles from an equatorial pitch angle of 90° down to lower values. However, this mechanism has not been uniquely identified yet. Here we investigate the mechanism of bounce resonance with equatorial noise (or fast magnetosonic waves). A test particle simulation is used to examine the effects of monochromatic magnetosonic waves on the equatorially mirroring energetic electrons, with a special interest in characterizing the effectiveness of bounce resonances. Our analysis shows that bounce resonances can occur at the first three harmonics of the bounce frequency (nωb, n = 1, 2, and 3) and can effectively reduce the equatorial pitch angle to values where resonant scattering by whistler mode waves becomes possible. We demonstrate that the nature of bounce resonance is nonlinear, and we propose a nonlinear oscillation model for characterizing bounce resonances using two key parameters, effective wave amplitude 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°.
NASA Astrophysics Data System (ADS)
Montemayor-Aldrete, J. A.; Morones-Ibarra, J. R.; Morales-Mori, A.; Ugalde-Velez, P.; Mendoza-Allende, A.; Cabrera-Bravo, E.; Montemayor-Varela, A.
2013-03-01
It is shown that the entropy of the low density monochromatic gravitational waves which stabilize gravitationally the crystalline structure of vacuum cosmic space varies with the volume in the same way as the entropy of an ideal gas formed by particles. This implies that close enough to the local Big-Bang event the energy of all the gravitational waves which stabilizes the crystalline structure of vacuum space behaves thermodynamically as though it is consisted of a number of independent energy or matter quanta (neutrons). Also it is shown that the diminishing in the gravitational energy of the waves which stabilize the crystalline vacuum space structure is the source of energy required to produce the electromagnetic radiation which is responsible for the hot matter expansion through a preexisting infinite cosmic space. Matter and antimatter is produced in equal quantities at the Big Bang region and there are no annihilation events between them during their initial stage of expansion through vacuum cosmic space due to the gravitational stress gradient pattern existing around the source region which has zero gravitational stress all the matter travels globally in one direction (For instance pointing to the long range tension gravitational stress cell-region) and all the antimatter corresponding to the contiguous compressed cell-region travels in the opposite direction. The obtained expression for the volumetric electromagnetic energy density resembles the classical one proportional to , obtained for the black body radiation in equilibrium conditions at temperature ; and at thermal equilibrium with baryons for the decoupling temperature between photons and matter, , electromagnetic energy of radiation has a value of photons per baryon. Also the evaluation of the Gibbs ´s free energy for the adiabatic compression process of transformation of gravitational stabilization waves of the crystalline vacuum space into baryons at the Big Bang gives a value of zero for the
Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation
Jing, Yun; Tao, Molei; Clement, Greg T.
2011-01-01
A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green’s function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed. PMID:21302985
Initiation of the Adiabatic Wave of Combustion for Obtaining the Substances with the Free Valence
NASA Astrophysics Data System (ADS)
Baideldonova, A.; Ksandopulo, G.; Mukhina, L.
2016-04-01
According to the task of obtaining substances with the free valence for the linkage of the nano-powders, the procedure of the synthesis of materials under the extreme nonequilibrium conditions is presented. The combustion of multilayer aluminothermic systems in the revolving reactor was investigated. Experiments were carried out in the reactor of high-temperature centrifuge. The initiation of process realizes by electric pulse in the effective layer. Further the wave of combustion was propagated along the axis of the reactor. The particles of the restored metal penetrated the underlayers of fresh mixture under the action of centrifugal acceleration and created the additional centers of ignition. The higher the density of metal, the higher speed and depth of penetration. An increase in the centrifugal acceleration strengthens the activity of process also. The speed of the motion of metallic particles grows. According the theoretical calculations it reaches 90 m/s in the case of tungsten.
Numerical simulation of nonlinear buoyancy waves in the lower atmosphere
NASA Astrophysics Data System (ADS)
Zhang, Pengfei
1997-09-01
A 2D dry incompressible vorticity-stream function model is developed and used to investigate nonlinear buoyancy waves, especially internal solitary waves and related phenomena in the lower atmosphere. Using this model some essential properties of internal solitary waves have been successfully simulated. For the first time reversed recirculation within large amplitude solitary waves has been found. The existence of recirculation enables large amplitude solitary waves to trap air and transport it. Meanwhile, due to viscosity the trapped air continuously leaks out during the transport. The influences of surface friction and ambient vertical wind shear on solitary waves are also studied. On the basis of the preceding studies, an internal solitary wave generated by a thunderstorm outflow, observed by NSSL's Doppler weather radar, a 444m tall tower and a surface network, is modeled. The simulation results show a quite good agreement with the observation in several aspects. The simulation also gives us a further understanding of the origin, propagation, and decay of the solitary wave, as well as its detailed kinematic and thermodynamic structure.
Benisti, Didier; Gremillet, Laurent
2008-03-15
The kinetic nonlinear dispersion relation, and frequency shift {delta}{omega}{sub srs}, of a plasma wave driven by stimulated Raman scattering are presented. Our theoretical calculations are fully electromagnetic, and use an adiabatic expression for the electron susceptibility which accounts for the change in phase velocity as the wave grows. When k{lambda}{sub D} > or approx. 0.35 (k being the plasma wave number and {lambda}{sub D} the Debye length), {delta}{omega}{sub srs} is significantly larger than could be inferred by assuming that the wave is freely propagating. Our theory is in excellent agreement with 1D Eulerian Vlasov-Maxwell simulations when 0.3{<=}k{lambda}{sub D}{<=}0.58, and allows discussion of previously proposed mechanisms for Raman saturation. In particular, we find that no ''loss of resonance'' of the plasma wave would limit the Raman growth rate, and that saturation through a phase detuning between the plasma wave and the laser drive is mitigated by wave number shifts.
Nonlinear interaction of kinetic Alfvén waves and ion acoustic waves in coronal loops
NASA Astrophysics Data System (ADS)
Sharma, Prachi; Yadav, Nitin; Sharma, R. P.
2016-05-01
Over the years, coronal heating has been the most fascinating question among the scientific community. In the present article, a heating mechanism has been proposed based on the wave-wave interaction. Under this wave-wave interaction, the high frequency kinetic Alfvén wave interacts with the low frequency ion acoustic wave. These waves are three dimensionally propagating and nonlinearly coupled through ponderomotive nonlinearity. A numerical code based on pseudo-spectral technique has been developed for solving these normalized dynamical equations. Localization of kinetic Alfvén wave field has been examined, and magnetic power spectrum has also been analyzed which shows the cascading of energy to higher wavenumbers, and this cascading has been found to have Kolmogorov scaling, i.e., k-5 /3 . A breakpoint appears after Kolmogorov scaling and next to this spectral break; a steeper scaling has been obtained. The presented nonlinear interaction for coronal loops plasmas is suggested to generate turbulent spectrum having Kolmogorov scaling in the inertial range and steepened scaling in the dissipation range. Since Kolmogorov turbulence is considered as the main source for coronal heating; therefore, the suggested mechanism will be a useful tool to understand the mystery of coronal loop heating through Kolmogorov turbulence and dissipation.
Nonlinear effects associated with kinetic Alfvén wave
NASA Astrophysics Data System (ADS)
Gaur, Nidhi; Sharma, R. P.
2015-04-01
The nonlinear phenomena are of striking importance in understanding the particle acceleration, heating, and turbulence in the interplanetary space. Kinetic Alfvén wave (KAW) is one of the strong candidates responsible for accelerating the solar wind and powering the solar wind turbulence. Therefore, the nonlinear properties of KAW are attracting a good attention. In the present work, we have investigated the nonlinear effects associated with KAW in the solar wind plasma at around 1 A.U. The ponderomotive force of (relatively high frequency, high power) pump KAW may be used to excite the low-frequency KAW (LKAW). For this purpose, we have derived the dynamical equations to analyze the nonlinear dynamics of relatively high frequency pump KAW in the presence of LKAW perturbation. The numerical solution has been carried out for the coupled system of equations by using the pseudospectral method for space integration and finite difference method along with the predictor corrector scheme for the evolution in time. The coupled system of nonlinear dynamical equations has been analyzed to study the nonlinear effects associated with pump KAW and the resulting turbulent spectra at 1 A.U.
Weakly nonlinear dynamics of near-CJ detonation waves
Bdzil, J.B.; Klein, R.
1993-02-01
The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature are running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.
Horizontal Lloyd mirror patterns from straight and curved nonlinear internal waves.
McMahon, K G; Reilly-Raska, L K; Siegmann, W L; Lynch, James F; Duda, T F
2012-02-01
Experimental observations and theoretical studies show that nonlinear internal waves occur widely in shallow water and cause acoustic propagation effects including ducting and mode coupling. Horizontal ducting results when acoustic modes travel between internal wave fronts that form waveguide boundaries. For small grazing angles between a mode trajectory and a front, an interference pattern may arise that is a horizontal Lloyd mirror pattern. An analytic description for this feature is provided along with comparisons between results from the formulated model predicting a horizontal Lloyd mirror pattern and an adiabatic mode parabolic equation. Different waveguide models are considered, including boxcar and jump sound speed profiles where change in sound speed is assumed 12 m/s. Modifications to the model are made to include multiple and moving fronts. The focus of this analysis is on different front locations relative to the source as well as on the number of fronts and their curvatures and speeds. Curvature influences mode incidence angles and thereby changes the interference patterns. For sources oriented so that the front appears concave, the areas with interference patterns shrink as curvature increases, while convexly oriented fronts cause patterns to expand.
Fast numerical treatment of nonlinear wave equations by spectral methods
Skjaeraasen, Olaf; Robinson, P. A.; Newman, D. L.
2011-02-15
A method is presented that accelerates spectral methods for numerical solution of a broad class of nonlinear partial differential wave equations that are first order in time and that arise in plasma wave theory. The approach involves exact analytical treatment of the linear part of the wave evolution including growth and damping as well as dispersion. After introducing the method for general scalar and vector equations, we discuss and illustrate it in more detail in the context of the coupling of high- and low-frequency plasma wave modes, as modeled by the electrostatic and electromagnetic Zakharov equations in multiple dimensions. For computational efficiency, the method uses eigenvector decomposition, which is particularly advantageous when the wave damping is mode-dependent and anisotropic in wavenumber space. In this context, it is shown that the method can significantly speed up numerical integration relative to standard spectral or finite difference methods by allowing much longer time steps, especially in the limit in which the nonlinear Schroedinger equation applies.
A nonlinear wave equation in nonadiabatic flame propagation
Booty, M.R.; Matalon, M.; Matkowsky, B.J.
1988-06-01
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 interaction of drift waves with driven plasma currents
Brandt, Christian; Grulke, Olaf; Klinger, Thomas
2010-03-15
In a cylindrical magnetized plasma, coherent drift wave modes are synchronized by a mode selective drive of plasma currents. Nonlinear effects of the synchronization are investigated in detail. Frequency pulling is observed over a certain frequency range. The dependence of the width of this synchronization range on the amplitude of the driven plasma currents forms Arnold tongues. The transition between complete and incomplete synchronization is indicated by the onset of periodic pulling and phase slippage. Synchronization is observed for driven current amplitudes, which are some percent of the typical value of parallel currents generated by drift waves.
Nonlinear generation of magnetostatic fluctuations by drift waves
NASA Astrophysics Data System (ADS)
Shukla, P. K.; Kaw, P. K.
1984-10-01
A self-consistent analysis of nonlinear coupling between drift waves and magnetostatic modes in tokomak discharges is presented. It is shown that an instability arises in the magnetostatic modes when they couple back to the drift waves. The disturbances are modeled with a parallel electron momentum equation and, in the case of a hydrogen plasma, have a growth rate close to 100 msec. The growth rate could, however, accelerate with higher electron densities, which may be a problem in current cold plasma toroidal devices which have a 5 msec confinement time.
Collapse of nonlinear electron plasma waves in a plasma layer
NASA Astrophysics Data System (ADS)
Grimalsky, V.; Koshevaya, S.; Rapoport, Yu; Kotsarenko, A.
2016-10-01
The excitation of nonlinear electron plasma waves in the plasma layer is investigated theoretically. This excitation is realized by means of initial oscillatory perturbations of the volume electron concentration or by initial oscillatory distributions of the longitudinal electron velocity. The amplitudes of the initial perturbations are small and the manifestation of the volume nonlinearity is absent. When the amplitudes of the initial perturbations exceed some thresholds, the values of the electron concentration near the plasma boundary increase catastrophically. The maxima of the electron concentration reach extremely high magnitudes, and sharp peaks in the electron concentration occur, which are localized both in the longitudinal and transverse directions. This effect is interpreted as wave collapse near the plasma boundary.
Nonlinear waves in coherently coupled Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Congy, T.; Kamchatnov, A. M.; Pavloff, N.
2016-04-01
We consider a quasi-one-dimensional two-component Bose-Einstein condensate subject to a coherent coupling between its components, such as realized in spin-orbit coupled condensates. We study how nonlinearity modifies the dynamics of the elementary excitations. The spectrum has two branches, which are affected in different ways. The upper branch experiences a modulational instability, which is stabilized by a long-wave-short-wave resonance with the lower branch. The lower branch is stable. In the limit of weak nonlinearity and small dispersion it is described by a Korteweg-de Vries equation or by the Gardner equation, depending on the value of the parameters of the system.
Discrete Element Method Simulation of Nonlinear Viscoelastic Stress Wave Problems
NASA Astrophysics Data System (ADS)
Tang, Zhiping; Horie, Y.; Wang, Wenqiang
2002-07-01
A DEM(Discrete Element Method) simulation of nonlinear viscoelastic stress wave problems is carried out. The interaction forces among elements are described using a model in which neighbor elements are linked by a nonlinear spring and a certain number of Maxwell components in parallel. By making use of exponential relaxation moduli, it is shown that numerical computation of the convolution integral does not require storing and repeatedly calculating strain history, so that the computational cost is dramatically reduced. To validate the viscoelastic DM2 code1, stress wave propagation in a Maxwell rod with one end subjected to a constant stress loading is simulated. Results excellently fit those from the characteristics calculation. The code is then used to investigate the problem of meso-scale damage in a plastic-bonded explosive under shock loading. Results not only show "compression damage", but also reveal a complex damage evolution. They demonstrate a unique capability of DEM in modeling heterogeneous materials.
Nonlinear compressional waves in a two-dimensional Yukawa lattice.
Avinash, K; Zhu, P; Nosenko, V; Goree, J
2003-10-01
A modified Korteweg-de Vries (KdV) equation is obtained for studying the propagation of nonlinear compressional waves and pulses in a chain of particles including the effect of damping. Suitably altering the linear phase velocity makes this equation useful also for the problem of phonon propagation in a two-dimensional (2D) lattice. Assuming a Yukawa potential, we use this method to model compressional wave propagation in a 2D plasma crystal, as in a recent experiment. By integrating the modified KdV equation the pulse is allowed to evolve, and good agreement with the experiment is found. It is shown that the speed of a compressional pulse increases with its amplitude, while the speed of a rarefactive pulse decreases. It is further discussed how the drag due to the background gas has a crucial role in weakening nonlinear effects and preventing the emergence of a soliton. PMID:14683049
Lattice Boltzmann model for generalized nonlinear wave equations
NASA Astrophysics Data System (ADS)
Lai, Huilin; Ma, Changfeng
2011-10-01
In this paper, a lattice Boltzmann model is developed to solve a class of the nonlinear wave equations. Through selecting equilibrium distribution function and an amending function properly, the governing evolution equation can be recovered correctly according to our proposed scheme, in which the Chapman-Enskog expansion is employed. We validate the algorithm on some problems where analytic solutions are available, including the second-order telegraph equation, the nonlinear Klein-Gordon equation, and the damped, driven sine-Gordon equation. It is found that the numerical results agree well with the analytic solutions, which indicates that the present algorithm is very effective and can be used to solve more general nonlinear problems.
NASA Technical Reports Server (NTRS)
Matsuda, Y.
1974-01-01
A low-noise plasma simulation model is developed and applied to a series of linear and nonlinear problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. It is demonstrated that use of the hybrid simulation model allows economical studies to be carried out in both the linear and nonlinear regimes with better quantitative results, for comparable computing time, than can be obtained by conventional particle simulation models, or direct solution of the Vlasov equation. The characteristics of the hybrid simulation model itself are first investigated, and it is shown to be capable of verifying the theoretical linear dispersion relation at wave energy levels as low as .000001 of the plasma thermal energy. Having established the validity of the hybrid simulation model, it is then used to study the nonlinear dynamics of monochromatic wave, sideband instability due to trapped particles, and satellite growth.
Fast neural solution of a nonlinear wave equation
NASA Technical Reports Server (NTRS)
Toomarian, Nikzad; Barhen, Jacob
1992-01-01
A neural algorithm for rapidly simulating a certain class of nonlinear wave phenomena using analog VLSI neural hardware is presented and applied to the Korteweg-de Vries partial differential equation. The corresponding neural architecture is obtained from a pseudospectral representation of the spatial dependence, along with a leap-frog scheme for the temporal evolution. Numerical simulations demonstrated the robustness of the proposed approach.
Fast Neural Solution Of A Nonlinear Wave Equation
NASA Technical Reports Server (NTRS)
Barhen, Jacob; Toomarian, Nikzad
1996-01-01
Neural algorithm for simulation of class of nonlinear wave phenomena devised. Numerically solves special one-dimensional case of Korteweg-deVries equation. Intended to be executed rapidly by neural network implemented as charge-coupled-device/charge-injection device, very-large-scale integrated-circuit analog data processor of type described in "CCD/CID Processors Would Offer Greater Precision" (NPO-18972).
Nonlinear Interactions between Gravity Waves in Water of Constant Depth
NASA Astrophysics Data System (ADS)
Szmidt, Kazimierz; Hedzielski, Benedykt
2015-06-01
The paper deals with interactions between water waves propagating in fluid of constant depth. In formulation of this problem, a nonlinear character of these interactions is taken into account. In particular, in order to simplify a solution to nonlinear boundary conditions at the free surface, a system of material coordinates is employed as independent variables in the description of the phenomenon. The main attention is focused on the transient solutions corresponding to fluid motion starting from rest. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in a finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of equations describing nonlinear waves, an approximate formulation is considered, which is based on a power series expansion of dependent variables with respect to a small parameter. Such a solution is assumed to be accurate in describing the main features of the phenomenon. Numerical experiments are conducted to illustrate the approximate formulation developed in this paper.
Quantum corrections to nonlinear ion acoustic wave with Landau damping
Mukherjee, Abhik; Janaki, M. S.; Bose, Anirban
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.
On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas
Nariyuki, Y.
2015-02-15
A multi-dimensional nonlinear evolution equation for Alfvén waves in weakly-expanding solar wind plasmas is derived by using the reductive perturbation method. The expansion of solar wind plasma parcels is modeled by an expanding box model, which includes the accelerating expansion. It is shown that the resultant equation agrees with the Wentzel-Kramers-Brillouin prediction of the low-frequency Alfvén waves in the linear limit. In the cold and one-dimensional limit, a modified derivative nonlinear Schrodinger equation is obtained. Direct numerical simulations are carried out to discuss the effect of the expansion on the modulational instability of monochromatic Alfvén waves and the propagation of Alfvén solitons. By using the instantaneous frequency, it is quantitatively shown that as far as the expansion rate is much smaller than wave frequencies, effects of the expansion are almost adiabatic. It is also confirmed that while shapes of Alfvén solitons temporally change due to the expansion, some of them can stably propagate after their collision in weakly-expanding plasmas.
NASA Astrophysics Data System (ADS)
Zuo, Peng; Zhou, Yu; Fan, Zheng
2016-07-01
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.
MJO: Asymptotically-Nondivergent Nonlinear Wave?: A Review
NASA Astrophysics Data System (ADS)
Yano, J. I.
2014-12-01
MJO is often considered a convectively-coupled wave. The present talk is going to argue that it is best understood primarily as a nonlinear solitary wave dominated by vorticity. Role of convection is secondary,though likely catalytic. According to Charney's (1963) scale analysis, the large-scale tropical circulations are nondivergent to the leading order, i.e., dominated by rotational flows. Yano et al (2009) demonstrate indeed that is the case for a period dominated by three MJO events. The scale analysis of Yano and Bonazzola (2009, JAS) demonstrates such an asymptotically nondivergent regime is a viable alternative to the traditionally-believed equatorial-wave regime. Wedi and Smolarkiewicz (2010, JAS) in turn, show by numerical computations of a dry system that a MJO-like oscillation for a similar period can indeed be generated by free solitary nonlinear equatorial Rossby-wave dynamicswithout any convective forcing to a system. Unfortunately, this perspective is slow to be accepted with people's mind so much fixed on the role of convection. This situation may be compared to a slow historical process of acceptance of Eady and Charney's baroclinicinstability simply because it does not invoke any convection Ironically, once the nonlinear free-wave view for MJO is accepted, interpretations can more easily be developed for a recent series of numerical model experiments under a global channel configuration overthe tropics with a high-resolution of 5-50 km with or without convection parameterization. All those experiments tend to reproduce observed large-scale circulations associated with MJO rather well, though most of time, they fail to reproduce convective coherency associated with MJO.These large-scale circulations appear to be generated by lateral forcing imposed at the latitudinal walls. These lateral boundaries are reasonably far enough (30NS) to induce any direct influence to the tropics. There is no linear dry equatorial wave that supports this period either
Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity.
Shao, Sihong; Quintero, Niurka R; Mertens, Franz G; Cooper, Fred; Khare, Avinash; Saxena, Avadh
2014-09-01
We consider the nonlinear Dirac equation in 1 + 1 dimension with scalar-scalar self interaction g(2)/κ+1(̅ΨΨ)(κ+1) and with mass m. Using the exact analytic form for rest frame solitary waves of the form Ψ(x,t)=ψ(x)e(-iωt) for arbitrary κ, we discuss the validity of various approaches to understanding stability that were successful for the nonlinear Schrödinger equation. In particular we study the validity of a version of Derrick's theorem and the criterion of Bogolubsky as well as the Vakhitov-Kolokolov criterion, and find that these criteria yield inconsistent results. Therefore, we study the stability by numerical simulations using a recently developed fourth-order operator splitting integration method. For different ranges of κ we map out the stability regimes in ω. We find that all stable nonlinear Dirac solitary waves have a one-hump profile, but not all one-hump waves are stable, while all waves with two humps are unstable. We also find that the time t(c), it takes for the instability to set in, is an exponentially increasing function of ω and t(c) decreases monotonically with increasing κ. PMID:25314512
Nonlinear Dirac equation solitary waves in external fields.
Mertens, Franz G; Quintero, Niurka R; Cooper, Fred; Khare, Avinash; Saxena, Avadh
2012-10-01
We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2/κ+1(Ψ[over ¯]Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP(t)/dq[over ̇](t)<0. Here P(t) is the momentum of the solitary wave, and q[over ̇] is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials that we always have dP(t)/dq[over ̇](t)>0, so, when instabilities do occur, they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that, when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations. We found that the time evolution of the collective coordinates of the solitary wave in our numerical simulations, namely the position of the average charge density and the momentum of the solitary wave, provide good indicators for when the solitary wave first becomes unstable. When these variables stop being smooth functions of time (t), then the solitary wave starts to distort
Nonlinear Dirac equation solitary waves in external fields.
Mertens, Franz G; Quintero, Niurka R; Cooper, Fred; Khare, Avinash; Saxena, Avadh
2012-10-01
We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2/κ+1(Ψ[over ¯]Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP(t)/dq[over ̇](t)<0. Here P(t) is the momentum of the solitary wave, and q[over ̇] is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials that we always have dP(t)/dq[over ̇](t)>0, so, when instabilities do occur, they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that, when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations. We found that the time evolution of the collective coordinates of the solitary wave in our numerical simulations, namely the position of the average charge density and the momentum of the solitary wave, provide good indicators for when the solitary wave first becomes unstable. When these variables stop being smooth functions of time (t), then the solitary wave starts to distort
Weakly nonlinear ion waves in striated electron temperatures.
Guio, P; Pécseli, H L
2016-04-01
The existence of low-frequency waveguide modes of electrostatic ion acoustic waves is demonstrated in magnetized plasmas for cases where the electron temperature is striated along magnetic field lines. For low frequencies, the temperature striation acts as waveguide that supports a trapped mode. For conditions where the ion cyclotron frequency is below the ion plasma frequency we find a dispersion relation having also a radiative frequency band, where waves can escape from the striation. Arguments for the formation and propagation of an equivalent of electrostatic shocks are presented and demonstrated numerically for these conditions. The shock represents here a balance between an external energy input maintained by ion injection and a dissipation mechanism in the form of energy leakage of the harmonics generated by nonlinear wave steepening. This is a reversible form for energy loss that can replace the time-irreversible losses in a standard Burgers equation. PMID:27176415
Nonlinear time-dependent simulation of helix traveling wave tubes
NASA Astrophysics Data System (ADS)
Peng, Wei-Feng; Yang, Zhong-Hai; Hu, Yu-Lu; Li, Jian-Qing; Lu, Qi-Ru; Li, Bin
2011-07-01
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.
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Lepri, Stefano; Pikovsky, Arkady
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
Modelling of nonlinear wave scattering in a delaminated elastic bar
Khusnutdinova, K. R.; Tranter, M. R.
2015-01-01
Integrity of layered structures, extensively used in modern industry, strongly depends on the quality of their interfaces; poor adhesion or delamination can lead to a failure of the structure. Can nonlinear waves help us to control the quality of layered structures? In this paper, we numerically model the dynamics of a long longitudinal strain solitary wave in a split, symmetric layered bar. The recently developed analytical approach, based on matching two asymptotic multiple-scales expansions and the integrability theory of the Korteweg–de Vries equation by the inverse scattering transform, is used to develop an effective semi-analytical numerical approach for these types of problems. We also employ a direct finite-difference method and compare the numerical results with each other, and with the analytical predictions. The numerical modelling confirms that delamination causes fission of an incident solitary wave and, thus, can be used to detect the defect. PMID:26730218
In-situ observations of nonlinear wave particle interaction of electromagnetic ion cyclotron waves
NASA Astrophysics Data System (ADS)
Shoji, M.; Miyoshi, Y.; Keika, K.; Katoh, Y.; Angelopoulos, V.; Nakamura, S.; Omura, Y.
2014-12-01
Direct measurement method for the electromagnetic wave and space plasma interaction has been suggested by a computer simulation study [Katoh et al., 2013], so-called Wave Particle Interaction Analysis (WPIA). We perform the WPIA for rising tone electromagnetic ion cyclotron (EMIC) waves (so-called EMIC triggered emissions), of which generation mechanism is essentially the same as the chorus emissions. THEMIS observation data (EFI, FGM, and ESA) are used for the WPIA. In the WPIA, we calculate (1) the inner product of the wave electric field and the velocity of the energetic protons: Wint, (2) the inner product of the wave magnetic field and the velocity of the energetic protons: WBint, and (3) the phase angle ζ between the wave magnetic field and the perpendicular velocity of the energetic protons. The values of (1) and (2) indicate the existence of the resonant currents inducing the nonlinear wave growth and the frequency change, respectively. We find the negative Wint and positive WBint at the nonlinear growing phase of the triggered emission as predicted in the theory [e.g. Omura and Nunn, 2011, Shoji and Omura, 2013]. In histogram of (3), we show the existence of the electromagnetic proton holes in the phase space generating the resonant currents. We also perform a hybrid simulation and evaluate WPIA method for EMIC waves. The simulation results show good agreement with the in-situ THEMIS observations.
Shear-driven Dynamo Waves in the Fully Nonlinear Regime
NASA Astrophysics Data System (ADS)
Pongkitiwanichakul, P.; Nigro, G.; Cattaneo, F.; Tobias, S. M.
2016-07-01
Large-scale dynamo action is well understood when the magnetic Reynolds number (Rm) is small, but becomes problematic in the astrophysically relevant large Rm limit since the fluctuations may control the operation of the dynamo, obscuring the large-scale behavior. Recent works by Tobias & Cattaneo demonstrated numerically the existence of large-scale dynamo action in the form of dynamo waves driven by strongly helical turbulence and shear. Their calculations were carried out in the kinematic regime in which the back-reaction of the Lorentz force on the flow is neglected. Here, we have undertaken a systematic extension of their work to the fully nonlinear regime. Helical turbulence and large-scale shear are produced self-consistently by prescribing body forces that, in the kinematic regime, drive flows that resemble the original velocity used by Tobias & Cattaneo. We have found four different solution types in the nonlinear regime for various ratios of the fluctuating velocity to the shear and Reynolds numbers. Some of the solutions are in the form of propagating waves. Some solutions show large-scale helical magnetic structure. Both waves and structures are permanent only when the kinetic helicity is non-zero on average.
Rotation-induced nonlinear wavepackets in internal waves
Whitfield, A. J. Johnson, E. R.
2014-05-15
The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets. It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.
Nonlinear interaction of kinetic Alfven wave with fast magnetosonic wave and turbulent spectrum
Modi, K. V.; Sharma, R. P.
2013-03-15
In the present paper, authors have investigated nonlinear interaction of kinetic Alfven wave (KAW) and fast magnetosonic wave for intermediate {beta}-plasma (m{sub e}/m{sub i} Much-Less-Than {beta} Much-Less-Than 1). Authors have developed the set of dimensionless equations in the presence of ponderomotive nonlinearity due to KAW in the dynamics of fast magnetosonic wave. Numerical simulation has been carried out to study the effect of nonlinear coupling and resulting turbulent/power spectrum for the different angles of propagation of fast magnetosonic wave applicable to solar wind at 1 AU. The localization of KAW has been found which becomes more complex as the angle of propagation of fast magnetosonic wave decreases. Results also reveal the steepening of power spectrum as the angle of propagation decreases which can be responsible for heating and acceleration of plasma particles in solar wind. Relevance of the obtained result is pointed out with observation received by Cluster spacecraft for the solar wind 1 AU.
Local computational strategies for predicting wave propagation in nonlinear media
NASA Astrophysics Data System (ADS)
Leamy, Michael J.; Autrusson, Thibaut B.; Staszewski, Wieslaw J.; Uhl, Tadeusz; Packo, Pawel
2014-03-01
Two local computational strategies for modeling elastic wave propagation, namely the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE), are compared and contrasted in analyzing bulk waves in two-dimensional nonlinear media. Each strategy formulates the problem from the perspective of a cell and its local interactions with other cells, leading to robust treatments of anisotropy, heterogeneity, and nonlinearity. The local approach also enables straight-forward parallelization on high performance computing clusters. While the two share a common local perspective, they differ in two major respects. The first is that CAFE employs both rectangular and triangular cells, while LISA considers only rectangular. The second is that LISA appeared much earlier than CAFE (early 1990's versus late 2000's), and as such has been developed to a much greater degree with a multitude of material models, cell-to-cell interactions, loading possibilities, and boundary treatments. A hybrid approach which combines the two is of great interest since the non-uniform mesh capability of the CAFE triangular cell can be readily coupled to LISA's rectangular grids, taking advantage of the built-in LISA features on the uniform portion of the domain. For linear material domains, the hybrid implementation appears straight-forward since both methods have been shown to recover the same equations in the rectangular case. For nonlinear material domains, the formulations cannot be put into a one-to-one correspondence, and hybrid implementation may be more problematic. This paper addresses these differences by first presenting the underlying formulations, and then computing results for growth of a second harmonic in an introduced bulk pressure wave. Rectangular cells are used in both LISA and CAFE. Results from both approaches are compared to an approximate, analytical solution based on a two-scale field representation. Differences in the LISA and CAFE computed
Nonlinear single Compton scattering of an electron wave packet
NASA Astrophysics Data System (ADS)
Angioi, A.; Mackenroth, F.; Di Piazza, A.
2016-05-01
Nonlinear single Compton scattering has been thoroughly investigated in the literature under the assumption that the electron initially has a definite momentum. Here, we study a more general initial state and consider the electron as a wave packet. In particular, we investigate the energy spectrum of the emitted radiation and show that, in typical experimental situations, some features of the spectra shown in previous works are almost completely washed out. Moreover, we show that, at comparable relative uncertainties, the one in the momentum of the incoming electron has a larger impact on the photon spectra at a fixed observation direction than the one on the laser frequency.
Subwavelength position sensing using nonlinear feedback and wave chaos.
Cohen, Seth D; Cavalcante, Hugo L D de S; Gauthier, Daniel J
2011-12-16
We demonstrate a position-sensing technique that relies on the inherent sensitivity of chaos, where we illuminate a subwavelength object with a complex structured radio-frequency field generated using wave chaos and nonlinear feedback. We operate the system in a quasiperiodic state and analyze changes in the frequency content of the scalar voltage signal in the feedback loop. This allows us to extract the object's position with a one-dimensional resolution of ~λ/10,000 and a two-dimensional resolution of ~λ/300, where λ is the shortest wavelength of the illuminating source.
Nonlinear wave propagation in discrete and continuous systems
NASA Astrophysics Data System (ADS)
Rothos, V. M.
2016-09-01
In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.
Cascading nonlinearities in optical four-wave mixing
NASA Astrophysics Data System (ADS)
Zgonik, M.; Günter, P.
1996-03-01
In a crystal without inversion symmetry there exist two-step indirect contributions to third-order nonlinear optical processes (cascading). Contributions to optical four-wave mixing occur through optical rectification and linear electro-optic effects. In contrast to cascading by second-harmonic generation, which has to satisfy strict phase-matching conditions, optical rectification is always allowed. In polar KNbO3 crystals we measured four-wave mixing in several geometries to evaluate the direct contribution of the third-order polarizabilities and the cascaded contribution. We present a theoretical model and show experimentally that the cascading effect is large and that contributing polarization gratings must be transversely polarized.
Quantifying wave-breaking dissipation using nonlinear phase-resolved wave-field simulations
NASA Astrophysics Data System (ADS)
Qi, Y.; Xiao, W.; Yue, D. K. P.
2014-12-01
We propose to understand and quantify wave-breaking dissipation in the evolution of general irregular short-crested wave-fields using direct nonlinear phase-resolved simulations based on a High-Order Spectral (HOS) method (Dommermuth & Yue 1987). We implement a robust phenomenological-based energy dissipation model in HOS to capture the effect of wave-breaking dissipation on the overall wave-field evolution (Xiao et al 2013). The efficacy of this model is confirmed by direct comparisons against measurements for the energy loss in 2D and 3D breaking events. By comparing simulated wave-fields with and without the dissipation model in HOS, we obtain the dissipation field δ(x,y,t), which provides the times, locations and intensity of wave breaking events (δ>δc). This is validated by comparison of HOS simulations with Airborne Terrain Mapper (ATM) measurements in the recent ONR Hi-Res field experiment. Figure (a) shows one frame of simulated wave-field (with dissipation model). Figure (b) is the corresponding measurement from ATM, where a large wave breaking event was captured. Figure (c) is the 3D view of the simulated wave-field with the colored region representing dissipation with δ>δc. The HOS predicted high-dissipation area is found to agree well with the measured breaking area. Based on HOS predicted high-dissipation area (δ>δc), we calculate Λ(c) (Phillips 1985), the distribution of total length of breaking wave front per unit surface area per unit increment of breaking velocity c. Figure (d) shows the distribution Λ(c) calculated from HOS. For breaking speeds c greater than 5m/s, the simulated Λ(c) is in qualitative agreement with Phillips theoretical power-law of Λ(c)~c-6. From δ(x,y,t), we further quantify wave breaking by calculating the whitecap coverage rate Wr(t) and energy dissipation rate ΔE'(t), and study the evolution of Wr and ΔE' to understand the role of wave breaking in nonlinear wave-field evolution. We obtain HOS simulations
Nonlinear interactions of electromagnetic waves with the auroral ionosphere
Wong, Alfred Y.
1999-09-20
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 CO{sub 2} through the use of ion cyclotron resonant heating.
Linear and nonlinear effects in detonation wave structure formation
NASA Astrophysics Data System (ADS)
Borisov, S. P.; Kudryavtsev, A. N.
2016-06-01
The role of linear and nonlinear effects in the process of formation of detonation wave structure is investigated using linear stability analysis and direct numerical simulation. A simple model with a one-step irreversible chemical reaction is considered. For linear stability computations, both the local iterative shooting procedure and the global Chebyshev pseudospectral method are employed. Numerical simulations of 1D pulsating instability are performed using a shock fitting approach based on a 5th order upwind-biased compact-difference discretization and a shock acceleration equation deduced from the Rankine-Hugoniot conditions. A shock capturing WENO scheme of the 5th order is used to simulate propagation of detonation wave in a plane channel. It is shown that the linear analysis predicts correctly the mode dominating on early stages of flow evolution and the size of detonation cells which emerge during these stages. Later, however, when a developed self-reproducing cellular structure forms, the cell size is approximately doubled due to nonlinear effects.
Nonlinear focusing of acoustic shock waves at a caustic cusp.
Marchiano, Régis; Coulouvrat, François; Thomas, Jean-Louis
2005-02-01
The present study investigates the focusing of acoustical weak shock waves incoming on a cusped caustic. The theoretical model is based on the Khokhlov-Zabolotskaya equation and its specific boundary conditions. Based on the so-called Guiraud's similitude law for a step shock, a new explanation about the wavefront unfolding due to nonlinear self-refraction is proposed. This effect is shown to be associated not only to nonlinearities, as expected by previous authors, but also to the nonlocal geometry of the wavefront. Numerical simulations confirm the sensitivity of the process to wavefront geometry. Theoretical modeling and numerical simulations are substantiated by an original experiment. This one is carried out in two steps. First, the canonical Pearcey function is synthesized in linear regime by the inverse filter technique. In the second step, the same wavefront is emitted but with a high amplitude to generate shock waves during the propagation. The experimental results are compared with remarkable agreement to the numerical ones. Finally, applications to sonic boom are briefly discussed. PMID:15759678
Solitary waves and nonlinear dynamic coherent structures in magnetic metamaterials
NASA Astrophysics Data System (ADS)
Tankeyev, A. P.; Smagin, V. V.; Borich, M. A.; Zhuravlev, A. S.
2009-03-01
Within the framework of the extended nonlinear Schrödinger equation (ENSE), two types of nonlinear states of magnetization in a ferromagnet-dielectric-metal metamagnetic structure have been obtained and investigated. These states have an internal structure; e.g., a periodic sequence of compound solitons is formed by kink-antikink pairs (shock waves), and coherent periodic breather structures are formed by “bright” quasi-solitons. Conditions have been found under which the envelope of these states is described by a modified Korteweg-de Vries (mKdV) equation. It is shown that the compound solitons are described by an mKdV equation with repulsion, and the breather structures, by an mKdV equation with attraction. It is shown also that the characteristic properties of the solutions are determined by the sign of the group-velocity dispersion rather than by the sign of the group velocity itself. The results obtained can be used for searching new nonlinear dynamic coherent structures, e.g., compound solitons and breathers in high-dispersion magnetic metamaterials.
Solitary and shock waves in discrete strongly nonlinear double power-law materials
NASA Astrophysics Data System (ADS)
Herbold, E. B.; Nesterenko, V. F.
2007-06-01
A laminar metamaterial supporting strongly nonlinear solitary and shock waves with impact energy mitigating capabilities is presented. It consists of steel plates with intermittent polymer toroidal rings acting as strongly nonlinear springs with large allowable strain. The force-displacement relationship of a compressed o-ring is described by the addition of two power-law relationships resulting in a solitary wave speed and width depending on the amplitude. This double nonlinearity allows splitting of an initial impulse into three separate strongly nonlinear solitary wave trains. Solitary and shock waves are observed experimentally and analyzed numerically in an assembly with Teflon o-rings.
The Wave Processes in the Media Having Inelastic Hysteresis with Saturation of The Nonlinear Loss
NASA Astrophysics Data System (ADS)
Nazarov, V. E.; Kiyashko, S. B.
2016-07-01
We study theoretically the nonlinear wave processes during excitation of a longitudinal harmonic wave in an unbounded medium and the rod resonator with inelastic hysteresis and saturation of the amplitude-dependent loss. The nonlinear-wave characteristics in such systems, namely, the amplitude-dependent loss, variation in the wave-propagation velocity, the resonant-frequency shift, and the higher-harmonic amplitudes are determined. The results of the theoretical and experimental studies of nonlinear effects in the rod resonator of annealed polycrystalline copper are compared. The effective parameters of the hysteretic nonlinearity of this metal are evaluated.
2D wave-front shaping in optical superlattices using nonlinear volume holography.
Yang, Bo; Hong, Xu-Hao; Lu, Rong-Er; Yue, Yang-Yang; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan
2016-07-01
Nonlinear volume holography is employed to realize arbitrary wave-front shaping during nonlinear processes with properly designed 2D optical superlattices. The concept of a nonlinear polarization wave in nonlinear volume holography is investigated. The holographic imaging of irregular patterns was performed using 2D LiTaO_{3} crystals with fundamental wave propagating along the spontaneous polarization direction, and the results agree well with the theoretical predictions. This Letter not only extends the application area of optical superlattices, but also offers an efficient method for wave-front shaping technology.
High-informative version of nonlinear transformation of Langmuir waves to electromagnetic waves
NASA Astrophysics Data System (ADS)
Erofeev, Vasily I.; Erofeev
2014-04-01
The concept of informativeness of nonlinear plasma physical scenario is discussed. Basic principles for heightening the informativeness of plasma kinetic models are explained. Former high-informative correlation analysis of plasma kinetics (Erofeev, V. 2011 High-Informative Plasma Theory, Saarbrücken: LAP) is generalized for studies of weakly turbulent plasmas that contain fields of solenoidal plasma waves apart from former potential ones. Respective machinery of plasma kinetic modeling is applied to an analysis of fusion of Langmuir waves with transformation to electromagnetic waves. It is shown that the customary version of this phenomenon (Terashima, Y. and Yajima, N. 1963 Prog. Theor. Phys. 30, 443; Akhiezer, I. A., Danelia, I. A. and Tsintsadze, N. L. 1964 Sov. Phys. JETP 19, 208; Al'tshul', L. M. and Karpman, V. I. 1965 Sov. Phys. JETP 20, 1043) substantially distorts the picture of merging of Langmuir waves with long wavelengths (λ >~ c/ωpe ).
NASA Technical Reports Server (NTRS)
Matda, Y.; Crawford, F. W.
1974-01-01
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.
NASA Astrophysics Data System (ADS)
Nguyen, Vu A.; Palo, Scott E.; Lieberman, Ruth S.; Forbes, Jeffrey M.; Ortland, David A.; Siskind, David E.
2016-07-01
Theory and past observations have provided evidence that atmospheric tides and other global-scale waves interact nonlinearly to produce additional secondary waves throughout the space-atmosphere interaction region. However, few studies have investigated the generation region of nonlinearly generated secondary waves, and as a result, the manifestation and impacts of these waves are still poorly understood. This study focuses on the nonlinear interaction between the quasi 2 day wave (2dayW3) and the migrating diurnal tide (DW1), two of the largest global-scale waves in the atmosphere. The fundamental goals of this effort are to characterize the forcing region of the secondary waves and to understand how it relates to their manifestation on a global scale. First, the Fast Fourier Synoptic Mapping method is applied to Thermosphere Ionosphere Mesosphere Energetics and Dynamics-Sounding of the Atmosphere using Broadband Emission Radiometry satellite observations to provide new evidence of secondary waves. These results show that secondary waves are only significant above 80 km. The nonlinear forcing for each secondary wave is then computed by extracting short-term primary wave information from a reanalysis model. The estimated nonlinear forcing quantities are used to force a linearized tidal model in order to calculate numerical secondary wave responses. Model results show that the secondary waves are significant from the upper mesosphere to the middle thermosphere, highlighting the implications for the atmosphere-space weather coupling. The study also concludes that the secondary wave response is most sensitive to the nonlinear forcing occurring in the lower and middle mesosphere and not coincident with the regions of strongest nonlinear forcing.
NASA Astrophysics Data System (ADS)
Gupta, Samit Kumar; Sarma, Amarendra K.
2016-07-01
In this work, we have studied the peregrine rogue wave dynamics, with a solitons on finite background (SFB) ansatz, in the recently proposed (Ablowitz and Musslimani, (2013) [31]) continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity. We have found that the continuous nonlinear Schrödinger system with PT-symmetric nonlinearity also admits Peregrine soliton solution. Motivated by the fact that Peregrine solitons are regarded as prototypical solutions of rogue waves, we have studied Peregrine rogue wave dynamics in the c-PTNLSE model. Upon numerical computation, we observe the appearance of low-intense Kuznetsov-Ma (KM) soliton trains in the absence of transverse shift (unbroken PT-symmetry) and well-localized high-intense Peregrine rogue waves in the presence of transverse shift (broken PT-symmetry) in a definite parametric regime.
Rayleigh scattering and nonlinear inversion of elastic waves
Gritto, R.
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 {minus}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{sub 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.
Threshold for electron trapping nonlinearity in Langmuir waves
Strozzi, D. J.; Williams, E. A.; Hinkel, D. E.; Langdon, A. B.; Banks, J. W.; Rose, H. A.
2012-11-15
We assess when electron trapping nonlinearity is expected to be important in Langmuir waves. The basic criterion is that the inverse of the detrapping rate {nu}{sub d} of electrons in the trapping region of velocity space must exceed the bounce period of deeply trapped electrons, {tau}{sub B}{identical_to}(n{sub e}/{delta}n){sup 1/2}2{pi}/{omega}{sub pe}. A unitless figure of merit, the 'bounce number'N{sub B}{identical_to}1/{nu}{sub d}{tau}{sub B}, encapsulates this condition and defines a trapping threshold amplitude for which N{sub B}=1. The detrapping rate is found for convective loss (transverse and longitudinal) out of a spatially finite Langmuir wave. Simulations of driven waves with a finite transverse profile, using the 2D-2V Vlasov code LOKI, show trapping nonlinearity increases continuously with N{sub B} for transverse loss, and is significant for N{sub B} Almost-Equal-To 1. The detrapping rate due to Coulomb collisions (both electron-electron and electron-ion) is also found, with pitch-angle scattering and parallel drag and diffusion treated in a unified manner. A simple way to combine convective and collisional detrapping is given. Application to underdense plasma conditions in inertial confinement fusion targets is presented. The results show that convective transverse loss is usually the most potent detrapping process in a single f/8 laser speckle. For typical plasma and laser conditions on the inner laser cones of the National Ignition Facility, local reflectivities {approx}3% are estimated to produce significant trapping effects.
Suret, Pierre; Picozzi, Antonio; Randoux, Stéphane
2011-08-29
We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a statistically stationary state. The evolution of the power spectrum of the field is characterized by the rapid growth of spectral tails that exhibit damped oscillations, until the whole spectrum ultimately reaches a steady state. The kinetic approach allows us to derive an analytical expression of the damped oscillations, which is found in agreement with the numerical simulations of both the NLS and kinetic equations. We report the experimental observation of this peculiar relaxation process of the integrable NLS equation.
Suret, Pierre; Picozzi, Antonio; Randoux, Stéphane
2011-08-29
We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a statistically stationary state. The evolution of the power spectrum of the field is characterized by the rapid growth of spectral tails that exhibit damped oscillations, until the whole spectrum ultimately reaches a steady state. The kinetic approach allows us to derive an analytical expression of the damped oscillations, which is found in agreement with the numerical simulations of both the NLS and kinetic equations. We report the experimental observation of this peculiar relaxation process of the integrable NLS equation. PMID:21935152
Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves.
Salerno, D; Minardi, S; Trull, J; Varanavicius, A; Tamosauskas, G; Valiulis, G; Dubietis, A; Caironi, D; Trillo, S; Piskarskas, A; Di Trapani, P
2003-10-01
We investigate experimentally the competition between spatial and temporal breakup due to modulational instability in chi((2)) nonlinear mixing. The modulation of the wave packets caused by the energy exchange between fundamental and second-harmonic components is found to be the prevailing trigger mechanism which, according to the relative weight of diffraction and dispersion, leads to the appearance of a multisoliton pattern in the low-dimensional spatial or temporal domain.
Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Auxiliary Equation Method
NASA Astrophysics Data System (ADS)
Kaplan, Melike; Akbulut, Arzu; Bekir, Ahmet
2015-10-01
The auxiliary equation method presents wide applicability to handling nonlinear wave equations. In this article, we establish new exact travelling wave solutions of the nonlinear Zoomeron equation, coupled Higgs equation, and equal width wave equation. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions, and rational functions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Throughout the article, all calculations are made with the aid of the Maple packet program.
Pair-tunneling induced localized waves in a vector nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Zhao, Li-Chen; Ling, Liming; Yang, Zhan-Ying; Liu, Jie
2015-06-01
We investigate localized waves of coupled two-mode nonlinear Schrödinger equations with a pair-tunneling term representing strongly interacting particles can tunnel between the modes as a fragmented pair. Facilitated by Darboux transformation, we have derived exact solution of nonlinear vector waves such as bright solitons, Kuznetsov-Ma soliton, Akhmediev breathers and rogue waves and demonstrated their interesting temporal-spatial structures. A phase diagram that demarcates the parameter ranges of the nonlinear waves is obtained. Possibilities to observe these localized waves are discussed in a two species Bose-Einstein condensate.
NASA Astrophysics Data System (ADS)
Demidov, V. E.; Hansen, U.-F.; Dzyapko, O.; Koulev, N.; Demokritov, S. O.; Slavin, A. N.
2006-09-01
Formation of stationary longitudinal amplitude patterns by propagating nonlinear spin waves has been discovered and studied experimentally by means of space-resolved Brillouin light scattering spectroscopy. The pattern formation is observed for spin waves propagating in narrow, longitudinally magnetized yttrium iron garnet stripes, characterized by attractive nonlinearity in both the longitudinal and transverse directions. A clear crossover of the effective dimensionality describing the propagation of spin waves in the stripe is observed with increase of the wave amplitude.
A flexible genuinely nonlinear approach for nonlinear wave propagation, breaking and run-up
NASA Astrophysics Data System (ADS)
Filippini, A. G.; Kazolea, M.; Ricchiuto, M.
2016-04-01
In this paper we evaluate hybrid strategies for the solution of the Green-Naghdi system of equations for the simulation of fully nonlinear and weakly dispersive free surface waves. We consider a two step solution procedure composed of: a first step where the non-hydrostatic source term is recovered by inverting the elliptic coercive operator associated to the dispersive effects; a second step which involves the solution of the hyperbolic shallow water system with the source term, computed in the previous phase, which accounts for the non-hydrostatic effects. Appropriate numerical methods, that can be also generalized on arbitrary unstructured meshes, are used to discretize the two stages: the standard C0 Galerkin finite element method for the elliptic phase; either third order Finite Volume or third order stabilized Finite Element method for the hyperbolic phase. The discrete dispersion properties of the fully coupled schemes obtained are studied, showing accuracy close to or better than that of a fourth order finite difference method. The hybrid approach of locally reverting to the nonlinear shallow water equations is used to recover energy dissipation in breaking regions. To this scope we evaluate two strategies: simply neglecting the non-hydrostatic contribution in the hyperbolic phase; imposing a tighter coupling of the two phases, with a wave breaking indicator embedded in the elliptic phase to smoothly turn off the dispersive effects. The discrete models obtained are thoroughly tested on benchmarks involving wave dispersion, breaking and run-up, showing a very promising potential for the simulation of complex near shore wave physics in terms of accuracy and robustness.
Dual variational principles for nonlinear traveling waves in multifluid plasmas
Webb, G. M.; McKenzie, J. F.; Mace, R. L.; Ko, C. M.; Zank, G. P.
2007-08-15
A Hamiltonian description of nonlinear, obliquely propagating traveling waves in a charge neutral, electron-proton, multifluid plasma is developed. The governing equations are written as a dual spatial Hamiltonian system. In the first formulation, the Hamiltonian is identified with the longitudinal, x-momentum flux integral P{sub x}=const, in which the energy integral {epsilon}={epsilon}{sub 0} acts as a constraint, and the Hamiltonian evolution operator is d/dx, where x is the position coordinate in the wave frame. In the second Hamiltonian formulation, the Hamiltonian is proportional to the conserved energy integral {epsilon}, in which the momentum integral P{sub x}=const acts as a constraint, and the Hamiltonian evolution operator d/d{tau}=u{sub x}d/dx is the Lagrangian time derivative where u{sub x} is the x component of the electron and proton fluids. The analysis is facilitated by using the de Hoffman-Teller frame of magnetohydrodynamic shock theory to simplify the transverse electron and proton momentum equations. The system is exactly integrable in cases in which the total transverse momentum fluxes of the system are zero in the de Hoffman-Teller frame. The implications of this constraint for the Alfven Mach number of the traveling wave are discussed. The physical conditions for the formation of whistler oscillitons based on the whistler dispersion equation are discussed.
McKenzie, J. F.; Doyle, T. B.; Rajah, S. S.
2012-11-15
The theory of fully nonlinear stationary electrostatic ion cyclotron waves is further developed. The existence of two fundamental constants of motion; namely, momentum flux density parallel to the background magnetic field and energy density, facilitates the reduction of the wave structure equation to a first order differential equation. For subsonic waves propagating sufficiently obliquely to the magnetic field, soliton solutions can be constructed. Importantly, analytic expressions for the amplitude of the soliton show that it increases with decreasing wave Mach number and with increasing obliquity to the magnetic field. In the subsonic, quasi-parallel case, periodic waves exist whose compressive and rarefactive amplitudes are asymmetric about the 'initial' point. A critical 'driver' field exists that gives rise to a soliton-like structure which corresponds to infinite wavelength. If the wave speed is supersonic, periodic waves may also be constructed. The aforementioned asymmetry in the waveform arises from the flow being driven towards the local sonic point in the compressive phase and away from it in the rarefactive phase. As the initial driver field approaches the critical value, the end point of the compressive phase becomes sonic and the waveform develops a wedge shape. This feature and the amplitudes of the compressive and rarefactive portions of the periodic waves are illustrated through new analytic expressions that follow from the equilibrium points of a wave structure equation which includes a driver field. These expressions are illustrated with figures that illuminate the nature of the solitons. The presently described wedge-shaped waveforms also occur in water waves, for similar 'transonic' reasons, when a Coriolis force is included.
Wave excitation by nonlinear coupling among shear Alfvén waves in a mirror-confined plasma
Ikezoe, R. Ichimura, M.; Okada, T.; Hirata, M.; Yokoyama, T.; Iwamoto, Y.; Sumida, S.; Jang, S.; Takeyama, K.; Yoshikawa, M.; Kohagura, J.; Shima, Y.; Wang, X.
2015-09-15
A shear Alfvén wave at slightly below the ion-cyclotron frequency overcomes the ion-cyclotron damping and grows because of the strong anisotropy of the ion temperature in the magnetic mirror configuration, and is called the Alfvén ion-cyclotron (AIC) wave. Density fluctuations caused by the AIC waves and the ion-cyclotron range of frequencies (ICRF) waves used for ion heating have been detected using a reflectometer in a wide radial region of the GAMMA 10 tandem mirror plasma. Various wave-wave couplings are clearly observed in the density fluctuations in the interior of the plasma, but these couplings are not so clear in the magnetic fluctuations at the plasma edge when measured using a pick-up coil. A radial dependence of the nonlinearity is found, particularly in waves with the difference frequencies of the AIC waves; bispectral analysis shows that such wave-wave coupling is significant near the core, but is not so evident at the periphery. In contrast, nonlinear coupling with the low-frequency background turbulence is quite distinct at the periphery. Nonlinear coupling associated with the AIC waves may play a significant role in the beta- and anisotropy-limits of a mirror-confined plasma through decay of the ICRF heating power and degradation of the plasma confinement by nonlinearly generated waves.
Analysis and modeling of broadband airgun data influenced by nonlinear internal waves.
Frank, Scott D; Badiey, Mohsen; Lynch, James F; Siegmann, William L
2004-12-01
To investigate acoustic effects of nonlinear internal waves, the two southwest tracks of the SWARM 95 experiment are considered. An airgun source produced broadband acoustic signals while a packet of large nonlinear internal waves passed between the source and two vertical linear arrays. The broadband data and its frequency range (10-180 Hz) distinguish this study from previous work. Models are developed for the internal wave environment, the geoacoustic parameters, and the airgun source signature. Parabolic equation simulations demonstrate that observed variations in intensity and wavelet time-frequency plots can be attributed to nonlinear internal waves. Empirical tests are provided of the internal wave-acoustic resonance condition that is the apparent theoretical mechanism responsible for the variations. Peaks of the effective internal wave spectrum are shown to coincide with differences in dominant acoustic wavenumbers comprising the airgun signal. The robustness of these relationships is investigated by simulations for a variety of geoacoustic and nonlinear internal wave model parameters.
A nonlinear model of ionic wave propagation along microtubules.
Satarić, M V; Ilić, D I; Ralević, N; Tuszynski, Jack Adam
2009-06-01
Microtubules (MTs) are important cytoskeletal polymers engaged in a number of specific cellular activities including the traffic of organelles using motor proteins, cellular architecture and motility, cell division and a possible participation in information processing within neuronal functioning. How MTs operate and process electrical information is still largely unknown. In this paper we investigate the conditions enabling MTs to act as electrical transmission lines for ion flows along their lengths. We introduce a model in which each tubulin dimer is viewed as an electric element with a capacitive, inductive and resistive characteristics arising due to polyelectrolyte nature of MTs. Based on Kirchhoff's laws taken in the continuum limit, a nonlinear partial differential equation is derived and analyzed. We demonstrate that it can be used to describe the electrostatic potential coupled to the propagating localized ionic waves. PMID:19259657
Standing waves for supercritical nonlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Dávila, Juan; del Pino, Manuel; Musso, Monica; Wei, Juncheng
Let V(x) be a non-negative, bounded potential in R, N⩾3 and p supercritical, p>{N+2}/{N-2}. We look for positive solutions of the standing-wave nonlinear Schrödinger equation Δu-V(x)u+u=0 in R, with u(x)→0 as |x|→+∞. We prove that if V(x)=o(|) as |x|→+∞, then for N⩾4 and p>{N+1}/{N-3} this problem admits a continuum of solutions. If in addition we have, for instance, V(x)=O(|) with μ>N, then this result still holds provided that N⩾3 and p>{N+2}/{N-2}. Other conditions for solvability, involving behavior of V at ∞, are also provided.
Nonlinear standing Alfven wave current system at Io: Theory
Neubauer, F.M.
1980-03-01
We present a nonlinear analytical model of the Alfven current tubes continuing the currents through Io (or rather its ionosphere) generated by the unipolar inductor effect due to Io's motion relative to the magnetospheric plasma. We thereby extend the linear work by Drell et al. (1965) to the fully nonlinear, sub-Alfvenic situation also including flow which is not perpendicular to the background magnetic field. The following principal results have been obtained: (1) The portion of the currents feeding Io is aligned with the Alfven characteristics at an angle theta/sub A/ is the Alfven Mach number. (2) The Alfven tubes act like an external conductance ..sigma../sub A/=1/(..mu../sub 0/V/sub A/(1+M/sub A//sup 2/+2M/sub A/ sin theta)/sup 1/2/ where V/sub A/ is the Alfven wave propagation. Hence the Jovian ionospheric conductivity is not necessary for current closure. (3) In addition, the Alfven tubes may be reflected from either the torus boundary or the Jovian ionosphere. The efficiency of the resulting interaction with these boundaries varies with Io position. The interaction is particularly strong at extreme magnetic latitudes, thereby suggesting a mechanism for the Io control of decametric emissions. (4) The reflected Alfven waves may heat both the torus plasma and the Jovian ionosphere as well as produce increased diffusion of high-energy particles in the torus. (5) From the point of view of the electrodynamic interaction, Io is unique among the Jovian satellites for several reasons: these include its ionosphere arising from ionized volcanic gases, a high external Alfvenic conductance ..sigma../sub A/, and a high corotational voltage in addition to the interaction phenomenon with a boundary. (6) We find that Amalthea is probably strongly coupled to Jupiter's ionosphere while the outer Galilean satellites may occasionally experience super-Alfvenic conditions.
Yao, Yu-Qin; Li, Ji; Han, Wei; Wang, Deng-Shan; Liu, Wu-Ming
2016-01-01
The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning.
Yao, Yu-Qin; Li, Ji; Han, Wei; Wang, Deng-Shan; Liu, Wu-Ming
2016-01-01
The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning. PMID:27403634
Nonlinear mechanisms for drift wave saturation and induced particle transport
Dimits, A.M. . Lab. for Plasma Research); Lee, W.W. . Plasma Physics Lab.)
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 {times} 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.
Han Jiuning; He Yonglin; Chen Yan; Zhang Kezhi; Ma Baohong
2013-01-15
By using the model of Cairns et al.[Geophys. Rev. Lett. 22, 2709 (1995)], the head-on collision of cylindrical/spherical ion-acoustic solitary waves in an unmagnetized non-planar plasma consisting of warm adiabatic ions and nonthermally distributed electrons is investigated. The extended Poincare-Lighthill-Kuo perturbation method is used to derive the modified Korteweg-de Vries equations for ion-acoustic solitary waves in this plasma system. The effects of the plasma geometry m, the ion to electron temperature ratio {sigma}, and the nonthermality of the electron distribution {alpha} on the interaction of the colliding solitary waves are studied. It is found that the plasma geometries have a big impact on the phase shifts of solitary waves. Also it is important to note that the phase shifts induced by the collision of compressive and rarefactive solitary waves are very different. We point out that this study is useful to the investigations about the observations of electrostatic solitary structures in astrophysical as well as in experimental plasmas with nonthermal energetic electrons.
New Traveling Wave Solutions for a Class of Nonlinear Evolution Equations
NASA Astrophysics Data System (ADS)
Bai, Cheng-Jie; Zhao, Hong; Xu, Heng-Ying; Zhang, Xia
The deformation mapping method is extended to solve a class of nonlinear evolution equations (NLEEs). Many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, and Jacobian elliptic function solutions, are obtained by a simple algebraic transformation relation between the solutions of the NLEEs and those of the cubic nonlinear Klein-Gordon (NKG) equation.
Numerical and experimental investigation of nonlinear ultrasonic Lamb waves at low frequency
NASA Astrophysics Data System (ADS)
Zuo, Peng; Zhou, Yu; Fan, Zheng
2016-07-01
Nonlinear ultrasonic Lamb waves are popular to characterize the nonlinearity of materials. However, the widely used nonlinear Lamb mode suffers from two associated complications: inherent dispersive and multimode natures. To overcome these, the symmetric Lamb mode (S0) at low frequency region is explored. At the low frequency region, the S0 mode is little dispersive and easy to generate. However, the secondary mode still exists, and increases linearly for significant distance. Numerical simulations and experiments are used to validate the nonlinear features and therefore demonstrate an easy alternative for nonlinear Lamb wave applications.
NASA Astrophysics Data System (ADS)
Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei
2016-07-01
Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.
Automatic computation of the travelling wave solutions to nonlinear PDEs
NASA Astrophysics Data System (ADS)
Liang, Songxin; Jeffrey, David J.
2008-05-01
Various extensions of the tanh-function method and their implementations for finding explicit travelling wave solutions to nonlinear partial differential equations (PDEs) have been reported in the literature. However, some solutions are often missed by these packages. In this paper, a new algorithm and its implementation called TWS for solving single nonlinear PDEs are presented. TWS is implemented in MAPLE 10. It turns out that, for PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases. Program summaryProgram title:TWS Catalogue identifier:AEAM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAM_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:1250 No. of bytes in distributed program, including test data, etc.:78 101 Distribution format:tar.gz Programming language:Maple 10 Computer:A laptop with 1.6 GHz Pentium CPU Operating system:Windows XP Professional RAM:760 Mbytes Classification:5 Nature of problem:Finding the travelling wave solutions to single nonlinear PDEs. Solution method:Based on tanh-function method. Restrictions:The current version of this package can only deal with single autonomous PDEs or ODEs, not systems of PDEs or ODEs. However, the PDEs can have any finite number of independent space variables in addition to time t. Unusual features:For PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases. Additional comments:It is easy to use. Running time:Less than 20 seconds for most cases, between 20 to 100 seconds for some cases, over 100 seconds for few cases. References: [1] E.S. Cheb-Terrab, K. von
Macrosimulation of nonlinear dynamic systems for wave-shaping applications
NASA Astrophysics Data System (ADS)
Ogrodzki, Jan; Bieńkowski, Piotr
2014-11-01
Macromodeling is a technique widely used in circuits simulation. Macromodels usually describe complex, repetitive parts of large systems. They are often created on the base of original circuits by their simplification, e.g. macromodels of operational amplifiers. Another group of macromodels makes use of the circuit response approximation. This approach is called behavioral macromodeling. Low numerical complexity of behavioral macromodels is especially useful in CAD systems where circuit simulation must be run many times. In this paper the behavioral macromodeling technique has been applied to the whole circuit not to its part. This technique may be understood as shaping of the circuit output response and so belongs to a class of wave-shaping methods. We have used it to nonlinear, dynamic circuits with periodic signals of finite spectra, as e.g. in audio systems. The macromodels shape their frequency and spectral characteristics with a sufficient simplicity to omit unwanted distortions and with a sufficient efficiency to run the simulator in real time. Elaboration of this wave-shaping simulator is based on dynamic circuits identification, Fourier approximation of signals and harmonic balance technique. The obtained macromodel can be run as a software substitute for a hardware audio system.
Slabko, Vitaly V; Popov, Alexander K; Tkachenko, Viktor A; Myslivets, Sergey A
2016-09-01
Three-wave mixing of ordinary and backward electromagnetic waves in a pulsed regime is investigated in the metamaterials that enable the coexistence and phase-matching of such waves. It is shown that the opposite direction of phase velocity and energy flux in backward waves gives rise to extraordinary transient processes due to greatly enhanced optical parametric amplification and frequency up- and down-shifting nonlinear reflectivity. The differences are illustrated through comparison with the counterparts in ordinary, co-propagating settings.
Nonlinear transient wave excitation as a new tool in model testing
Clauss, G.F.; Kuehnlein, W.L.
1996-12-31
Short extension transient waves with tailor-made spectra are extremely efficient for model testing. For small water elevations a linear description of the wave field is satisfactory. With higher transient wave trains, however, the linear description becomes increasingly inaccurate, and a new numerical technique must be developed. Such a new method is based on the fact that short and high wave groups with strong nonlinear characteristics evolve from long and low wave groups, which are characterized by linear principles. As the total energy of the transient wave is invariant during its metamorphosis, the initial linear Fourier spectrum is selected as the backbone of wave information or as the primordial cell from which all nonlinearities are hatched. Based on the initial Fourier spectrum which is the core of the wave information operator the shape variation of the linear transient wave train during propagation is calculated. At selected positions the nonlinear expansion is accomplished by solving the mutually dependent particle motion equations in time domain. The proposed new method uses a numerical nonlinear description of transient wave trains as a function of time or space for any fixed or moving reference point. At its primordial state it is based on a linear superposition of wave information which is complemented by an expanded velocity potential to calculate nonlinear surface elevations, particle motions, velocities, and accelerations. After the nonlinear wave trains converge and pass the concentration point only to diverge and fade away as long, low and linear wave groups, the primordial linear Fourier spectrum can be found again at the end of the development. This step can be used to monitor the transformation. Wave energy spectra and the shape of the wave train can be designed with special regard to the proposed task. Based on these data the entire wave field can be determined.
Kittell, Aaron W.; Camenisch, Theodore G.; Ratke, Joseph J.; Sidabras, Jason W.; Hyde, James S.
2011-01-01
A continuous wave (CW) electron paramagnetic resonance (EPR) spectrum is typically displayed as the first harmonic response to the application of 100 kHz magnetic field modulation, which is used to enhance sensitivity by reducing the level of 1/f noise. However, magnetic field modulation of any amplitude causes spectral broadening and sacrifices EPR spectral intensity by at least a factor of two. In the work presented here, a CW rapid-scan spectroscopic technique that avoids these compromises and also provides a means of avoiding 1/f noise is developed. This technique, termed non-adiabatic rapid sweep (NARS) EPR, consists of repetitively sweeping the polarizing magnetic field in a linear manner over a spectral fragment with a small coil at a repetition rate that is sufficiently high that receiver noise, microwave phase noise, and environmental microphonics, each of which has 1/f characteristics, are overcome. Nevertheless, the rate of sweep is sufficiently slow that adiabatic responses are avoided and the spin system is always close to thermal equilibrium. The repetitively acquired spectra from the spectral fragment are averaged. Under these conditions, undistorted pure absorption spectra are obtained without broadening or loss of signal intensity. A digital filter such as a moving average is applied to remove high frequency noise, which is approximately equivalent in bandwidth to use of an integrating time constant in conventional field modulation with lock-in detection. Nitroxide spectra at L- and X-band are presented. PMID:21741868
The Effect of Crack Orientation on the Nonlinear Interaction of a P-wave with an S-wave
TenCate, J. A.; Malcolm, A. E.; Feng, X.; Fehler, M. C.
2016-06-06
Cracks, joints, fluids, and other pore-scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore-scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presencemore » and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low-amplitude P wave probe by a high-amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.« less
The effect of crack orientation on the nonlinear interaction of a P wave with an S wave
NASA Astrophysics Data System (ADS)
TenCate, J. A.; Malcolm, A. E.; Feng, X.; Fehler, M. C.
2016-06-01
Cracks, joints, fluids, and other pore-scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore-scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presence and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low-amplitude P wave probe by a high-amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.
Laboratory Study of Nonlinear Trapping of Magnetized Langmuir Waves Inside a Density Depletion
Starodubtsev, Mikhail V.; Nazarov, Vladimir V.; Kostrov, Alexander V.
2007-05-11
The formation of a small-scale plasma density depletion region extended along the ambient magnetic field and caused by the nonlinear interaction of the upper-hybrid plasma waves with a magnetoplasma has been observed under laboratory conditions modeling the ionospheric heating experiments. Plasma waves are trapped inside the depletion due to their specific dispersion properties. The threshold of the nonlinear wave trapping significantly increases in the vicinity of the harmonics of the electron gyrofrequency.
The nonlinear equatorial Kelvin wave. [in coastal currents of El Nino and Gulf of Guinea
NASA Technical Reports Server (NTRS)
Boyd, J. P.
1980-01-01
Using the method of strained coordinates, a uniformly valid approximation to the nonlinear equatorial Kelvin wave is derived. It is shown that nonlinear effects are negligible for the Kelvin waves associated with the Gulf of Guinea upwelling. The Kelvin waves involved in El Nino, however, are significantly distorted both in shape and speed. The leading edge is smoothed and expanded rather than steepened, but the trailing edge will form sharp fronts and eventually break.
Bazzani, A.; Turchetti, G.; Benedetti, C.; Rambaldi, S.; Servizi, G.
2005-06-08
In a high intensity circular accelerator the synchrotron dynamics introduces a slow modulation in the betatronic tune due to the space-charge tune depression. When the transverse motion is non-linear due to the presence of multipolar effects, resonance islands move in the phase space and change their amplitude. This effect introduces the trapping and detrapping phenomenon and a slow diffusion in the phase space. We apply the neo-adiabatic theory to describe this diffusion mechanism that can contribute to halo formation.
Propagation of Long Extensional Nonlinear Waves in a Hyper-Elastic Layer
NASA Astrophysics Data System (ADS)
Teymür, Mevlüt
Propagation of small but finite amplitude waves in a nonlinear hyper-elastic plate of uniform thickness is considered. By employing a perturbation expansion, extensional waves are examined under the long wave limit. It is shown that the asymptotic wave field is governed by a Korteweg-DeVries (K-dV) equation. Then the propagation characteristics of the asymptotic waves are discussed via the well known solutions of the K-dV equation.
NASA Technical Reports Server (NTRS)
Koons, H. C.; Roeder, J. L.; Bauer, O. H.; Haerendel, G.; Treumann, R.
1987-01-01
Nonlinear wave decay processes have been detected in the solar wind by the plasma wave experiment aboard the Active Magnetospheric Particle Tracer Explorers (AMPTE) IRM spacecraft. The main process is the generation of ultralow-frequency ion acoustic waves from the decay of Langmuir waves near the electron plasma frequency. Frequently, this is accompanied by an enhancement of emissions near twice the plasma frequency. This enhancement is most likely due to the generation of electromagnetic waves from the coalescence of two Langmuir waves. These processes occur within the electron foreshock in front of the earth's bow shock.
Evidence of nonlinear interaction between quasi 2 day wave and quasi-stationary wave
NASA Astrophysics Data System (ADS)
Gu, Sheng-Yang; Liu, Han-Li; Li, Tao; Dou, Xiankang; Wu, Qian; Russell, James M.
2015-02-01
The nonlinear interaction between the westward quasi 2 day wave (QTDW) with zonal wave number s = 3 (W3) and stationary planetary wave with s = 1 (SPW1) is first investigated using both Thermosphere, Ionosphere, and Mesosphere Electric Dynamics (TIMED) satellite observations and the thermosphere-ionosphere-mesosphere electrodynamics general circulation model (TIME-GCM) simulations. A QTDW with westward s = 2 (W2) is identified in the mesosphere and lower thermosphere (MLT) region in TIMED/Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) temperature and TIMED/TIMED Doppler Imager (TIDI) wind observations during 2011/2012 austral summer period, which coincides with a strong SPW1 episode at high latitude of the northern winter hemisphere. The temperature perturbation of W2 QTDW reaches a maximum amplitude of ~8 K at ~30°S and ~88 km in the Southern Hemisphere, with a smaller amplitude in the Northern Hemisphere at similar latitude and minimum amplitude at the equator. The maximum meridional wind amplitude of the W2 QTDW is observed to be ~40 m/s at 95 km in the equatorial region. The TIME-GCM is utilized to simulate the nonlinear interactions between W3 QTDW and SPW1 by specifying both W3 QTDW and SPW1 perturbations at the lower model boundary. The model results show a clear W2 QTDW signature in the MLT region, which agrees well with the TIMED/SABER temperature and TIMED/TIDI horizontal wind observations. We conclude that the W2 QTDW during the 2011/2012 austral summer period results from the nonlinear interaction between W3 QTDW and SPW1.
NASA Astrophysics Data System (ADS)
Hu, Tao; Ma, Li
2010-09-01
An internal wave observation experiment was performed near the south of Hai-Nan Island in the South China Sea in July 2004. Three vertical thermistor arrays were moored to estimate internal wave propagation direction and velocity. A nonlinear internal wave packet was observed in this experiment. It appeared at flood tide time of wee hours. Computation indicated that the nonlinear internal wave packet's velocity was 0.54 m/s and its propagation direction was northwest. From its propagation direction, we estimated that the nonlinear internal wave packet was generated near Xi-Sha Islands. The dnoidal model of KdV(Korteweg-deVries) equation was used to simulate the waveform of thid nonlinear internal wave. Measured data shows the crest interval of nonlinear internal waves was shorter when they propagated. In the last section of this paper we simulate a nonlinear internal wave packet's effect on sound propagation and analyzed mode coupling led by the nonlinear internal wave packet.
Guided wave methods and apparatus for nonlinear frequency generation
Durfee, III, Charles G.; Rundquist, Andrew; Kapteyn, Henry C.; Murnane, Margaret M.
2000-01-01
Methods and apparatus are disclosed for the nonlinear generation of sum and difference frequencies of electromagnetic radiation propagating in a nonlinear material. A waveguide having a waveguide cavity contains the nonlinear material. Phase matching of the nonlinear generation is obtained by adjusting a waveguide propagation constant, the refractive index of the nonlinear material, or the waveguide mode in which the radiation propagates. Phase matching can be achieved even in isotropic nonlinear materials. A short-wavelength radiation source uses phase-matched nonlinear generation in a waveguide to produce high harmonics of a pulsed laser.
NASA Astrophysics Data System (ADS)
Verweij, Martin D.; Demi, Libertario; van Dongen, Koen W. A.
2012-09-01
The Iterative Nonlinear Contrast Source (INCS) method is a full-wave method for the accurate computation of wide-angle, pulsed, nonlinear ultrasound fields appearing in, e.g., medical echoscopy. The method is based on the Westervelt equation and considers the occurring nonlinear term as a distributed contrast source that operates in a linear background medium. This formulation leads to an integral equation, which is solved in an iterative way. The original INCS method uses a Neumann scheme to successively approximate the nonlinear wave field in homogeneous, lossless, nonlinear media. To cope with attenuative and/or inhomogeneous nonlinear media, additional contrast sources may be introduced. Since these deteriorate the convergence rate of the Neumann scheme, more advanced iterative solution schemes like Bi-CGSTAB are required. To overcome the difficulty that such schemes only apply to linear integral equations, the nonlinear contrast source is linearized, at the cost of a significant systematic error in the fourth and higher harmonics. In this paper, a strategy is proposed in which the relevant iterative solution scheme is restarted with an updated version of the linearized contrast source. Results demonstrate the effectiveness of this strategy in eliminating the systematic error. In addition, it is shown that the same approach also improves the convergence rate in case of nonlinear propagation in media with attenuation.
Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves
NASA Technical Reports Server (NTRS)
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.
Linear versus nonlinear response of a forced wave turbulence system.
Cadot, Olivier; Touzé, Cyril; Boudaoud, Arezki
2010-10-01
A vibrating plate is set into a chaotic state of wave turbulence by a forcing having periodic and random components. Both components are weighted in order to explore continuously intermediate forcing from the periodic to the random one, but keeping constant its rms value. The transverse velocity of the plate is measured at the application point of the force. It is found that whatever the detail of the forcing is, the velocity spectra exhibit a universal cascade for frequencies larger than the forcing frequency range. In contrast, the velocity spectra strongly depend on the nature of the forcing within the range of forcing frequencies. The coherence function is used to extract the contribution of the velocity fluctuations that display a linear relationship with the forcing. The nonlinear contribution to the velocity fluctuations is found to be almost constant, about 55% of the total velocity fluctuations whatever the nature of the forcing from random to periodic. On the other hand, the nonlinear contribution to the fluctuations of the injected power depends on the nature of the forcing; it is significantly larger for the periodic forcing (60%) and decreases continuously as the randomness is increased, reaching a value of 40% for the pure random forcing. For all the cases of intermediate forcing from random to periodic, a simple model of the velocity response recovers in a fairly good agreement the probability density function of the injected power. The consequence of the existence of a linear-response component is discussed in the context of the fluctuation-dissipation theorem validation in experiments of out-of-equilibrium systems. PMID:21230369
Eliasson, Bengt; Shukla, P K
2010-07-01
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the modulational instability for long-crested wave trains, which agrees well with recent large-scale experiments in wave basins, where it was found that narrower directional spectra lead to self-focusing of ocean waves and an enhanced probability of extreme events. We find that the modulational instability is nonlinearly saturated by a broadening of the wave spectrum, which leads to the stabilization of the water-wave system. Applications of our results to other fields of physics, such as nonlinear optics and plasma physics, are discussed.
Do nonlinear waves evolve in a universal manner in dusty and other plasma environments?
NASA Astrophysics Data System (ADS)
Bharuthram, R.; Singh, S. V.; Maharaj, S. K.; Moolla, S.; Lazarus, I. J.; Reddy, R. V.; Lakhina, G. S.; Lakhina
2014-12-01
Using a fluid theory approach, this article provides a comparative study on the evolution of nonlinear waves in dusty plasmas, as well as other plasma environments, viz electron-ion, and electron-positron plasmas. Where applicable, relevance to satellite measurements is pointed out. A range of nonlinear waves from low frequency (ion acoustic and ion cyclotron waves), high frequency (electron acoustic and electron cyclotron waves) in electron-ion plasmas, ultra-low frequency (dust acoustic and dust cyclotron waves) in dusty plasmas and in electron-positron plasmas are discussed. Depending upon the plasma parameters, saw-tooth and bipolar structures are shown to evolve.
Rogue waves: from nonlinear Schrödinger breather solutions to sea-keeping test.
Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco
2013-01-01
Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.
Verification of nonlinear particle simulation of radio frequency waves in tokamak
Kuley, A. Lin, Z.; Bao, J.; Wei, X. S.; Xiao, Y.; Zhang, W.; Sun, G. Y.; Fisch, N. J.
2015-10-15
Nonlinear simulation model for radio frequency waves in fusion plasmas has been developed and verified using fully kinetic ion and drift kinetic electron. Ion cyclotron motion in the toroidal geometry is implemented using Boris push in the Boozer coordinates. Linear dispersion relation and nonlinear particle trapping are verified for the lower hybrid wave and ion Bernstein wave (IBW). Parametric decay instability is observed where a large amplitude pump wave decays into an IBW sideband and an ion cyclotron quasimode (ICQM). The ICQM induces an ion perpendicular heating, with a heating rate proportional to the pump wave intensity.
Evolution of nonlinear dust-ion-acoustic waves in an inhomogeneous plasma
NASA Astrophysics Data System (ADS)
Xiao, De-long; Ma, J. X.; Li, Yang-fang; Xia, Yinhua; Yu, M. Y.
2006-05-01
The propagation of nonlinear dust-ion-acoustic waves in an inhomogeneous dusty plasma is studied. At small but finite amplitudes, the wave evolution is governed by a modified Korteweg-deVries Burgers equation, whose coefficients are space dependent. The properties of the evolution equation are analyzed and the behavior of the corresponding shock and soliton solutions is numerically studied. If dust-charge perturbation is neglected, there exists a zero-nonlinearity point where the coefficient of the nonlinear term changes from negative to positive. At that point the nonlinear wave also undergoes structural deformation. If the dust-charge perturbation is taken into account, the zero-nonlinearity point may not appear and the soliton or shock wave will retain its form during the propagation.
Evolution of nonlinear dust-ion-acoustic waves in an inhomogeneous plasma
Xiao Delong; Ma, J.X.; Li Yangfang; Xia Yinhua; Yu, M.Y.
2006-05-15
The propagation of nonlinear dust-ion-acoustic waves in an inhomogeneous dusty plasma is studied. At small but finite amplitudes, the wave evolution is governed by a modified Korteweg-deVries Burgers equation, whose coefficients are space dependent. The properties of the evolution equation are analyzed and the behavior of the corresponding shock and soliton solutions is numerically studied. If dust-charge perturbation is neglected, there exists a zero-nonlinearity point where the coefficient of the nonlinear term changes from negative to positive. At that point the nonlinear wave also undergoes structural deformation. If the dust-charge perturbation is taken into account, the zero-nonlinearity point may not appear and the soliton or shock wave will retain its form during the propagation.
Garnier, Josselin; Picozzi, Antonio
2010-03-15
This article presents a unified kinetic formulation of partially coherent nonlinear optical waves propagating in a noninstantaneous response Kerr medium. We derive a kinetic equation that combines the weak Langmuir turbulence kinetic equation and a Vlasov-like equation within a general framework: It describes the evolution of the spectrum of a random field that exhibits a quasistationary statistics in the presence of a noninstantaneous nonlinear response. The kinetic equation sheds new light on the dynamics of partially coherent nonlinear waves and allows for a qualitative interpretation of the interplay between the noninstantaneous nonlinearity and the nonstationary statistics of the incoherent field. It is shown that the incoherent modulational instability of a random nonlinear wave can be suppressed by the noninstantaneous nonlinear response. Moreover, incoherent modulational instability can prevent the generation of spectral incoherent solitons.
Numerical study of material nonlinearity assessment based on non-collinear ultrasonic wave mixing
NASA Astrophysics Data System (ADS)
Zhang, Ziyin; Nagy, Peter B.; Hassan, Waled
2015-03-01
Recent research has indicated that non-collinear ultrasonic wave mixing can be exploited for the measurement of both bulk material nonlinearity and localized interface nonlinearity. In the particular configuration considered in this study, two oblique shear waves are mixed to generate a third longitudinal wave as a result of nonlinear interaction with the material. In contrast with the nonlinearity parameter (β) measured with conventional longitudinal wave harmonic generation, the mixed signal depends only on the second Murnaghan coefficient (m). A simple analytical approximation was developed to determine the amplitude of the mixed signal. It was shown that in the presence of a perfectly reflecting interface the bulk nonlinearity decreases due to the complex linear reflection coefficient of such an interface above the longitudinal critical angle. It was also found that a nonlinear interface produces an additional symmetric nonlinear scattered wave that is the same for both the reflected and transmitted fields. This excess nonlinearity can be exploited to characterize the interface, especially from the reflected part of the mixed signal that is essentially free of bulk nonlinearity contribution from the surrounding host material.
Cross-polarized wave generation by effective cubic nonlinear optical interaction.
Petrov, G I; Albert, O; Etchepare, J; Saltiel, S M
2001-03-15
A new cubic nonlinear optical effect in which a linearly polarized wave propagating in a single quadratic medium is converted into a wave that is cross polarized to the input wave is observed in BBO crystal. The effect is explained by cascading of two different second-order processes: second-harmonic generation and difference frequency mixing.
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. PMID:25871222
Extreme physical information and the nonlinear wave equation
NASA Astrophysics Data System (ADS)
Frieden, B. R.
1995-09-01
The nonlinear wave equation an be derived from a principle of extreme physical information (EPI) K. This is for a scenario where a probe electron moves through a medium in a weak magnetic field. The field is caused by a probabilistic line current source. Assume that the probability current density S of the electron is approximately constant, and directed parallel to the current source. Both the source probability amplitudes (rho) and the electron probability amplitudes (phi) are unknowns (called 'modes') of the problem. The net physical information K here consists of two components: functional K1[(phi) ] due to modes (phi) and K2[(rho) ] due to modes (rho) , respectively. To form K1[(phi) ], the Fisher information functional I1[(phi) ] for the electron modes is first constructed. This is of a fixed mathematical form. Then, a unitary transformation on (phi) to a physical space is sought that leaves I1 invariant, as form J1. This is, of course, the Fourier transformation, where the transform coordinates are momenta and I1 is essentially the mean-square electron momentum. Information K1[(phi) ] is then defined as (I1 - J1). Information K2 is formed similarly. The total information K is formed as the sum of the two components K1[(phi) ] and K2[(rho) ], by the additivity of Fisher information, and is then extremized in both (phi) and (rho) . Extremizing first in (rho) gives a Taylor series in powers of (phi) n*(phi) n, which is cut off at the quadratic term. Back-substituting this into the total Lagrangian gives one that is quadratic in (phi) n*(phi) n. Now varying (phi) * gives the required cubic wave equation in (phi) .
Nonlinear response of tension leg platforms in random sea waves
Ma, R.; Li, G.
1995-12-31
The nonlinear dynamic analysis of a tension leg platform is carried out by using nonlinear spectral analysis in this paper. The nonlinear response spectrum is obtained by introducing Hermite polynomial. The study indicates that it is possible to solve nonlinear vibration problems by using spectral analysis directly. It is not necessary to linearize the nonlinear terms in this method so that the errors introduced by linearization can be eliminated. This method will provide a convenient and accurate tool for solving nonlinear random vibration problems.
Local absorbing boundary conditions for nonlinear wave equation on unbounded domain.
Li, Hongwei; Wu, Xiaonan; Zhang, Jiwei
2011-09-01
The numerical solution of the nonlinear wave equation on unbounded spatial domain is considered. The artificial boundary method is introduced to reduce the nonlinear problem on unbounded spatial domain to an initial boundary value problem on a bounded domain. Using the unified approach, which is based on the operator splitting method, we construct the efficient nonlinear local absorbing boundary conditions for the nonlinear wave equation, and give the stability analysis of the resulting boundary conditions. Finally, several numerical examples are given to demonstrate the effectiveness of our method.
Nonlinear evolution of interacting oblique waves on two-dimensional shear layers
NASA Technical Reports Server (NTRS)
Goldstein, M. E.; Choi, S.-W.
1989-01-01
The effects of critical layer nonlinearity are considered on spatially growing oblique instability waves on nominally two-dimensional shear layers between parallel streams. The analysis shows that three-dimensional effects cause nonlinearity to occur at much smaller amplitudes than it does in two-dimensional flows. The nonlinear instability wave amplitude is determined by an integro-differential equation with cubic type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. The numerical solutions always end in a singularity at a finite downstream distance.
Modeling Nonlinear Acoustic Standing Waves in Resonators: Theory and Experiments
NASA Technical Reports Server (NTRS)
Raman, Ganesh; Li, Xiaofan; Finkbeiner, Joshua
2004-01-01
The overall goal of the cooperative research with NASA Glenn is to fundamentally understand, computationally model, and experimentally validate non-linear acoustic waves in enclosures with the ultimate goal of developing a non-contact acoustic seal. The longer term goal is to transition the Glenn acoustic seal innovation to a prototype sealing device. Lucas and coworkers are credited with pioneering work in Resonant Macrosonic Synthesis (RMS). Several Patents and publications have successfully illustrated the concept of Resonant Macrosonic Synthesis. To utilize this concept in practical application one needs to have an understanding of the details of the phenomenon and a predictive tool that can examine the waveforms produced within resonators of complex shapes. With appropriately shaped resonators one can produce un-shocked waveforms of high amplitude that would result in very high pressures in certain regions. Our goal is to control the waveforms and exploit the high pressures to produce an acoustic seal. Note that shock formation critically limits peak-to-peak pressure amplitudes and also causes excessive energy dissipation. Proper shaping of the resonator is thus critical to the use of this innovation.
Self-switching of displacement waves in elastic nonlinearly deformed materials
NASA Astrophysics Data System (ADS)
Rushchitsky, Jeremiah
The problem of self-switching plane waves in elastic nonlinearly deformed materials is formulated. Reduced and evolution equations, which describe the interaction of two waves the power pumping wave and the faint signal wave are obtained. For the case of wave numbers matching the pumping and signal waves, a procedure of finding the exact solution of evolution equations is described. The solution is expressed by elliptic Jacobi functions. The existence of the power wave self-switching is shown and commented. To cite this article: J. Rushchitsky, C. R. Mecanique 330 (2002) 175-180.
NASA Astrophysics Data System (ADS)
Ass'ad, A. I.; Ashour, H. S.; Shabat, M. M.
Magnetostatic surface waves have been investigated in a layered system of a nonlinear nonmagnetic negative permittivity material (NPM) and Ferrite (YIG). We derived the dispersion relation before numerically solving the dispersion relation of the TE nonlinear magnetostatic surface waves (NMSSW) in the proposed structure and the power flow. We found out that the wave effective nonlinear refractive index is much smaller in the forward direction than in the backward direction and consequently, the power flow is lower for the forward direction than the backward direction.
Small amplitude nonlinear electron acoustic solitary waves in weakly magnetized plasma
Dutta, Manjistha; Khan, Manoranjan; Ghosh, Samiran; Roychoudhury, Rajkumar; Chakrabarti, Nikhil
2013-01-15
Nonlinear propagation of electron acoustic waves in homogeneous, dispersive plasma medium with two temperature electron species is studied in presence of externally applied magnetic field. The linear dispersion relation is found to be modified by the externally applied magnetic field. Lagrangian transformation technique is applied to carry out nonlinear analysis. For small amplitude limit, a modified KdV equation is obtained, the modification arising due to presence of magnetic field. For weakly magnetized plasma, the modified KdV equation possesses stable solitary solutions with speed and amplitude increasing temporally. The solutions are valid upto some finite time period beyond which the nonlinear wave tends to wave breaking.
Weakly nonlinear dust ion-acoustic shock waves in a dusty plasma with nonthermal electrons
Berbri, Abderrezak; Tribeche, Mouloud
2009-05-15
Weakly nonlinear dust ion-acoustic (DIA) shock waves are investigated in a dusty plasma with nonthermal electrons. A modified Korteweg-de Vries equation with a cubic nonlinearity is derived. Due to the net negative dust charge {mu}Z{sub d} and electron nonthermality, the present plasma model can admit compressive and rarefactive weak DIA shock waves. The effect of increasing {mu}Z{sub d} is to lower the critical nonthermal parameter {beta}{sub c} above which only rarefactive DIA shock waves are admitted. Our investigation may help to understand the nonlinear structures observed in the auroral acceleration regions.
Wave propagation in photonic crystals and metamaterials: Surface waves, nonlinearity and chirality
Wang, Bingnan
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.
Analytical Solitons for Langmuir Waves in Plasma Physics with Cubic Nonlinearity and Perturbations
NASA Astrophysics Data System (ADS)
Zhou, Qin; Mirzazadeh, M.
2016-09-01
We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schrödinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on the G'/G-expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.
NASA Astrophysics Data System (ADS)
Selim, M. M.; El-Depsy, A.; El-Shamy, E. F.
2015-12-01
Properties of nonlinear ion-acoustic travelling waves propagating in a three-dimensional multicomponent magnetoplasma system composed of positive ions, negative ions and superthermal electrons are considered. Using the reductive perturbation technique (RPT), the Zkharov-Kuznetsov (ZK) equation is derived. The bifurcation theory of planar dynamical systems is applied to investigate the existence of the solitary wave solutions and the periodic travelling wave solutions of the resulting ZK equation. It is found that both compressive and rarefactive nonlinear ion-acoustic travelling waves strongly depend on the external magnetic field, the unperturbed positive-to-negative ions density ratio, the direction cosine of the wave propagation vector with the Cartesian coordinates, as well as the superthermal electron parameter. The present model may be useful for describing the formation of nonlinear ion-acoustic travelling wave in certain astrophysical scenarios, such as the D and F-regions of the Earth's ionosphere.
Nonlinear trapping and self-guiding of magnetized Langmuir waves due to thermal plasma filamentation
Nazarov, Vladimir V.; Starodubtsev, Mikhail V.; Kostrov, Alexander V.
2007-12-15
Nonlinear interaction of Langmuir waves with a laboratory magnetoplasma has been studied under the conditions relevant to the ionospheric heating experiments. Self-guiding of magnetized Langmuir waves is observed at critical plasma density ({omega}={omega}{sub p}): Langmuir waves are trapped inside a narrow, magnetic-field-aligned plasma density depletion region, which is formed by trapped waves due to thermal plasma nonlinearity, i.e., due to local plasma heating and consequent thermodiffusion. Magnetized Langmuir waves are trapped inside the depletion region through their specific dispersion properties; this fact has been shown using the kinetically modified dispersion relation. The threshold of the nonlinear wave trapping exhibits significant growth in the vicinity of harmonics of the electron gyrofrequency.
Nonlinear coherent structures of Alfvén wave in a collisional plasma
NASA Astrophysics Data System (ADS)
Jana, Sayanee; Ghosh, Samiran; Chakrabarti, Nikhil
2016-07-01
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.
Propagation of Long-Wavelength Nonlinear Slow Sausage Waves in Stratified Magnetic Flux Tubes
NASA Astrophysics Data System (ADS)
Barbulescu, M.; Erdélyi, R.
2016-05-01
The propagation of nonlinear, long-wavelength, slow sausage waves in an expanding magnetic flux tube, embedded in a non-magnetic stratified environment, is discussed. The governing equation for surface waves, which is akin to the Leibovich-Roberts equation, is derived using the method of multiple scales. The solitary wave solution of the equation is obtained numerically. The results obtained are illustrative of a solitary wave whose properties are highly dependent on the degree of stratification.
Nonlinear wave collapse, shock, and breather formation in an electron magnetohydrodynamic plasma.
Ghosh, Samiran; Chakrabarti, Nikhil
2014-12-01
Low-frequency nonlinear wave dynamics is investigated in a two-dimensional inhomogeneous electron magnetohydrodynamic (EMHD) plasma in the presence of electron viscosity. In the long-wavelength limit, the dynamics of the wave is found to be governed by a novel nonlinear equation. The result of the moving-frame nonlinear analysis is noteworthy, which shows that this nonlinear equation does have a breather solution and electron viscosity is responsible for the breather. A breather is a nonlinear wave in which energy accumulates in a localized and oscillatory manner. Analytical solution and time-dependent numerical simulation of this novel equation reveal the collapse of a soliton (localized pulse) into a weak noise shelf and formation of shocklike structures.
Basic principles approach for studying nonlinear Alfven wave-alpha particle dynamics
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.
High-order rogue waves in vector nonlinear Schrödinger equations.
Ling, Liming; Guo, Boling; Zhao, Li-Chen
2014-04-01
We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber. PMID:24827185
Role of Convective Cells in Nonlinear Interaction of Kinetic Alfven Waves
NASA Astrophysics Data System (ADS)
Luk, Onnie
The convective cells are observed in the auroral ionosphere and they could play an important role in the nonlinear interaction of Alfven waves and disrupt the kinetic Alfven wave (KAW) turbulence. Zonal fields, which are analogous to convective cells, are generated by microturbulence and regulate microturbulence inside toroidally confined plasmas. It is important to understand the role of convective cells in the nonlinear interaction of KAW leading to perpendicular cascade of spectral energy. A nonlinear gyrokinetic particle simulation has been developed to study the perpendicular spectral cascade of kinetic Alfven wave. However, convective cells were excluded in the study. In this thesis project, we have modified the formulation to implement the convective cells to study their role in the nonlinear interactions of KAW. This thesis contains detail description of the code formulation and convergence tests performed, and the simulation results on the role of convective cells in the nonlinear interactions of KAW. In the single KAW pump wave simulations, we observed the pump wave energy cascades to waves with shorter wavelengths, with three of them as dominant daughter waves. Convective cells are among those dominant daughter waves and they enhance the rate of energy transfer from pump to daughter waves. When zonal fields are present, the growth rates of the dominant daughter waves are doubled. The convective cell (zonal flow) of the zonal fields is shown to play a major role in the nonlinear wave interaction, while the linear zonal vector potential has little effects. The growth rates of the daughter waves linearly depends on the pump wave amplitude and the square of perpendicular wavenumber. On the other hand, the growth rates do not depend on the parallel wavenumber in the limit where the parallel wavenumber is much smaller than the perpendicular wavenumber. The nonlinear wave interactions with various perpendicular wavenumbers are also studied in this work. When
Rogue waves for a system of coupled derivative nonlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Chan, Hiu Ning; Malomed, Boris; Chow, Kwok Wing
2015-11-01
Previous works in the literature on water waves have demonstrated that the fourth-order evolution of gravity waves in deep water will be governed by a higher order nonlinear Schrödinger equation. In the presence of two wave trains, the system is described by a higher order coupled nonlinear Schrödinger system. Through a gauge transformation, these evolution equations are reduced to a coupled derivative nonlinear Schrödinger system. The goal here is to study rogue waves, unexpectedly large displacements from an equilibrium position, through the Hirota bilinear transformation theoretically. The connections between the onset of rogue waves and modulation instability are investigated. The range of cubic nonlinearity allowing rogue wave formation is elucidated. Under a finite group velocity mismatch between the two components, the existence regime for rogue waves is extended as compared to the case with a single wave train. The amplification ratio of the amplitude can be higher than that of the single component nonlinear Schrödinger equation. Partial financial support has been provided by the Research Grants Council through contracts HKU711713E and HKU17200815.
Stability of Traveling Waves of Nonlinear Schrödinger Equation with Nonzero Condition at Infinity
NASA Astrophysics Data System (ADS)
Lin, Zhiwu; Wang, Zhengping; Zeng, Chongchun
2016-10-01
We study the stability of traveling waves of the nonlinear Schrödinger equation with nonzero condition at infinity obtained via a constrained variational approach. Two important physical models for this are the Gross-Pitaevskii (GP) equation and the cubic-quintic equation. First, under a non-degeneracy condition we prove a sharp instability criterion for 3D traveling waves of (GP), which had been conjectured in the physical literature. This result is also extended for general nonlinearity and higher dimensions, including 4D (GP) and 3D cubic-quintic equations. Second, for cubic-quintic type nonlinearity, we construct slow traveling waves and prove their nonlinear instability in any dimension. For dimension two, the non-degeneracy condition is also proved for these slow traveling waves. For general traveling waves without vortices (that is nonvanishing) and with general nonlinearity in any dimension, we find a sharp condition for linear instability. Third, we prove that any 2D traveling wave of (GP) is transversally unstable, and we find the sharp interval of unstable transversal wave numbers. Near unstable traveling waves of all of the above cases, we construct unstable and stable invariant manifolds.
Theoretical study of nonlinear waves and shock-like phenomena in hot plasmas
NASA Technical Reports Server (NTRS)
Fried, B. D.; Banos, A., Jr.; Kennel, C. F.
1973-01-01
Summaries are presented of research in basic plasma physics. Nonlinear waves and shock-like phenomena were studied which are pertinent to space physics applications, and include specific problems of magnetospheric and solar wind plasma physics.
Nonlinear airglow signatures of ducted gravity waves in the mesosphere and lower thermosphere
NASA Astrophysics Data System (ADS)
Snively, J. B.; Hickey, M. P.; Taylor, M. J.
2010-12-01
Signatures of short-period gravity waves are detected frequently in airglow data, revealing typical horizontal wavelengths of ˜15-35 km and periods of ˜4-8 minutes [e.g., Simkhada et al., Ann. Geophys., 27, 3213, 2009]. Many of such waves are ducted within the mesosphere and lower thermosphere (MLT) region [e.g., Walterscheid and Hickey, 114, D19109, 2009], and typical airglow intensity perturbations suggest amplitudes on the order of a few to tens of Kelvin within the airglow layers. At these amplitudes, trapped small-scale waves may be intermittently subject to nonlinear dissipation, potentially contributing to the local small-scale dynamics and variability of the lower thermosphere. For exceptionally strong small-scale waves, nonlinear behavior may become detectable in airglow data, including examples of wave breakdown [e.g., Yamada et al., GRL, 28(11), 2153, 2001], or apparent bore formation [e.g., Smith et al., JGR, 108(A2), 1083, 2003]. For moderately strong gravity waves with principally-linear propagation characteristics, however, airglow signatures may also exhibit nonlinearity in the form of harmonics, due to strong perturbations of reacting minor species at steep gradients of density [Huang et al., JGR, 108(A5), 1173, 2003; Snively et al., JGR, In Press, 2010]. Two scenarios are investigated numerically, using a nonlinear photochemical-dynamical model to simulate ducted gravity wave perturbations to the hydroxyl airglow layer. First, signatures of ducted waves are considered that exhibit nonlinearity associated with the wave perturbations to minor species participating in the emission processes. In this case, the nonlinear signatures are not indicative of changes in the wave packet spectrum. Second, we consider signatures of ducted waves at sufficient amplitudes to exhibit nonlinear propagation as they approach dissipation. In this second case, observable nonlinearity in the airglow signatures arise simultaneously from the overall wave perturbation and
Numerical solution of the nonlinear Schrödinger equation with wave operator on unbounded domains.
Li, Hongwei; Wu, Xiaonan; Zhang, Jiwei
2014-09-01
In this paper, we generalize the unified approach proposed in Zhang et al. [J. Zhang, Z. Xu, and X. Wu, Phys. Rev. E 78, 026709 (2008)] to design the nonlinear local absorbing boundary conditions (LABCs) for the nonlinear Schrödinger equation with wave operator on unbounded domains. In fact, based on the methodology underlying the unified approach, we first split the original equation into two parts-the linear equation and the nonlinear equation-then achieve a one-way operator to approximate the linear equation to make the wave outgoing, and finally combine the one-way operator with the nonlinear equation to achieve the nonlinear LABCs. The stability of the equation with the nonlinear LABCs is also analyzed by introducing some auxiliary variables, and some numerical examples are presented to verify the accuracy and effectiveness of our proposed method.
Nonlinear oscillations of semigeostrophic Eady waves in the presence of diffusivity
NASA Astrophysics Data System (ADS)
Xu, Qin; Gu, Wei; Shouting, Gao
2005-01-01
Analyses are performed to examine the physical processes involved in nonlinear oscillations of Eady baroclinic waves obtained from viscous semigeostrophic models with two types of boundary conditions (freeslip and non-slip). By comparing with previous studies for the case of the free-slip boundary condition, it is shown that the nonlinear oscillations are produced mainly by the interaction between the baroclinic wave and zonal-mean state (total zonal-mean flow velocity and buoyancy stratification) but the timescale of the nonlinear oscillations is largely controlled by the diffusivity. When the boundary condition is non-slip, the nonlinear oscillations are further damped and slowed by the diffusive process. Since the free-slip (non-slip) boundary condition is the zero drag (infinite drag) limit of the more realistic drag boundary condition, the nonlinear oscillations obtained with the two types of boundary conditions are two extremes for more realistic nonlinear oscillations.
On the Stability of Self-Similar Solutions to Nonlinear Wave Equations
NASA Astrophysics Data System (ADS)
Costin, Ovidiu; Donninger, Roland; Glogić, Irfan; Huang, Min
2016-04-01
We consider an explicit self-similar solution to an energy-supercritical Yang-Mills equation and prove its mode stability. Based on earlier work by one of the authors, we obtain a fully rigorous proof of the nonlinear stability of the self-similar blowup profile. This is a large-data result for a supercritical wave equation. Our method is broadly applicable and provides a general approach to stability problems related to self-similar solutions of nonlinear wave equations.
A nonlinear acoustic metamaterial: Realization of a backwards-traveling second-harmonic sound wave.
Quan, Li; Qian, Feng; Liu, Xiaozhou; Gong, Xiufen
2016-06-01
An ordinary waveguide with periodic vibration plates and side holes can realize an acoustic metamaterial that simultaneously possesses a negative bulk modulus and a negative mass density. The study is further extended to a nonlinear case and it is predicted that a backwards-traveling second-harmonic sound wave can be obtained through the nonlinear propagation of a sound wave in such a metamaterial.
A nonlinear acoustic metamaterial: Realization of a backwards-traveling second-harmonic sound wave.
Quan, Li; Qian, Feng; Liu, Xiaozhou; Gong, Xiufen
2016-06-01
An ordinary waveguide with periodic vibration plates and side holes can realize an acoustic metamaterial that simultaneously possesses a negative bulk modulus and a negative mass density. The study is further extended to a nonlinear case and it is predicted that a backwards-traveling second-harmonic sound wave can be obtained through the nonlinear propagation of a sound wave in such a metamaterial. PMID:27369164
Analytical solutions and rogue waves in (3+1)-dimensional nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Ma, Zheng-Yi; Ma, Song-Hua
2012-03-01
Analytical solutions in terms of rational-like functions are presented for a (3+1)-dimensional nonlinear Schrödinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.
New solitary wave solutions of some nonlinear evolution equations with distinct physical structures
NASA Astrophysics Data System (ADS)
Sakthivel, Rathinasamy; Chun, Changbum
2008-12-01
In this paper, we obtain solitary wave solutions for some nonlinear partial differential equations. The Exp-function method is used to establish solitary wave solutions for Calogero-Bogoyavlenskii-Schiff and general modified Degasperis-Procesi and Camassa-Holm equations. The result shows that the Exp-function method yields new and more general solutions. Moreover, this method with the aid of symbolic computation provides a very effective and powerful mathematical tool for solving nonlinear evolution equations arising in mathematical physics.
Wave breaking of nonlinear electron oscillations in a warm magnetized plasma
Pramanik, Sourav; Maity, Chandan; Chakrabarti, Nikhil
2014-02-15
Wave breaking phenomena of nonlinear electron oscillations around a homogeneous background of massive ions have been studied in a warm magnetized plasma by using Lagrangian variables. An inhomogeneity in the background magnetic field is shown to induce phase mixing and thus breaking of the oscillations. A nonlinear analysis in Lagrangian variables predicts that wave breaking may disappear above a critical value of the electron temperature. An estimate for the critical temperature has been provided.
Hong, Ming; Su, Zhongqing; Wang, Qiang; Cheng, Li; Qing, Xinlin
2014-03-01
A dedicated modeling technique for comprehending nonlinear characteristics of ultrasonic waves traversing in a fatigued medium was developed, based on a retrofitted constitutive relation of the medium by considering the nonlinearities originated from material, fatigue damage, as well as the "breathing" motion of fatigue cracks. Piezoelectric wafers, for exciting and acquiring ultrasonic waves, were integrated in the model. The extracted nonlinearities were calibrated by virtue of an acoustic nonlinearity parameter. The modeling technique was validated experimentally, and the results showed satisfactory consistency in between, both revealing: the developed modeling approach is able to faithfully simulate fatigue crack-incurred nonlinearities manifested in ultrasonic waves; a cumulative growth of the acoustic nonlinearity parameter with increasing wave propagation distance exists; such a parameter acquired via a sensing path is nonlinearly related to the offset distance from the fatigue crack to that sensing path; and neither the incidence angle of the probing wave nor the length of the sensing path impacts on the parameter significantly. This study has yielded a quantitative characterization strategy for fatigue cracks using embeddable piezoelectric sensor networks, facilitating deployment of structural health monitoring which is capable of identifying small-scale damage at an embryo stage and surveilling its growth continuously.
On the spectral-spatial instability of a light wave in a medium with cubic nonlinearity
Afanas'ev, Anatolii A; Volkov, V M
2003-11-30
Based on the analysis of frequency-nondegenerate four-photon parametric scattering, the spectral-angular dependences of the increments of perturbing modes are obtained in the field of an intense light wave propagating in a medium with cubic nonlinearity. (nonlinear optical phenomena)
Is DNA a nonlinear dynamical system where solitary conformational waves are possible?
Yakushevich, L V
2001-09-01
DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The history of the approach, the main results, and arguments in favour and against are presented. Perspectives are discussed pertaining to studies of DNA's nonlinear properties. PMID:11568475
Nonlinear effects associated with the dispersive Alfven waves in space plasmas
Kumar, Sanjay; Sharma, R. P.
2010-03-15
This paper presents the model equations governing the nonlinear dynamics of the dispersive Alfven wave (DAW) in the low-beta plasmas (beta<
Nonlinear internal tidal waves in a semi-enclosed sea (Gulf of California)
NASA Astrophysics Data System (ADS)
Novotryasov, Vadim; Filonov, Anatoliy; Lavín, Miguel F.
2011-12-01
This paper studies the nonlinear transformation of the semidiurnal internal tidal waves in the northern Gulf of California, based on spectral analysis of temperature and current fluctuations from moored instruments, and analytical simulation. Observations showed that: (a) The spectrum presented a quasilinear structure with peaks at frequencies ωn = n ω0, where ω0 is the frequency of the tidal harmonic M2 and n = 1, 2… is the subharmonics number. (b) The amplitudes of the even subharmonics M4 and M8 were of the same order, as were those of the odd subharmonics M6 and M10, but the last two were larger. (c) The energy of the subharmonics decreased as ω-3 with increasing n. These features were simulated by an analytical model spectrum of nonlinear internal waves; it produced a line structure formed by the harmonics whose energy depends on the distance traveled by the wave from the area of generation. In the approximation of quadratic nonlinearity, the spectrum of nonlinear long internal waves in the zone of wave breaking is asymptotically ˜ωn-2,6. Allowance for cubic nonlinearity leads to a non-monotonic decay of subharmonics energy depending on their number n, similar to the observed spectrum, which indicates that the internal semidiurnal tide in the northern Gulf of California is a cubically nonlinear wave.
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients.
Abdel-Gawad, Hamdy I; Osman, Mohamed
2015-07-01
In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg-de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE's.
Shukla, P K; Eliasson, B
2007-08-31
We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schrödinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.
Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves.
Bayındır, Cihan
2016-02-25
In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions.
The evolution of nonlinear Alfven waves subject to growth and damping
NASA Technical Reports Server (NTRS)
Spangler, S. R.
1986-01-01
The effects of wave amplification (by streaming particle distributions) and damping (by ion-cyclotron resonance absorption) on the nonlinear evolution of Alfven waves are investigated theoretically. The results of numerical simulations based on the derivative-Schroedinger-equation model of Spangler and Sheerin (1983 and 1985) are presented graphically and characterized in detail, with an emphasis on astrophysical applications. Three phases of wave-packet evolution (linear, nonlinear-saturation, and postsaturation quasi-steady) are identified, and nonlinearity is found to transfer wave energy from growing or amplified wavenumbers to wavenumbers affected by damping. It is pointed out that although there are similarities between the solitonlike pulses predicted by the simulations and short-wavelength shocklet structures observed in the earth bow shock, the model does not explain why low-frequency waves stop growing in the vicinity of the bow shock.
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients
Abdel-Gawad, Hamdy I.; Osman, Mohamed
2014-01-01
In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg–de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE’s. PMID:26199750
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients.
Abdel-Gawad, Hamdy I; Osman, Mohamed
2015-07-01
In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg-de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE's. PMID:26199750
Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves.
Bayındır, Cihan
2016-01-01
In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions. PMID:26911357
Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves
Bayındır, Cihan
2016-01-01
In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions. PMID:26911357
Nonlinear interaction of near-planar TS waves and longitudinal vortices in boundary-layer transition
NASA Technical Reports Server (NTRS)
Smith, F. T.
1988-01-01
The nonlinear interactions that evolve between a planar or nearly planar Tollmien-Schlichting (TS) wave and the associated longitudinal vortices are considered theoretically for a boundary layer at high Reynolds number. The vortex flow is either induced by the TS nonlinear forcing or is input upstream, and similarly for the nonlinear wave development. Three major kinds of nonlinear spatial evolution, Types 1-3, are found. Each can start from secondary instability and then become nonlinear, Type 1 proving to be relatively benign but able to act as a pre-cursor to the Types 2, 3 which turn out to be very powerful nonlinear interactions. Type 2 involves faster stream-wise dependence and leads to a finite-distance blow-up in the amplitudes, which then triggers the full nonlinear 3-D triple-deck response, thus entirely altering the mean-flow profile locally. In contrast, Type 3 involves slower streamwise dependence but a faster spanwise response, with a small TS amplitude thereby causing an enhanced vortex effect which, again, is substantial enough to entirely alter the meanflow profile, on a more global scale. Streak-like formations in which there is localized concentration of streamwise vorticity and/or wave amplitude can appear, and certain of the nonlinear features also suggest by-pass processes for transition and significant changes in the flow structure downstream. The powerful nonlinear 3-D interactions 2, 3 are potentially very relevant to experimental findings in transition.
Fatigue damage localization using time-domain features extracted from nonlinear Lamb waves
NASA Astrophysics Data System (ADS)
Hong, Ming; Su, Zhongqing; Lu, Ye; Cheng, Li
2014-03-01
Nonlinear guided waves are sensitive to small-scale fatigue damage that may hardly be identified by traditional techniques. A characterization method for fatigue damage is established based on nonlinear Lamb waves in conjunction with the use of a piezoelectric sensor network. Theories on nonlinear Lamb waves for damage detection are first introduced briefly. Then, the ineffectiveness of using pure frequency-domain information of nonlinear wave signals for locating damage is discussed. With a revisit to traditional gross-damage localization techniques based on the time of flight, the idea of using temporal signal features of nonlinear Lamb waves to locate fatigue damage is introduced. This process involves a time-frequency analysis that enables the damage-induced nonlinear signal features, which are either undiscernible in the original time history or uninformative in the frequency spectrum, to be revealed. Subsequently, a finite element modeling technique is employed, accounting for various sources of nonlinearities in a fatigued medium. A piezoelectric sensor network is configured to actively generate and acquire probing Lamb waves that involve damageinduced nonlinear features. A probability-based diagnostic imaging algorithm is further proposed, presenting results in diagnostic images intuitively. The approach is experimentally verified on a fatigue-damaged aluminum plate, showing reasonably good accuracy. Compared to existing nonlinear ultrasonics-based inspection techniques, this approach uses a permanently attached sensor network that well accommodates automated online health monitoring; more significantly, it utilizes time-domain information of higher-order harmonics from time-frequency analysis, and demonstrates a great potential for quantitative characterization of small-scale damage with improved localization accuracy.
Slabko, Vitaly V; Popov, Alexander K; Tkachenko, Viktor A; Myslivets, Sergey A
2016-09-01
Three-wave mixing of ordinary and backward electromagnetic waves in a pulsed regime is investigated in the metamaterials that enable the coexistence and phase-matching of such waves. It is shown that the opposite direction of phase velocity and energy flux in backward waves gives rise to extraordinary transient processes due to greatly enhanced optical parametric amplification and frequency up- and down-shifting nonlinear reflectivity. The differences are illustrated through comparison with the counterparts in ordinary, co-propagating settings. PMID:27607951
NASA Astrophysics Data System (ADS)
Rauter, N.; Lammering, R.
2015-04-01
In order to detect micro-structural damages accurately new methods are currently developed. A promising tool is the generation of higher harmonic wave modes caused by the nonlinear Lamb wave propagation in plate like structures. Due to the very small amplitudes a cumulative effect is used. To get a better overview of this inspection method numerical simulations are essential. Previous studies have developed the analytical description of this phenomenon which is based on the five-constant nonlinear elastic theory. The analytical solution has been approved by numerical simulations. In this work first the nonlinear cumulative wave propagation is simulated and analyzed considering micro-structural cracks in thin linear elastic isotropic plates. It is shown that there is a cumulative effect considering the S1-S2 mode pair. Furthermore the sensitivity of the relative acoustical nonlinearity parameter regarding those damages is validated. Furthermore, an influence of the crack size and orientation on the nonlinear wave propagation behavior is observed. In a second step the micro-structural cracks are replaced by a nonlinear material model. Instead of the five-constant nonlinear elastic theory hyperelastic material models that are implemented in commonly used FEM software are used to simulate the cumulative effect of the higher harmonic Lamb wave generation. The cumulative effect as well as the different nonlinear behavior of the S1-S2 and S2-S4 mode pairs are found by using these hyperelastic material models. It is shown that, both numerical simulations, which take into account micro-structural cracks on the one hand and nonlinear material on the other hand, lead to comparable results. Furthermore, in comparison to the five-constant nonlinear elastic theory the use of the well established hyperelastic material models like Neo-Hooke and Mooney-Rivlin are a suitable alternative to simulate the cumulative higher harmonic generation.
Chatterjee, Debjani; Misra, A P
2015-12-01
The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' q-nonextensive statistics. In particular, the previous linear theory of Langmuir oscillations in EP plasmas [Saberian and Esfandyari-Kalejahi, Phys. Rev. E 87, 053112 (2013)] is rectified and modified. Applying the multiple scale technique (MST), it is shown that the evolution of electrostatic wave envelopes is governed by a nonlinear Schrödinger (NLS) equation with a nonlocal nonlinear term ∝P∫|ϕ(ξ',τ)|(2)dξ'ϕ/(ξ-ξ') [where P denotes the Cauchy principal value, ϕ is the small-amplitude electrostatic (complex) potential, and ξ and τ are the stretched coordinates in MST], which appears due to the wave-particle resonance. It is found that a subregion 1/3wave frequency can turn over with the group velocity going to zero and then to negative values. The effects of the nonlocal nonlinear term and the nonextensive parameter q are examined on the modulational instability of wave envelopes, as well as on the solitary wave solution of the NLS equation. It is found that the modulated wave packet is always unstable (nonlinear Landau damping) due to the nonlocal nonlinearity in the NLS equation. Furthermore, the effect of the nonlinear Landau damping is to slow down the amplitude of the wave envelope, and the corresponding decay rate can be faster the larger is the number of superthermal particles in pair plasmas.
Chatterjee, Debjani; Misra, A P
2015-12-01
The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' q-nonextensive statistics. In particular, the previous linear theory of Langmuir oscillations in EP plasmas [Saberian and Esfandyari-Kalejahi, Phys. Rev. E 87, 053112 (2013)] is rectified and modified. Applying the multiple scale technique (MST), it is shown that the evolution of electrostatic wave envelopes is governed by a nonlinear Schrödinger (NLS) equation with a nonlocal nonlinear term ∝P∫|ϕ(ξ',τ)|(2)dξ'ϕ/(ξ-ξ') [where P denotes the Cauchy principal value, ϕ is the small-amplitude electrostatic (complex) potential, and ξ and τ are the stretched coordinates in MST], which appears due to the wave-particle resonance. It is found that a subregion 1/3wave frequency can turn over with the group velocity going to zero and then to negative values. The effects of the nonlocal nonlinear term and the nonextensive parameter q are examined on the modulational instability of wave envelopes, as well as on the solitary wave solution of the NLS equation. It is found that the modulated wave packet is always unstable (nonlinear Landau damping) due to the nonlocal nonlinearity in the NLS equation. Furthermore, the effect of the nonlinear Landau damping is to slow down the amplitude of the wave envelope, and the corresponding decay rate can be faster the larger is the number of superthermal particles in pair plasmas. PMID:26764841
NASA Astrophysics Data System (ADS)
Chatterjee, Debjani; Misra, A. P.
2015-12-01
The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' q -nonextensive statistics. In particular, the previous linear theory of Langmuir oscillations in EP plasmas [Saberian and Esfandyari-Kalejahi, Phys. Rev. E 87, 053112 (2013), 10.1103/PhysRevE.87.053112] is rectified and modified. Applying the multiple scale technique (MST), it is shown that the evolution of electrostatic wave envelopes is governed by a nonlinear Schrödinger (NLS) equation with a nonlocal nonlinear term ∝P ∫|ϕ (ξ',τ ) |2d ξ'ϕ /(ξ -ξ') [where P denotes the Cauchy principal value, ϕ is the small-amplitude electrostatic (complex) potential, and ξ and τ are the stretched coordinates in MST], which appears due to the wave-particle resonance. It is found that a subregion 1 /3 wave frequency can turn over with the group velocity going to zero and then to negative values. The effects of the nonlocal nonlinear term and the nonextensive parameter q are examined on the modulational instability of wave envelopes, as well as on the solitary wave solution of the NLS equation. It is found that the modulated wave packet is always unstable (nonlinear Landau damping) due to the nonlocal nonlinearity in the NLS equation. Furthermore, the effect of the nonlinear Landau damping is to slow down the amplitude of the wave envelope, and the corresponding decay rate can be faster the larger is the number of superthermal particles in pair plasmas.
Nonlinear waves on the free surface of a dielectric liquid in an oblique electric field
Gashkov, M. A.; Zubarev, N. M. Kochurin, E. A.
2015-09-15
The nonlinear dynamics of the free surface of an ideal dielectric liquid that is exposed to an external oblique electric field has been studied theoretically. In the framework of the Hamiltonian formalism, a system of nonlinear integro-differential equations has been derived that describes the dynamics of nonlinear waves in the small-angle approximation. It is established that for a liquid with high dielectric permittivity, these equations have a solution in the form of plane waves of arbitrary shape that propagate without distortion in the direction of the horizontal component of the external field.
General analytic results for nonlinear waves and solitons in molecular clouds
NASA Technical Reports Server (NTRS)
Adams, Fred C.; Fatuzzo, Marco; Watkins, Richard
1994-01-01
We study nonlinear wave phenomena in self-gravitating fluid systems, with a particular emphasis on applications to molecular clouds. This paper presents analytical results for one spatial dimension. We show that a large class of physical systems can be described by theories with a 'charge density' q(rho); this quantity replaces the density on the right-hand side of the Poisson equation for the gravitational potential. We use this formulation to prove general results about nonlinear wave motions in self-gravitating systems. We show that in order for stationary waves to exist, the total charge (the integral of the charge density over the wave profile) must vanish. This 'no-charge' property for solitary waves is related to the capability of a system to be stable to gravitational perturbations for arbitrarily long wavelengths. We find necessary and sufficient conditions on the charge density for the existence of solitary waves and stationary waves. We study nonlinear wave motions for Jeans-type theories (where q(rho) = rho-rho(sub 0)) and find that nonlinear waves of large amplitude are confined to a rather narrow range of wavelengths. We also study wave motions for molecular clouds threaded by magnetic fields and show how the allowed range of wavelengths is affected by the field strength. Since the gravitational force in one spatial dimension does not fall off with distance, we consider two classes of models with more realistic gravity: Yukawa potentials and a pseudo two-dimensional treatment. We study the allowed types of wave behavior for these models. Finally, we discuss the implications of this work for molecular cloud structure. We argue that molecular clouds can support a wide variety of wave motions and suggest that stationary waves (such as those considered in this paper) may have already been observed.
Dissipative effects on nonlinear waves in rotating fluids.
NASA Technical Reports Server (NTRS)
Leibovich, S.; Randall, J. D.
1971-01-01
Modifications to the existing inviscid theory of long-wave propagation in rotating fluids are studied. A modification to the Korteweg-deVries equation is found to describe weak dissipation in long waves in a swirling fluid. General features of solutions are discussed, and a solution for the damping of solitary waves is presented.
NASA Astrophysics Data System (ADS)
Schönecker, Stephan; Li, Xiaoqing; Johansson, Börje; Vitos, Levente
2016-08-01
The strained Fe-Co alloy in body-centered tetragonal (bct) structure has raised considerable interest due to its giant uniaxial magnetocrystalline anisotropy energy. On the basis of the classical Heisenberg Hamiltonian with ab initio interatomic exchange interactions, we perform a theoretical study of fundamental finite temperature magnetic properties of Fe1 -xCox alloy films as a function of three variables: chemical composition 0.3 ≤x ≤0.8 , bct geometry [a ,c (a )] arising from in-plane strain and associated out-of-plane relaxation, and atomic long-range order (ALRO). The Curie temperatures TC(x ,a ) obtained from Monte Carlo simulations display a competition between a pronounced dependence on tetragonality, strong ferromagnetism in the Co-rich alloy, and the beginning instability of ferromagnetic order in the Fe-rich alloy when c /a →√{2 } . Atomic ordering enhances TC and arises mainly due to different distributions of atoms in neighboring coordination shells rather than altering exchange interactions significantly. We investigate the ordering effect on the shape of the adiabatic spin-wave spectrum for selected pairs (x ,a ) . Our results indicate that long-wavelength acoustic spin-wave excitations show dependencies on x , a , and ALRO similar to those of TC. The directional anisotropy of the spin-wave stiffness d (x ,a ) peaks in narrow ranges of composition and tetragonality. ALRO exhibits a strong effect on d for near equiconcentration Fe-Co. We also discuss our findings in the context of employing Fe-Co as perpendicular magnetic recording medium.
Startup of distillation columns using profile position control based on nonlinear wave model
Han, M.; Park, S. |
1999-04-01
Startup of distillation columns is a very challenging control problem because of its strong nonlinearity and a wide operating range during the transient period. A nonlinear wave model captures the essential dynamic behavior of the distillation process so that it is possible to deal with the difficulties encountered during startup operation. This paper is concerned with the startup of distillation systems using nonlinear wave model based control developed by Han and Park. This control scheme uses profile positions as controlled variables and is based on the nonlinear wave model by Hwang and generic model control scheme by Lee and Sullivan. It can be applied to a binary or a multicomponent distillation system that can be represented as a pseudobinary. The proposed control scheme is shown by simulation studies to provide a safe and economic startup operation not only for dual composition control of a simple distillation column but also for a complex distillation configuration.
NASA Technical Reports Server (NTRS)
Mcdonald, B. Edward; Plante, Daniel R.
1989-01-01
The nonlinear progressive wave equation (NPE) model was developed by the Naval Ocean Research and Development Activity during 1982 to 1987 to study nonlinear effects in long range oceanic propagation of finite amplitude acoustic waves, including weak shocks. The NPE model was applied to propagation of a generic shock wave (initial condition provided by Sandia Division 1533) in a few illustrative environments. The following consequences of nonlinearity are seen by comparing linear and nonlinear NPE results: (1) a decrease in shock strength versus range (a well-known result of entropy increases at the shock front); (2) an increase in the convergence zone range; and (3) a vertical meandering of the energy path about the corresponding linear ray path. Items (2) and (3) are manifestations of self-refraction.
Delrue, Steven; Van Den Abeele, Koen
2015-12-01
Interaction of ultrasonic guided waves with kissing bonds (closed delaminations and incipient surface breaking cracks) gives rise to nonlinear features at the defect location. This causes higher harmonic frequency ultrasonic radiation into the ambient air, often referred to as Nonlinear Air-Coupled Emission (NACE), which may serve as a nonlinear tag to detect the defects. This paper summarizes the results of a numerical implementation and simulation study of NACE. The developed model combines a 3D time domain model for the nonlinear Lamb wave propagation in delaminated samples with a spectral solution for the nonlinear air-coupled emission. A parametric study is conducted to illustrate the potential of detecting defect location, size and shape by studying the NACE acoustic radiation patterns in different orientation planes. The simulation results prove that there is a good determination potential for the defect parameters, especially when the radiated frequency matches one of the resonance frequencies of the delaminated layer, leading to a Local Defect Resonance (LDR). PMID:26208725
Detection and analysis of coherent groups in three-dimensional fully-nonlinear potential wave fields
NASA Astrophysics Data System (ADS)
Sanina, E. V.; Suslov, S. A.; Chalikov, D.; Babanin, A. V.
2016-07-01
We investigate the emergence of coherent groups in three-dimensional fully-nonlinear potential deep water waves whose initial spectrum is assumed to be of the JONSWAP type with directional distribution given by cos nθ, where n is the integer varying from 1 to 16. The analysis is based on the results of long-term wave simulations performed using a numerical solution of a three-dimensional Laplace equation for the velocity potential subject to nonlinear kinematic and dynamic boundary conditions at the free surface. The main characteristics of wave groups such as their average velocity, maximum group wave height, lifetime and length are analysed. The statistics of extreme waves occurring in the detected groups are discussed. Spatial and temporal scale characteristics of wave groups are compared to the previous results.
Nonlinear damping of a finite amplitude whistler wave due to modified two stream instability
Saito, Shinji; Nariyuki, Yasuhiro; Umeda, Takayuki
2015-07-15
A two-dimensional, fully kinetic, particle-in-cell simulation is used to investigate the nonlinear development of a parallel propagating finite amplitude whistler wave (parent wave) with a wavelength longer than an ion inertial length. The cross field current of the parent wave generates short-scale whistler waves propagating highly oblique directions to the ambient magnetic field through the modified two-stream instability (MTSI) which scatters electrons and ions parallel and perpendicular to the magnetic field, respectively. The parent wave is largely damped during a time comparable to the wave period. The MTSI-driven damping process is proposed as a cause of nonlinear dissipation of kinetic turbulence in the solar wind.
Kim, Kihong; Phung, D K; Rotermund, F; Lim, H
2008-01-21
We develop a generalized version of the invariant imbedding method, which allows us to solve the electromagnetic wave equations in arbitrarily inhomogeneous stratified media where both the dielectric permittivity and magnetic permeability depend on the strengths of the electric and magnetic fields, in a numerically accurate and efficient manner. We apply our method to a uniform nonlinear slab and find that in the presence of strong external radiation, an initially uniform medium of positive refractive index can spontaneously change into a highly inhomogeneous medium where regions of positive or negative refractive index as well as metallic regions appear. We also study the wave transmission properties of periodic nonlinear media and the influence of nonlinearity on the mode conversion phenomena in inhomogeneous plasmas. We argue that our theory is very useful in the study of the optical properties of a variety of nonlinear media including nonlinear negative index media fabricated using wires and split-ring resonators.
TRIADS: A phase-resolving model for nonlinear shoaling of directional wave spectra
NASA Astrophysics Data System (ADS)
Sheremet, Alex; Davis, Justin R.; Tian, Miao; Hanson, Jeffrey L.; Hathaway, Kent K.
2016-03-01
We investigate the performance of TRIADS, a numerical implementation of a phase-resolving, nonlinear, spectral model describing directional wave evolution in intermediate and shallow water. TRIADS simulations of shoaling waves generated by Hurricane Bill, 2009 are compared to directional spectral estimates based on observations collected at the Field Research Facility of the US Army Corps Of Engineers, at Duck, NC. Both the ability of the model to capture the processes essential to the nonlinear wave evolution, and the efficiency of the numerical implementations are analyzed and discussed.
Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis
NASA Astrophysics Data System (ADS)
Li, Tong; Wang, Zhi-An
In this paper, we establish the existence and the nonlinear stability of traveling wave solutions to a system of conservation laws which is transformed, by a change of variable, from the well-known Keller-Segel model describing cell (bacteria) movement toward the concentration gradient of the chemical that is consumed by the cells. We prove the existence of traveling fronts by the phase plane analysis and show the asymptotic nonlinear stability of traveling wave solutions without the smallness assumption on the wave strengths by the method of energy estimates.
Nonlinear propagation of electromagnetic waves in a plasma containing random irregularities.
NASA Technical Reports Server (NTRS)
Liu, C. H.
1973-01-01
The problem of propagation of finite-amplitude electromagnetic waves in a plasma containing random irregularities is studied. Using a recently developed perturbation technique, a general equation for finite amplitude coherent waves is derived. Included in this equation are both the effects of quasi-harmonic nonlinear heating of electrons and random scattering by irregularities. The equation is solved in general by the equivalent linearization procedure. The amplitude of the coherent wave is found to be attenuated by collision and scattering. Both attenuation are affected by the nonlinear heating of the electrons. Curves showing the results for a specific example will be presented.
Weakly nonlinear ion-sound waves in inhomogeneous electron temperature, magnetized plasmas
NASA Astrophysics Data System (ADS)
Pecseli, H. L.; Guio, P.
2009-12-01
Low frequency electrostatic waves are studied in magnetized plasmas for the case where the electron temperature varies with position in a direction perpendicular to the magnetic field. We analyze guided waves with characteristic frequencies below the ion cyclotron and ion plasma frequencies. A Korteweg-deVries equation is derived for the weakly nonlinear waves, and the results compared to numerical simulations. We study two different models for the electron distribution: one where the electrons are assumed to be in local Boltzmann equilibrium at all times, while the other model assumes a nonthermal-distribution for the electrons. The nonlinear space-time evolution of the electrostatic potential differs for the two cases.
Nonlinear shear wave in a non Newtonian visco-elastic medium
Banerjee, D.; Janaki, M. S.; Chakrabarti, N.
2012-06-15
An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau-Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries equation. This model has application from laboratory to astrophysical plasmas as well as in biological systems.
Difference-frequency generation in nonlinear scattering of acoustic waves by a rigid sphere.
Silva, Glauber T; Bandeira, Anderson
2013-02-01
In this paper, the partial-wave expansion method is applied to describe the difference-frequency pressure generated in a nonlinear scattering of two acoustic waves with an arbitrary wavefront by means of a rigid sphere. Particularly, the difference-frequency generation is analyzed in the nonlinear scattering with a spherical scatterer involving two intersecting plane waves in the following configurations: collinear, crossing at right angles, and counter-propagating. For the sake of simplicity, the plane waves are assumed to be spatially located in a spherical region which diameter is smaller than the difference-frequency wavelength. Such arrangements can be experimentally accomplished in vibro-acoustography and nonlinear acoustic tomography techniques. It turns out to be that when the sphere radius is of the order of the primary wavelengths, and the downshift ratio (i.e. the ratio between the fundamental frequency and the difference-frequency) is larger than five, difference-frequency generation is mostly due to a nonlinear interaction between the primary scattered waves. The exception to this is the collinear scattering for which the nonlinear interaction of the primary incident waves is also relevant. In addition, the difference-frequency scattered pressure in all scattering configurations decays as r(-1)lnr and 1/r, where r is the radial distance from the scatterer to the observation point.
Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma
NASA Astrophysics Data System (ADS)
Ghosh, Samiran; Chakrabarti, Nikhil
2016-08-01
The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev-Petviashvili solitons.
Nonlinear disintegration of sine wave in the framework of the Gardner equation
NASA Astrophysics Data System (ADS)
Kurkin, Andrey; Talipova, Tatiana; Kurkina, Oxana; Rouvinskaya, Ekaterina; Pelinovsky, Efim
2016-04-01
Nonlinear disintegration of sine wave is studied in the framework of the Gardner equation (extended version of the Korteweg - de Vries equation with both quadratic and cubic nonlinear terms). Undular bores appear here as an intermediate stage of wave evolution. Our numerical computations demonstrate the features of undular bore developing for different signs of the cubic nonlinear term. If cubic nonlinear term is negative, and initial wave amplitude is large enough, two undular bores are generated from the two breaking points formed on both crest slopes (within dispersionless Gardner equation). Undular bore consists of one table-top soliton and a group of small soliton-like waves passing through the table-top soliton. If the cubic nonlinear term is positive and again the wave amplitude is large enough, the breaking points appear on crest and trough generating groups of positive and negative solitary-like pulses. It is shown that nonlinear interaction of waves happens according to one of scenarios of two-soliton interaction of "exchange" or "overtake" types with a phase shift. If small-amplitude pulses interact with large-amplitude soliton-like pulses, their speed in average is negative in the case when "free" velocity is positive. Nonlinear interaction leads to the generation of higher harmonics and spectrum width increases with amplitude increase independently of the sign of cubic nonlinear term. The breaking asymptotic k4/3 predicted within the dispersionless Gardner equation emerges during the process of undular bore development. The formation of soliton-like perturbations leads to appearance of several spectral peaks which are downshifting with time.
Nonlinear wave propagation in a strongly coupled collisional dusty plasma
Ghosh, Samiran; Gupta, Mithil Ranjan; Chakrabarti, Nikhil; Chaudhuri, Manis
2011-06-15
The propagation of a nonlinear low-frequency mode in a strongly coupled dusty plasma is investigated using a generalized hydrodynamical model. For the well-known longitudinal dust acoustic mode a standard perturbative approach leads to a Korteweg-de Vries (KdV) soliton. The strong viscoelastic effect, however, introduced a nonlinear forcing and a linear damping in the KdV equation. This novel equation is solved analytically to show a competition between nonlinear forcing and dissipative damping. The physical consequence of such a solution is also sketched.
Nonlinear wave propagation in a strongly coupled collisional dusty plasma.
Ghosh, Samiran; Gupta, Mithil Ranjan; Chakrabarti, Nikhil; Chaudhuri, Manis
2011-06-01
The propagation of a nonlinear low-frequency mode in a strongly coupled dusty plasma is investigated using a generalized hydrodynamical model. For the well-known longitudinal dust acoustic mode a standard perturbative approach leads to a Korteweg-de Vries (KdV) soliton. The strong viscoelastic effect, however, introduced a nonlinear forcing and a linear damping in the KdV equation. This novel equation is solved analytically to show a competition between nonlinear forcing and dissipative damping. The physical consequence of such a solution is also sketched. PMID:21797497
Covariances and spectra of the kinematics and dynamics of nonlinear waves
NASA Technical Reports Server (NTRS)
Tung, C. C.; Huang, N. E.
1985-01-01
Using the Stokes waves as a model of nonlinear waves and considering the linear component as a narrow-band Gaussian process, the covariances and spectra of velocity and acceleration components and pressure for points in the vicinity of still water level were derived taking into consideration the effects of free surface fluctuations. The results are compared with those obtained earlier using linear Gaussian waves.
Nonlinear evolution of a large-amplitude circularly polarized Alfven wave: High beta
NASA Technical Reports Server (NTRS)
Ghosh, S.; Vinas, A. F.; Goldstein, M. L.
1994-01-01
The nonlinear dynamics following saturation of the parametric instabilities of a monochromatic field-aligned large-amplitude circularly polarized Alfven wave is investigated via direct numerical simulation in the case of high plasma beta and no wave dispersion. The magnetohydrodynamic (MHD) code permits nonlinear couplings in the parallel direction to the ambient magnetic field and one perpendicular direction. Compressibility is included in the form of a polytropic equation of state. Turbulent cascades develop after saturation of two coupled oblique three-wave parametric instabilities; one of which is an oblique filamentationlike instability reported earlier. Remnants of the parametric processes, as well as of the original Alfven pump wave, persist during late nonlinear times. Nearly incompressible MHD features such as spectral anisotropies appear as well.
Evolution of nonlinear ion-acoustic solitary wave propagation in rotating plasma
Das, G. C.; Nag, Apratim
2006-08-15
A simple unmagnetized plasma rotating around an axis at an angle {theta} with the propagation direction of the acoustic mode has been taken. The nonlinear wave mode has been derived as an equivalent Sagdeev potential equation. A special procedure, known as the tanh method, has been developed to study the nonlinear wave propagation in plasma dynamics. Further, under small amplitude approximation, the nonlinear plasma acoustic mode has been exploited to study the evolution of soliton propagation in the plasma. The main emphasis has been given to the interaction of Coriolis force on the changes of coherent structure of the soliton. The solitary wave solution finds the different nature of solitons called compressive and rarefactive solitons as well as its explosions or collapses along with soliton dynamics and these have been showing exciting observations in exhibiting a narrow wave packet with the generation of high electric pressure and the growth of high energy which, in turn, yields the phenomena of radiating soliton in dynamics.
NASA Astrophysics Data System (ADS)
Wang, Bin; Su, Zhenpeng; Zhang, Yan; Shi, Shengwei; Wang, Geng
2016-04-01
In response to solar wind disturbances, radiation belt (a few hundreds of keV to several MeV) electron fluxes can be depleted significantly over the entire equatorial pitch angle range. The frequently mentioned cyclotron resonant scattering is applicable only for electrons mirroring off the equator. Here we propose a new physical mechanism, nonlinear Landau resonance with oblique electromagnetic ion cyclotron (EMIC) waves, to effectively scatter the near equatorially mirroring electrons. Our test particle simulations show that the nonlinear Landau trapping can occur over a wide energy range and yield the net decrease in equatorial pitch angle Δαeq≈10° within several seconds. Our parametric studies further reveal that this nonlinear Landau-trapping process is favored by a low plasma density, an intense wave field, a high wave frequency close to ion gyrofrequencies, and a large wave normal angle.
Nonlinear modulation of an extraordinary wave under the conditions of parametric decay
Dorofeenko, V. G.; Krasovitskiy, V. B.; Turikov, V. A.
2012-06-15
A self-consistent set of Hamilton equations describing nonlinear saturation of the amplitude of oscillations excited under the conditions of parametric decay of an elliptically polarized extraordinary wave in cold plasma is solved analytically and numerically. It is shown that the exponential increase in the amplitude of the secondary wave excited at the half-frequency of the primary wave changes into a reverse process in which energy is returned to the primary wave and nonlinear oscillations propagating across the external magnetic field are generated. The system of 'slow' equations for the amplitudes, obtained by averaging the initial equations over the high-frequency period, is used to describe steady-state nonlinear oscillations in plasma.
Shortcuts to adiabaticity in quantum many-body systems: a quantum dynamical microscope
NASA Astrophysics Data System (ADS)
Del Campo, Adolfo
2014-03-01
The evolution of a quantum system induced by a shortcut to adiabaticity mimics the adiabatic dynamics without the requirement of slow driving. Engineering it involves diagonalizing the instantaneous Hamiltonian of the system and results in the need of auxiliary non-local interactions for matter-waves. Here experimentally realizable driving protocols are found for a large class of single-particle, many-body, and non-linear systems without demanding the spectral properties as an input. The method is applied to the expansion of a trapped ultracold gas which spatially scales up the size of the cloud while conserving the quantum correlations of the initial many-body state. This shortcut to adiabatic expansions acts as a quantum dynamical microscope.
Nonlinear propagation of Rossby-Khantadze electromagnetic planetary waves in the ionospheric E-layer
NASA Astrophysics Data System (ADS)
Futatani, S.; Horton, W.; Kaladze, T. D.
2013-10-01
Nonlinear vortex propagation of electromagnetic coupled Rossby and Khantadze planetary waves in the weakly ionized ionospheric E-layer is investigated with numerical simulations. Large scale, finite amplitude vortex structures are launched as initial conditions at low, mid, and high latitudes. For each k-vector the linear dispersion relation has two eigenmodes corresponding to the slow magnetized Rossby wave and the fast magnetic Khantadze wave. Both waves propagate westward with local speeds of the order of 10-20 m/s for the slow wave and of the order of 500-1000 km/s for the fast wave. We show that for finite amplitudes there are dipole solitary structures emitted from the initial conditions. These structures are neutrally stable, nonlinear states that avoid radiating waves by propagating faster than the corresponding linear wave speeds. The condition for these coherent structures to occur is that their amplitudes are such that the nonlinear convection around the core of the disturbance is faster than the linear wave speed for the corresponding dominant Fourier components of the initial disturbance. The presence of the solitary vortex states is indicative of an initial strong disturbance such as that from a solar storm or a tectonic plate movement. We show that for generic, large amplitude initial disturbances both slow and fast vortex structures propagate out of the initial structure.
Ion-acoustic nonlinear periodic waves in electron-positron-ion plasma
Chawla, J. K.; Mishra, M. K.
2010-10-15
Ion-acoustic nonlinear periodic waves, namely, ion-acoustic cnoidal waves have been studied in electron-positron-ion plasma. Using reductive perturbation method and appropriate boundary condition for nonlinear periodic waves, the Korteweg-de Vries (KdV) equation is derived for the system. The cnoidal wave solution of the KdV equation is discussed in detail. It is found that the frequency of the cnoidal wave is a function of its amplitude. It is also found that the positron concentration modifies the properties of the ion-acoustic cnoidal waves. The existence regions for ion-acoustic cnoidal wave in the parameters space (p,{sigma}), where p and {sigma} are the positron concentration and temperature ratio of electron to positron, are discussed in detail. In the limiting case these ion-acoustic cnoidal waves reduce to the ion-acoustic soliton solutions. The effect of other parameters on the characteristics of the nonlinear periodic waves is also discussed.
Nonlinear propagation of Rossby-Khantadze electromagnetic planetary waves in the ionospheric E-layer
Futatani, S.; Horton, W.; Kaladze, T. D.
2013-10-15
Nonlinear vortex propagation of electromagnetic coupled Rossby and Khantadze planetary waves in the weakly ionized ionospheric E-layer is investigated with numerical simulations. Large scale, finite amplitude vortex structures are launched as initial conditions at low, mid, and high latitudes. For each k-vector the linear dispersion relation has two eigenmodes corresponding to the slow magnetized Rossby wave and the fast magnetic Khantadze wave. Both waves propagate westward with local speeds of the order of 10–20 m/s for the slow wave and of the order of 500–1000 km/s for the fast wave. We show that for finite amplitudes there are dipole solitary structures emitted from the initial conditions. These structures are neutrally stable, nonlinear states that avoid radiating waves by propagating faster than the corresponding linear wave speeds. The condition for these coherent structures to occur is that their amplitudes are such that the nonlinear convection around the core of the disturbance is faster than the linear wave speed for the corresponding dominant Fourier components of the initial disturbance. The presence of the solitary vortex states is indicative of an initial strong disturbance such as that from a solar storm or a tectonic plate movement. We show that for generic, large amplitude initial disturbances both slow and fast vortex structures propagate out of the initial structure.
Characterizing the nonlinear interaction of S- and P-waves in a rock sample
NASA Astrophysics Data System (ADS)
Gallot, Thomas; Malcolm, Alison; Szabo, Thomas L.; Brown, Stephen; Burns, Daniel; Fehler, Michael
2015-01-01
The nonlinear elastic response of rocks is known to be caused by the rocks' microstructure, particularly cracks and fluids. This paper presents a method for characterizing the nonlinearity of rocks in a laboratory scale experiment with a unique configuration. This configuration has been designed to open up the possibility of using the nonlinear characterization of rocks as an imaging tool in the field. In our experiment, we study the nonlinear interaction of two traveling waves: a low-amplitude 500 kHz P-wave probe and a high-amplitude 50 kHz S-wave pump in a room-dry 15 × 15 × 3 cm slab of Berea sandstone. Changes in the arrival time of the P-wave probe as it passes through the perturbation created by the traveling S-wave pump were recorded. Waveforms were time gated to simulate a semi-infinite medium. The shear wave phase relative to the P-wave probe signal was varied with resultant changes in the P-wave probe arrival time of up to 100 ns, corresponding to a change in elastic properties of 0.2%. In order to estimate the strain in our sample, we also measured the particle velocity at the sample surface to scale a finite difference linear elastic simulation to estimate the complex strain field in the sample, on the order of 10-6, induced by the S-wave pump. We derived a fourth order elastic model to relate the changes in elasticity to the pump strain components. We recover quadratic and cubic nonlinear parameters: β ˜ = - 872 and δ ˜ = - 1.1 × 10 10 , respectively, at room-temperature and when particle motions of the pump and probe waves are aligned. Temperature fluctuations are correlated to changes in the recovered values of β ˜ and δ ˜ , and we find that the nonlinear parameter changes when the particle motions are orthogonal. No evidence of slow dynamics was seen in our measurements. The same experimental configuration, when applied to Lucite and aluminum, produced no measurable nonlinear effects. In summary, a method of selectively determining the
Degenerate adiabatic perturbation theory: Foundations and applications
NASA Astrophysics Data System (ADS)
Rigolin, Gustavo; Ortiz, Gerardo
2014-08-01
We present details and expand on the framework leading to the recently introduced degenerate adiabatic perturbation theory [Phys. Rev. Lett. 104, 170406 (2010), 10.1103/PhysRevLett.104.170406], and on the formulation of the degenerate adiabatic theorem, along with its necessary and sufficient conditions [given in Phys. Rev. A 85, 062111 (2012), 10.1103/PhysRevA.85.062111]. We start with the adiabatic approximation for degenerate Hamiltonians that paves the way to a clear and rigorous statement of the associated degenerate adiabatic theorem, where the non-Abelian geometric phase (Wilczek-Zee phase) plays a central role to its quantitative formulation. We then describe the degenerate adiabatic perturbation theory, whose zeroth-order term is the degenerate adiabatic approximation, in its full generality. The parameter in the perturbative power-series expansion of the time-dependent wave function is directly associated to the inverse of the time it takes to drive the system from its initial to its final state. With the aid of the degenerate adiabatic perturbation theory we obtain rigorous necessary and sufficient conditions for the validity of the adiabatic theorem of quantum mechanics. Finally, to illustrate the power and wide scope of the methodology, we apply the framework to a degenerate Hamiltonian, whose closed-form time-dependent wave function is derived exactly, and also to other nonexactly solvable Hamiltonians whose solutions are numerically computed.
NASA Technical Reports Server (NTRS)
Goodrich, C. C.; Scudder, J. D.
1984-01-01
The adiabatic energy gain of electrons in the stationary electric and magnetic field structure of collisionless shock waves was examined analytically in reference to conditions of the earth's bow shock. The study was performed to characterize the behavior of electrons interacting with the cross-shock potential. A normal incidence frame (NIF) was adopted in order to calculate the reversible energy change across a time stationary shock, and comparisons were made with predictions made by the de Hoffman-Teller (HT) model (1950). The electron energy gain, about 20-50 eV, is demonstrated to be consistent with a 200-500 eV potential jump in the bow shock quasi-perpendicular geometry. The electrons lose energy working against the solar wind motional electric field. The reversible energy process is close to that modeled by HT, which predicts that the motional electric field vanishes and the electron energy gain from the electric potential is equated to the ion energy loss to the potential.
Spatial Frequency Clustering in Nonlinear Dust-Density Waves
Menzel, K. O.; Arp, O.; Piel, A.
2010-06-11
Self-excited density waves were studied in a strongly coupled dusty plasma of a radio-frequency discharge under microgravity conditions. The spatiotemporal evolution of the complicated three-dimensional wave field was investigated and analyzed for two different situations. The reconstructed instantaneous phase information of the wave field revealed a partial synchronization within multiple distinct domains. The boundaries of these regions coincide with the locations of topological defects.
Nonlinear Generation of Electromagnetic Waves through Induced Scattering by Thermal Plasma.
Tejero, E M; Crabtree, C; Blackwell, D D; Amatucci, W E; Mithaiwala, M; Ganguli, G; Rudakov, L
2015-01-01
We demonstrate the conversion of electrostatic pump waves into electromagnetic waves through nonlinear induced scattering by thermal particles in a laboratory plasma. Electrostatic waves in the whistler branch are launched that propagate near the resonance cone. When the amplitude exceeds a threshold ~5 × 10(-6) times the background magnetic field, wave power is scattered below the pump frequency with wave normal angles (~59°), where the scattered wavelength reaches the limits of the plasma column. The scattered wave has a perpendicular wavelength that is an order of magnitude larger than the pump wave and longer than the electron skin depth. The amplitude threshold, scattered frequency spectrum, and scattered wave normal angles are in good agreement with theory. The results may affect the analysis and interpretation of space observations and lead to a comprehensive understanding of the nature of the Earth's plasma environment. PMID:26647962
Nonlinear Generation of Electromagnetic Waves through Induced Scattering by Thermal Plasma.
Tejero, E M; Crabtree, C; Blackwell, D D; Amatucci, W E; Mithaiwala, M; Ganguli, G; Rudakov, L
2015-01-01
We demonstrate the conversion of electrostatic pump waves into electromagnetic waves through nonlinear induced scattering by thermal particles in a laboratory plasma. Electrostatic waves in the whistler branch are launched that propagate near the resonance cone. When the amplitude exceeds a threshold ~5 × 10(-6) times the background magnetic field, wave power is scattered below the pump frequency with wave normal angles (~59°), where the scattered wavelength reaches the limits of the plasma column. The scattered wave has a perpendicular wavelength that is an order of magnitude larger than the pump wave and longer than the electron skin depth. The amplitude threshold, scattered frequency spectrum, and scattered wave normal angles are in good agreement with theory. The results may affect the analysis and interpretation of space observations and lead to a comprehensive understanding of the nature of the Earth's plasma environment.
Nonlinear Generation of Electromagnetic Waves through Induced Scattering by Thermal Plasma
Tejero, E. M.; Crabtree, C.; Blackwell, D. D.; Amatucci, W. E.; Mithaiwala, M.; Ganguli, G.; Rudakov, L.
2015-01-01
We demonstrate the conversion of electrostatic pump waves into electromagnetic waves through nonlinear induced scattering by thermal particles in a laboratory plasma. Electrostatic waves in the whistler branch are launched that propagate near the resonance cone. When the amplitude exceeds a threshold ~5 × 10−6 times the background magnetic field, wave power is scattered below the pump frequency with wave normal angles (~59°), where the scattered wavelength reaches the limits of the plasma column. The scattered wave has a perpendicular wavelength that is an order of magnitude larger than the pump wave and longer than the electron skin depth. The amplitude threshold, scattered frequency spectrum, and scattered wave normal angles are in good agreement with theory. The results may affect the analysis and interpretation of space observations and lead to a comprehensive understanding of the nature of the Earth’s plasma environment. PMID:26647962
Combination of nonlinear ultrasonics and guided wave tomography for imaging the micro-defects.
Li, Weibin; Cho, Younho
2016-02-01
The use of guided wave tomography has become an attractive alternative to convert ultrasonic wave raw data to visualized results for quantitative signal interpretation. For more accurate life prediction and efficient management strategies for critical structural components, there is a demand of imaging micro-damages in early stage. However, there is rarely investigation on guided wave tomographic imaging of micro-defects. One of the reasons for this might be that it becomes challenging to monitor tiny signal difference coefficient in a reliable manner for wave propagation in the specimens with micro-damages. Nonlinear acoustic signal whose frequency differs from that of the input signal can be found in the specimens with micro-damages. Therefore, the combination of guided wave tomography and nonlinear acoustic response induced by micro-damages could be a feasibility study for imaging micro-damages. In this paper, the nonlinear Rayleigh surface wave tomographic method is investigated to locate and size micro-corrosive defect region in an isotropic solid media. The variations of acoustic nonlinear responses of ultrasonic waves in the specimens with and without defects are used in guided wave tomographic algorithm to construct the images. The comparisons between images obtained by experimental signals and real defect region induced by hydrogen corrosion are presented in this paper. Results show that the images of defect regions with different shape, size and location are successfully obtained by this novel technique, while there is no visualized result constructed by conventional linear ultrasonic tomographic one. The present approach shows a potential for inspecting, locating and imaging micro-defects by nonlinear Rayleigh surface wave tomography.
Strategies for reliable second harmonic of nonlinear acoustic wave through cement-based materials
NASA Astrophysics Data System (ADS)
Xie, Fan; Guo, Zhiwei; Zhang, Jinwei
2014-07-01
The strategies for retrieving reliable nonlinear second harmonic in cement-based materials are proposed in this paper using high-performance test system, piezoelectric transducers with central frequency in MHz, monochromatic tone-burst excitation and robust data process method.The Fundamental and second-order harmonics are measured to retrieve reliable acoustic nonlinearity with the input power level increased from ∼50 V to ∼280 V. About 173 times repeatable measurements are conducted to verify the stability of the experimental system. Specimens with three distinct aggregate sizes are used to measure the acoustic nonlinearity under uniaxial load. The results show a decrease in the measured acoustic nonlinearity at early damage stage, then a slight increase when large cracks coalesce. The rapid increase in acoustic nonlinearity at the final stage indicates the imminent failure. Our results also suggest that the nonlinear ultrasonic method is more sensitive than P-wave velocity for damage evaluation.
Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory.
Gnutzmann, Sven; Waltner, Daniel
2016-03-01
In this paper we present a general framework for solving the stationary nonlinear Schrödinger equation (NLSE) on a network of one-dimensional wires modeled by a metric graph with suitable matching conditions at the vertices. A formal solution is given that expresses the wave function and its derivative at one end of an edge (wire) nonlinearly in terms of the values at the other end. For the cubic NLSE this nonlinear transfer operation can be expressed explicitly in terms of Jacobi elliptic functions. Its application reduces the problem of solving the corresponding set of coupled ordinary nonlinear differential equations to a finite set of nonlinear algebraic equations. For sufficiently small amplitudes we use canonical perturbation theory, which makes it possible to extract the leading nonlinear corrections over large distances.
Dust-ion acoustic cnoidal waves and associated nonlinear ion flux in a nonthermal dusty plasma
NASA Astrophysics Data System (ADS)
Ur-Rehman, Hafeez; Mahmood, S.
2016-09-01
The dust-ion acoustic nonlinear periodic (cnoidal) waves and solitons are investigated in a dusty plasma containing dynamic cold ions, superthermal kappa distributed electrons and static charged dust particles. The massive dust particles can have positive or negative charge depending on the plasma environment. Using reductive perturbation method (RPM) with appropriate periodic boundary conditions, the evolution equations for the first and second order nonlinear potentials are derived. The first order potential is determined through Korteweg-de Vries (KdV) equation which gives dust-ion acoustic cnoidal waves and solitons structures. The solution of second order nonlinear potential is obtained through an inhomogeneous differential equation derived from collecting higher order terms of dynamic equations, which is linear for second order electrostatic potential. The nonlinear ion flux associated with the cnoidal waves is also found out numerically. The numerical plots of the dust-ion acoustic cnoidal wave and soliton structures for both positively and negatively charged dust particles cases and nonthermal electrons are also presented for illustration. It is found that only compressive nonlinear electrostatic structures are formed in case of positively dust charged particles while both compressive and rarefactive nonlinear structures are obtained in case of negatively charged particles depending on the negatively charged dust density in a nonthermal dusty plasma. The numerical results are obtained using data of the ionospheric region containing dusty plasma exist in the literature.
Near-planar TS waves and longitudinal vortices in channel flow: Nonlinear interaction and focusing
NASA Technical Reports Server (NTRS)
Hall, P.; Smith, F. T.
1989-01-01
The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, is studied the most here and it usually produces spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This then points to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 correspond to still higher amplitudes, with 3 being related to 2, while 4 is connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an 0(1) relative amount. All the types of nonlinear interaction however can result in the formation of focussed responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude.
Near-planar TS waves and longitudinal vortices in channel flow - Nonlinear interaction and focussing
NASA Technical Reports Server (NTRS)
Hall, Philip; Smith, Frank T.
1990-01-01
The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, is studied the most here and it usually produces spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This then points to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 correspond to still higher amplitudes, with 3 being related to 2, while 4 is connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an O(1) relative amount. All the types of nonlinear interaction, however, can result in the formation of focused responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude.
Force-controlled absorption in a fully-nonlinear numerical wave tank
Spinneken, Johannes Christou, Marios; Swan, Chris
2014-09-01
An active control methodology for the absorption of water waves in a numerical wave tank is introduced. This methodology is based upon a force-feedback technique which has previously been shown to be very effective in physical wave tanks. Unlike other methods, an a-priori knowledge of the wave conditions in the tank is not required; the absorption controller being designed to automatically respond to a wide range of wave conditions. In comparison to numerical sponge layers, effective wave absorption is achieved on the boundary, thereby minimising the spatial extent of the numerical wave tank. In contrast to the imposition of radiation conditions, the scheme is inherently capable of absorbing irregular waves. Most importantly, simultaneous generation and absorption can be achieved. This is an important advance when considering inclusion of reflective bodies within the numerical wave tank. In designing the absorption controller, an infinite impulse response filter is adopted, thereby eliminating the problem of non-causality in the controller optimisation. Two alternative controllers are considered, both implemented in a fully-nonlinear wave tank based on a multiple-flux boundary element scheme. To simplify the problem under consideration, the present analysis is limited to water waves propagating in a two-dimensional domain. The paper presents an extensive numerical validation which demonstrates the success of the method for a wide range of wave conditions including regular, focused and random waves. The numerical investigation also highlights some of the limitations of the method, particularly in simultaneously generating and absorbing large amplitude or highly-nonlinear waves. The findings of the present numerical study are directly applicable to related fields where optimum absorption is sought; these include physical wavemaking, wave power absorption and a wide range of numerical wave tank schemes.
Ottaviani, C.; Corbalan, R.; Mompart, J.; Ahufinger, V.
2010-04-15
We show that the adiabatic dynamics of a Bose-Einstein condensate (BEC) in a double-well potential can be described in terms of a dark variable resulting from the combination of the population imbalance and the spatial atomic coherence between the two wells. By means of this dark variable, we extend, to the nonlinear matter-wave case, the recent proposal by Vitanov and Shore [Phys. Rev. A 73, 053402 (2006)] on adiabatic passage techniques to coherently control the population of two internal levels of an atom or molecule. We investigate the conditions to adiabatically split or transport a BEC as well as to prepare an adiabatic self-trapping state by the optimal delayed temporal variation of the tunneling rate via either the energy bias between the two wells or the BEC nonlinearity. The emergence of nonlinear eigenstates and unstable stationary solutions of the system as well as their role in the breaking down of the adiabatic dynamics is investigated in detail.
Nonlinear evolution of a large-amplitude circularly polarized Alfven wave: Low beta
NASA Technical Reports Server (NTRS)
Ghosh, S.; Goldstein, M. L.
1994-01-01
The nature of turbulent cascades arising from the parametric instabilities of a monochromatic field-aligned large-amplitude circularly polarized Alfven wave is investigated via direct numerical simulation for the case of low plasma Beta and no wave dispersion. The magnetohydrodynamic code permits nonlinear couplings in the parallel direction to the ambient magnetic field and one perpendicular direction. Compressibility is included in the form of a polytropic equation of state. Anisotropic turbulent cascades, similar to those found in early incompressible two-dimensional simulations, occur after nonlinear saturation of the parallel propagating decay instability. The turbulent spectrum can be divided into three regimes: the lowest wave numbers are dominated by lower sideband remnants of the parametric process, intermediate wave numbers display nearly incompressible dynamics, and the highest wave numbers are dominated by acoustic turbulence.
NASA Astrophysics Data System (ADS)
Chillara, Vamshi Krishna; Lissenden, Cliff J.
2016-01-01
Interest in using the higher harmonic generation of ultrasonic guided wave modes for nondestructive evaluation continues to grow tremendously as the understanding of nonlinear guided wave propagation has enabled further analysis. The combination of the attractive properties of guided waves with the attractive properties of higher harmonic generation provides a very unique potential for characterization of incipient damage, particularly in plate and shell structures. Guided waves can propagate relatively long distances, provide access to hidden structural components, have various displacement polarizations, and provide many opportunities for mode conversions due to their multimode character. Moreover, higher harmonic generation is sensitive to changing aspects of the microstructures such as to the dislocation density, precipitates, inclusions, and voids. We review the recent advances in the theory of nonlinear guided waves, as well as the numerical simulations and experiments that demonstrate their utility.
Linear and nonlinear dynamics of current-driven waves in dusty plasmas
Ahmad, Ali; Ali Shan, S.; Haque, Q.; Saleem, H.
2012-09-15
The linear and nonlinear dynamics of a recently proposed plasma mode of dusty plasma is studied using kappa distribution for electrons. This electrostatic wave can propagate in the plasma due to the sheared flow of electrons and ions parallel to the external magnetic field in the presence of stationary dust. The coupling of this wave with the usual drift wave and ion acoustic wave is investigated. D'Angelo's mode is also modified in the presence of superthermal electrons. In the nonlinear regime, the wave can give rise to dipolar vortex structures if the shear in flow is weaker and tripolar vortices if the flow has steeper gradient. The results have been applied to Saturn's magnetosphere corresponding to negatively charged dust grains. But the theoretical model is applicable for positively charged dust as well. This work will be useful for future observations and studies of dusty environments of planets and comets.
NASA Astrophysics Data System (ADS)
Dimitrova, Zlatinka I.
2015-12-01
We investigate flow of incompressible fluid in a cylindrical tube with elastic walls. The radius of the tube may change along its length. The discussed problem is connected to the fluid-structure interaction in large human arteries and especially to nonlinear effects. The long-wave approximation is applied to solve model equations. The obtained model Korteweg-deVries equation possessing a variable coefficient is reduced to a nonlinear dynamical system of three first order differential equations. The low probability of a solitary wave arising is shown. Periodic wave solutions of the model system of equations are studied and it is shown that the waves, that are consequence of the irregular heart pulsations may be modelled by a sequence of parts of such periodic wave solutions.
Ion-acoustic cnoidal wave and associated non-linear ion flux in dusty plasma
Jain, S. L.; Tiwari, R. S.; Mishra, M. K.
2012-10-15
Using reductive perturbation method with appropriate boundary conditions, coupled evolution equations for first and second order potentials are derived for ion-acoustic waves in a collisionless, un-magnetized plasma consisting of hot isothermal electrons, cold ions, and massive mobile charged dust grains. The boundary conditions give rise to renormalization term, which enable us to eliminate secular contribution in higher order terms. Determining the non secular solution of these coupled equations, expressions for wave phase velocity and averaged non-linear ion flux associated with ion-acoustic cnoidal wave are obtained. Variation of the wave phase velocity and averaged non-linear ion flux as a function of modulus (k{sup 2}) dependent wave amplitude are numerically examined for different values of dust concentration, charge on dust grains, and mass ratio of dust grains with plasma ions. It is found that for a given amplitude, the presence of positively (negatively) charged dust grains in plasma decreases (increases) the wave phase velocity. This behavior is more pronounced with increase in dust concentrations or increase in charge on dust grains or decrease in mass ratio of dust grains. The averaged non-linear ion flux associated with wave is positive (negative) for negatively (positively) charged dust grains in the plasma and increases (decreases) with modulus (k{sup 2}) dependent wave amplitude. For given amplitude, it increases (decreases) as dust concentration or charge of negatively (positively) charged dust grains increases in the plasma.
NASA Astrophysics Data System (ADS)
Bona, J. L.; Chen, M.; Saut, J.-C.
2004-05-01
In part I of this work (Bona J L, Chen M and Saut J-C 2002 Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory J. Nonlinear Sci. 12 283-318), a four-parameter family of Boussinesq systems was derived to describe the propagation of surface water waves. Similar systems are expected to arise in other physical settings where the dominant aspects of propagation are a balance between the nonlinear effects of convection and the linear effects of frequency dispersion. In addition to deriving these systems, we determined in part I exactly which of them are linearly well posed in various natural function classes. It was argued that linear well-posedness is a natural necessary requirement for the possible physical relevance of the model in question. In this paper, it is shown that the first-order correct models that are linearly well posed are in fact locally nonlinearly well posed. Moreover, in certain specific cases, global well-posedness is established for physically relevant initial data. In part I, higher-order correct models were also derived. A preliminary analysis of a promising subclass of these models shows them to be well posed.
Simulation of nonlinear ultrasound wave propagation in Fourier domain
NASA Astrophysics Data System (ADS)
Varray, F.; Basset, O.; Cachard, C.
2015-10-01
The nonlinear ultrasound field distortion occurs in all biological media and reminds of great interest in all nonlinear imaging strategies as harmonic or contrast agent imaging. From the various set of methods that compute this propagation, the angular spectrum one is the fastest in term of computation time but the harmonics calculation is less accurate compared to other strategies. In this work, a new formulation based on a slowly varying envelope approximation is proposed to evaluate the full nonlinear spectrum distortion during the propagation. This tool is compared to a previous published angular method and the resulting pressure fields are very close which validate the proposed strategy, with a maximal error inferior to 2 dB. In term of computation time, the proposed tools is as fast as the previous one, but compute the full spectrum in once.
Excitation of vortices using linear and nonlinear magnetostatic waves.
Boardman, A D; Rapoport, Yu G; Grimalsky, V V; Ivanov, B A; Koshevaya, S V; Velasco, L; Zaspel, C E
2005-02-01
It is shown that stationary vortex structures can be excited in a ferrite film, in the important centimeter and millimeter wavelength ranges. It is shown that both linear and nonlinear structures can be excited using a three-beam interaction created with circular antennas. These give rise to a special phase distribution created by linear and nonlinear mixing. An interesting set of three clockwise rotating vortices joined by one counter-rotating one presents itself in the linear regime: a scenario that is only qualitatively changed by the onset of nonlinearity. It is pointed out that control of the vortex structure, through parametric coupling, based upon a microwave resonator, is possible and that there are many interesting possibilities for applications.
A Weakly Nonlinear Model for the Damping of Resonantly Forced Density Waves in Dense Planetary Rings
NASA Astrophysics Data System (ADS)
Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki
2016-10-01
In this paper, we address the stability of resonantly forced density waves in dense planetary rings. Goldreich & Tremaine have already argued that density waves might be unstable, depending on the relationship between the ring’s viscosity and the surface mass density. In the recent paper Schmidt et al., we have pointed out that when—within a fluid description of the ring dynamics—the criterion for viscous overstability is satisfied, forced spiral density waves become unstable as well. In this case, linear theory fails to describe the damping, but nonlinearity of the underlying equations guarantees a finite amplitude and eventually a damping of the wave. We apply the multiple scale formalism to derive a weakly nonlinear damping relation from a hydrodynamical model. This relation describes the resonant excitation and nonlinear viscous damping of spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients. The model consistently predicts density waves to be (linearly) unstable in a ring region where the conditions for viscous overstability are met. Sufficiently far away from the Lindblad resonance, the surface mass density perturbation is predicted to saturate to a constant value due to nonlinear viscous damping. The wave’s damping lengths of the model depend on certain input parameters, such as the distance to the threshold for viscous overstability in parameter space and the ground state surface mass density.
Localized waves in three-component coupled nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Xu, Tao; Chen, Yong
2016-09-01
We study the generalized Darboux transformation to the three-component coupled nonlinear Schrödinger equation. First- and second-order localized waves are obtained by this technique. In first-order localized wave, we get the interactional solutions between first-order rogue wave and one-dark, one-bright soliton respectively. Meanwhile, the interactional solutions between one-breather and first-order rogue wave are also given. In second-order localized wave, one-dark-one-bright soliton together with second-order rogue wave is presented in the first component, and two-bright soliton together with second-order rogue wave are gained respectively in the other two components. Besides, we observe second-order rogue wave together with one-breather in three components. Moreover, by increasing the absolute values of two free parameters, the nonlinear waves merge with each other distinctly. These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system. Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things, China (Grant No. ZF1213).
Localized waves in three-component coupled nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Xu, Tao; Chen, Yong
2016-09-01
We study the generalized Darboux transformation to the three-component coupled nonlinear Schrödinger equation. First- and second-order localized waves are obtained by this technique. In first-order localized wave, we get the interactional solutions between first-order rogue wave and one-dark, one-bright soliton respectively. Meanwhile, the interactional solutions between one-breather and first-order rogue wave are also given. In second-order localized wave, one-dark-one-bright soliton together with second-order rogue wave is presented in the first component, and two-bright soliton together with second-order rogue wave are gained respectively in the other two components. Besides, we observe second-order rogue wave together with one-breather in three components. Moreover, by increasing the absolute values of two free parameters, the nonlinear waves merge with each other distinctly. These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system. Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things, China (Grant No. ZF1213).
Nonlinear trans-resonant waves, vortices and patterns: From microresonators to the early Universe.
Galiev, Sh. U.; Galiyev, T. Sh.
2001-09-01
Perturbed wave equations are considered. Approximate general solutions of these equations are constructed, which describe wave phenomena in different physical and chemical systems. Analogies between surface waves, nonlinear and atom optics, field theories and acoustics of the early Universe can be seen in the similarities between the general solutions that govern each system. With the help of the general solutions and boundary conditions and/or resonant conditions we have derived the basic highly nonlinear ordinary differential equation or the basic algebraic equation for traveling waves. Then, approximate analytic resonant solutions are constructed, which describe the trans-resonant transformation of harmonic waves into traveling shock-, jet-, or mushroom-like waves. The mushroom-like waves can evolve into cloud-like and vortex-like structures. The motion and oscillations of these waves and structures can be very complex. Under parametric excitation these waves can vary their velocity, stop, and change the direction of their motion. Different dynamic patterns are yielded by these resonant traveling waves in the x-t and x-y planes. They simulate many patterns observed in liquid layers, optical systems, superconductors, Bose-Einstein condensates, micro- and electron resonators. The harmonic excitation may be compressed and transformed inside the resonant band into traveling or standing particle-like waves. The area of application of these solutions and results may possibly vary from the generation of nuclear particles, acoustical turbulence, and catastrophic seismic waves to the formation of galaxies and the Universe. In particular, the formation of galaxies and galaxy clusters may be connected with nonlinear and resonant phenomena in the early Universe. (c) 2001 American Institute of Physics.
Wavenumber shift due to nonlinear plasma and wave interaction
NASA Astrophysics Data System (ADS)
Gan, Chunyun; Xiang, Nong; Yu, Zhi; Yang, Youlei; Ou, Jing
2016-06-01
Wavenumber shift of the ion Bernstein wave has been observed in the particle-in-cell simulations when the input power of the injected wave is sufficiently large. It is demonstrated that the increase of the total kinetic energy of ions, including both the thermal energy related to the random thermal motion and the oscillation energy due to the coherent motion with the wave, gives rise to such change of the wavenumber. However, the velocity distribution function of the ions can approximately be fitted as a Maxwellian distribution function, and thus, the linear dispersion relation still holds, provided that the initial ion temperature is replaced by the effective temperature measured in the simulation.
Assessment of precipitation in alloy steel using nonlinear Rayleigh surface waves
NASA Astrophysics Data System (ADS)
Thiele, Sebastian; Matlack, Kathryn H.; Kim, Jin-Yeon; Qu, Jianmin; Wall, James J.; Jacobs, Laurence J.
2014-02-01
Nonlinear ultrasonic waves have shown to be sensitive to various microstructural changes in metals including coherent precipitates; these precipitates introduce a strain field in the lattice structure. The thermal aging of certain alloy steels leads to the formation of coherent precipitates, which pin dislocations and contribute to the generation of a second harmonic component. A precipitate hardenable material namely 17-4 PH stainless steel is thermally treated in this research to obtain different precipitation stages, and then the influence of precipitates on the acoustic nonlinearity parameter is assessed. Conclusions about the microstrucutural changes in the material are drawn based on the results from a nonlinear Rayleigh surface wave measurement and complementary thermo-electric power, hardness and ultrasonic velocity measurements. The results show that the nonlinear parameter is sensitive to coherent precipitates in the material and moreover that precipitation characteristics can be characterized based on the obtained experimental data.
Evolution of higher order nonlinear equation for the dust ion-acoustic waves in nonextensive plasma
Yasmin, S.; Asaduzzaman, M.; Mamun, A. A.
2012-10-15
There are three different types of nonlinear equations, namely, Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and mixed modified K-dV (mixed mK-dV) equations, for the nonlinear propagation of the dust ion-acoustic (DIA) waves. The effects of electron nonextensivity on DIA solitary waves propagating in a dusty plasma (containing negatively charged stationary dust, inertial ions, and nonextensive q distributed electrons) are examined by solving these nonlinear equations. The basic features of mixed mK-dV (higher order nonlinear equation) solitons are found to exist beyond the K-dV limit. The properties of mK-dV solitons are compared with those of mixed mK-dV solitons. It is found that both positive and negative solitons are obtained depending on the q (nonextensive parameter).
Quantum and classical dynamics in adiabatic computation
NASA Astrophysics Data System (ADS)
Crowley, P. J. D.; Äńurić, T.; Vinci, W.; Warburton, P. A.; Green, A. G.
2014-10-01
Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialized state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose ground state encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimization algorithms and quantum adiabatic optimization. This perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We apply these to the D-Wave Vesuvius machine with revealing—though inconclusive—results.
Role of convective cell in nonlinear interaction of kinetic Alfvén waves
NASA Astrophysics Data System (ADS)
Luk, O. O.; Lin, Z.
2016-10-01
Gyrokinetic particle simulations show that electrostatic convective cell (CC) can be generated by kinetic Alfvén waves and plays a dominant role in the nonlinear interactions underlying perpendicular spectral cascade. The CC growth rate increases linearly with the field amplitude of the pump waves and has a small but finite threshold, and decreases with the parallel wavevector. The CC growth is proportional to the perpendicular wavevector when there are two pump waves, but proportional to the square of the perpendicular wavevector when there is a single pump wave.
Nonlinear saturation spectra of electric fields and density fluctuations in drift wave turbulence
NASA Technical Reports Server (NTRS)
Kelley, M. C.
1982-01-01
The detection of drift waves in the nonlinear evolution of a space plasma process driven at long wavelengths is considered, adducing measurements of the electric field and density fluctuation power spectra as evidence. Since the driving mechanism is clearly at long wavelengths, the detection of drift waves suggests that they may play an important role in the transfer of wave energy from long to short wavelengths in a low beta plasma. The saturated spectral density is compared with theoretical results in order to estimate the anomalous diffusion rate. The observed spectral form and amplitude is in excellent agreement with drift wave predictions.
Exact Traveling Wave Solutions of a Higher-Dimensional Nonlinear Evolution Equation
NASA Astrophysics Data System (ADS)
Lee, Jonu; Sakthivel, Rathinasamy; Wazzan, Luwai
The exact traveling wave solutions of (4 + 1)-dimensional nonlinear Fokas equation is obtained by using three distinct methods with symbolic computation. The modified tanh-coth method is implemented to obtain single soliton solutions whereas the extended Jacobi elliptic function method is applied to derive doubly periodic wave solutions for this higher-dimensional integrable equation. The Exp-function method gives generalized wave solutions with some free parameters. It is shown that soliton solutions and triangular solutions can be established as the limits of the Jacobi doubly periodic wave solutions.
Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
NASA Astrophysics Data System (ADS)
Kim, E.; Li, F.; Chong, C.; Theocharis, G.; Yang, J.; Kevrekidis, P. G.
2015-03-01
In the present work, we experimentally implement, numerically compute with, and theoretically analyze a configuration in the form of a single column woodpile periodic structure. Our main finding is that a Hertzian, locally resonant, woodpile lattice offers a test bed for the formation of genuinely traveling waves composed of a strongly localized solitary wave on top of a small amplitude oscillatory tail. This type of wave, called a nanopteron, is not only motivated theoretically and numerically, but is also visualized experimentally by means of a laser Doppler vibrometer. This system can also be useful for manipulating stress waves at will, for example, to achieve strong attenuation and modulation of high-amplitude impacts without relying on damping in the system.
Nonlinear disintegration of sine wave in the framework of the Gardner equation
NASA Astrophysics Data System (ADS)
Kurkina, Oxana; Rouvinskaya, Ekaterina; Talipova, Tatiana; Kurkin, Andrey; Pelinovsky, Efim
2016-10-01
Internal tidal wave entering shallow waters transforms into an undular bore and this process can be described in the framework of the Gardner equation (extended version of the Korteweg-de Vries equation with both quadratic and cubic nonlinear terms). Our numerical computations demonstrate the features of undular bore developing for different signs of the cubic nonlinear term. If cubic nonlinear term is negative, and initial wave amplitude is large enough, two undular bores are generated from the two breaking points formed on both crest slopes (within dispersionless Gardner equation). Undular bore consists of one table-top soliton and a group of small soliton-like waves passing through the table-top soliton. If the cubic nonlinear term is positive and again the wave amplitude is large enough, the breaking points appear on crest and trough generating groups of positive and negative soliton-like pulses. This is the main difference with respect to the classic Korteweg-de Vries equation, where the breaking point is single. It is shown also that nonlinear interaction of waves happens similarly to one of scenarios of two-soliton interaction of "exchange" or "overtake" types with a phase shift. If small-amplitude pulses interact with large-amplitude soliton-like pulses, their speed in average is negative in the case when "free" velocity is positive. Nonlinear interaction leads to the generation of higher harmonics and spectrum width increases with amplitude increase independently of the sign of cubic nonlinear term. The breaking asymptotic k 4 / 3 predicted within the dispersionless Gardner equation emerges during the process of undular bore development. The formation of soliton-like perturbations leads to appearance of several spectral peaks which are downshifting with time.
Numerical schemes for a model for nonlinear dispersive waves
NASA Technical Reports Server (NTRS)
Bona, J. L.; Pritchard, W. G.; Scott, L. R.
1985-01-01
A description is given of a number of numerical schemes to solve an evolution equation (Korteweg-deVries) that arises when modelling the propagation of water waves in a channel. The discussion also includes the results of numerical experiments made with each of the schemes. It is suggested, on the basis of these experiments, that one of the schemes may have (discrete) solitary-wave solutions.
Kengne, E; Bozic, V; Viana, M; Vaillancourt, R
2008-08-01
In the semidiscrete limit and in suitably scaled coordinates, the voltage of a system of coupled nonlinear dispersive transmission lines is described by a nonlinear Schrödinger equation. This equation is used to study the transverse stability of solitary waves of the system. Exact results for the growth rate and the corresponding perturbation function of linear transverse perturbations are obtained in terms of the network's and soliton's parameters.
Nonlinear Breit-Wheeler process in the collision of a photon with two plane waves
NASA Astrophysics Data System (ADS)
Wu, Yuan-Bin; Xue, She-Sheng
2014-07-01
The nonlinear Breit-Wheeler process of electron-positron pair production off a probe photon colliding with a low-frequency and a high-frequency electromagnetic wave that propagate in the same direction is analyzed. We calculate the pair-production probability and the spectra of the created pair in the nonlinear Breit-Wheeler processes of pair production off a probe photon colliding with two plane waves or one of these two plane waves. The differences of these two cases are discussed. We evidently show, in the two-wave case, the possibility of Breit-Wheeler pair production with simultaneous photon emission into the low-frequency wave and the high multiphoton phenomena: (i) Breit-Wheeler pair production by absorption of the probe photon and a large number of photons from the low-frequency wave, in addition to the absorption of one photon from the high-frequency wave; (ii) Breit-Wheeler pair production by absorption of the probe photon and one photon from the high-frequency wave with simultaneous emission of a large number of photons into the low-frequency wave. The phenomenon of photon emission into the wave cannot happen in the one-wave case. Compared with the one-wave case, the contributions from high multiphoton processes are largely enhanced in the two-wave case. The results presented in this article show a possible way to access the observations of the phenomenon of photon emission into the wave and high multiphoton phenomenon in Breit-Wheeler pair production even with the laser-beam intensity of order 1018 W/cm2.
High-order Two-way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering
NASA Technical Reports Server (NTRS)
Fibich, Gadi; Tsynkov, Semyon
2000-01-01
When solving linear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, by linear superposition, the original problem is reduced to one that involves only the scattered waves driven by the values of the impinging field at the surface of the obstacles. In addition, when the original domain is unbounded, special artificial boundary conditions (ABCs) that would guarantee the reflectionless propagation of waves have to be set at the outer boundary of the finite computational domain. The situation becomes conceptually different when the propagation equation is nonlinear. In this case the impinging and scattered waves can no longer be separated, and the problem has to be solved in its entirety. In particular, the boundary on which the incoming field values are prescribed, should transmit the given incoming waves in one direction and simultaneously be transparent to all the outgoing waves that travel in the opposite direction. We call this type of boundary conditions two-way ABCs. In the paper, we construct the two-way ABCs for the nonlinear Helmholtz equation that models the laser beam propagation in a medium with nonlinear index of refraction. In this case, the forward propagation is accompanied by backscattering, i.e., generation of waves in the direction opposite to that of the incoming signal. Our two-way ABCs generate no reflection of the backscattered waves and at the same time impose the correct values of the incoming wave. The ABCs are obtained for a fourth-order accurate discretization to the Helmholtz operator; the fourth-order grid convergence is corroborated experimentally by solving linear model problems. We also present solutions in the nonlinear case using the two-way ABC which, unlike the traditional Dirichlet boundary condition, allows for direct calculation of the magnitude of backscattering.