Adiabatic nonlinear waves with trapped particles. II. Wave dispersion
Dodin, I. Y.; Fisch, N. J.
2012-01-15
A general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is generalized, and the nonlinear kinetic frequency shift {omega}{sub NL} is found analytically as a function of the wave amplitude a. Smooth distributions yield {omega}{sub NL}{proportional_to}{radical}(a), as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation. Such beams are formed whenever the phase velocity changes, because the trapped distribution is in autoresonance and thus evolves differently from the passing distribution. Hence, even adiabatic {omega}{sub NL}(a) is generally nonlocal.
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.
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
Extensive Adiabatic Invariants for Nonlinear Chains
NASA Astrophysics Data System (ADS)
Giorgilli, Antonio; Paleari, Simone; Penati, Tiziano
2012-09-01
We look for extensive adiabatic invariants in nonlinear chains in the thermodynamic limit. Considering the quadratic part of the Klein-Gordon Hamiltonian, by a linear change of variables we transform it into a sum of two parts in involution. At variance with the usual method of introducing normal modes, our constructive procedure allows us to exploit the complete resonance, while keeping the extensive nature of the system. Next we construct a nonlinear approximation of an extensive adiabatic invariant for a perturbation of the discrete nonlinear Schrödinger model. The fluctuations of this quantity are controlled via Gibbs measure estimates independent of the system size, for a large set of initial data at low specific energy. Finally, by numerical calculations we show that our adiabatic invariant is well conserved for times much longer than predicted by our first order theory, with fluctuation much smaller than expected according to standard statistical estimates.
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.
Cabaret, J; Béquin, P; Theocharis, G; Andreev, V; Gusev, V E; Tournat, V
2015-07-31
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. PMID:26274421
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.
Nonlinear effects generation in non-adiabatically tapered fibres
NASA Astrophysics Data System (ADS)
Palací, Jesús; Mas, Sara; Monzón-Hernández, David; Martí, Javier
2015-12-01
Nonlinear effects are observed in a non-adiabatically tapered optical fibre. The designed structure allows for the introduction of self-phase modulation, which is observed through pulse breaking and spectral broadening, in approximately a centimetre of propagation using a commercial telecom laser. These devices are simple to fabricate and suitable to generate and control a variety of nonlinear effects in practical applications because they do not experience short-term degradation as previously reported approaches. Experimental and theoretical results are obtained, showing a good agreement.
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.
The dynamic instability of adiabatic blast waves
NASA Astrophysics Data System (ADS)
Ryu, Dongsu; Vishniac, Ethan T.
1991-02-01
Adiabatic blastwaves, which have a total energy injected from the center E varies as tq and propagate through a preshock medium with a density rhoE varies as r-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 trapping in coupled kinetic Alfven-acoustic waves
Shah, H. A.; Ali, Z.; Masood, W.
2013-03-15
In the present work, we have discussed the effects of adiabatic trapping of electrons on obliquely propagating Alfven waves in a low {beta} plasma. Using the two potential theory and employing the Sagdeev potential approach, we have investigated the existence of arbitrary amplitude coupled kinetic Alfven-acoustic solitary waves in both the sub and super Alfvenic cases. The results obtained have been analyzed and presented graphically and can be applied to regions of space where the low {beta} assumption holds true.
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
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
2016-01-01
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
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.
Adiabatic femtosecond pulse compression and control by using quadratic cascading nonlinearity
NASA Astrophysics Data System (ADS)
Zeng, Xianglong; Ashihara, Satoshi; Shimura, Tsutomu; Kuroda, Kazuo
2008-01-01
We experimentally demonstrate that adiabatic compression of femtosecond pulse can be achieved by employing the management of quadratic cascading nonlinearity in quasi-phase-matching gratings. Cascading nonlinearity is not a simple analogy with third-order optical nonlinearity in term of the engineering properties of the magnitude and focusing (or defocusing) nonlinearity. Femtosecond pulse compression is investigated based on type-I (e: o + o) collinear QPM geometry of aperiodically poled MgO-doped LiNbO 3 (MgO: LN). Group-velocity-matching condition is chosen to generate quadratic femtosecond soliton consisting of fundamental (FF) and second harmonic (SH) pulses. Adiabatic-like compression process is observed in the length of 50 mm linearly chirped QPM. Cascading nonlinearity is local managed, instead of dispersion management used in fiber adiabatic soliton compression. Quadratic soliton including FF and SH pulses are obtained from the compression of 95 fs FF pulse in the initial experiments. Dependence on the phase mismatch and group velocity mismatch, cascading nonlinearity has a flexible property and presents a new challenge for exploring femtosecond pulse shaping and control. The demonstrated pulse compression and control based on cascading nonlinearity is useful for generation of shorter pulses with clean temporal profiles, efficient femtosecond second harmonic generation and group-velocity control.
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.
Nonlinear Adiabatic Passage from Fermion Atoms to Boson Molecules
Pazy, E.; Tikhonenkov, I.; Band, Y.B.; Vardi, A.; Fleischhauer, M.
2005-10-21
We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction {gamma} on the sweep rate {alpha} varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number N. The power law is linear, {gamma}{proportional_to}{alpha}, when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and {gamma}{proportional_to}{alpha}{sup 1/3} when it is larger. Experimental data agree well with a linear dependence, but do not conclusively rule out the Landau-Zener model.
Acoustic solitary waves in dusty and/or multi-ion plasmas with cold, adiabatic, and hot constituents
Verheest, Frank; Hellberg, Manfred A.; Kourakis, Ioannis
2008-11-15
Large nonlinear acoustic waves are discussed in a four-component plasma, made up of two superhot isothermal species, and two species with lower thermal velocities, being, respectively, adiabatic and cold. First a model is considered in which the isothermal species are electrons and ions, while the cooler species are positive and/or negative dust. Using a Sagdeev pseudopotential formalism, large dust-acoustic structures have been studied in a systematic way, to delimit the compositional parameter space in which they can be found, without restrictions on the charges and masses of the dust species and their charge signs. Solitary waves can only occur for nonlinear structure velocities smaller than the adiabatic dust thermal velocity, leading to a novel dust-acoustic-like mode based on the interplay between the two dust species. If the cold and adiabatic dust are oppositely charged, only solitary waves exist, having the polarity of the cold dust, their parameter range being limited by infinite compression of the cold dust. However, when the charges of the cold and adiabatic species have the same sign, solitary structures are limited for increasing Mach numbers successively by infinite cold dust compression, by encountering the adiabatic dust sonic point, and by the occurrence of double layers. The latter have, for smaller Mach numbers, the same polarity as the charged dust, but switch at the high Mach number end to the opposite polarity. Typical Sagdeev pseudopotentials and solitary wave profiles have been presented. Finally, the analysis has nowhere used the assumption that the dust would be much more massive than the ions and hence, one or both dust species can easily be replaced by positive and/or negative ions and the conclusions will apply to that plasma model equally well. This would cover a number of different scenarios, such as, for example, very hot electrons and ions, together with a mix of adiabatic ions and dust (of either polarity) or a very hot electron
Transition time of nonlinear Landau-Zener model in adiabatic limit
NASA Astrophysics Data System (ADS)
Liu, Xuan-Zuo; Tian, Dong-Ping; Chong, Bo
2016-06-01
The impact of nonlinear interaction on the loop structure of lower energy level and on the time evolution curve of canonical momentum which corresponds to the lower eigenstate are analyzed respectively. We find that the curve changes from single-valued to multi-valued as nonlinear interaction grows. The fascinating part is that the time range delimited by turning points in the loop of energy level and the period between two inflexion points on the multi-valued part of the evolution curve of canonical momentum are the same. Therefore, we propose a characteristic time in the transition process of nonlinear Landau-Zener model in adiabatic limit. Last, the physical meaning of the transition time as a measure of how much time the system experiences a structural change which directly results in the breakdown of adiabaticity is 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.
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.
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.
Stationary nonlinear Alfven waves and solitons
NASA Technical Reports Server (NTRS)
Hada, T.; Kennel, C. F.; Buti, B.
1989-01-01
Stationary solutions of the derivative nonlinear Schroedinger equation are discussed and classified by using a pseudopotential formulation. The solutions consist of a rich family of nonlinear Alfven waves and solitons with parallel and oblique propagation directions. Expressions for the envelope and the phase of nonlinear waves with periodic envelope modulation, and 'hyperbolic' and 'algebraic' solitons are given. The propagation angle for the slightly modulated elliptic, periodic waves and for oblique solitons is evaluated.
Dust-acoustic solitary waves in a four-component adiabatic magnetized dusty plasma
Akhter, T. Mannan, A.; Mamun, A. A.
2013-07-15
Theoretical investigation has been made on obliquely propagating dust-acoustic (DA) solitary waves (SWs) in a magnetized dusty plasma which consists of non-inertial adiabatic electron and ion fluids, and inertial negatively as well as positively charged adiabatic dust fluids. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation which admits a solitary wave solution for small but finite amplitude limit. It has been shown that the basic features (speed, height, thickness, etc.) of such DA solitary structures are significantly modified by adiabaticity of plasma fluids, opposite polarity dust components, and the obliqueness of external magnetic field. The SWs have been changed from compressive to rarefactive depending on the value of {mu} (a parameter determining the number of positive dust present in this plasma model). The present investigation can be of relevance to the electrostatic solitary structures observed in various dusty plasma environments (viz. cometary tails, upper mesosphere, Jupiter's magnetosphere, etc.)
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.
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
High-fidelity composite adiabatic passage in nonlinear two-level systems
NASA Astrophysics Data System (ADS)
Dou, Fu-Quan; Cao, Hui; Liu, Jie; Fu, Li-Bin
2016-04-01
We investigate the composite adiabatic passage (CAP) reported by B. T. Torosov et al. [Phys. Rev. Lett. 106, 233001 (2011), 10.1103/PhysRevLett.106.233001] in a nonlinear two-level system in which the level energies depend on the occupation of the levels, representing a mean-field type of interaction between the particles. A high-fidelity, fast, and robust quantum manipulation is achieved in the system. We consider the effect of interparticle interaction and find that it tends to increase the number of the pulse sequences. The CAP technique can suppress the nonadiabatic oscillations below the quantum-information benchmark 10-4, as long as there exist sufficiently long composite sequences. We analyze the robustness against the variations in the field parameters. The difference between the nonlinear and linear systems on the CAP technique is also discussed.
Nonlinear evolution of astrophysical Alfven waves
Spangler, S.R.
1984-11-01
Nonlinear Alfven waves were studied using the derivative nonlinear Schrodinger equation as a model. The evolution of initial conditions, such as envelope solitons, amplitude-modulated waves, and band-limited noise was investigated. The last two furnish models for naturally occurring Alfven waves in an astrophysical plasma. A collapse instability in which a wave packet becomes more intense and of smaller spatial extent was analyzed. It is argued that this instability leads to enhanced plasma heating. In studies in which the waves are amplified by an electron beam, the instability tends to modestly inhibit wave growth. (ESA)
Nonlinear evolution of astrophysical Alfven waves
NASA Technical Reports Server (NTRS)
Spangler, S. R.
1984-01-01
Nonlinear Alfven waves were studied using the derivative nonlinear Schrodinger equation as a model. The evolution of initial conditions, such as envelope solitons, amplitude-modulated waves, and band-limited noise was investigated. The last two furnish models for naturally occurring Alfven waves in an astrophysical plasma. A collapse instability in which a wave packet becomes more intense and of smaller spatial extent was analyzed. It is argued that this instability leads to enhanced plasma heating. In studies in which the waves are amplified by an electron beam, the instability tends to modestly inhibit wave growth.
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.
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.
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
Nonlinear spreading of Farley-Buneman waves
NASA Astrophysics Data System (ADS)
Litt, S. K.; Bains, A. S.; Smolyakov, A. I.; Onishchenko, O. G.; Pokhotelov, O. A.
2015-11-01
Nonlinear coupling of Farley-Buneman (FB) waves is studied using the method of modulational decay instabilities. Dispersion relation for the growth of the secondary Farley-Buneman waves has been derived. It is shown that the primary wave is unstable with respect to the modulational instability decay, producing the secondary waves with a finite flow angle with respect to the direction of the electron E × B flow. This process leads to the nonlinear spreading of the primary FB waves into the linearly stable region which is consistent with the previous numerical simulations and some observations.
NASA Astrophysics Data System (ADS)
Nunn, David; Omura, Yoshiharu
2015-04-01
Most previous work on nonlinear wave-particle interactions between energetic electrons and VLF waves in the Earth's magnetosphere has assumed parallel propagation, the underlying mechanism being nonlinear trapping of cyclotron resonant electrons in a parabolic magnetic field inhomogeneity. Here nonlinear wave-particle interaction in oblique whistlers in the Earth's magnetosphere is investigated. The study is nonself-consistent and assumes an arbitrarily chosen wave field. We employ a "continuous wave" wave field with constant frequency and amplitude, and a model for an individual VLF chorus element. We derive the equations of motion and trapping conditions in oblique whistlers. The resonant particle distribution function, resonant current, and nonlinear growth rate are computed as functions of position and time. For all resonances of order n, resonant electrons obey the trapping equation, and provided the wave amplitude is big enough for the prevailing obliquity, nonlinearity manifests itself by a "hole" or "hill" in distribution function, depending on the zero-order distribution function and on position. A key finding is that the n = 1 resonance is relatively unaffected by moderate obliquity up to 25°, but growth rates roll off rapidly at high obliquity. The n = 1 resonance saturates due to the adiabatic effect and here reaches a maximum growth at ~20 pT, 2000 km from the equator. Damping due to the n = 0 resonance is not subject to adiabatic effects and maximizes at some 8000 km from the equator at an obliquity ~55°.
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.
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
Nonlinear waves in an Alfven waveguide
Dmitrienko, I.S.
1992-06-01
A nonlinear Schroedinger equation is derived for the envelopes of weakly nonlinear quasilongitudinal (k{sub 1}<{radical}{omega}/{omega}{sub i}k{sub {parallel}}) Alfven waves in a waveguide, the existence of which is ensured by the presence of ion inertia (m{sub i}{ne}0) in a plasma with a transverse density gradient. It is shown that the nonlinear properties of such waves are associated with the presence of transverse structure in the waveguide modes. Estimates show that weakly nonlinear processes can have a significant effect on the dynamics of Pc 1 geomagnetic pulsations. 7 refs.
Nonlinear progressive acoustic-gravity waves: Exact solutions
NASA Astrophysics Data System (ADS)
Godin, Oleg
2013-04-01
We consider finite-amplitude mechanical waves in an inhomogeneous, compressible fluid in a uniform gravity field. The fluid is assumed to be inviscid, and wave motion is considered as an adiabatic thermodynamic process. The fluid either occupies an unbounded domain or has free and/or rigid boundaries. Wave motion is described by the momentum, continuity, and state equations in Lagrangian coordinates. We consider generic inhomogeneous fluids; no specific assumptions are made regarding the equation of state or spatial variations of the mass density or the sound speed in the absence of waves. The density and the sound speed are piece-wise continuous functions of position. The discontinuities represent fluid-fluid interfaces, such as the air-sea interface. Following a recent work on linear acoustic-gravity waves [O. A. Godin, Incompressible wave motion of compressible fluids, Phys. Rev. Lett., 108, 194501 (2012)], here we investigate a particular class of non-linear wave motions in fluids, in which pressure remains constant in each moving fluid parcel. Exact, analytic solutions of the non-linear hydrodynamics equations are obtained for two distinct scenarios. In the first scenario, the fluid is either unbounded or has a free surface. In the latter case, the exact analytic solution can be interpreted as a progressive surface wave. In the second scenario, the fluid has a free surface and a sloping, plane rigid boundary. Then the exact analytic solution represents an edge wave propagating horizontally along the rigid boundary. In both scenarios, the flow field associated with the finite-amplitude waves is rotational. When the sound speed tends to infinity, our results reduce to well-known finite-amplitude waves in incompressible fluids. In another limit, when the wave amplitude tends to zero, the exact solutions reduce to known results for linear waves in compressible fluids. The possibility of extending the theory to rotating fluids and fluids with a shearing background
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.
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
Nonlinear waves and solitons in molecular clouds
NASA Technical Reports Server (NTRS)
Adams, Fred C.; Fatuzzo, Marco
1993-01-01
We begin a study of nonlinear wave phenomena in molecular clouds. These clouds exhibit highly nonlinear structure that is often described in terms of 'clumps' and 'filaments' which are bouncing around, twisting, and colliding within the cloud. These clouds are important because they ultimately produce the initial conditions for the star formation process. Our motivation is to explore the possibility that solitons (i.e., spatially localized, single-hump wave entities which often exhibit remarkable stability) can live in these molecular clouds and produce their observed structure. In this paper we focus on the case of one spatial dimension, and we show that a rich variety of nonlinear waves can exist in molecular cloud fluid systems (where self-gravity is included). We show that in the absence of magnetic fields no true soliton solutions are allowed, although highly nonlinear waves (whose crests become widely spaced and thus soliton-like) do exist. For clouds with embedded magnetic fields, we derive a model equation which describes the behavior of wave phenomena; this model equation allows solutions which correspond to nonlinear waves, solitons, and topological solitons. We briefly consider the stability of these wave entities and discuss the possible role they play in molecular cloud dynamics.
Domain wall motion driven by adiabatic spin transfer torque through excitation of nonlinear dynamics
NASA Astrophysics Data System (ADS)
Wang, D.; Dong, Yulan; Yan, Zhou; Wang, Xi-guang; He, Jun; Guo, Guang-hua
2016-05-01
Domain wall dynamics under the joint action of a linearly polarized microwave magnetic field and spin transfer torque was analysed in terms of the domain wall collective coordinates. It was found that a microwave-assisted steady domain wall motion driven by adiabatic spin transfer torque can be adequately described by three domain wall collective coordinates. Analytical expression for the domain wall velocity showed that there are two contributions to the steady domain wall motion. One is derived from the nonlinear oscillation of domain wall width excited by the microwave field, and the other is from the heterodyne process between the width oscillation and the microwave field. The former always propels a domain wall to move in the positive direction, which is defined as the direction of the applied current. The latter contribution to the domain wall velocity can be positive or negative, depending on the polarization of the microwave field. The final domain wall velocity is determined by the competition between those two contributions, which indicates that by simply changing the polarization of the microwave field, the direction of the domain wall motion can be reversed. Our analysis demonstrated that the characteristics of domain wall motion can be tuned by selective excitation of nonlinear domain wall dynamics.
Nonlinear self-contraction of electron waves
NASA Technical Reports Server (NTRS)
Intrator, T.; Chan, C.; Hershkowitz, N.; Diebold, D.
1984-01-01
Laboratory evidence is presented of modulationally unstable electron wave packets which can be described by a nonlinear geometrical optics theory. Growth times for self-contraction are found to be much faster than ion response times and the bursts do not appear to be related to Zakharov Langmuir-wave collapse.
Nonlinear Evolution of Alfvenic Wave Packets
NASA Technical Reports Server (NTRS)
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
Nonlinear Talbot effect of rogue waves
NASA Astrophysics Data System (ADS)
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. PMID:23005044
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 sharpening during superposition of surface waves
NASA Astrophysics Data System (ADS)
Chalikov, Dmitry; Babanin, Alexander V.
2016-06-01
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.
Neural field theory of nonlinear wave-wave and wave-neuron processes
NASA Astrophysics Data System (ADS)
Robinson, P. A.; Roy, N.
2015-06-01
Systematic expansion of neural field theory equations in terms of nonlinear response functions is carried out to enable a wide variety of nonlinear wave-wave and wave-neuron processes to be treated systematically in systems involving multiple neural populations. The results are illustrated by analyzing second-harmonic generation, and they can also be applied to wave-wave coalescence, multiharmonic generation, facilitation, depression, refractoriness, and other nonlinear processes.
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.
Nonlinear Unstable Wave Disturbances in Fluidized Beds
NASA Astrophysics Data System (ADS)
Liu, J. T. C.
1983-10-01
Instabilities in fluidized beds are interpreted from the two-phase continuum theory of linearized hydrodynamic stability as the result of interactions between wave hierarchies for which the stability condition is violated; that is, in which the lower-order waves propagate at speeds exceeding those of the higher-order waves. For weak nonlinearities a hierarchy of Burgers-like equations is obtained. The nonlinear modifications to the wave speeds point towards the restoration of the stability condition in the linearized sense. A weakly nonlinear hydrodynamic stability analysis yields an amplitude equation that is of second order. It is argued, however, that the major history of the disturbance development may be expressed by a simpler first-order amplitude equation. The Landau-Stuart constant obtained is intimately related to the nonlinear modifications of the wave speeds of the higher- and lower-order wave operators. It is shown that for supercritical disturbances, amplitude and phase velocity equilibration is possible, and that the levels of the equilibration depend on the initial amplification rate, in agreement with observations. The equilibration occurs by cascades of the fundamental wave disturbance into its harmonics.
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.
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.
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.
Time-Averaged Adiabatic Potentials: Versatile Matter-Wave Guides and Atom Traps
NASA Astrophysics Data System (ADS)
Lesanovsky, Igor; von Klitzing, Wolf
2007-08-01
We demonstrate a novel class of trapping potentials, time-averaged adiabatic potentials (TAAP), which allows the generation of a large variety of traps for quantum gases and matter-wave guides for atom interferometers. Examples include stacks of pancakes, rows of cigars, and multiple rings or sickles. The traps can be coupled through controllable tunneling barriers or merged altogether. We present analytical expressions for pancake-, cigar-, and ring-shaped traps. The ring geometry is of particular interest for guided matter-wave interferometry as it provides a perfectly smooth waveguide of widely tunable diameter and thus adjustable sensitivity of the interferometer. The flexibility of the TAAP would make possible the use of Bose-Einstein condensates as coherent matter waves in large-area atom interferometers.
Time-averaged adiabatic potentials: versatile matter-wave guides and atom traps.
Lesanovsky, Igor; von Klitzing, Wolf
2007-08-24
We demonstrate a novel class of trapping potentials, time-averaged adiabatic potentials (TAAP), which allows the generation of a large variety of traps for quantum gases and matter-wave guides for atom interferometers. Examples include stacks of pancakes, rows of cigars, and multiple rings or sickles. The traps can be coupled through controllable tunneling barriers or merged altogether. We present analytical expressions for pancake-, cigar-, and ring-shaped traps. The ring geometry is of particular interest for guided matter-wave interferometry as it provides a perfectly smooth waveguide of widely tunable diameter and thus adjustable sensitivity of the interferometer. The flexibility of the TAAP would make possible the use of Bose-Einstein condensates as coherent matter waves in large-area atom interferometers. PMID:17930945
Time-Averaged Adiabatic Potentials: Versatile Matter-Wave Guides and Atom Traps
Lesanovsky, Igor; Klitzing, Wolf von
2007-08-24
We demonstrate a novel class of trapping potentials, time-averaged adiabatic potentials (TAAP), which allows the generation of a large variety of traps for quantum gases and matter-wave guides for atom interferometers. Examples include stacks of pancakes, rows of cigars, and multiple rings or sickles. The traps can be coupled through controllable tunneling barriers or merged altogether. We present analytical expressions for pancake-, cigar-, and ring-shaped traps. The ring geometry is of particular interest for guided matter-wave interferometry as it provides a perfectly smooth waveguide of widely tunable diameter and thus adjustable sensitivity of the interferometer. The flexibility of the TAAP would make possible the use of Bose-Einstein condensates as coherent matter waves in large-area atom interferometers.
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.
Kinetic Electrostatic Electron Nonlinear Waves in Laser
NASA Astrophysics Data System (ADS)
Afeyan, Bedros
2004-11-01
A new type of coherent self-sustaining nonlinear kinetic wave has been discovered, well below the plasma frequency, which we call Kinetic Electrostatic Electron Nonlinear (KEEN) waves. Vlasov-Poisson and Vlasov-Maxwell simulations where KEEN waves were excited by ponderomotive forces of short duration, generated by the beating of counter-propagating lasers of the appropriate colors [1-2], show that these waves persist without decay well after the driving fields are turned off. The resulting phase space vortical structures are reminiscent in certain respects to BGK modes proposed in 1957 [3]. However, KEEN waves are not stationary and higher harmonics which are an essential part of their make up have wider and wider frequency content. KEEN waves constitute a generalization and clarification of concepts previously invoked to help explain stimulated electron acoustic wave scattering in the presence of SRS [4,5]. However, in the case of KEEN waves, no flattened (zero slope) electron velocity distribution function need be invoked and no single mode behavior is observed. There is a threshold drive which is necessary in order to create KEEN waves. A reduced model based on a phase space coupled mode theory with 3-4 modes will be shown to capture the phase locked multimode nonlinear nature of KEEN waves. We have also successfully completed a series of experiments to generate via optical mixing and observe via 4ω Thomson scattering KEEN waves on Trident at LANL. Our latest results from this campaign will be shown. [1] B. Afeyan, et al., "Kinetic Electrostatic " Proc. IFSA Conf. (2004). [2] B. Afeyan, et al., submitted to PRL (2004) [3] I. Bernstein et al., Phys. Rev. 108. 546 (1957). [4] D. S. Montgomery et al., PRL 87, 155001 (2001). [5] H. A, Rose and D. A. Russell, Phys. Plasmas 8, 4784 (2001).
Nonlinear Biot waves in granular media
NASA Astrophysics Data System (ADS)
Dazel, Olivier; Tournat, V.
2010-01-01
The nonlinear propagation through unconsolidated model granular media is investigated in the frame of the Biot-Allard theory extended to the case of a nonlinear quadratic behavior of the solid frame (the elastic beads and their contacts). We evaluate the importance of mode coupling between solid and fluid waves, depending on the actual fluid and the bead diameter. The application of these results to other media supporting Biot's waves (trabecular bones, porous ceramics, polymer foams...) is straightforward, provided the parameters of the Biot-Allard model are available for these media.
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.
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 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.
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.
Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave
Sharma, R. P. Sharma, Swati Gaur, Nidhi
2014-07-15
The nonlinear phenomena are of prominent interests in understanding the particle acceleration and transportation in the interplanetary space. The ponderomotive nonlinearity causing the filamentation of the parallel propagating circularly polarized dispersive Alfvén wave having a finite frequency may be one of the mechanisms that contribute to the heating of the plasmas. The contribution will be different of the left (L) handed mode, the right (R) handed mode, and the mix mode. The contribution also depends upon the finite frequency of the circularly polarized waves. In the present paper, we have investigated the effect of the nonlinear coupling of the L and R circularly polarized dispersive Alfvén wave on the localized structures formation and the respective power spectra. The dynamical equations are derived in the presence of the ponderomotive nonlinearity of the L and R pumps and then studied semi-analytically as well as numerically. The ponderomotive nonlinearity accounts for the nonlinear coupling between both the modes. In the presence of the adiabatic response of the density fluctuations, the nonlinear dynamical equations satisfy the modified nonlinear Schrödinger equation. The equations thus obtained are solved in solar wind regime to study the coupling effect on localization and the power spectra. The effect of coupling is also studied on Faraday rotation and ellipticity of the wave caused due to the difference in the localization of the left and the right modes with the distance of propagation.
Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice
Abdullaev, F. Kh.; Tomio, Lauro; Gammal, A.; Luz, H. L. F. da
2007-10-15
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.
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.
Quantum Lattice Fluctuations in the Charge Density Wave State beyond the Adiabatic Approximation
NASA Astrophysics Data System (ADS)
Shida, Keisuke; Watanabe, Yuko; Gomi, Hiroki; Takahashi, Akira; Tomita, Norikazu
2015-12-01
We have developed a tractable numerical method in which large-amplitude quantum lattice fluctuations can be described beyond the adiabatic approximation using the coherent state representation of phonons. A many-body wave function is constructed by the superposition of direct products of non-orthogonal Slater determinants for electrons and coherent states of phonons. Both orbitals in all the Slater determinants and the amplitudes of all the coherent states are simultaneously optimized. We apply the method to the one-dimensional Su-Schrieffer-Heeger model with the on-site and nearest-neighbor-site Coulomb interactions. It is shown the lattice fluctuations in doped charge density wave (CDW) systems are described by the translational and vibrational motion of lattice solitons. Such lattice solitons induce bond alternation in the doped CDW system while the lattice becomes equidistant in the half-filled CDW system.
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.
Effects of Wave Nonlinearity on Wave Attenuation by Vegetation
NASA Astrophysics Data System (ADS)
Wu, W. C.; Cox, D. T.
2014-12-01
The need to explore sustainable approaches to maintain coastal ecological systems has been widely recognized for decades and is increasingly important due to global climate change and patterns in coastal population growth. Submerged aquatic vegetation and emergent vegetation in estuaries and shorelines can provide ecosystem services, including wave-energy reduction and erosion control. Idealized models of wave-vegetation interaction often assume rigid, vertically uniform vegetation under the action of waves described by linear wave theory. A physical model experiment was conducted to investigate the effects of wave nonlinearity on the attenuation of random waves propagating through a stand of uniform, emergent vegetation in constant water depth. The experimental conditions spanned a relative water depth from near shallow to near deep water waves (0.45 < kh <1.49) and wave steepness from linear to nonlinear conditions (0.03 < ak < 0.18). The wave height to water depth ratios were in the range 0.12 < Hs/h < 0.34, and the Ursell parameter was in the range 2 < Ur < 68. Frictional losses from the side wall and friction were measured and removed from the wave attenuation in the vegetated cases to isolate the impact of vegetation. The normalized wave height attenuation decay for each case was fit to the decay equation of Dalrymple et al. (1984) to determine the damping factor, which was then used to calculate the bulk drag coefficients CD. This paper shows that the damping factor is dependent on the wave steepness ak across the range of relative water depths from shallow to deep water and that the damping factor can increase by a factor of two when the value of ak approximately doubles. In turn, this causes the drag coefficient CD to decrease on average by 23%. The drag coefficient can be modeled using the Keulegan-Carpenter number using the horizontal orbital wave velocity estimate from linear wave theory as the characteristic velocity scale. Alternatively, the Ursell
Stratification effects on nonlinear elastic surface waves
NASA Astrophysics Data System (ADS)
Parker, D. F.
1988-01-01
On a homogeneous elastic half-space, linear surface waves are nondispersive. In each direction, waves having any profile travel without distortion. Nonlinearity causes intermodulation between the various wavelengths so that the signal distorts. Even when nonlinearity is small, sinusoidal profiles do not remain approximately sinusoidal. The absence of dispersion means that profiles suffer cumulative distortion, until the surface slope and strain become locally unbounded. Although this behaviour is typical of many signals, there are some signals for which intermodulation is constructive. These signals can travel coherently over large distances. For seismological applications, it is important to study the effects due to stratification. Dependence of the material constants on depth modifies the nonlinear evolution equations previously derived for homogeneous media. It has a smaller effect on higher frequencies than on lower frequencies. An approximate theory for short wavelength (high frequency) signals is introduced. Calculations show that when nonlinearity is no more important than dispersion, initially sinusoidal profiles propagate with surface slope remaining finite. When dispersion is small compared to nonlinearity, certain sharp peaked profiles can travel large distances while suffering little distortion.
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 holography for acoustic wave detection
NASA Astrophysics Data System (ADS)
Bortolozzo, U.; Dolfi, D.; Huignard, J. P.; Molin, S.; Peigné, A.; Residori, S.
2015-03-01
A liquid crystal medium is used to perform nonlinear dynamic holography and is coupled with multimode optical fibers for optical sensing applications. Thanks to the adaptive character of the nonlinear holography, and to the sensitivity of the multimode fibers, we demonstrate that the system is able to perform efficient acoustic wave detection even with noisy signals. The detection limit is estimated and multimode versus monomode optical fiber are compared. Finally, a wavelength multiplexing protocol is implemented for the spatial localization of the acoustic disturbances.
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 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
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.
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.
On Nonlinear Properties of Waves Predicted by a Boussinesq Model
NASA Astrophysics Data System (ADS)
Shi, F.; Kirby, J. T.; Dalrymple, R. A.; Chen, Q.
2002-12-01
In this study, a fully nonlinear Boussinesq model (Wei, et al., 1995) is used to investigate nonlinear wave features observed in a physical model study of Ponce de Leon Inlet, Florida. The experiment was conducted and the laboratory data were provided by the U.S. Army Engineer Research and Development Center. We employ a curvilinear version of the fully nonlinear Boussinesq model and use a curvilinear grid which is able to resolve a broad spectrum of waves in the computational domain. Eighteen cases with monochromatic input waves and TMA spectral waves are carried out. To show the superiority of the Boussinesq model to other conventional wave models, we focus on examinations of wave nonlinearity in the study. Secondary wave crest features are presented by snapshots of the computed wave field and time series of surface elevations in both the physical model and the numerical model. Spectral analyses of spectral wave cases also show the wave energy transfer from the original peak frequencies to the corresponding harmonic frequencies. As another indicator of wave nonlinearity, the probability distributions of wave surface elevations are computed from both the measured data and numerical results and show similar deviations from their Gaussian distributions. Other measures of wave nonlinearity, such as wave skewness and asymmetry, are also examined in the study. The fairly good agreement between modeled and measured indicators of wave nonlinearity demonstrates the capability of the Boussinesq model for predicting nonlinear wave transformation in the nearshore region.
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.
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.
NASA Astrophysics Data System (ADS)
Clary, D. C.; Connor, J. N. L.
Rotationally adiabatic distorted wave (RADW) and vibrationally adiabatic distorted wave (VADW) calculations of total and differential cross sections are reported for the three-dimensional H + H2(v=0, j=0) →H2(v'=0, j') + H and D + H2(v=0, j=0) →DH(v'=0, j') + H chemical reactions. Both the Porter-Karplus (PK) and the Siegbahn-Liu-Truhlar-Horowitz (SLTH) potential energy surfaces are used. The RADW results for D+H2 on the SLTH potential surface agree well with those obtained by Yung et al. In calculations using the PK surface, we obtain poor agreement with the RADW results reported for the H + H2 reaction by Choi and Tang, and for the D + H2 reaction by Tang and Choi. Reasons for these discrepancies are discussed. The absolute total RADW cross sections for the H + H2 reaction using both potential surfaces fall well below those obtained in accurate quantum calculations while the VADW total cross sections are smaller in magnitude than the RADW cross sections. The RADW and VADW results for relative rotational population distributions and for normalized differential cross sections are almost identical, and agree well with accurate quantum calculations for these quantities for the H + H2 reaction using the PK potential surface.
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.
Nonlinear surface acoustic waves in cubic crystals
NASA Astrophysics Data System (ADS)
Kumon, Ronald Edward
Model equations developed by Hamilton, Il'inskii, and Zabolotskaya [J. Acoust. Soc. Am. 105, 639-651 (1999)] are used to perform theoretical and numerical studies of nonlinear surface acoustic waves in a variety of nonpiezoelectric cubic crystals. The basic theory underlying the model equations is outlined, quasilinear solutions of the equations are derived, and expressions are developed for the shock formation distance and nonlinearity coefficient. A time-domain equation corresponding to the frequency-domain model equations is derived and shown to reduce to a time-domain equation introduced previously for Rayleigh waves [E. A. Zabolotskaya, J. Acoust. Soc. Am. 91, 2569-2575 (1992)]. Numerical calculations are performed to predict the evolution of initially monofrequency surface waves in the (001), (110), and (111) planes of the crystals RbCl, KCl, NaCl, CaF2, SrF2, BaF2, C (diamond), Si, Ge, Al, Ni, Cu in the moverline 3m point group, and the crystals Cs-alum, NH4- alum, and K-alum in the moverline 3 point group. The calculations are based on measured second- and third- order elastic constants taken from the literature. Nonlinearity matrix elements which describe the coupling strength of harmonic interactions are shown to provide a powerful tool for characterizing waveform distortion. Simulations in the (001) and (110) planes show that in certain directions the velocity waveform distortion may change in sign, generation of one or more harmonies may be suppressed and shock formation postponed, or energy may be transferred rapidly to the highest harmonics and shock formation enhanced. Simulations in the (111) plane show that the nonlinearity matrix elements are generally complex-valued, which may lead to asymmetric distortion and the appearance of low frequency oscillations near the peaks and shocks in the velocity waveforms. A simple transformation based on the phase of the nonlinearity matrix is shown to provide a reasonable approximation of asymmetric waveform
Strongly nonlinear waves in capillary electrophoresis
NASA Astrophysics Data System (ADS)
Chen, Zhen; Ghosal, Sandip
2012-05-01
In capillary electrophoresis, sample ions migrate along a microcapillary filled with a background electrolyte under the influence of an applied electric field. If the sample concentration is sufficiently high, the electrical conductivity in the sample zone could differ significantly from the background. Under such conditions, the local migration velocity of sample ions becomes concentration-dependent, resulting in a nonlinear wave that exhibits shocklike features. If the nonlinearity is weak, the sample concentration profile, under certain simplifying assumptions, can be shown to obey Burgers’ equation [Ghosal and Chen, Bull. Math. Biol.BMTBAP0092-824010.1007/s11538-010-9527-2 72, 2047 (2010)], which has an exact analytical solution for arbitrary initial condition. In this paper, we use a numerical method to study the problem in the more general case where the sample concentration is not small in comparison to the concentration of background ions. In the case of low concentrations, the numerical results agree with the weakly nonlinear theory presented earlier, but at high concentrations, the wave evolves in a way that is qualitatively different.
Nonlinear wave function expansions : a progress report.
Shepard, R.; Minkoff, M.; Brozell, S. R.; Chemistry
2007-12-01
Some recent progress is reported for a novel nonlinear expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions using the Graphical Unitary Group Approach and the wave function is expanded in a basis of product functions, allowing application to closed and open shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational expansion that depends on a relatively small number of nonlinear parameters called arc factors. Efficient recursive procedures for the computation of reduced one- and two-particle density matrices, overlap matrix elements, and Hamiltonian matrix elements result in a very efficient computational procedure that is applicable to very large configuration state function (CSF) expansions. A new energy-based optimization approach is presented based on product function splitting and variational recombination. Convergence of both valence correlation energy and dynamical correlation energy with respect to the product function basis dimension is examined. A wave function analysis approach suitable for very large CSF expansions is presented based on Shavitt graph node density and arc density. Some new closed-form expressions for various Shavitt Graph and Auxiliary Pair Graph statistics are presented.
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.
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 density waves in the single-wave model
Marinov, Kiril B.; Tzenov, Stephan I.
2011-03-15
The single-wave model equations are transformed to an exact hydrodynamic closure by using a class of solutions to the Vlasov equation corresponding to the waterbag model. The warm fluid dynamic equations are then manipulated by means of the renormalization group method. As a result, amplitude equations for the slowly varying wave amplitudes are derived. Since the characteristic equation for waves has in general three roots, two cases are examined. If all the three roots of the characteristic equation are real, the amplitude equations for the eigenmodes represent a system of three coupled nonlinear equations. In the case where the dispersion equation possesses one real and two complex conjugate roots, the amplitude equations take the form of two coupled equations with complex coefficients. The analytical results are then compared to the exact system dynamics obtained by solving the hydrodynamic equations numerically.
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.
Spin waves cause non-linear friction
NASA Astrophysics Data System (ADS)
Magiera, M. P.; Brendel, L.; Wolf, D. E.; Nowak, U.
2011-07-01
Energy dissipation is studied for a hard magnetic tip that scans a soft magnetic substrate. The dynamics of the atomic moments are simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation numerically. The local energy currents are analysed for the case of a Heisenberg spin chain taken as substrate. This leads to an explanation for the velocity dependence of the friction force: The non-linear contribution for high velocities can be attributed to a spin wave front pushed by the tip along the substrate.
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 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
Moll, Jochen
2016-09-01
This work is based on the experimental observation that the phase and group velocity of the fundamental antisymmetric wave mode in a composite structure with linearly varying thickness changes as it propagates along the nonuniform waveguide (Moll et al., 2015). This adiabatic wave motion leads to systematic damage localization errors of conventional algorithms because a constant wave velocity is assumed in the reconstruction process. This paper presents a generalized beamforming approach for composite structures with nonuniform cross section that eliminates this systematic error. Damage localization results will be presented and discussed in comparison to existing techniques. PMID:27317966
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
Experiments on nonlinear wave propagation in disordered media
NASA Astrophysics Data System (ADS)
McKenna, M. J.; Keat, Justin; Wang, Jun; Maynard, J. D.
1994-02-01
A fundamental question concerning systems which are both disordered and nonlinear is whether or not Anderson localization is weakened by the nonlinearity. Theory predicts that localized eigenstates will survive nonlinearity, whereas nonlinear pulses may or may not experience the effects of localization depending on the relative magnitude of the Anderson localization length and the characteristic width of the pulse. We have used nonlinear surface waves on a superfluid helium film to obtain results in agreement with the theoretical predictions.
Nonlinear low frequency (LF) waves - Comets and foreshock phenomena
NASA Technical Reports Server (NTRS)
Tsurutani, Bruce T.
1991-01-01
A review is conducted of LF wave nonlinear properties at comets and in the earth's foreshock, engaging such compelling questions as why there are no cometary cyclotron waves, the physical mechanism responsible for 'dispersive whiskers', and the character of a general description of linear waves. Attention is given to the nonlinear properties of LF waves, whose development is illustrated by examples of waves and their features at different distances from the comet, as well as by computer simulation results. Also discussed is a curious wave mode detected from Comet Giacobini-Zinner, both at and upstream of the bow shock/wave.
NASA Astrophysics Data System (ADS)
Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru
2015-12-01
We first calculate the ground-state molecular wave function of 1D model H2 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.
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.
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.
Nonlinear interaction of energetic ring current protons with magnetospheric hydromagnetic waves
Chan, A.A.; Chen, Liu; White, R.B.
1989-09-01
In order to study nonlinear wave-particle interactions in the earth's magnetosphere we have derived Hamiltonian equations for the gyrophase-averaged nonrealistic motion of charged particles in a perturbed dipole magnetic field. We assume low frequency (less than the proton gyrofrequency) fully electromagnetic perturbations, and we retain finite Larmor radius effects. Analytic and numerical results for the stochastic threshold of energetic protons ({approx gt} 100 keV) in compressional geomagnetic pulsations in the Pc 5 range of frequencies (150--600 seconds) are presented. These protons undergo a drift-bounce resonance with the Pc 5 waves which breaks the second (longitudinal) and third (flux) adiabatic invariants, while the first invariant (the magnetic moment) and the proton energy are approximately conserved. The proton motion in the observed spectrum of waves is found to be strongly diffusive, due to the overlap of neighboring primary resonances. 17 refs., 2 figs.
Nonlinear interaction of energetic ring current protons with magnetospheric hydromagnetic waves
Chan, A.A.; Chen, L.; White, R.B. )
1989-10-01
In order to study nonlinear wave-particle interactions in the Earth's magnetosphere we have derived Hamiltonian equations for the gyrophase-averaged nonrelativistic motion of charged particles in a perturbed dipole magnetic field. We assume low frequency (less than the proton gyrofrequency) fully electromagnetic perturbations, and we retain finite Larmor radius effects. Analytic and numerical results for the stochastic threshold of energetic protons ({approx gt}100 keV) in compressional geomagnetic pulsations in the Pc 5 range of frequencies 150--600 seconds are presented. These protons undergo a drift-bounce resonance with the Pc 5 waves which breaks the second (longitudinal) and third (flux) adiabatic invariants, while the first invariant (the magnetic moment) and the proton energy are approximately conserved. The proton motion in the observed spectrum of waves is found to be strongly diffusive, due to the overlap of neighboring primary resonances. {copyright} American Geophysical Union 1989
Nonlinear 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.
Nonlinear Landau damping of transverse electromagnetic waves in dusty plasmas
Tsintsadze, N. L.; Chaudhary, Rozina; Shah, H. A.; Murtaza, G.
2009-04-15
High-frequency transverse electromagnetic waves in a collisionless isotropic dusty plasma damp via nonlinear Landau damping. Taking into account the latter we have obtained a generalized set of Zakharov equations with local and nonlocal terms. Then from this coupled set of Zakharov equations a kinetic nonlinear Schroedinger equation with local and nonlocal nonlinearities is derived for special cases. It is shown that the modulation of the amplitude of the electromagnetic waves leads to the modulation instability through the nonlinear Landau damping term. The maximum growth rate is obtained for the special case when the group velocity of electromagnetic waves is close to the dust acoustic velocity.
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.
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.
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.
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.
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"
The effect of nonlinear traveling waves on rotating machinery
NASA Astrophysics Data System (ADS)
Jauregui-Correa, Juan Carlos
2013-08-01
The effect of the housing stiffness on nonlinear traveling waves is presented in this work. It was found that the housing controls the synchronization of nonlinear elements and it allows nonlinear waves to travel through the structure. This phenomenon was observed in a gearbox with a soft housing, and the phenomenon was reproduced with a lump-mass dynamic model. The model included a pair of gears, the rolling bearings and the housing. The model considered all the nonlinear effects. Numerical and experimental results were analyzed with a time-frequency method using the Morlet wavelet function. A compound effect was observed when the nonlinear waves travel between the gears and the bearings: the waves increased the dynamic load amplitude and add another periodic load.
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.
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
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.
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.
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.
Fully efficient adiabatic frequency conversion of broadband Ti:sapphire oscillator pulses.
Moses, Jeffrey; Suchowski, Haim; Kärtner, Franz X
2012-05-01
By adiabatic difference-frequency generation in an aperiodically poled nonlinear crystal-a nonlinear optical analog of rapid adiabatic passage in a two-level atomic system-we demonstrate the conversion of a 110 nm band from an octave-spanning Ti:sapphire oscillator to the infrared, spanning 1550 to 2450 nm, with near-100% internal conversion efficiency. The experiment proves the principle of complete Landau-Zener adiabatic transfer in nonlinear optical wave mixing. Our implementation is a practical approach to the seeding of high-energy ultrabroadband optical parametric chirped pulse amplifiers. PMID:22555747
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.
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.
Nonlinear electrostatic solitary waves in electron-positron plasmas
NASA Astrophysics Data System (ADS)
Lazarus, I. J.; Bharuthram, R.; Moolla, S.; Singh, S. V.; Lakhina, G. S.
2016-02-01
The generation of nonlinear electrostatic solitary waves (ESWs) is explored in a magnetized four component two-temperature electron-positron plasma. Fluid theory is used to derive a set of nonlinear equations for the ESWs, which propagate obliquely to an external magnetic field. The electric field structures are examined for various plasma parameters and are shown to yield sinusoidal, sawtooth and bipolar waveforms. It is found that an increase in the densities of the electrons and positrons strengthen the nonlinearity while the periodicity and nonlinearity of the wave increases as the cool-to-hot temperature ratio increases. Our results could be useful in understanding nonlinear propagation of waves in astrophysical environments and related laboratory experiments.
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
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.
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 mixing of electromagnetic waves in plasmas.
Stefan, V; Cohen, B I; Joshi, C
1989-01-27
Recently, a strong research effort has been focused on applications of beat waves in plasma interactions. This research has important implications for various aspects of plasma physics and plasma technology. This article reviews the present status of the field and comments on plasma probing, heating of magnetically confined and laser plasmas, ionospheric plasma modification, beat-wave particle acceleration, beat-wave current drive in toroidal devices, beat wave-driven free-electron lasers, and phase conjugation with beat waves. PMID:17799185
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.
Capillary waves in the subcritical nonlinear Schroedinger equation
Kozyreff, G.
2010-01-15
We expand recent results on the nonlinear Schroedinger equation with cubic-quintic nonlinearity to show that some solutions are described by the Bernoulli equation in the presence of surface tension. As a consequence, capillary waves are predicted and found numerically at the interface between regions of large and low amplitude.
Non-linear interaction of elastic waves in rocks
NASA Astrophysics Data System (ADS)
Kuvshinov, B. N.; Smit, T. J. H.; Campman, X. H.
2013-09-01
We study theoretically the interaction of elastic waves caused by non-linearities of rock elastic moduli, and assess the possibility to use this phenomenon in hydrocarbon exploration and in the analysis of rock samples. In our calculations we use the five-constant model by Gol'dberg. It is shown that the interaction of plane waves in isotropic solids is completely described by five coupling coefficients, which have the same order of magnitude. By considering scattering of compressional waves generated by controlled sources at the Earth surface from a non-linear layer at the subsurface, we conclude that non-linear signals from deep formations are unlikely to be measured with the current level of technology. Our analysis of field tests where non-linear signals were measured, suggests that these signals are generated either in the shallow subsurface or in the vicinity of sources. Non-linear wave interaction might be observable in lab tests with focused ultrasonic beams. In this case, the non-linear response is generated in the secondary parametric array formed by linear beams scattered from inclusions. Although the strength of this response is controlled by non-linearity of the surrounding medium rather than by non-linearity of inclusions, its measurement can help to obtain better images of rock samples.
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 slow magnetoacoustic waves in coronal plasma structures
NASA Astrophysics Data System (ADS)
Afanasyev, A. N.; Nakariakov, V. M.
2015-01-01
Context. There is abundant observational evidence of longitudinal waves in the plasma structures of the solar corona. These essentially compressive waves are confidently interpreted as slow magnetoacoustic waves. The use of the slow waves in plasma diagnostics and estimating their possible contribution to plasma heating and acceleration require detailed theoretical modelling. Aims: We investigate the role of obliqueness and magnetic effects in the evolution of slow magnetoacoustic waves, also called tube waves, in field-aligned plasma structures. Special attention is paid to the wave damping caused by nonlinear steepening. Methods: We considered an untwisted straight axisymmetric field-aligned plasma cylinder and analysed the behaviour of the slow magnetoacoustic waves that are guided by this plasma structure. We adopted a thin flux tube approximation. We took into account dissipation caused by viscosity, resistivity and thermal conduction, and nonlinearity. Effects of stratification and dispersion caused by the finite radius of the flux tube were neglected. Results: We derive the Burgers-type evolutionary equation for tube waves in a uniform plasma cylinder. Compared with a plane acoustic wave, the formation of shock fronts in tube waves is found to occur at a larger distance from the source. In addition, tube waves experience stronger damping. These effects are most pronounced in plasmas with the parameter β at about or greater than unity. In a low-β plasma, the evolution of tube waves can satisfactorily be described with the Burgers equation for plane acoustic waves. Conclusions:
Nonlinear spin-wave excitations at low magnetic bias fields
NASA Astrophysics Data System (ADS)
Woltersdorf, Georg
We investigate experimentally and theoretically the nonlinear magnetization dynamics in magnetic films at low magnetic bias fields. Nonlinear magnetization dynamics is essential for the operation of numerous spintronic devices ranging from magnetic memory to spin torque microwave generators. Examples are microwave-assisted switching of magnetic structures and the generation of spin currents at low bias fields by high-amplitude ferromagnetic resonance. In the experiments we use X-ray magnetic circular dichroism to determine the number density of excited magnons in magnetically soft Ni80Fe20 thin films. Our data show that the common Suhl instability model of nonlinear ferromagnetic resonance is not adequate for the description of the nonlinear behavior in the low magnetic field limit. Here we derive a model of parametric spin-wave excitation, which correctly predicts nonlinear threshold amplitudes and decay rates at high and at low magnetic bias fields. In fact, a series of critical spin-wave modes with fast oscillations of the amplitude and phase is found, generalizing the theory of parametric spin-wave excitation to large modulation amplitudes. For these modes, we also find pronounced frequency locking effects that may be used for synchronization purposes in magnonic devices. By using this effect, effective spin-wave sources based on parametric spin-wave excitation may be realized. Our results also show that it is not required to invoke a wave vector-dependent damping parameter in the interpretation of nonlinear magnetic resonance experiments performed at low bias fields.
Instabilities in nonlinear internal waves on the Washington continental shelf
NASA Astrophysics Data System (ADS)
Zhang, Shuang; Alford, Matthew H.
2015-07-01
Previous studies have identified two primary mechanisms (shear instability and convective instability) by which nonlinear internal waves (NLIWs) induce mixing on continental shelves. To determine the relative importance of these and their dependence on background flow conditions, we examine a much longer (6 month) data set from a moored ADCP/thermistor chain with 2 m vertical spacing in which over 600 NLIWs are detected. Turbulent properties of the 318 waves with detectable overturning instabilities are documented using Thorpe scales. The 130 waves detected while an ADCP was functioning are classified based on a Froude number criterion (Fr =
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.
Perturbation approach to dispersion curves calculation for nonlinear Lamb waves
NASA Astrophysics Data System (ADS)
Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2015-05-01
Analysis of elastic wave propagation in nonlinear media has gained recent research attention due to the recognition of their amplitude-dependent behavior. This creates opportunities for increased accuracy of damage detection and localization, development of new structural monitoring strategies, and design of new structures with desirable acoustic behavior (e.g., amplitude-dependent frequency bandgaps, wave beaming, and filtering). This differs from more traditional nonlinear analysis approaches which target the prediction of higher harmonic growth. Of particular interest in this work is the analysis of amplitude-dependent shifts in Lamb wave dispersion curves. Typically, dispersion curves are calculated for nominally linear material parameters and geometrical features of a waveguide, even when the constitutive law is nonlinear. Instead, this work employs a Lindstedt - Poincare perturbation approach to calculate amplitude-dependent dispersion curves, and shifts thereof, for nonlinearly-elastic plates. As a result, a set of first order corrections to frequency (or equivalently wavenumber) are calculated. These corrections yield significant amplitude dependence in the spectral characteristics of the calculated waves, especially for high frequency waves, which differs fundamentally from linear analyses. Numerical simulations confirm the analytical shifts predicted. Recognition of this amplitude-dependence in Lamb wave dispersion may suggest, among other things, that the analysis of guided wave propagation phenomena within a fully nonlinear framework needs to revisit mode-mode energy flux and higher harmonics generation conditions.
Switchable nonlinear metasurfaces for absorbing high power surface waves
NASA Astrophysics Data System (ADS)
Kim, Sanghoon; Wakatsuchi, Hiroki; Rushton, Jeremiah J.; Sievenpiper, Daniel F.
2016-01-01
We demonstrate a concept of a nonlinear metamaterial that provides power dependent absorption of incident surface waves. The metasurface includes nonlinear circuits which transform it from a low loss to high loss state when illuminated with high power waves. The proposed surface allows low power signals to propagate but strongly absorbs high power signals. It can potentially be used on enclosures for electric devices to protest against damage. We experimentally verify that the nonlinear metasurface has two distinct states controlled by the incoming signal power. We also demonstrate that it inhibits the propagation of large signals and dramatically decreases the field that is leaked through an opening in a conductive enclosure.
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
Travelling waves in nonlinear magneto-inductive lattices
NASA Astrophysics Data System (ADS)
Agaoglou, M.; Fečkan, M.; Pospíšil, M.; Rothos, V. M.; Susanto, H.
2016-01-01
We consider a lattice equation modelling one-dimensional metamaterials formed by a discrete array of nonlinear resonators. We focus on periodic travelling waves due to the presence of a periodic force. The existence and uniqueness results of periodic travelling waves of the system are presented. Our analytical results are found to be in good agreement with direct numerical computations.
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.
Nonlinear isothermal waves in a degenerate electron plasma
Dubinov, A. E.; Dubinova, A. A.
2008-05-15
A nonlinear differential equation describing oscillations of the chemical potential in a one-dimensional steady-state wave propagating in a degenerate electron gas against an immobile neutralizing ion background is derived, investigated, and solved exactly. It is found that the wave phase velocity is bounded below by a critical velocity, whose exact value is obtained.
Nonlinear wave propagation in strongly coupled dusty plasmas.
Veeresha, B M; Tiwari, S K; Sen, A; Kaw, P K; Das, A
2010-03-01
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. PMID:20365882
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.
Nonlinear spin-wave excitations at low magnetic bias fields
Bauer, Hans G.; Majchrak, Peter; Kachel, Torsten; Back, Christian H.; Woltersdorf, Georg
2015-01-01
Nonlinear magnetization dynamics is essential for the operation of numerous spintronic devices ranging from magnetic memory to spin torque microwave generators. Examples are microwave-assisted switching of magnetic structures and the generation of spin currents at low bias fields by high-amplitude ferromagnetic resonance. Here we use X-ray magnetic circular dichroism to determine the number density of excited magnons in magnetically soft Ni80Fe20 thin films. Our data show that the common model of nonlinear ferromagnetic resonance is not adequate for the description of the nonlinear behaviour in the low magnetic field limit. Here we derive a model of parametric spin-wave excitation, which correctly predicts nonlinear threshold amplitudes and decay rates at high and at low magnetic bias fields. In fact, a series of critical spin-wave modes with fast oscillations of the amplitude and phase is found, generalizing the theory of parametric spin-wave excitation to large modulation amplitudes. PMID:26374256
Nonlinear current response of a d-wave superfluid
NASA Astrophysics Data System (ADS)
Dahm, T.; Scalapino, D. J.
1999-11-01
Despite several efforts the nonlinear Meissner effect in d-wave superconductors, as has been discussed by Yip and Sauls in 1992, has not been verified experimentally in high-Tc superconductors at present. Here, we reinvestigate the nonlinear response expected in a d-wave superconductor. While the linear \\|H-->\\| field dependence of the penetration depth, predicted by Yip and Sauls, is restricted by the lower critical field and can be masked by nonlocal effects, we argue that the upturn of the nonlinear coefficient of the quadratic field dependence is more stable and remains observable over a broader range of parameters. We investigate this by studying the influence of nonmagnetic impurities on the nonlinear response. We discuss the difficulties of observing this intrinsic d-wave signature in present day high-Tc films and single crystals.
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.
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.
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.
Nonlinear periodic space-charge waves in plasma
Kovalev, V. A.
2009-05-15
A solution is obtained in the form of coupled nonlinear periodic space-charge waves propagating in a magnetoactive plasma. The wave spectrum in the vicinity of the critical point, where the number of harmonics increases substantially, is found to fall with harmonic number as {proportional_to} s{sup -1/3}. Periodic space-charge waves are invoked to explain the zebra pattern in the radio emission from solar flares.
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.
Modelization of highly nonlinear waves in coastal regions
NASA Astrophysics Data System (ADS)
Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre
2015-04-01
The proposed work deals with the development of a highly non-linear model for water wave propagation in coastal regions. The accurate modelization of surface gravity waves is of major interest in ocean engineering, especially in the field of marine renewable energy. These marine structures are intended to be settled in coastal regions where the effect of variable bathymetry may be significant on local wave conditions. This study presents a numerical model for the wave propagation with complex bathymetry. It is based on High-Order Spectral (HOS) method, initially limited to the propagation of non-linear wave fields over flat bottom. Such a model has been developed and validated at the LHEEA Lab. (Ecole Centrale Nantes) over the past few years and the current developments will enlarge its application range. This new numerical model will keep the interesting numerical properties of the original pseudo-spectral approach (convergence, efficiency with the use of FFTs, …) and enable the possibility to propagate highly non-linear wave fields over long time and large distance. Different validations will be provided in addition to the presentation of the method. At first, Bragg reflection will be studied with the proposed approach. If the Bragg condition is satisfied, the reflected wave generated by a sinusoidal bottom patch should be amplified as a result of resonant quadratic interactions between incident wave and bottom. Comparisons will be provided with experiments and reference solutions. Then, the method will be used to consider the transformation of a non-linear monochromatic wave as it propagates up and over a submerged bar. As the waves travel up the front slope of the bar, it steepens and high harmonics are generated due to non-linear interactions. Comparisons with experimental data will be provided. The different test cases will assess the accuracy and efficiency of the method proposed.
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.
NASA Astrophysics Data System (ADS)
Xie, Xi-Yang; Tian, Bo; Wang, Yu-Feng; Sun, Ya; Jiang, Yan
2015-11-01
In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable-coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.
Low-loss adiabatically-tapered high-contrast gratings for slow-wave modulators on SOI
NASA Astrophysics Data System (ADS)
Sciancalepore, Corrado; Hassan, Karim; Ferrotti, Thomas; Harduin, Julie; Duprez, Hélène; Menezo, Sylvie; Ben Bakir, Badhise
2015-02-01
In this communication, we report about the design, fabrication, and testing of Silicon-based photonic integrated circuits (Si-PICs) including low-loss flat-band slow-light high-contrast-gratings (HCGs) waveguides at 1.31 μm. The light slowdown is achieved in 300-nm-thick silicon-on-insulator (SOI) rib waveguides by patterning adiabatically-tapered highcontrast gratings, capable of providing slow-light propagation with extremely low optical losses, back-scattering, and Fabry-Pérot noise. In detail, the one-dimensional (1-D) grating architecture is capable to provide band-edge group indices ng ~ 25, characterized by overall propagation losses equivalent to those of the index-like propagation regime (~ 1-2 dB/cm). Such photonic band-edge slow-light regime at low propagation losses is made possible by the adiabatic apodization of such 1-D HCGs, thus resulting in a win-win approach where light slow-down regime is reached without additional optical losses penalty. As well as that, a tailored apodization optimized via genetic algorithms allows the flattening of slow-light regime over the wavelength window of interest, therefore suiting well needs for group index stability for modulation purposes and non-linear effects generation. In conclusion, such architectures provide key features suitable for power-efficient high-speed modulators in silicon as well as an extremely low-loss building block for non-linear optics (NLO) which is now available in the Si photonics toolbox.
Nonlinear diffusion waves in high magnetic fields
NASA Astrophysics Data System (ADS)
Oreshkin, V. I.; Chaikovsky, S. A.; Labetskaya, N. A.; Datsko, I. M.; Rybka, D. V.; Ratakhin, N. A.; Khishchenko, K. V.
2015-11-01
The nonlinear diffusion of a magnetic field and the large-scale instabilities arising upon an electrical explosion of conductors in a superstrong (2-3 MG) magnetic field were investigated experimentally on the MIG high-current generator (up to 2.5 peak current, 100 ns current rise time). It was observed that in the nonlinear stage of the process, the wavelength of thermal instabilities (striations) increased with a rate of 1.5-3 km/s.
Nonlinear electron magnetohydrodynamics physics. II. Wave propagation and wave-wave interactions
Urrutia, J. M.; Stenzel, R. L.; Strohmaier, K. D.
2008-04-15
The propagation of low-frequency whistler modes with wave magnetic field exceeding the ambient field is investigated experimentally. Such nonlinear waves are excited with magnetic loop antennas whose axial field is aligned with the background magnetic field and greatly exceeds its strength. The oscillatory antenna field excites propagating wave packets with field topologies alternating between whistler spheromaks and mirrors. The propagation speed of spheromaks is observed to decrease with amplitude while that of mirrors increases with amplitude. The field distribution varies with amplitude: Spheromaks contract axially while mirrors spread out compared to linear whistlers. Consequently, the peak magnetic field and current densities in spheromaks exceed that of mirrors. Wave-wave interactions of nonlinear whistler modes is also studied. Counterpropagating spheromaks collide inelastically and form a stationary field-reversed configuration. The radius of the toroidal current ring depends on current and can be larger than that of the loop antenna. A tilted field-reversed configuration precesses in the direction of the electron drift. The free magnetic energy is dissipated in the plasma volume and converted into electron heat.
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.
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 internal wave penetration via parametric subharmonic instability
NASA Astrophysics Data System (ADS)
Ghaemsaidi, S. J.; Joubaud, S.; Dauxois, T.; Odier, P.; Peacock, T.
2016-01-01
We present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially periodic boundary forcing from above of a density stratification comprising a strongly stratified, thin upper layer sitting atop a weakly stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly stratified lower layer. We find that around 10% of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study.
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
NASA Astrophysics Data System (ADS)
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), 10.1017/jfm.2013.584] 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.
Second harmonic generation using nonlinear Rayleigh surface waves in stone
NASA Astrophysics Data System (ADS)
Smith, Margaret; Kim, Gun; Kim, Jin-Yeon; Kurtis, Kimberly; Jacobs, Laurence
2015-03-01
This research tests the potential application of the Second Harmonic Generation (SHG) method using nonlinear Rayleigh surface waves to nondestructively quantify surface microstructural changes in thin stone. The acoustic nonlinearity parameter (β) has been assessed as a meaningful indicator for characterizing the nonlinearity of civil engineering materials; additionally, Rayleigh waves offer the opportunity to isolate a material's near surface microstructural status. Sandstone was selected for testing due to its relative uniformity and small grain size compared to other stone types; the sample thickness was 2 inches to reflect the minimum panel thickness recommended by the Indiana Limestone Institute. For this research, initially fully non-contact generation and detection techniques are evaluated before a 100kHz wedge transmitter and a 200kHz air-coupled receiver are employed for generation and detection of nonlinear Rayleigh waves. Non-contact transmitters and receivers have advantages such as removing the irregularities associated with coupling as well as not leaving residues, which in stone applications can be considered aesthetically damaging. The experimental results show that the nonlinear parameter, β, can be effectively isolated using the wedge transmitter and non-contact set up and that too much of the signal strength is lost in the fully non-contact method to extract meaningful results for this stone and stones with slow wave speeds. This indicates that the proposed SHG technique is effective for evaluating the nonlinearity parameter, β, and can next be applied to characterize near surface microstructural changes in thin applications of dimensioned stone.
Prospect of Nonlinear Freak Tsunami Waves from Stochastic Earthquake Sources
NASA Astrophysics Data System (ADS)
Geist, E. L.
2014-12-01
The prospect of freak (or rogue) tsunami edge waves from continental subduction zone earthquakes is examined. Although the hydrodynamics that govern tsunamis are formulated from the shallow-water wave equations, the dispersion relation for edge waves is similar to that for deep-water waves. As a result, freak waves can result from many of the same mechanisms as for deep-water waves: spatial focusing, dispersive (temporal) focusing, modulation instability, and mode coupling from resonant interaction. The focus of this study is on determining the likelihood of freak edge waves from the two nonlinear mechanisms: modulation instability and mode coupling. The initial conditions are provided by coseismic vertical displacement from a subduction thrust earthquake. A two-dimensional stochastic slip model is used to generate a range of coseismic displacement realizations. The slip model is defined by a power-law wavenumber spectrum and Lévy-law distributed random variables. Tsunami edge waves produced by this source model have a broader spectrum with energy distributed across many more modes compared to edge waves derived from the simplified earthquake sources used in the past. To characterize modulation instability, methods developed for a random sea are modified for seismogenic edge waves. The Benjamin-Feir parameter constrains how many unstable wave packets are possible in a time series of finite length. In addition, because seismogenic tsunami edge wave energy is distributed across a number of modes, nonlinear mode coupling can result both in the collinear case and in the counter-propagating case where edge waves are reflected by coastline irregularities. Mode coupling results in the appearance of a third edge wave mode that can greatly increase the variability in wave heights. Determination of possible freak tsunami edge waves is important for assessing the tsunami hazard at longshore locations distant from the rupture zone of continental subduction zone earthquakes.
Nonlinear inertial Alfven wave in dusty plasmas
Mahmood, S.; Saleem, H.
2011-11-29
Solitary inertial Alfven wave in the presence of positively and negatively charged dust particles is studied. It is found that electron density dips are formed in the super Alfvenic region and wave amplitude is increased for the case of negatively charged dust particles in comparison with positively charged dust particles in electron-ion plasmas.
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.
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.
Nonlinear surface wave instability for electrified Kelvin fluids.
El-Dib, Yusry O; Abd El-Latif, Osama E
2005-05-15
A weakly nonlinear approach is utilized here to discuss surface wave instability for two superposed electrified fluids of Kelvin type. The influence of a vertical electric field is discussed. The linear form for equations of motion is solved in the light of nonlinear boundary conditions. The method of multiple scales is used for the purpose of nonlinear perturbation. The surface wave response is governed by the well-known nonlinear Ginzburg-Landau equation rather than the transcendental dispersion relation in the linear scope. Although linear stability conditions are not available for arbitrary viscosity, the nonlinear analysis allowed deriving necessary and sufficient stability conditions. Moreover, at the marginal state, the nonlinear scope for stability is discussed through its dependence on the wavetrain frequency, in which short-wave disturbance is assumed to relax the linear transcendental terms. Besides the linear stability constraint, the nonlinear scope gives an additional constraint on the wavetrain frequency. Nonlinear stability criteria are derived and are performed in view of a nondimensional form. Furthermore, the nonlinear analysis is repeated for an arbitrary wave disturbance. A suitable choice for dimensionless form made it possible to relax transcendental terms included in stability conditions. Numerical calculations at the marginal state show that both the vertical electric field and the stratified fluid density play a dual role in the stability criteria. This dual role is the opposite to the dual role that the stratified viscosity plays in the stability profile. For the marginal state representation, numerical examination shows that elasticity plays a dual role in the stability criteria in a manner similar to that of the viscosity behavior. PMID:15837494
On the Cauchy problem for strongly nonlinear intense wave groups
NASA Astrophysics Data System (ADS)
Slunyaev, Alexey
2015-04-01
Stable long-living nonlinear groups of gravity water waves (very steep and very short envelope solitons) were first observed in numerical simulations [1, 2] and then - in laboratory conditions [3]. In [2] their interaction was shown to be almost elastic in some (but not all) situations. Therefore the Cauchy problem for localized wave groups beyond the weakly nonlinear assumption is of interest. In general, the formation of a few solitary wave groups from the initial condition may take place [4]. We have focused on the unidentified reason, why some experimental tests of solitary wave groups in [3] were not successful (while other runs with slightly different experimental parameters were successful). In this paper we consider the initial problem, when the initial condition is taken in the form of a scaled intense envelope soliton of the nonlinear Schrodinger equation, and is simulated by means of the fully nonlinear code of potential Euler equations. The result of the long-term evolution (which is generally represented by a solitary wave group and smaller scale waves) is compared with the prediction of the weakly nonlinear theory. We show reasonable agreement between the weakly nonlinear theory and the strongly nonlinear simulations. In particular, a 10% decrease of the initial perturbation results in 20% smaller amplitude of the eventual envelope soliton. This fact explains the failure of reproduction of envelope solitons in some experimental tests in the finite-depth flume [3]. The solution of the nonlinear Schrodinger equation for finite-depth water may be transformed to the infinite-depth solution with reduced amplitude. [1] A.I. Dyachenko, V.E. Zakharov, On the formation of freak waves on the surface of deep water. J. Exp. Theor. Phys. Lett. 88, 307-311 (2008). [2] A.V. Slunyaev, Numerical simulation of "limiting" envelope solitons of gravity waves on deep water. JETP 109, 676-686 (2009). [3] A. Slunyaev, G.F. Clauss, M. Klein, M. Onorato, Simulations and
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.
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. PMID:19518527
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
NASA Astrophysics Data System (ADS)
Marino, F.; Maitland, C.; Vocke, D.; Ortolan, A.; Faccio, D.
2016-03-01
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Torello, David; Kim, Jin-Yeon; Qu, Jianmin; Jacobs, Laurence J.
2015-03-01
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 β11 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 β117075/β112024 measure of 1.363 agrees well with previous literature and earlier work.
Nonlinear waves on a string with inhomogeneous properties
NASA Astrophysics Data System (ADS)
Arredondo, Robert
Nonlinear waves on an infinite string with a rapid change in properties at one location are treated. The string is an idealized version of more complex configurations in both fluids and solids. This idealized version treats the property change as an interface with a discontinuity in properties. Packets of waves are then considered with a reduced model, here a set of nonlinear Schrodinger (NLS) equations. The stress and the displacement must both be matched at the interface, resulting in dynamic and kinematic interfacial conditions. The dynamic condition produces an inhomogeneous effect that cannot be treated successfully with separation-of-variables. This inhomogeneity is treated here with a time-evolution approach using Laplace transforms. The results show that this inhomogeneity creates a mean longitudinal displacement on both sides of the interface and a shift in the position of the interface as the waves transit the interface. This mean longitudinal displacement corresponds to a sustained strain in the string. The mean longitudinal displacement develops three distinct features. One feature has a length scale that is half the wave-length of the incident waves, while the lengths of the other two features have the same order as the length of the wave packet. The position of maximum strain as a result of this mean is often at the interface, depending on parameter values. These results apply to a variety of applications, such as waves in ocean ice, Rayleigh waves caused by earthquakes, internal waves in the oceans and atmosphere, as well as waves in stretched cables.
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.
Numerical modelling of nonlinear full-wave acoustic propagation
NASA Astrophysics Data System (ADS)
Velasco-Segura, Roberto; Rendón, Pablo L.
2015-10-01
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.
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.
Exact traveling wave solutions for system of nonlinear evolution equations.
Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H
2016-01-01
In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis. PMID:27347461
Nonlinear interaction of atmospheric, surface-gravity, and hydroacoustic waves
NASA Astrophysics Data System (ADS)
Kadri, Usama
2016-04-01
We discuss the generation of hydroacoustic waves by the mutual interaction of atmospheric and surface-gravity waves, through nonlinear resonant triad interaction. To this end, we consider a two fluid problem, with a half-space air layer over a compressible water layer of finite depth, and a rigid bottom. The governing equations comprise a quadratic compressible wave equation, and the standard associated boundary conditions. Using a multiple scale approach we derive at the amplitude evolution equations for all three triad members. It is shown that the energy input by the atmospheric wave is transferred to the acoustic mode, with no noticeable effect on the surface gravity mode.
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.
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.
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 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.
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.
Nonlinearly driven oscillations in the gyrotron traveling-wave amplifier
Chiu, C. C.; Pao, K. F.; Yan, Y. C.; Chu, K. R.; Barnett, L. R.; Luhmann, N. C. Jr.
2008-12-15
By delivering unprecedented power and gain, the gyrotron traveling-wave amplifier (gyro-TWT) offers great promise for advanced millimeter wave radars. However, the underlying physics of this complex nonlinear system is yet to be fully elucidated. Here, we report a new phenomenon in the form of nonlinearly driven oscillations. A zero-drive stable gyro-TWT is shown to be susceptible to a considerably reduced dynamic range at the band edge, followed by a sudden transition into driven oscillations and then a hysteresis effect. An analysis of this unexpected behavior and its physical interpretation are presented.
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.
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.
Matter-wave soliton interferometer based on a nonlinear splitter
NASA Astrophysics Data System (ADS)
Sakaguchi, Hidetsugu; Malomed, Boris A.
2016-02-01
We elaborate a model of the interferometer which, unlike previously studied ones, uses a local (δ-functional) nonlinear repulsive potential, embedded into a harmonic-oscillator trapping potential, as the splitter for the incident soliton. An estimate demonstrates that this setting may be implemented by means of the localized Feshbach resonance controlled by a focused laser beam. The same system may be realized as a nonlinear waveguide in optics. Subsequent analysis produces an exact solution for scattering of a plane wave in the linear medium on the δ -functional nonlinear repulsive potential, and an approximate solution for splitting of the incident soliton when the ambient medium is nonlinear. The most essential result, obtained by means of systematic simulations, is that the use of the nonlinear splitter provides the sensitivity of the soliton-based interferometer to the target, inserted into one of its arms, which is much higher than the sensitivity provided by the usual linear splitter.
Study of solar wind spectra by nonlinear waves interaction
NASA Astrophysics Data System (ADS)
Dwivedi, Navin; Sharma, Rampal; Narita, Yasuhito
2014-05-01
The nature of small-scale turbulent fluctuations in the solar wind (SW) turbulence is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations predict the evidence of the dominance of kinetic Alfvén waves (KAW) at sub-ion scales with frequency below than ion cyclotron frequency, while other studies suggest that the KAW mode cannot carry the turbulence cascade down to electron scales and that the whistler mode is more relevant. In the present work, nonlinear interaction of kinetic Alfvén wave with whistler wave is considered as one of the possible cause responsible for the solar wind turbulence. A set of coupled dimensionless equations are derived for the intermediate beta plasmas and the nonlinear interaction between these two wave modes has been studied. As a consequence of ponderomotive nonlinearity, the pump KAW becomes filamented when its power exceeds the threshold for the filamentation instability. Whistler is considered to be weak and thus doesn't have enough intensity to initiate its own localization. It gets localized while propagating through the density channel created by KAW localization. In addition, spectral scales of power spectra of KAW and whistler are also calculated. The steeper spectra are found with scaling greater than -5/3. This type of nonlinear interaction between different wave modes and steeper spectra is one of the reasons for the solar wind turbulence and particles acceleration. This work is partially supported by DST (India) and FP7/STORM (313038)
Nonlinear Waves in Hall MHD: Analysis and Comparison to Known Linear Waves
NASA Astrophysics Data System (ADS)
Pino, Jesse; Mahajan, Swadesh; Dorland, William
2004-11-01
Recently, a novel set of nonlinear waves were found to satisfy the Hall-Magnetohydrodynamic (HMHD) equations. The Mahajan-Krishan solution is a generalization of the classic Walén Nonlinear Alvén wave, of the form b=±αv. The implications of this mode are studied, including polarization and superposition. In particular, the gyrokinetic limit (k_⊥≫ k_\\|) is used in an attempt to match the MK wave to known Kinetic Alfvén waves and introduce FLR effects.
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.
Air-coupled detection of nonlinear Rayleigh surface waves to assess material nonlinearity.
Thiele, Sebastian; Kim, Jin-Yeon; Qu, Jianmin; Jacobs, Laurence J
2014-08-01
This research presents a new technique for nonlinear Rayleigh surface wave measurements that uses a non-contact, air-coupled ultrasonic transducer; this receiver is less dependent on surface conditions than laser-based detection, and is much more accurate and efficient than detection with a contact wedge transducer. A viable experimental setup is presented that enables the robust, non-contact measurement of nonlinear Rayleigh surface waves over a range of propagation distances. The relative nonlinearity parameter is obtained as the slope of the normalized second harmonic amplitudes plotted versus propagation distance. This experimental setup is then used to assess the relative nonlinearity parameters of two aluminum alloy specimens (Al 2024-T351 and Al 7075-T651). These results demonstrate the effectiveness of the proposed technique - the average standard deviation of the normalized second harmonic amplitudes, measured at locations along the propagation path, is below 2%. Experimental validation is provided by a comparison of the ratio of the measured nonlinearity parameters of these specimens with ratios from the absolute nonlinearity parameters for the same materials measured by capacitive detection of nonlinear longitudinal waves. PMID:24836962
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
On the nature of kinetic electrostatic electron nonlinear (KEEN) waves
NASA Astrophysics Data System (ADS)
Dodin, I. Y.; Fisch, N. J.
2014-03-01
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.
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.
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
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.
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.
Optimization of a finite difference method for nonlinear wave equations
NASA Astrophysics Data System (ADS)
Chen, Miaochao
2013-07-01
Wave equations have important fluid dynamics background, which are extensively used in many fields, such as aviation, meteorology, maritime, water conservancy, etc. This paper is devoted to the explicit difference method for nonlinear wave equations. Firstly, a three-level and explicit difference scheme is derived. It is shown that the explicit difference scheme is uniquely solvable and convergent. Moreover, a numerical experiment is conducted to illustrate the theoretical results of the presented method.
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. PMID:11910107
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.
Multidimensional detonation propagation modeled via nonlinear shock wave superposition
NASA Astrophysics Data System (ADS)
Higgins, Andrew; Mehrjoo, Navid
2010-11-01
Detonation waves in gases are inherently multidimensional due to their cellular structure, and detonations in liquids and heterogeneous solids are often associated with instabilities and stochastic, localized reaction centers (i.e., hot spots). To explore the statistical nature of detonation dynamics in such systems, a simple model that idealizes detonation propagation as an ensemble of interacting blast waves originating from spatially random point sources has been proposed. Prior results using this model exhibited features that have been observed in real detonating systems, such as anomalous scaling between axisymmetric and two-dimensional geometries. However, those efforts used simple linear superposition of the blast waves. The present work uses a model of blast wave superposition developed for multiple-source explosions (the LAMB approximation) that incorporates the nonlinear interaction of shock waves analytically, permitting the effect of a more physical model of blast wave interaction to be explored. The results are suggestive of a universal behavior in systems of spatially randomized energy sources.
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.
Analysis of nonlinear internal waves in the New York Bight
NASA Technical Reports Server (NTRS)
Liu, Antony K.
1988-01-01
An analysis of the nonlinear-internal-wave evolution in the New York Bight was performed on the basis of current meter mooring data obtained in the New York Bight during the SAR Internal Wave Signature Experiment (SARSEX). The solitary wave theory was extended to include dissipation and shoaling effects, and a series of numerical experiments were performed by solving the wave evolution equation, with waveforms observed in the SARSEX area as initial conditions. The results of calculations demonstrate that the relative balance of dissipation and shoaling effects is crucial to the detailed evolution of internal wave packets. From an observed initial wave packet at the upstream mooring, the numerical evolution simulation agreed reasonably well with the measurements at the distant mooring for the leading two large solitons.
Parameter spaces for linear and nonlinear whistler-mode waves
Summers, Danny; Tang, Rongxin; Omura, Yoshiharu; Lee, Dong-Hun
2013-07-15
We examine the growth of magnetospheric whistler-mode waves which comprises a linear growth phase followed by a nonlinear growth phase. We construct time-profiles for the wave amplitude that smoothly match at the transition between linear and nonlinear wave growth. This matching procedure can only take place over a limited “matching region” in (N{sub h}/N{sub 0},A{sub T})-space, where A{sub T} is the electron thermal anisotropy, N{sub h} is the hot (energetic) electron number density, and N{sub 0} is the cold (background) electron number density. We construct this matching region and determine how the matching wave amplitude varies throughout the region. Further, we specify a boundary in (N{sub h}/N{sub 0},A{sub T})-space that separates a region where only linear chorus wave growth can occur from the region in which fully nonlinear chorus growth is possible. We expect that this boundary should prove of practical use in performing computationally expensive full-scale particle simulations, and in interpreting experimental wave data.
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. PMID:25360922
Travelling Waves for the Nonlinear Schrödinger Equation with General Nonlinearity in Dimension Two
NASA Astrophysics Data System (ADS)
Chiron, David; Scheid, Claire
2016-02-01
We investigate numerically the two-dimensional travelling waves of the nonlinear Schrödinger equation for a general nonlinearity and with nonzero condition at infinity. In particular, we are interested in the energy-momentum diagrams. We propose a numerical strategy based on the variational structure of the equation. The key point is to characterize the saddle points of the action as minimizers of another functional that allows us to use a gradient flow. We combine this approach with a continuation method in speed in order to obtain the full range of velocities. Through various examples, we show that even though the nonlinearity has the same behaviour as the well-known Gross-Pitaevskii nonlinearity, the qualitative properties of the travelling waves may be extremely different. For instance, we observe cusps, a modified KP-I asymptotic in the transonic limit, various multiplicity results and "one-dimensional spreading" phenomena.
Nonlinear Bloch waves in metallic photonic band-gap filaments
Kaso, Artan; John, Sajeev
2007-11-15
We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10-50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell's equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament.
Weak localization with nonlinear bosonic matter waves
Hartmann, Timo; Michl, Josef; Petitjean, Cyril; Wellens, Thomas; Urbina, Juan-Diego; Richter, Klaus; Schlagheck, Peter
2012-08-15
We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the nonlinear Gross-Pitaevskii equation, we develop a diagrammatic theory for the self-consistent stationary scattering state of the interacting condensate, which is combined with the semiclassical representation of the single-particle Green function in terms of chaotic classical trajectories within the billiard. This analytical approach predicts a universal dephasing of weak localization in the presence of a small interaction strength between the atoms, which is found to be in good agreement with the numerically computed reflection and transmission probabilities of the propagating condensate. The numerical simulation of this quasi-stationary scattering process indicates that this interaction-induced dephasing mechanism may give rise to a signature of weak antilocalization, which we attribute to the influence of non-universal short-path contributions. - Highlights: Black-Right-Pointing-Pointer Numerical simulation of scattering of Bose-Einstein condensate through billiards. Black-Right-Pointing-Pointer Novel analytical semiclassical theory for nonlinear coherent scattering. Black-Right-Pointing-Pointer Inversion of weak localization due to mean-field interaction within the condensate. Black-Right-Pointing-Pointer Relevance of non-universal short-path contributions.
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.
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
Phase space lattices and integrable nonlinear wave equations
NASA Astrophysics Data System (ADS)
Tracy, Eugene; Zobin, Nahum
2003-10-01
Nonlinear wave equations in fluids and plasmas that are integrable by Inverse Scattering Theory (IST), such as the Korteweg-deVries and nonlinear Schrodinger equations, are known to be infinite-dimensional Hamiltonian systems [1]. These are of interest physically because they predict new phenomena not present in linear wave theories, such as solitons and rogue waves. The IST method provides solutions of these equations in terms of a special class of functions called Riemann theta functions. The usual approach to the theory of theta functions tends to obscure the underlying phase space structure. A theory due to Mumford and Igusa [2], however shows that the theta functions arise naturally in the study of phase space lattices. We will describe this theory, as well as potential applications to nonlinear signal processing and the statistical theory of nonlinear waves. 1] , S. Novikov, S. V. Manakov, L. P. Pitaevskii and V. E. Zakharov, Theory of solitons: the inverse scattering method (Consultants Bureau, New York, 1984). 2] D. Mumford, Tata lectures on theta, Vols. I-III (Birkhauser); J. Igusa, Theta functions (Springer-Verlag, New York, 1972).
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.
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.
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
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.
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.
The nonlinear evolution of rogue waves generated by means of wave focusing technique
NASA Astrophysics Data System (ADS)
Hu, HanHong; Ma, Ning
2011-01-01
Generating the rogue waves in offshore engineering is investigated, first of all, to forecast its occurrence to protect the offshore structure from being attacked, to study the mechanism and hydrodynamic properties of rouge wave experimentally as well as the rouge/structure interaction for the structure design. To achieve these purposes demands an accurate wave generation and calculation. In this paper, we establish a spatial domain model of fourth order nonlinear Schrödinger (NLS) equation for describing deep-water wave trains in the moving coordinate system. In order to generate rogue waves in the experimental tank efficiently, we take care that the transient water wave (TWW) determines precisely the concentration of time/place. First we simulate the three-dimensional wave using TWW in the numerical tank and modeling the deepwater basin with a double-side multi-segmented wave-maker in Shanghai Jiao Tong University (SJTU) under the linear superposing theory. To discuss its nonlinearity for guiding the experiment, we set the TWW as the initial condition of the NLS equation. The differences between the linear and nonlinear simulations are presented. Meanwhile, the characteristics of the transient water wave, including water particle velocity and wave slope, are investigated, which are important factors in safeguarding the offshore structures.
Solitary waves in nonlinear coupled incommensurate chains
NASA Astrophysics Data System (ADS)
Dikandé, A. M.; Kofané, T. C.
1994-01-01
We present dynamical theory of soliton excitations in nonlinear coupled incommensurate chains which consists of two deformable chains of different atomic species, each with its own chemical potential, on the same substrate. In the continuum approximation, the motion equations are a set of coupled Sine-Gordon equations. The soliton solutions of these coupled equations are studied in detail. It has been shown that the frequency of the internal oscillations depends on the coupling parameter. The interaction energy between the two weakly coupled Sine-Gordon systems has been found. Results of the dynamical theory have been related to the transport properties in organic conductors such as TTF-TCNQ, KCP and others. Indeed, we have calculated some meaningful physical parameters of these compounds within the soliton limit, and discussed different types of behaviors shown at the transition with respect to variations of the physical parameters.
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'.
Acoustic nonlinear periodic waves in pair-ion plasmas
NASA Astrophysics Data System (ADS)
Mahmood, Shahzad; Kaladze, Tamaz; Ur-Rehman, Hafeez
2013-09-01
Electrostatic acoustic nonlinear periodic (cnoidal) waves and solitons are investigated in unmagnetized pair-ion plasmas consisting of same mass and oppositely charged ion species with different temperatures. Using reductive perturbation method and appropriate boundary conditions, the Korteweg-de Vries (KdV) equation is derived. The analytical solutions of both cnoidal wave and soliton solutions are discussed in detail. The phase plane plots of cnoidal and soliton structures are shown. It is found that both compressive and rarefactive cnoidal wave and soliton structures are formed depending on the temperature ratio of positive and negative ions in pair-ion plasmas. In the special case, it is revealed that the amplitude of soliton may become larger than it is allowed by the nonlinear stationary wave theory which is equal to the quantum tunneling by particle through a potential barrier effect. The serious flaws in the earlier published results by Yadav et al., [PRE 52, 3045 (1995)] and Chawla and Misra [Phys. Plasmas 17, 102315 (2010)] of studying ion acoustic nonlinear periodic waves are also pointed out.
Nonlinear 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 wave interactions in swept wing flows
NASA Technical Reports Server (NTRS)
Elhady, Nabil M.
1988-01-01
An analysis is presented which examines the modulation of different instability modes satisfying the triad resonance condition in time and space in a three-dimensional boundary layer flow. Detuning parameters are used for the wave numbers and the frequencies. The nonparallelism of the mean flow is taken into account in the analysis. At the leading-edge region of an infinite swept wing, different resonant triads are investigated that are comprised of travelling crossflow, vertical vorticity and Tollmein-Schlichting modes. The spatial evolution of the resonating triad components are studied.
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.
Attenuation characteristics of nonlinear pressure waves propagating in pipes
NASA Technical Reports Server (NTRS)
Shih, C. C.
1974-01-01
A series of experiments was conducted to investigate temporal and spatial velocity distributions of fluid flow in 3-in. open-end pipes of various lengths up to 210 ft, produced by the propagation of nonlinear pressure waves of various intensities. Velocity profiles across each of five sections along the pipes were measured as a function of time with the use of hot-film and hot-wire anemometers for two pressure waves produced by a piston. Peculiar configurations of the velocity profiles across the pipe section were noted, which are uncommon for steady pipe flow. Theoretical consideration was given to this phenomenon of higher velocity near the pipe wall for qualitative confirmation. Experimentally time-dependent velocity distributions along the pipe axis were compared with one-dimensional theoretical results obtained by the method of characteristics with or without diffusion term for the purpose of determining the attenuation characteristics of the nonlinear wave propagation in the pipes.
Features of fluid flows in strongly nonlinear internal solitary waves
NASA Astrophysics Data System (ADS)
Semin, S.; Kurkina, O.; Kurkin, A.; Talipova, T.; Pelinovsky, E.; Churaev, E.
2014-12-01
The characteristics of highly nonlinear solitary internal waves (solitons) are calculated within the fully nonlinear numerical model of the Massachusetts Institute of Technology. The verification and adaptation of the model is based on the data from laboratory experiments. The present paper also compares the results of our calculations with the calculations performed in the framework of the fully nonlinear Bergen Ocean Model. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in the numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the pycnocline and near the bottom are computed.
Graefe, E. M.; Korsch, H. J.; Witthaut, D.
2006-01-15
We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning.
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
Evolution of Random Nonlinear Infragravity Waves in Coastal Waters
NASA Astrophysics Data System (ADS)
Tian, Miao; Sheremet, Alex; Shrira, Victor
2014-05-01
The observed spectra of nearshore infragravity waves are typically mixed, with a discrete component (edge waves, trapped waves, propagating parallel to the coast) and a continuous one (leaky waves, that propagate from, and radiate back into, the deep ocean. See e.g., Oltman-Shay and Guza, 1987). The evolution of infragravity spectrum is driven by three general processes: 1) edge-leaky interactions, that transfer energy to the system from shorter waves; 2) energy redistribution through edge-edge and edge-leaky interactions; 3) and energy dissipation due to processes such as bottom friction. Previous studies treated either the edge and leaky system, in isolation from the other one, and focused on phase-resolving dynamical equation. Following Whitham (1976), who derived the nonlinear edge-wave solutions for the shallow water equations, theoretical work on the nonlinear edge-edge interaction resulted in many significant extensions (e.g., Kirby et. al. 1998, Pelinovsky et. al. 2010). The interaction between standing edge waves and a normally incident wave has been investigated both within the framework of the shallow-water equation (Guza and Davis 1974) and full water wave theory (Minzoni and Whitham, 1977). Here, we derive a general dynamical equation for the full mixed edge-leaky spectrum over a laterally uniform beach based on Zakharov's (1968, 1999) Hamiltonian formalism. The introduction of canonical variables in this formalism significantly simplifies the complicated derivation of the nonlinear interaction coefficient in the previous work (Kirby et. al. 1998, Pelinovsky et. al. 2010). The subharmonic resonance mechanism for edge-wave excitation (Guza and Davis, 1974) is retrieved from the model equation as a special case. The effects of dissipation induced by bottom friction are included using a perturbation approach. A kinetic equation for Zakharov's (1999) canonical variables can be derived, that reduces to the stochastic nonlinear mild-slope model of Agnon and
Evolution of Random Nonlinear Infragravity Waves in Coastal Waters
NASA Astrophysics Data System (ADS)
Tian, M.; Sheremet, A.; Shrira, V. I.
2014-12-01
The observed spectra of nearshore infragravity waves are typically mixed, with a discrete component (edge waves, trapped waves, propagating parallel to the coast) and a continuous one (leaky waves, that propagate from, and radiate back into, the deep ocean. See e.g., Oltman-Shay and Guza, 1987). The evolution of infragravity spectrum is driven by three general processes: 1) edge-leaky interactions, that transfer energy to the system from shorter waves; 2) energy redistribution through edge-edge and edge-leaky interactions; 3) and energy dissipation due to processes such as bottom friction. Previous studies treated either the edge and leaky system, in isolation from the other one, and focused on phase-resolving dynamical equation. Following Whitham (1976), who derived the nonlinear edge-wave solutions for the shallow water equations, theoretical work on the nonlinear edge-edge interaction resulted in many significant extensions (e.g., Kirby et. al. 1998, Pelinovsky et. al. 2010). The interaction between standing edge waves and a normally incident wave has been investigated both within the framework of the shallow-water equation (Guza and Davis 1974) and full water wave theory (Minzoni and Whitham, 1977). Here, we derive a general dynamical equation for the full mixed edge-leaky spectrum over a laterally uniform beach based on Zakharov's (1968, 1999) Hamiltonian formalism. The introduction of canonical variables in this formalism significantly simplifies the complicated derivation of the nonlinear interaction coefficient in the previous work (Kirby et. al. 1998, Pelinovsky et. al. 2010). The subharmonic resonance mechanism for edge-wave excitation (Guza and Davis, 1974) is retrieved from the model equation as a special case. The effects of dissipation induced by bottom friction are included using a perturbation approach. A kinetic equation for Zakharov's (1999) canonical variables can be derived, that reduces to the stochastic nonlinear mild-slope model of Agnon and
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.
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.
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.
Interaction of highly nonlinear solitary waves with linear elastic media
NASA Astrophysics Data System (ADS)
Yang, Jinkyu; Silvestro, Claudio; Khatri, Devvrath; de Nardo, Luigi; Daraio, Chiara
2011-04-01
We study the interaction of highly nonlinear solitary waves propagating in granular crystals with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary and secondary reflected waves. Experimental tests are performed to correlate the linear medium geometry, materials, and mass with the formation and propagation of reflected waves. We compare the experimental results with theoretical analysis based on the long-wavelength approximation and with numerical predictions obtained from discrete particle models. Experimental results are found to be in agreement with theoretical analysis and numerical simulations. This preliminary study establishes the foundation for utilizing reflected solitary waves as novel information carriers in nondestructive evaluation of elastic material systems.
Interaction of highly nonlinear solitary waves with linear elastic media.
Yang, Jinkyu; Silvestro, Claudio; Khatri, Devvrath; De Nardo, Luigi; Daraio, Chiara
2011-04-01
We study the interaction of highly nonlinear solitary waves propagating in granular crystals with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary and secondary reflected waves. Experimental tests are performed to correlate the linear medium geometry, materials, and mass with the formation and propagation of reflected waves. We compare the experimental results with theoretical analysis based on the long-wavelength approximation and with numerical predictions obtained from discrete particle models. Experimental results are found to be in agreement with theoretical analysis and numerical simulations. This preliminary study establishes the foundation for utilizing reflected solitary waves as novel information carriers in nondestructive evaluation of elastic material systems. PMID:21599325
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.
Nonlinear wave packet interferometry and molecular state reconstruction
NASA Astrophysics Data System (ADS)
Humble, Travis Selby
Nonlinear wave packet interferometry (WPI) uses two phase-locked pulse-pairs to excite a molecular electronic population and measures those contributions arising from a one-pulse nuclear wave packet overlapping with a three-pulse nuclear wave packet. The interferogram quantifies the wave-packet interference at the probability-amplitude level and, with knowledge of the three-pulse (reference) wave packets, enables reconstruction of the one-pulse (target) wave packet. In one-color nonlinear WPI, both pulse-pairs resonate with the same electronic transition and the interferogram measures a sum of wave-packet overlaps. Experimental conditions often minimize mixing of these overlaps and hence permit molecular state reconstruction, as demonstrated by numerical calculations for model harmonic and photodissociative systems. Yet, a one-color reconstruction technique requires information about the Hamiltonian under which the target and reference states propagate. The latter knowledge obviates the practical need for experimental state determination, since computational methods are then a viable, alternative solution. Two-color nonlinear WPI, in which the pulse-pairs drive different electronic transitions, circumvents the need for information about the target-state Hamiltonian by using an auxiliary electronic level for preparing the reference states. Furthermore, in a two-color experiment, the interferogram measures a single wave-packet overlap, definitely identifying the information necessary for molecular state reconstruction. These features suggest two-color nonlinear WPI could serve as a diagnostic tool for identifying optically-controlled, yet unknown, molecular dynamics. Simulations for model systems and the lithium dimer demonstrate that target states can be reconstructed in the presence of signal noise, thermal mixtures, and rovibrational coupling and in the absence of information about the target-state Hamiltonian. In the presence of electronic-energy transfer, the
Nonlinear waves and shocks in a rigid acoustical guide.
Fernando, Rasika; Druon, Yann; Coulouvrat, François; Marchiano, Régis
2011-02-01
A model is developed for the propagation of finite amplitude acoustical waves and weak shocks in a straight duct of arbitrary cross section. It generalizes the linear modal solution, assuming mode amplitudes slowly vary along the guide axis under the influence of nonlinearities. Using orthogonality properties, the model finally reduces to a set of ordinary differential equations for each mode at each of the harmonics of the input frequency. The theory is then applied to a two-dimensional waveguide. Dispersion relations indicate that there can be two types of nonlinear interactions either called "resonant" or "non-resonant." Resonant interactions occur dominantly for modes propagating at a rather large angle with respect to the axis and involve mostly modes propagating with the same phase velocity. In this case, guided propagation is similar to nonlinear plane wave propagation, with the progressive steepening up to shock formation of the two waves that constitute the mode and reflect onto the guide walls. Non-resonant interactions can be observed as the input modes propagate at a small angle, in which case, nonlinear interactions involve many adjacent modes having close phase velocities. Grazing propagation can also lead to more complex phenomena such as wavefront curvature and irregular reflection. PMID:21361419
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.
Amplitude-dependent contraction/elongation of nonlinear Lamb waves
NASA Astrophysics Data System (ADS)
Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2016-04-01
Nonlinear elastic guided waves find application in various disciplines of science and engineering, such as non- destructive testing and structural health monitoring. Recent recognition and quantification of their amplitude- dependent changes in spectral properties has contributed to the development of new monitoring concepts for mechanical structures. The focus of this work is to investigate and predict amplitude-dependent shifts in Lamb wave dispersion curves. The theory for frequency/wavenumber shifts for plate waves, based on a Lindstedt-Poincaré perturbation approach, was presented by the authors in previous years. Equivalently, spectral properties changes can be seen as wavelength contraction/elongation. Within the proposed framework, the wavelength of a Lamb wave depends on several factors; e.g., wave amplitude and second-, third- and fourth-order elastic constants, and others. Various types of nonlinear effects are considered in presented studies. Sensitivity studies for model parameters, i.e. higher-order elastic constants, are performed to quantify their influence on Lamb wave frequency/wavenumber shifting, and to identify the key parameters governing wavelength tuning.
Feasibility of using nonlinear guided waves to measure acoustic nonlinearity of aluminum
NASA Astrophysics Data System (ADS)
Matlack, Kathryn H.; Kim, Jin-Yeon; Jacobs, Laurence J.; Qu, Jianmin
2011-04-01
This research investigates the feasibility of measuring acoustic nonlinearity in aluminum with different ultrasonic guided wave modes. Acoustic nonlinearity is manifested by generation of a second harmonic component in an originally monochromatic ultrasonic wave signal, and previous research has shown this correlates to an intrinsic material property. This parameter has been shown to increase with accumulated material damage - specifically in low- and high-cycle fatigue - prior to crack initiation, whereas other ultrasonic nondestructive evaluation (NDE) techniques measuring linear parameters are unable to detect damage prior to crack initiation. In structural components such as jet engines and aircraft structures subjected to fatigue damage, crack initiation does not occur until ~80% of a component's life. Thus, there is a need for structural health monitoring (SHM) techniques that can characterize material damage state prior to crack initiation, and therefore nonlinear ultrasonic techniques have the potential to be powerful NDE and SHM tools. Experimental results using Rayleigh and Lamb guided wave modes to measure acoustic nonlinearity in undamaged aluminum 6061 samples are presented, and a comparison of the efficiency of these modes to measure acoustic nonlinearity is given.
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.
On the instability of Goertler vortices to nonlinear travelling waves
NASA Technical Reports Server (NTRS)
Seddougui, Sharon O.; Bassom, Andrew P.
1990-01-01
Recent theoretical work by Hall and Seddougui (1989) has shown that strongly nonlinear, high wavenumber Goertler vortices developing within a boundary layer flow are susceptible to a secondary instability which takes the form of travelling waves confined to a thin region centered at the outer edge of the vortex. The case is considered in which the secondary mode could be satisfactorily described by a linear stability theory and herein the objective is to extend this investigation of Hall and Seddougui (1989) into the nonlinear regime. It was found that at this stage not only does the secondary mode become nonlinear but it also interacts with itself so as to modify the governing equations for the primary Goertler vortex. In this case then, the vortex and the travelling wave drive each other and, indeed, the whole flow structure is described by an infinite set of coupled, nonlinear differential equations. A Stuart-Watson type of weakly nonlinear analysis of these equations is undertaken and concluded, in particular, that on this basis there exist stable flow configurations in which the travelling mode is of finite amplitude. Implications of the findings for practical situations are discussed and it is shown that the theoretical conclusions drawn here are in good qualitative agreement with available experimental observations.
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.
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°.
Experiments on nonlinear coastal shelf waves in a rotating annulus
NASA Astrophysics Data System (ADS)
Stewart, Andrew; Dellar, Paul; Johnson, Ted
2010-05-01
In many coastal regions, the ocean depth increases very rapidly at a 'shelf break' running approximately parallel to the coastline. A shelf break marks the edge of the continental shelf, and separates the deep ocean from the relatively shallow near-coastal ocean. Shelf breaks play an important rôle in steering coastal currents, such as the Aghulas current which flows southwest along the eastern coast of Africa at speeds of up to 1 ms-1. To investigate the effect of shelf breaks in stabilising coastal currents, we have carried out laboratory experiments to generate nonlinear topographic Rossby waves that propagate along a shelf break in the presence of a mean current. Our experiments use an annular channel in a rotating cylindrical tank. We model the shelf break with a tank floor that undergoes a sharp drop at a certain radius Rh. The tank was filled with homogeneous fluid, and set rotating with constant angular velocity until the fluid inside rotated as a solid body. We then induced horizontal perturbations to the fluid, which caused Taylor columns to move inwards and outwards across the shelf. Conservation of potential vorticity forces these columns to acquire relative vorticity as they cross the shelf, which allows waves to propagate around the tank. These waves are known as topographic Rossby shelf waves. The large-scale flow around shelf breaks has been the subject of a series of theoretical investigations. These commonly approximate the sharp drop in the depth by a discontinuity, on the assumption that the horizontal length scale of the flow is much larger than the width of the shelf break. However, the fluid is still assumed to move in columns, as in shallow water theory, even as it crosses the shelf. Our present work aims to consolidate a theoretical model for nonlinear waves propagating along a depth discontinuity in the context of our laboratory experiments. We assume that rotational effects are dominant, and that fluid velocities are small compared with
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.
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.
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 electron-acoustic waves in quantum plasma
Sah, O. P.; Manta, J.
2009-03-15
The nonlinear wave structure of electron-acoustic waves (EAWs) is investigated in a three component unmagnetized dense quantum plasma consisting of two distinct groups of electrons (one inertial cold electron, and other inertialess hot electrons) and immobile ions. By employing one dimensional quantum hydrodynamic model and standard reductive perturbation technique, a Korteweg-de-Vries equation governing the dynamics of EAWs is derived. Both compressive and rarefactive solitons along with periodical potential structures are found to exist for various ranges of dimensionless quantum parameter H. The quantum mechanical effects are also examined numerically on the profiles of the amplitude and the width of electron-acoustic solitary waves. It is observed that both the amplitude and the width of electron-acoustic solitary waves are significantly affected by the parameter H. The relevance of the present investigation to the astrophysical ultradense plasmas is also discussed.
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.
Weakly nonlinear dynamics of near-CJ detonation waves
Bdzil, J.B. ); Klein, R. . Inst. fuer Technische Mechanik)
1993-01-01
The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature 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.
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.
Non-linear wave interaction in a plasma column
NASA Technical Reports Server (NTRS)
Larsen, J.-M.; Crawford, F. W.
1979-01-01
Non-linear three-wave interaction is analysed for propagation along a cylindrical plasma column surrounded by an infinite dielectric, in the absence of a static magnetic field. An averaged-Lagrangian method is used, and the results are specialized to parametric interaction and mode conversion, assuming an undepleted pump wave. The theory for these two types of interactions is extended to include imperfect synchronism, and the effects of loss. Computations are presented indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma column parameters.
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.
The Nonlinear Landau Damping Rate of a Driven Plasma Wave
Benisti, D; Strozzi, D J; Gremillet, L; Morice, O
2009-08-04
In this Letter, we discuss the concept of the nonlinear Landau damping rate, {nu}, of a driven electron plasma wave, and provide a very simple, practical, analytic formula for {nu} which agrees very well with results inferred from Vlasov simulations of stimulated Raman scattering. {nu} actually is more complicated an operator than a plain damping rate, and it may only be seen as such because it assumes almost constant values before abruptly dropping to 0. The decrease of {nu} to 0 is moreover shown to occur later when the wave amplitude varies in the direction transverse to its propagation.
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.
Discrete Element Method Simulation of Nonlinear Viscoelastic Stress Wave Problems
NASA Astrophysics Data System (ADS)
Wang, Wenqiang; Tang, Zhiping; Horie, Y.
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 code[1], 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
Modulational development of nonlinear gravity-wave groups
NASA Technical Reports Server (NTRS)
Chereskin, T. K.; Mollo-Christensen, E.
1985-01-01
Observations of the development of nonlinear surface gravity-wave groups are presented, and the amplitude and phase modulations are calculated using Hilbert-transform techniques. With increasing propagation distance and wave steepness, the phase modulation develops local phase reversals whose locations correspond to amplitude minima or nodes. The concomitant frequency modulation develops jumps or discontinuities. The observations are compared with recent similar results for wavetrains. The observations are modelled numerically using the cubic nonlinear Schroedinger equation. The motivation is twofold: to examine quantitatively the evolution of phase as well as amplitude modulation, and to test the inviscid predictions for the asymptotic behavior of groups versus long-time observations. Although dissipation rules out the recurrence, there is a long-time coherence of the groups. The phase modulation is found to distinguish between dispersive and soliton behavior.
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.
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
Numerical study of nonlinear streaming inside a standing wave resonator
NASA Astrophysics Data System (ADS)
Daru, V.; Carlès, D. Baltean; Weisman, C.
2012-09-01
The acoustic streaming associated to standing waves in a cylindrical resonator is studied for increasing nonlinear Reynolds numbers by numerically solving the compressible Navier-Stokes equations, using a high resolution finite difference scheme. The resonator is excited by shaking it along the axis at imposed frequency, corresponding to the fundamental resonance frequency of the waveguide. For sufficiently large acoustic velocities, shocks are visible. The mean field is computed by time-averaging over the main acoustic period. When the nonlinear Reynolds number increases, the center of the outer streaming cells are pushed toward the acoustic velocity nodes and two additional vortices per quarter-wavelength are generated on the axis, near the velocity antinodes. This result differs from linear models and is in agreement with several recent experimental measurement performed in the nonlinear regime. The mean temperature field evolution within the resonator is also investigated.
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.
Observation of Laser-Pulse Shortening in Nonlinear Plasma Waves
Faure, J.; Glinec, Y.; Santos, J.J.; Ewald, F.; Rousseau, J.-P.; Malka, V.; Kiselev, S.; Pukhov, A.; Hosokai, T.
2005-11-11
We have measured the temporal shortening of an ultraintense laser pulse interacting with an underdense plasma. When interacting with strongly nonlinear plasma waves, the laser pulse is shortened from 38{+-}2 fs to the 10-14 fs level, with a 20% energy efficiency. The laser ponderomotive force excites a wakefield, which, along with relativistic self-phase modulation, broadens the laser spectrum and subsequently compresses the pulse. This mechanism is confirmed by 3D particle in cell simulations.
Observation of laser-pulse shortening in nonlinear plasma waves.
Faure, J; Glinec, Y; Santos, J J; Ewald, F; Rousseau, J-P; Kiselev, S; Pukhov, A; Hosokai, T; Malka, V
2005-11-11
We have measured the temporal shortening of an ultraintense laser pulse interacting with an underdense plasma. When interacting with strongly nonlinear plasma waves, the laser pulse is shortened from 38 +/- 2 fs to the 10-14 fs level, with a 20% energy efficiency. The laser ponderomotive force excites a wakefield, which, along with relativistic self-phase modulation, broadens the laser spectrum and subsequently compresses the pulse. This mechanism is confirmed by 3D particle in cell simulations. PMID:16384066
NASA Astrophysics Data System (ADS)
Medvedev, M. V.
1998-11-01
The magnetic field fluctuations frequently observed in the Solar Wind and Interstellar Medium are likely to be nonlinear Alfvén waves, in which the ponderomotive coupling of Alfvénic magnetic energy to ion-acoustic quasi-modes has modified the phase velocity vA and caused wave-front steepening. In the warm, collisionless Solar Wind plasma the resonant particle-wave interactions result in relatively rapid (compared to the particle bounce time) formation of quasi-stationary Alfvénic Rotational Discontinuities, (M.V. Medvedev, P.H. Diamond, V.I. Shevchenko, and V.L. Galinsky, Phys. Rev. Lett. 78), 4934 (1997) and references therein. which have been the subject of intense satellite observations and theoretical investigations, and whose emergence and dynamics has not been previously understood. These discontinuities are shown to be quasi-stationary wave-form remnants of nonlinearly evolved coherent Alfvén waves. In long-time asymptotics, however, the particle distribution function (PDF) is affected by wave magnetic fields. Indeed, the resonant particles are trapped in the quasi-stationary Alfvénic discontinuities by mirroring forces giving rise to the nonlinear Landau damping and, ultimately, to a formation of a plateau on the PDF, so that the linear collisionless damping vanishes. Using Virial theorem for trapped particles, it is analytically demonstrated (M.V. Medvedev, P.H. Diamond, M.N. Rosenbluth, and V.I. Shevchenko, Submitted to Phys. Rev. Lett. (1998).) that their effect on the nonlinear dynamics of such discontinuities is highly non-trivial and forces a significant departure of the theory from the conventional paradigm. Considering the strongly compressible MHD (Alfvénic) Solar Wind turbulence as an ensemble of randomly interacting Alfvénic discontinuities and nonlinear waves, it is also shown (M.V. Medvedev and P.H. Diamond, Phys. Rev. E 56), R2371 (1997). that there exist two different phases of turbulence which are due to the collisionless (Landau
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.
Nonlinear active wave modulation approach for microdamage detection
NASA Astrophysics Data System (ADS)
Wu, Hwai-Chung; Warnemuende, Kraig
2001-07-01
Several nondestructive testing methods can be used to estimate the extents of damage in a concrete structure. Pulse-velocity and amplitude attenuation, are very common in nondestructive ultrasonic evaluation. Velocity of propagation is not very sensitive to the degrees of damage unless a great deal of micro-damage having evolving into localized macro-damage. Amplitude attenuation is potentially more sensitive than pulse-velocity. However, this method depends strongly on the coupling conditions between transducers and concrete, hence unreliable. A new active modulation approach, Nonlinear Active Wave Modulation Spectroscopy, is adopted in our study. In this procedure, a probe wave will be passed through the system in a similar fashion to regular acoustics. Simultaneously, a second, low frequency modulating wave will be applied to the system to effectively change the size and stiffness of flaws microscopically and cyclically, thereby causing the frequency modulation to change cyclically as well. The resulting amplified modulations will be correlated to the extents of damage with the effect that even slight damage should become quantifiable. This study unveils the potential of nonlinear frequency analysis methods for micro-damage detection and evaluation using actively modulated acoustic signals. This method can interrogate materials exaggerating the nonlinearly that exists due to microcracking and deterioration.
Numerical study of nonlinear full wave acoustic propagation
NASA Astrophysics Data System (ADS)
Velasco-Segura, Roberto; Rendon, Pablo L.
2013-11-01
With the aim of describing nonlinear acoustic phenomena, a form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A CLAWPACK based, 2D finite-volume method using Roe's linearization has been implemented to obtain numerically the solution of the proposed equations. In order to validate the code, two different tests have been performed: one against a special Taylor shock-like analytic solution, the other against published results on a HIFU system, both with satisfactory results. The code is written for parallel execution on a GPU and improves performance by a factor of over 50 when compared to the standard CLAWPACK Fortran code. This code can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from modest models of diagnostic and therapeutic HIFU, parametric acoustic arrays, to acoustic wave guides. A couple of examples will be presented showing shock formation and oblique interaction. DGAPA PAPIIT IN110411, PAEP UNAM 2013.
Prakash, Vijay S; Sonti, Venkata R
2015-11-01
Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrödinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. PMID:26627797
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
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.
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
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.
Probing an S-wave with a P-wave: experimental developments for understanding rock nonlinearities
NASA Astrophysics Data System (ADS)
Brown, S. R.; Gallot, T.; Malcolm, A. E.; Fehler, M. C.; Szabo, T.; Burns, D.; Zhu, Z.
2012-12-01
The nonlinear characterization of rocks is a research topic applicable to several geophysical problems such as erthquake source physics, reservoir fracturing processes or imaging. Recently, dynamic methods have been shown to reveal new information about the nonlinear response of materials. Existing methods generally rely on vibrating a sample at a fixed resonant frequency to create a low frequency strain (the pump). During a cycle of the pump, the nonlinear response of the material is measured via a high frequency wave (the probe). In a similar method, the standing wave is replaced by a pulsed wave. This method extends the so-called Dynamic Acousto-Elastic Testing (DAET) to semi-infinite media and allows for frequency scans of the non linear response. We have performed laboratory experiments in rocks (berea sandstones) to explore the possibility of using such method for Earth imaging. For the pump, we use a shear wave with frequencies in the tens of kHz and the probe is a compressional pulse in the hundreds of kHz range. In this configuration, we are interested in the delay of the probe caused by the pump via a nonlinear interaction. The results highlight a fast rectification effect and a slow weakening effect, respectively related to classical non linearities and conditioning of the material. The dynamics of the conditioning can be studied with this pulsed method. Using a shear wave pump also gives us the opportunity to study the effect of the relative orientation of the pump.
Internal Nonlinear Tidal Waves on the Mexican Pacific Shelf
NASA Astrophysics Data System (ADS)
Filonov, A.; Tereshchenko, I.; Anis, A.; Internal Nonlinear Tidal Waves
2013-05-01
Dynamics of semidiurnal internal tides on the Mexican Pacific shelf are discussed using data obtained from moored instruments and vessel transects. The internal tides were dominated by inclined waves, propagating upward and onshore. These waves underwent nonlinear transformations and overturns resulting in intense mixing and eventually the creation of homogeneous temperature layers up to 20 m thick. Spectral analysis of temperature and velocity fluctuations revealed a -5/3 slope, consistent with the existence of an inertial sub range in the turbulence spectra. Observation was conducted in Navidad Bay, on the Pacific Mexican shelf from 17-28 May, 2010. Time series of temperature and water-currents were collected from moorings instrumented with thermistors and acoustic Doppler current profilers (ADCPs). Two acoustic Doppler velocimeters (ADVs), a CTD, and a self-contained autonomous turbulence profiler provided high-frequency velocity and temperature fluctuations for estimation of turbulence parameters. Temperature, salinity, and current transects were performed with a towed CTD profiler and ADCP. The analysis indicates that inclined semidiurnal internal tides propagating upward and onshore dominates on the narrow shelf and adjacent continental slope. These waves undergo nonlinear transformation in two ways: 1). Overturning of wave crests producing strong mixing and resulting in the formation of homogeneous layers up to 20 m thick and with horizontal extents of a few kilometers. 2). Formation of groups of near-bottom solitons.
Warm wave breaking of nonlinear plasma waves with arbitrary phase velocities
Schroeder, C.B.; Esarey, E.; Shadwick, B.A.
2005-11-01
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.
Warm wave breaking of nonlinear plasma waves with arbitrary phase velocities.
Schroeder, C B; Esarey, E; Shadwick, B A
2005-11-01
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. PMID:16383678
Nonlinear collisionless damping of Weibel turbulence in relativistic blast waves
NASA Astrophysics Data System (ADS)
Lemoine, Martin
2015-01-01
The Weibel/filamentation instability is known to play a key role in the physics of weakly magnetized collisionless shock waves. From the point of view of high energy astrophysics, this instability also plays a crucial role because its development in the shock precursor populates the downstream with a small-scale magneto-static turbulence which shapes the acceleration and radiative processes of suprathermal particles. The present work discusses the physics of the dissipation of this Weibel-generated turbulence downstream of relativistic collisionless shock waves. It calculates explicitly the first-order nonlinear terms associated to the diffusive nature of the particle trajectories. These corrections are found to systematically increase the damping rate, assuming that the scattering length remains larger than the coherence length of the magnetic fluctuations. The relevance of such corrections is discussed in a broader astrophysical perspective, in particular regarding the physics of the external relativistic shock wave of a gamma-ray burst.
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
Weakly nonlinear ion waves in striated electron temperatures
NASA Astrophysics Data System (ADS)
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.
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.
Current structure of strongly nonlinear interfacial solitary waves
NASA Astrophysics Data System (ADS)
Semin, Sergey; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim; Churaev, Egor
2015-04-01
The characteristics of highly nonlinear solitary internal waves (solitons) in two-layer flow are computed within the fully nonlinear Navier-Stokes equations with use of numerical model of the Massachusetts Institute of Technology (MITgcm). The verification and adaptation of the model is based on the data from laboratory experiments [Carr & Davies, 2006]. The present paper also compares the results of our calculations with the computations performed in the framework of the fully nonlinear Bergen Ocean Model [Thiem et al, 2011]. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the interface and near the bottom are computed. The results demonstrated completely different trajectories at different depths of the model area. Thus, in the surface layer is observed the largest displacement of Lagrangian particles, which can be more than two and a half times larger than the characteristic width of the soliton. Located at the initial moment along the middle pycnocline fluid particles move along the elongated vertical loop at a distance of not more than one third of the width of the solitary wave. In the bottom layer of the fluid moves in the opposite direction of propagation of the internal wave, but under the influence of the reverse flow, when the bulk of the velocity field of the soliton ceases to influence the trajectory, it moves in the opposite direction. The magnitude of displacement of fluid particles in the bottom layer is not more than the half-width of the solitary wave. 1. Carr, M., and Davies, P.A. The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Phys. Fluids, 2006, vol. 18, No. 1, 1 - 10. 2. Thiem, O., Carr
Nonlinear instability and chaos in plasma wave-wave interactions, I., Introduction
Kueny, C.S.; Morrison, P.J.
1994-11-01
Conventional linear stability analyses may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper [submitted to Physics of Plasmas], this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various (integrable) systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper.
Propagation of nonlinear waves over submerged step: wave separation and subharmonic generation
NASA Astrophysics Data System (ADS)
Monsalve, Eduardo; Maurel, Agnes; Pagneux, Vincent; Petitjeans, Philippe
2015-11-01
Water waves can be described in simplified cases by the Helmholtz equation. However, even in these cases, they present a high complexity, among which their dispersive character and their nonlinearities are the subject of the present study. Using Fourier Transform Profilometry, we study experimentally the propagation of waves passing over a submerged step. Because of the small water depth after the step, the wave enters in a nonlinear regime. In the shallow water region, the second harmonic leads to two types of waves: bound waves which are slaves of the fundamental frequency with wavenumber 2 k (ω) , and free waves which propagate according to the usual dispersion relation with wavenumber k (2 ω) . Because of the presence of these two waves, beats are produced at the second harmonic with characteristic beat length. In this work, for the first time we extended this analysis to the third and higher harmonics. Next, the region after the step is limited to a finite size L with a reflecting wall. For certain frequencies and L- values, the spectral component becomes involved, with the appearance of sub harmonics. This regime is analyzed in more details, suggesting a transition to a chaotic and quasi-periodic wave behavior.
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.
Observations of the parametric decay instability of nonlinear magnetohydrodynamic waves
Spangler, S.R.; Leckband, J.A.; Cairns, I.H.
1997-03-01
One of the most important nonlinear processes for Alfven and fast magnetosonic waves is the decay instability, in which a forward propagating magnetohydrodynamic (MHD) wave is converted into a forward propagating ion acoustic wave and a backward propagating MHD wave. Despite an extensive theoretical literature and numerous computer simulations of the process, there is minimal experimental or observational evidence for its existence. In this paper we report an extensive search for evidence of the decay instability in the MHD wave field upstream of the Earth`s bow shock. Twenty intervals of spacecraft magnetometer and density data with durations between 21 and 168 min were examined. The observational signature of the decay instability sought was a quasi-monochromatic feature in the density power spectrum, attributable to the daughter ion acoustic wave, at a frequency higher than the main wave features in the magnetic power spectra. Such a feature was in fact observed for the interval in which the theoretically predicted instability growth rate was highest, as well as in a second interval for which the instability was permitted with a slower growth rate. However, the data set also contains three long intervals of data in which the {open_quotes}decay line{close_quotes} signature is not seen, although theoretically permitted. The decay line is also absent in four shorter intervals in which the plasma {beta} is less than unity, and the instability accordingly facilitated. Possible reasons for the absence of the instability in these intervals are discussed, such as a finite bandwidth for the parent wave field and plasma kinetic effects. {copyright} {ital 1997 American Institute of Physics.}
Observations of the parametric decay instability of nonlinear magnetohydrodynamic waves
NASA Astrophysics Data System (ADS)
Spangler, Steven R.; Leckband, James A.; Cairns, Iver H.
1997-03-01
One of the most important nonlinear processes for Alfvén and fast magnetosonic waves is the decay instability, in which a forward propagating magnetohydrodynamic (MHD) wave is converted into a forward propagating ion acoustic wave and a backward propagating MHD wave. Despite an extensive theoretical literature and numerous computer simulations of the process, there is minimal experimental or observational evidence for its existence. In this paper we report an extensive search for evidence of the decay instability in the MHD wave field upstream of the Earth's bow shock. Twenty intervals of spacecraft magnetometer and density data with durations between 21 and 168 min were examined. The observational signature of the decay instability sought was a quasi-monochromatic feature in the density power spectrum, attributable to the daughter ion acoustic wave, at a frequency higher than the main wave features in the magnetic power spectra. Such a feature was in fact observed for the interval in which the theoretically predicted instability growth rate was highest, as well as in a second interval for which the instability was permitted with a slower growth rate. However, the data set also contains three long intervals of data in which the "decay line'' signature is not seen, although theoretically permitted. The decay line is also absent in four shorter intervals in which the plasma β is less than unity, and the instability accordingly facilitated. Possible reasons for the absence of the instability in these intervals are discussed, such as a finite bandwidth for the parent wave field and plasma kinetic effects.
Freak waves in nonlinear unidirectional wave trains over a sloping bottom
NASA Astrophysics Data System (ADS)
Trulsen, Karsten; Raustøl, Anne; Bæverfjord Rye, Lisa
2015-04-01
Water surface waves evolving on constant depth experience decreasing nonlinear modulation with decreasing depth, and it is anticipated that the occurrence of freak waves is similarly reduced (e.g. Mori & Janssen 2006; Janssen & Onorato 2007; Janssen 2009). Waves evolving on non-uniform depth will additionally experience non-equilibrium effects, having to adapt to a new depth along their path. This may cause interesting behavior with respect to freak wave occurrence, different from that suggested above. For waves propagating from quite shallow to even more shallow water over a slope, Sergeeva et al. (2011) found a local maximum of extreme waves on the shallow end of the slope. For waves propagating from quite deep to shallower water over a very long slope, Zeng & Trulsen (2012) found no local maximum of extreme waves on the shallow end of the slope. They found that the waves may need a considerable distance of propagation before reaching their new equilibrium statistics. They even found some cases of a local minimum of extreme wave occurrence at the shallow end of the slope. Experimental evidence of a local maximum of extreme wave statistics on the shallow end of the slope was found by Trulsen et al. (2012), and corresponding numerical simulations were later done by Gramstad et al. (2013). The works cited above appear to suggest two different regimes, the presence of a local maximum of extreme waves at the shallow end of a slope, or the lack of such a maximum, possibly depending on the depths involved, or possibly depending on the length of the slope. We have carried out a set of carefully controlled experiments with irregular waves propagating over variable depth as suggested in the figure. A movable array of 16 ultrasound probes was used to measure surface elevation, such that high resolution was achieved to catch the location of local maxima and minima of extreme wave occurrence. We have found that there are indeed two different regimes depending on the depth
Nonlinear radiation damping of nuclear spin waves and magnetoelastic waves in antiferromagnets
NASA Astrophysics Data System (ADS)
Andrienko, Alexander V.; Safonov, Vladimir L.
2016-03-01
Parallel pumping of nuclear spin waves in antiferromagnetic CsMnF3 at liquid helium temperatures and magnetoelastic waves in antiferromagnetic FeBO3 at liquid nitrogen temperature in a helical resonator was studied. It was found that the absorbed microwave power is approximately equal to the irradiated power from the sample and that the main restriction mechanism of absorption in both cases is defined by the nonlinear radiation damping predicted about two decades ago. Nonlinear radiation damping is sure to be a common feature of the parallel pumping technique for all normal magnetic excitations and it must be taken into account for interpretation of nonlinear phenomena in parametrically excited magnetic systems.
DEM Modelling of Non-linear Viscoelastic Stress Waves
NASA Astrophysics Data System (ADS)
Wang, Wenqiang; Tang, Zhiping; Horie, Yasuyuki
2001-06-01
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, and can reduce the computational cost dramatically. To validate the viscoelastic DM2 code, 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. Satisfactory results are also obtained in the simulation of one-dimensional plane wave in a plastic bonded explosive. The code is then used to investigate the problem of meso-scale damage in this 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.
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.
Molecular dynamics simulation of complex plasmas: interaction of nonlinear waves
NASA Astrophysics Data System (ADS)
Durniak, Celine; Samsonov, Dmitry
2008-11-01
Complex plasmas consist of micron sized microspheres immersed into ordinary ion-electron plasmas. They exist in solid, liquid, gaseous states and exhibit a range of dynamic phenomena such as waves, solitons, phase transitions, heat transfer. These phenomena can be modelled in complex plasmas at the microscopic or ``molecular'' scale, which is almost impossible in ordinary solids and liquids. We simulate a monolayer complex plasma consisting of 3000 negatively-charged particles (or grains) with the help of molecular dynamics computer simulations. The equations of grain motion are solved using a 5^th order Runge Kutta method taking into account interaction of every grain with each other via a Yukawa potential. The grains are confined more strongly in the vertical direction than in the horizontal. After seeding the grains randomly the code is run until the equilibrium is reached as the grain kinetics energy reduces due to damping force equal to the neutral friction in the experiments and a monolayer crystal lattice is formed. Then we investigate interactions between nonlinear waves in a monolayer strongly coupled complex plasma moving in three dimensions. Different excitations are applied during a short time symmetrically on both sides of the lattice. Structural properties and nonlinear waves characteristics are examined as the pulses propagate across the complex plasma in opposite directions.
Computation of Transient Nonlinear Ship Waves Using AN Adaptive Algorithm
NASA Astrophysics Data System (ADS)
Çelebi, M. S.
2000-04-01
An indirect boundary integral method is used to solve transient nonlinear ship wave problems. A resulting mixed boundary value problem is solved at each time-step using a mixed Eulerian- Lagrangian time integration technique. Two dynamic node allocation techniques, which basically distribute nodes on an ever changing body surface, are presented. Both two-sided hyperbolic tangent and variational grid generation algorithms are developed and compared on station curves. A ship hull form is generated in parametric space using a B-spline surface representation. Two-sided hyperbolic tangent and variational adaptive curve grid-generation methods are then applied on the hull station curves to generate effective node placement. The numerical algorithm, in the first method, used two stretching parameters. In the second method, a conservative form of the parametric variational Euler-Lagrange equations is used the perform an adaptive gridding on each station. The resulting unsymmetrical influence coefficient matrix is solved using both a restarted version of GMRES based on the modified Gram-Schmidt procedure and a line Jacobi method based on LU decomposition. The convergence rates of both matrix iteration techniques are improved with specially devised preconditioners. Numerical examples of node placements on typical hull cross-sections using both techniques are discussed and fully nonlinear ship wave patterns and wave resistance computations are presented.
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.
Shock-wave structure using nonlinear model Boltzmann equations.
NASA Technical Reports Server (NTRS)
Segal, B. M.; Ferziger, J. H.
1972-01-01
The structure of strong plane shock waves in a perfect monatomic gas was studied using four nonlinear models of the Boltzmann equation. The models involved the use of a simplified collision operator with velocity-independent collision frequency, in place of the complicated Boltzmann collision operator. The models employed were the BGK and ellipsoidal models developed by earlier authors, and the polynomial and trimodal gain function models developed during the work. An exact set of moment equations was derived for the density, velocity, temperature, viscous stress, and heat flux within the shock. This set was reduced to a pair of coupled nonlinear integral equations and solved using specially adapted numerical techniques. A new and simple Gauss-Seidel iteration was developed during the work and found to be as efficient as the best earlier iteration methods.
NASA Technical Reports Server (NTRS)
Kim, H.; Crawford, F. W.
1977-01-01
It is pointed out that the conventional iterative analysis of nonlinear plasma wave phenomena, which involves a direct use of Maxwell's equations and the equations describing the particle dynamics, leads to formidable theoretical and algebraic complexities, especially for warm plasmas. As an effective alternative, the Lagrangian method may be applied. It is shown how this method may be used in the microscopic description of small-signal wave propagation and in the study of nonlinear wave interactions. The linear theory is developed for an infinite, homogeneous, collisionless, warm magnetoplasma. A summary is presented of a perturbation expansion scheme described by Galloway and Kim (1971), and Lagrangians to third order in perturbation are considered. Attention is given to the averaged-Lagrangian density, the action-transfer and coupled-mode equations, and the general solution of the coupled-mode equations.
A Heterogeneous Nonlinear Attenuating Full-Wave Model of Ultrasound
Pinton, Gianmarco F.; Dahl, Jeremy; Rosenzweig, Stephen; Trahey, Gregg E.
2015-01-01
A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain (FDTD). Three-dimensional solutions of the equation are verified with water tank measurements of a commercial diagnostic ultrasound transducer and are shown to be in excellent agreement in terms of the fundamental and harmonic acoustic fields and the power spectrum at the focus. The linear and nonlinear components of the algorithm are also verified independently. In the linear nonattenuating regime solutions match results from Field II, a well established software package used in transducer modeling, to within 0.3 dB. Nonlinear plane wave propagation is shown to closely match results from the Galerkin method up to 4 times the fundamental frequency. In addition to thermoviscous attenuation we present a numerical solution of the relaxation attenuation laws that allows modeling of arbitrary frequency dependent attenuation, such as that observed in tissue. A perfectly matched layer (PML) is implemented at the boundaries with a numerical implementation that allows the PML to be used with high-order discretizations. A −78 dB reduction in the reflected amplitude is demonstrated. The numerical algorithm is used to simulate a diagnostic ultrasound pulse propagating through a histologically measured representation of human abdominal wall with spatial variation in the speed of sound, attenuation, nonlinearity, and density. An ultrasound image is created in silico using the same physical and algorithmic process used in an ultrasound scanner: a series of pulses are transmitted through heterogeneous scattering tissue and the received echoes are used in a delay-and-sum beam-forming algorithm to generate a images. The resulting harmonic image exhibits characteristic improvement in lesion boundary definition and contrast when compared with the fundamental image. We demonstrate a mechanism of harmonic image quality
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.
Joint photon and wave statistics in nonlinear optical couplers
NASA Astrophysics Data System (ADS)
Peřina, Jan; Křepelka, Jaromír
2014-09-01
Nonlinear optical couplers based on optical parametric processes and Raman-Brillouin scattering are discussed from the point of view of their nonclassical behaviour using joint photon-number and integrated-intensity probability distributions and derived quantum statistical quantities. Employing these tools quantum entanglement of modes and their nonclassical properties are demonstrated by means of conditional probability distributions and their Fano factors, difference-number probability distributions, quantum oscillations, squeezing of vacuum fluctuations and negative values of the joint wave probability quasidistributions in time evolution. Sub-Poissonian and sub-shot-noise properties are determined for initial coherent, chaotic and squeezed light.
Nonlinear positron-acoustic waves in fully relativistic degenerate plasmas
NASA Astrophysics Data System (ADS)
Hossen, M. A.; Mamun, A. A.
2016-03-01
The nonlinear positron-acoustic (PA) waves propagating in a fully relativistic electron-positron-ion (EPI) plasma (containing degenerate electrons and positrons, and immobile heavy ions) have been theoretically investigated. A fully relativistic hydrodynamic model, which is consistent with the relativistic principle has been used, and the reductive perturbation method is employed to derive the dynamical Korteweg-de Vries equation. The dynamics of electrons as well as positrons, and the presence of immobile heavy ions are taken into account. It is found that the effects of relativistic degeneracy of electrons and positrons, static heavy ions, plasma particles velocity, enthalpy, etc have significantly modified the basic properties of the PA solitary waves propagating in the fully relativistic EPI plasmas. The application of the results of our present work in astrophysical compact objects such as white dwarfs and neutron stars, etc are briefly discussed.
Nonlinear interactions of electromagnetic waves with the auroral ionosphere
NASA Astrophysics Data System (ADS)
Wong, Alfred Y.
1999-09-01
The ionosphere provides us with an opportunity to perform plasma experiments in an environment with long confinement times, very large-scale lengths, and no confining walls. The auroral ionosphere with its nearly vertical magnetic field geometry is uniquely endowed with large amount of free energy from electron and ion precipitation along the magnetic field and mega-ampere current across the magnetic field. To take advantage of this giant outdoor laboratory, two facilities HAARP and HIPAS, with frequencies ranging from the radio to optical bands, are now available for active probing of and interaction with this interesting region. The ponderomotive pressures from the self-consistent wave fields have produced significant local perturbations of density and particle distributions at heights where the incident EM frequency matches a plasma resonance. This paper will review theory and experiments covering the nonlinear phenomena of parametric decay instability to wave collapse processes. At HF frequencies plasma lenses can be created by preconditioning pulses to focus what is a normally divergent beam into a high-intensity spot to further enhance nonlinear phenomena. At optical wavelengths a large rotating liquid metal mirror is used to focus laser pulses up to a given height. Such laser pulses are tuned to the same wavelengths of selected atomic and molecular resonances, with resulting large scattering cross sections. Ongoing experiments on dual-site experiments and excitation of ELF waves will be presented. The connection of such basic studies to environmental applications will be discussed. Such applications include the global communication using ELF waves, the ozone depletion and remediation and the control of atmospheric CO2 through the use of ion cyclotron resonant heating.
Nonlinear 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.
Weakly nonlinear analysis of impulsively-forced Faraday waves.
Catllá, Anne; Porter, Jeff; Silber, Mary
2005-11-01
Parametrically-excited surface waves, forced by a repeating sequence of delta-function impulses, are considered within the framework of the Zhang-Viñals model [W. Zhang and J. Viñals, J. Fluid Mech. 336, 301 (1997)]. With impulsive forcing, the linear stability analysis can be carried out exactly and leads to an implicit equation for the neutral stability curves. As noted previously [J. Bechhoefer and B. Johnson, Am. J. Phys. 64, 1482 (1996)], in the simplest case of N=2 equally-spaced impulses per period (which alternate up and down) there are only subharmonic modes of instability. The familiar situation of alternating subharmonic and harmonic resonance tongues emerges only if an asymmetry in the spacing between the impulses is introduced. We extend the linear analysis for N=2 impulses per period to the weakly nonlinear regime, where we determine the leading order nonlinear saturation of one-dimensional standing waves as a function of forcing strength. Specifically, an analytic expression for the cubic Landau coefficient in the bifurcation equation is derived as a function of the dimensionless spacing between the two impulses and the fluid parameters that appear in the Zhang-Viñals model. As the capillary parameter is varied, one finds a parameter regime of wave amplitude suppression, which is due to a familiar 1:2 spatiotemporal resonance between the subharmonic mode of instability and a damped harmonic mode. This resonance occurs for impulsive forcing even when harmonic resonance tongues are absent from the neutral stability curves. The strength of this resonance feature can be tuned by varying the spacing between the impulses. This finding is interpreted in terms of a recent symmetry-based analysis of multifrequency forced Faraday waves [J. Porter, C. M. Topaz, and M. Silber, Phys. Lett. 93, 034502 (2004); C. M. Topaz, J. Porter, and M. Silber, Phys. Rev. E 70, 066206 (2004)]. PMID:16383732
Flow separation and resuspension beneath shoaling nonlinear internal waves
NASA Astrophysics Data System (ADS)
Boegman, Leon; Ivey, Gregory N.
2009-02-01
Laboratory observations are presented showing the structure and dynamics of the turbulent bottom boundary layer beneath nonlinear internal waves (NLIWs) of depression shoaling upon sloping topography. The adverse pressure gradient beneath the shoaling waves causes the rear face to steepen, flow separation to occur, and wave-induced near-bottom vortices to suspend bed material. The resuspension is directly attributed to the near-bed viscous stress and to near-bed patches of elevated positive Reynolds stress generated by the vortical structures. These results are consistent with published field observations of resuspension events beneath shoaling NLIWs. Elevated near-bed viscous stresses are found throughout the domain at locations that are not correlated to the resuspension events. Near-bed viscous stress is thus required for incipient sediment motion but is not necessarily a precursor for resuspension. Resuspension is dependent on the vertical velocity field associated with positive Reynolds stress and is also found to occur where the mean (wave-averaged) vertical velocity is directed away from the bed. The results are interpreted by analogy to the eddy-stress and turbulent bursting resuspension models developed for turbulent channel flows.
Evolution of the derivative skewness for nonlinearly propagating waves.
Reichman, Brent O; Muhlestein, Michael B; Gee, Kent L; Neilsen, Tracianne B; Thomas, Derek C
2016-03-01
The skewness of the first time derivative of a pressure waveform, or derivative skewness, has been used previously to describe the presence of shock-like content in jet and rocket noise. Despite its use, a quantitative understanding of derivative skewness values has been lacking. In this paper, the derivative skewness for nonlinearly propagating waves is investigated using analytical, numerical, and experimental methods. Analytical expressions for the derivative skewness of an initially sinusoidal plane wave are developed and, along with numerical data, are used to describe its behavior in the preshock, sawtooth, and old-age regions. Analyses of common measurement issues show that the derivative skewness is relatively sensitive to the effects of a smaller sampling rate, but less sensitive to the presence of additive noise. In addition, the derivative skewness of nonlinearly propagating noise is found to reach greater values over a shorter length scale relative to sinusoidal signals. A minimum sampling rate is recommended for sinusoidal signals to accurately estimate derivative skewness values up to five, which serves as an approximate threshold indicating significant shock formation. PMID:27036276
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
Spin-orbit interaction with nonlinear wave functions.
Brozell, S. R.; Shepard, R.; Zhang, Z.; Stanford Univ.
2007-12-01
The computation of the spin-orbit interaction is discussed for electronic wave functions expressed in the new nonlinear expansion form. This form is based on spin eigenfunctions using the graphical unitary group approach (GUGA). The nodes of a Shavitt graph in GUGA are connected by arcs, and a Configuration State Function (CSF) is represented as a walk along arcs from the vacuum node to a head node. The wave function is a linear combination of product functions each of which is a linear combination of all CSFs, wherein each CSF coefficient is a product of nonlinear arc factors. When the spin-orbit interaction is included the Shavitt graph is a union of single-headed Shavitt graphs each with the same total number of electrons and orbitals. Thus spin-orbit Shavitt graphs are multiheaded. For full-CI multiheaded Shavitt graphs, analytic expressions are presented for the number of walks, the number of nodes, the number of arcs, and the number of node pairs in the associated auxiliary pair graph.
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.
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.
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. PMID:27367067
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.
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
Experimental study of nonlinear behaviors of a free-floating body in waves
NASA Astrophysics Data System (ADS)
He, Ming; Ren, Bing; Qiu, Da-hong
2016-04-01
Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relatively wide range of wave nonlinearities. A charge-coupled device (CCD) camera was used to capture the real-time motion of the floating body. The measurement data show that the sway, heave and roll motions of the floating body are all harmonic oscillations while the equilibrium position of the sway motion drifts in the wave direction. The drift speed is proportional to wave steepness when the size of the floating body is comparable to the wavelength, while it is proportional to the square of wave steepness when the floating body is relatively small. In addition, the drift motion leads to a slightly longer oscillation period of the floating body than the wave period of nonlinear wave and the discrepancy increases with the increment of wave steepness.
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.
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.
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.
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
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.
On triad nonlinear resonant interactions of deep water waves trapped by jet currents
NASA Astrophysics Data System (ADS)
Shrira, Victor; Slunyaev, Alexey
2014-05-01
We derive an asymptotic description of weakly nonlinear wave interactions between waves trapped by opposing jet currents by extending the asymptotic modal approach developed in Shrira & Slunyaev (2014). It is widely believed that to the leading order the nonlinear interactions between water waves in deep water are always quartic and potential. We show that for waves trapped on the jet currents it is not true: triad resonant interactions between trapped modes are always allowed. Moreover, the nonlinear evolution of the wave field is to the leading order determined by these triad interactions if the current is sufficiently strong or wave field nonlinearity is appropriately weak. To the leading order the corresponding interaction coefficients are controlled by the background vorticity due to the jet. More specifically, we consider waves upon a longitudinally uniform jet current; the current is assumed to be stationary and without vertical shear. The approximate separation of variables allows us to find the two-dimensional mode structure by means of one-dimensional boundary value problem (BVP) for wave Fourier harmonics along the current. The asymptotic weakly nonlinear theory taking into account quadratic nonlinearity for broad but not necessary weak currents is developed. The evolution equations for three interacting modes are written explicitly, the nonlinear interaction coefficients are computed. The three-wave interactions weaken when the current is weak. When the ratio of the current magnitude to wave celerity is of order of wave steepness the effects of 3-wave and 4-wave resonances appear at the same asymptotic order. These regimes, as well as the identified regimes where triad resonant interactions between trapped waves are dominant, lead to a qualitatively new wave dynamics which remains to be explored yet. V.I. Shrira, A.V. Slunyaev, Trapped waves on jet currents: asymptotic modal approach. J. Fluid Mech. 738, 65-104 (2014).
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
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
Creep damage characterization using nonlinear ultrasonic guided wave method: A mesoscale model
NASA Astrophysics Data System (ADS)
Xiang, Yanxun; Deng, Mingxi; Xuan, Fu-Zhen
2014-01-01
The early deformations in materials such as creep, plasticity, and fatigue damages have been proved to have a close relationship with the nonlinear effect of ultrasonic waves propagating in them. In the present paper, a theoretical mesoscale model of an ultrasonic non-destructive method has been proposed to evaluate creep deformed states based on nonlinear guided waves. The model developed here considers the nonlinear generation of Lamb waves response from precipitates variation in the dislocation network, which can be applicable to all precipitate stages including coherent and semi-coherent precipitates in the metallic alloy undergoing creep degradation. To verify the proposed model, experiments of titanium alloy Ti60 plates were carried out with different creep strains. An "increase-decrease" change of the acoustic nonlinearity of guided wave versus the creep life fraction has been observed. Based on microscopic images analyses, the mesoscale model was then applied to these creep damaged Ti60 specimens, which revealed a good accordance with the measured results of the nonlinear guided waves. It is shown that the change of the nonlinear Lamb wave depends on the variations of the α2 precipitation volume fraction, the dislocation density, the growth of the creep-voids, and the increasing mismatch of the phase velocities during the creep deformation process. The results indicate that the effect of the precipitate-dislocation interactions on the nonlinear guided wave is likely the dominant mechanism responsible for the change of nonlinear guided wave propagation in the crept materials.
Abe, H.; Okuda, H.
1993-08-01
In this Letter, we first present a new computer simulation model developed to study the propagation of electromagnetic waves in a dielectric medium in the linear and nonlinear regimes. The model is constructed by combining a microscopic model used in the semi-classical approximation for the dielectric media and the particle model developed for the plasma simulations. The model was then used for studying linear and nonlinear wave propagation in the dielectric medium such as an optical fiber. It is shown that the model may be useful for studying nonlinear wave propagation and harmonics generation in the nonlinear dielectric media.
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.
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.
Nonlinear theory of slow cyclotron wave interaction in folded waveguide
Ganguly, A.K.; Choi, J.J.
1995-12-31
A three-dimensional non-linear theory is presented for the generation of broadband radiation from slow cyclotron wave interaction in a folded waveguide. The serpentine structure is formed by folding a rectangular waveguide so that the orientation of the magnetic changes (H-plane bend) instead of the conventional E-plane bend configuration where the orientation of the electric field changes. The H-plane bend structure can use larger beam tunnel without distorting the rf field structure and generate higher output power. Numerical results will be shown for the TE{sub 10} mode propagation in an unridged and a double ridged waveguide. For a 61.5 kV, 3 A beam with {alpha}=1.0 and {Delta}v{sub z}/v{sub z}=0, calculations show an efficiency of 25% with 20% bandwidth and an efficiency of 35% at 10% bandwidth. The efficiency and bandwidth is relatively unchanged up to a beam axial velocity spread of 2%. The bandwidth can be further increased by mode coalescing techniques. Multistage operation is necessary to avoid backward wave oscillation.
A more general model equation of nonlinear Rayleigh waves and their quasilinear solutions
NASA Astrophysics Data System (ADS)
Zhang, Shuzeng; Li, Xiongbing; Jeong, Hyunjo
2016-03-01
A more general two-dimensional wave motion equation with consideration of attenuation and nonlinearity is proposed to describe propagating nonlinear Rayleigh waves of finite amplitude. Based on the quasilinear theory, the numerical solutions for the sound beams of fundamental and second harmonic waves are constructed with Green’s function method. Compared with solutions from the parabolic approximate equation, results from the general equation have more accuracy in both the near distance of the propagation direction and the far distance of the transverse direction, as quasiplane waves are used and non-paraxial Green’s functions are obtained. It is more effective to obtain the nonlinear Rayleigh sound beam distributions accurately with the proposed general equation and solutions. Brief consideration is given to the measurement of nonlinear parameter using nonlinear Rayleigh waves.
Numerical Simulation of Nonlinear Ultrasonic Waves Due to Bi-material Interface Contact
NASA Astrophysics Data System (ADS)
Hirose, S.; Saitoh, T.
2014-06-01
Boundary integral equations are formulated to investigate nonlinear waves generated by a debonding interface of bi-material subjected to an incident plane wave. For the numerical simulation, the IRK (Implicit Runge-Kutta method) based CQ-BEM (Convolution Quadrature-Boundary Element Method) is developed. The interface conditions for a debonding area, consisting of three phases of separation, stick, and slip, are developed for the simulation of nonlinear ultrasonic waves. Numerical results are obtained and discussed for normal incidence of a plane longitudinal wave onto the nonlinear interface with a static compressive stress.
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.
Nonlinear Alfvén wave dynamics at a 2D magnetic null point: ponderomotive force
NASA Astrophysics Data System (ADS)
Thurgood, J. O.; McLaughlin, J. A.
2013-07-01
Context. In the linear, β = 0 MHD regime, the transient properties of magnetohydrodynamic (MHD) waves in the vicinity of 2D null points are well known. The waves are decoupled and accumulate at predictable parts of the magnetic topology: fast waves accumulate at the null point; whereas Alfvén waves cannot cross the separatricies. However, in nonlinear MHD mode conversion can occur at regions of inhomogeneous Alfvén speed, suggesting that the decoupled nature of waves may not extend to the nonlinear regime. Aims: We investigate the behaviour of low-amplitude Alfvén waves about a 2D magnetic null point in nonlinear, β = 0 MHD. Methods: We numerically simulate the introduction of low-amplitude Alfvén waves into the vicinity of a magnetic null point using the nonlinear LARE2D code. Results: Unlike in the linear regime, we find that the Alfvén wave sustains cospatial daughter disturbances, manifest in the transverse and longitudinal fluid velocity, owing to the action of nonlinear magnetic pressure gradients (viz. the ponderomotive force). These disturbances are dependent on the Alfvén wave and do not interact with the medium to excite magnetoacoustic waves, although the transverse daughter becomes focused at the null point. Additionally, an independently propagating fast magnetoacoustic wave is generated during the early stages, which transports some of the initial Alfvén wave energy towards the null point. Subsequently, despite undergoing dispersion and phase-mixing due to gradients in the Alfvén-speed profile (∇cA ≠ 0) there is no further nonlinear generation of fast waves. Conclusions: We find that Alfvén waves at 2D cold null points behave largely as in the linear regime, however they sustain transverse and longitudinal disturbances - effects absent in the linear regime - due to nonlinear magnetic pressure gradients.
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.
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.
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.
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. PMID:20867450
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. PMID:23405086
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.
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.
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
Creep Damage Evaluation of Titanium Alloy Using Nonlinear Ultrasonic Lamb Waves
NASA Astrophysics Data System (ADS)
Xiang, Yan-Xun; Deng, Ming-Xi; Xuan, Fu-Zhen; Chen, Hu; Chen, Ding-Yue
2012-10-01
The creep damage in high temperature resistant titanium alloys Ti60 is measured using the nonlinear effect of an ultrasonic Lamb wave. The results show that the normalised acoustic nonlinearity of a Lamb wave exhibits a variation of the “increase-decrease" tendency as a function of the creep damage. The influence of microstructure evolution on the nonlinear Lamb wave propagation has been analyzed based on metallographic studies, which reveal that the normalised acoustic nonlinearity increases due to a rising of the precipitation volume fraction and the dislocation density in the early stage, and it decreases as a combined result of dislocation change and micro-void initiation in the material. The nonlinear Lamb wave exhibits the potential for the assessment of the remaining creep life in metals.
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.
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. PMID:18040322
Beach steepness effects on nonlinear infragravity-wave interactions: A numerical study
NASA Astrophysics Data System (ADS)
de Bakker, A. T. M.; Tissier, M. F. S.; Ruessink, B. G.
2016-01-01
The numerical model SWASH is used to investigate nonlinear energy transfers between waves for a diverse set of beach profiles and wave conditions, with a specific focus on infragravity waves. We use bispectral analysis to study the nonlinear triad interactions, and estimate energy transfers to determine energy flows within the spectra. The energy transfers are divided into four types of triad interactions, with triads including either one, two or three infragravity-frequency components, and triad interactions solely between sea-swell wave frequencies. The SWASH model is validated with a high-resolution laboratory data set on a gently sloping beach, which shows that SWASH is capable of modeling the detailed nonlinear interactions. From the simulations, we observe that especially the beach slope affects nonlinear infragravity-wave interactions. On a low-sloping beach, infragravity-wave energy dominates the water motion close to shore. Here infragravity-infragravity interactions dominate and generate higher harmonics that lead to the steepening of the infragravity wave and eventually breaking, causing large infragravity energy dissipation. On the contrary, on a steep-sloping beach, sea-swell wave energy dominates the water motion everywhere. Here infragravity frequencies interact with the spectral peak and spread energy to a wide range of higher frequencies, with relatively less infragravity energy dissipation. Although both beach types have different nonlinear interaction patterns during infragravity-wave dissipation, the amount of infragravity-wave reflection can be estimated by a single parameter, the normalized bed slope.
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
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.
Rogue wave modes for a derivative nonlinear Schrödinger model.
Chan, Hiu Ning; Chow, Kwok Wing; Kedziora, David Jacob; Grimshaw, Roger Hamilton James; Ding, Edwin
2014-03-01
Rogue waves in fluid dynamics and optical waveguides are unexpectedly large displacements from a background state, and occur in the nonlinear Schrödinger equation with positive linear dispersion in the regime of positive cubic nonlinearity. Rogue waves of a derivative nonlinear Schrödinger equation are calculated in this work as a long-wave limit of a breather (a pulsating mode), and can occur in the regime of negative cubic nonlinearity if a sufficiently strong self-steepening nonlinearity is also present. This critical magnitude is shown to be precisely the threshold for the onset of modulation instabilities of the background plane wave, providing a strong piece of evidence regarding the connection between a rogue wave and modulation instability. The maximum amplitude of the rogue wave is three times that of the background plane wave, a result identical to that of the Peregrine breather in the classical nonlinear Schrödinger equation model. This amplification ratio and the resulting spectral broadening arising from modulation instability correlate with recent experimental results of water waves. Numerical simulations in the regime of marginal stability are described. PMID:24730920
Nonlinear evolution of a baroclinic wave and imbalanced dissipation
NASA Astrophysics Data System (ADS)
Nadiga, Balu
2015-11-01
The question of how ocean circulation equilibrates in the presence of continuous large-scale forcing and a tendency of geostrophic turbulence to confine energy to large and intermediate scales is considered. By considering the nonlinear evolution of an unstable baroclinic wave at small Rossby and Froude numbers (small aspect ratio domain) at high resolutions, it is shown that submesoscale instabilities provide an interior pathway between the energetic oceanic mesoscales and smaller unbalanced scales. An estimate of the magnitude of this pathway is presented. Phenomenology-wise, mesoscale shear and strain resulting from the primary baroclinic instability drive frontogenesis; fronts in turn support ageostrophic secondary circulation and instabilities. These two processes together lead to a quick rise in dissipation rate which then reaches a peak and begins to fall as frontogenesis slows down; eventually balanced and imbalanced modes decouple. Dissipation of balanced energy by imbalanced processes is shown to scale exponentially with Rossby number of the base flow. Further, a break is seen in the total energy (TE) spectrum at small scales with a transition from k-3 to k - 5 / 3 reminiscent of the atmospheric spectra of Nastrom & Gage. For details see JFM 756, 965-1006.
Nonlinear dynamics of wind waves: multifractal phase/time effects
NASA Astrophysics Data System (ADS)
Mellen, R. H.; Leykin, I. A.
In addition to the bispectral coherence method, phase/time analysis of analytic signals is another promising avenue for the investigation of phase effects in wind waves. Frequency spectra of phase fluctuations obtained from both sea and laboratory experiments follow an F-β power law over several decades, suggesting that a fractal description is appropriate. However, many similar natural phenomena have been shown to be multifractal. Universal multifractals are quantified by two additional parameters: the Lévy index 0 < α < 2 for the type of multifractal and the co-dimension 0 < C1 < 1 for intermittence. The three parameters are a full statistical measure the nonlinear dynamics. Analysis of laboratory flume data is reported here and the results indicate that the phase fluctuations are 'hard multifractal' (α > 1). The actual estimate is close to the limiting value α = 2, which is consistent with Kolmogorov's lognormal model for turbulent fluctuations. Implications for radar and sonar backscattering from the sea surface are briefly considered.
Modeling Nonlinear Acoustic Standing Waves in Resonators: Theory and Experiments
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.
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.
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.
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.
El-Labany, S. K.; Moslem, Waleed M.; Safy, F. M.
2006-08-15
Nonlinear propagation of dust-acoustic solitary waves (DASWs) in a strong magnetized dusty plasma comprising warm adiabatic variable-charged dust particles, isothermal electrons, and two-temperature ions is investigated. Applying a reductive perturbation theory, a nonlinear Zakharov-Kuznetsov (ZK) equation for the first-order perturbed potential and a linear inhomogeneous ZK-type equation for the second-order perturbed potential are derived. However, at a certain value of high-temperature ion density, the coefficient of the nonlinear terms of both ZK and ZK-type equations vanishes. Therefore, a new set of expansion physical parameters and stretched coordinates are then used to derive a modified Zakharov-Kuznetsov (mZK) equation for the first-order perturbed potential and a mZK-type equation for the second-order perturbed potential. Stationary solutions of these equations are obtained using a renormalization method. A condition for two-temperature ions assumption is examined for various cosmic dust-laden plasma systems. It is found that this condition is satisfied for Saturn's F ring. The effects of two-temperature ions, magnetic field, and higher-order nonlinearity on the behavior of the DASWs are discussed. To obtain the stability condition of the waves, a method based on energy consideration is used and the condition for stable solitons is derived.
NASA Astrophysics Data System (ADS)
Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan
2016-02-01
We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.
Numerical experiments on the drift wave-zonal flow paradigm for nonlinear saturation
Waltz, R. E.; Holland, C.
2008-12-15
This paper confirms that ExB shearing from toroidally symmetric (toroidal mode number n=0) 'radial modes' provides the dominant nonlinear saturation mechanism for drift wave (n{ne}0) turbulence, which in turn nonlinearly drives the modes. In common usage, this is loosely referred to as the 'drift wave-zonal flow paradigm' for nonlinear saturation despite the fact that radial modes have several components distinguished in this paper: a residual or zero mean frequency 'zonal flow' part and an oscillatory 'geodesic acoustic mode' (GAM) part. Linearly, the zonal flows (and GAMs) are weakly damped only by ion-ion collisions, while the GAMs are strongly Landau damped only at low safety factor q. At high q the Hinton-Rosenbluth residual flow from an impulse vanishes and only the weakly damped GAMs remain. With the linear physics and driving rates of the finite-n transport modes unchanged, this paper argues that GAMs are only somewhat less effective than the residual zonal flows in providing the nonlinear saturation, and in some cases ExB shearing from GAMs (or at least the GAM physics) appears to dominate: transport appears to be nearly linear in the GAM frequency. By deleting the drift wave-drift wave nonlinear coupling, it is found that drift wave-radial mode nonlinear coupling triads account for most of the nonlinear saturation. Furthermore, the ExB shear components of the radial modes nonlinearly stabilize the finite-n modes, while the diamagnetic components nonlinearly destabilize them. Finally, from wave number spectral contour plots of the time average nonlinear entropy transfer function (and rates), it is shown that the peak in entropy generation coincides with the peak in transport production, while entropy dissipation (like Landau damping) is spread equally over all n modes (including n=0). Most of these conclusions appear to hold about equally well for all types of drift wave turbulence.
Quantitative Analysis of Nonlinear Water-Waves: A Perspective of an Experimentalist
NASA Astrophysics Data System (ADS)
Shemer, Lev
In the present review the emphasis is put on laboratory studies of propagating water waves where experiments were designed with the purpose to enable juxtaposing the measurement results with the theoretical predictions, thus providing a basis for evaluation of the domain of validity of various nonlinear theoretical model of different complexity. In particular, evolution of deterministic wave groups of different shapes and several values of characteristic nonlinearity is studied in deep and intermediate-depth water. Experiments attempting to generate extremely steep (rogue) waves are reviewed in greater detail. Relation between the kinematics of steep nonlinear waves and incipient breaking is considered. Discussion of deterministic wave systems is followed by review of laboratory experiments on propagation of numerous realizations of random wave groups with different initial spectra. The experimental results are compared with the corresponding Monte-Carlo numerical simulations based on different models.
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.
Evidence for Nonlinear VLF Wave Physics from Van Allen Probe Data
NASA Astrophysics Data System (ADS)
Crabtree, C. E.; Tejero, E. M.; Ganguli, G.; Hospodarsky, G. B.; Kletzing, C.
2015-12-01
VLF waves in the whistler mode branch in the Earth's radiation belts play a critical role in both the acceleration and loss of energetic electrons. VLF waves are often observed with magnetic field amplitudes that are a significant fraction of the background magnetic field suggesting that nonlinear effects may be important. We develop new Bayesian time-series analysis tools to investigate magnetic and electric field data from the EMFISIS instrument on board the Van Allen Probes. We also validate the analysis techniques through laboratory experiments. We apply these tools to Chorus waves to show that the picture of a single coherent plane wave is insufficient to explain EMFISIS data and that nonlinear collective wave interactions play an important role in moderating Chorus wave growth. We also apply these techniques to show that nonlinear induced scattering by thermal electrons can play a significant role in controlling the propagation of large amplitude lightning generated whistlers inside the plasmasphere.
NASA Astrophysics Data System (ADS)
Katoh, Y.; Kitahara, M.; Kojima, H.; Omura, Y.; Kasahara, S.; Hirahara, M.; Miyoshi, Y.; Seki, K.; Asamura, K.; Takashima, T.
2012-12-01
We study the statistical significance of the Wave Particle Interaction Analyzer (WPIA) for measurement of the energy transfer process between energetic electrons and whistler-mode chorus emissions in the Earth's inner magnetosphere. The WPIA measures a relative phase angle between the wave vector and velocity vector of each particle and computes an inner product W(t), while W(t) is equivalent to the variation of the kinetic energy of energetic electrons interacting with plasma waves. The WPIA measurements will be realized by the Software-type WPIA in the SPRINT-B/ERG satellite mission. In the present study, we evaluate the feasibility of WPIA by applying the WPIA analysis to the simulation results on whistler-mode chorus generation. We compute W(t) of a wave electric field observed at a fixed point assumed in the simulation system and a velocity vector of each energetic electron passing through the assumed point. By integrating W(t) in time, we obtain significant values of W_{int} in the kinetic energy and pitch angle ranges as expected from the evolution of chorus emissions in the simulation result. The statistical significance of the obtained W_{int} is evaluated by calculating the standard deviation σ_W of W_{int}. We show that W_{int} greater than σ_W is obtained in the velocity phase space corresponding to the wave generation and acceleration of relativistic electrons. We conduct another analysis of a distribution of energetic electrons in the wave phase space using the same dataset of the simulation results. We clarify that the deviation of the distribution in the wave phase space is found in the velocity phase space corresponding to the large W_{int} values, which is consistent with formation of nonlinear resonant currents assumed in the generation mechanism of chorus emissions. The present study suggests that the statistical significance of the WPIA can be evaluated by calculating σ_W of W_{int}, and reveals the feasibility of the WPIA, which will be on
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.
A nonlinear wave mixing method for detecting Alkali-Silica reactivity of aggregates
NASA Astrophysics Data System (ADS)
Liu, M.; Tang, G.; Jacobs, L. J.; Qu, J.
2012-05-01
Alkali-silica reaction (ASR) is a deleterious reaction in concrete. Significant ASR damage could undermine the durability of concrete structures and may result in reduced service life. Several nondestructive techniques based on ultrasound have been used to assess ASR damage. It has been shown that nonlinear ultrasound is more sensitive to internal stresses as well as to micro-cracks induced by ASR damage. In this investigation, we developed a co-linear wave mixing method for assessing ASR damage in concrete. By mixing two longitudinal waves, a new longitudinal wave with a lower frequency is generated. The amplitude of this new wave is proportional to the acoustic nonlinear parameter β which can then be obtained from the frequency spectrum of the newly generated longitudinal wave. Our experimental results show that (i) the acoustic nonlinearity parameter is closely correlated to ASR damage in concrete, (ii) the nonlinear wave mixing technique developed here is capable of measuring the changes in the acoustic nonlinearity parameter caused by ASR damage, even in its early stages, and (iii) the nonlinear wave mixing method has the potential to identify the different stages of ASR damage and to track the intrinsic characteristics of the ASR damage.
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.
Wave train generation of solitons in systems with higher-order nonlinearities.
Mohamadou, Alidou; LatchioTiofack, C G; Kofané, Timoléon C
2010-07-01
Considering the higher-order nonlinearities in a material can significantly change its behavior. We suggest the extended nonlinear Schrödinger equation to describe the propagation of ultrashort optical pulses through a dispersive medium with higher-order nonlinearities. Soliton trains are generated through the modulational instability and we point out the influence of the septic nonlinearity in the modulational instability gain. Experimental values are used for the numerical simulations and the input plane wave leads to the development of pulse trains, depending upon the sign of the septic nonlinearity. PMID:20866749
Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit
NASA Astrophysics Data System (ADS)
Liu, Xiang; Chraplyvy, A. R.; Winzer, P. J.; Tkach, R. W.; Chandrasekhar, S.
2013-07-01
Kerr nonlinearity imposes a limit on the achievable transmission performance and capacity of optical fibre communication links. We show that the nonlinear distortions of a pair of phase-conjugated twin waves are essentially anticorrelated, so cancellation of signal-to-signal nonlinear interactions can be achieved by coherently superimposing the twin waves at the end of the transmission line. We demonstrate that by applying this approach to fibre communication, nonlinear distortions can be reduced by >8.5 dB. In dispersive nonlinear transmission, the nonlinearity cancellation additionally requires a dispersion-symmetry condition that can be satisfied by appropriately predispersing the signals. By using these techniques we succeed in transmitting a 400 Gb s-1 superchannel over 12,800 km of fibre. We further show a connection between the nonlinearity cancellation and a nonlinear noise squeezing effect. The concept of using phase-conjugated twin waves to suppress nonlinear interactions may prove beneficial in other physical systems governed by the nonlinear Schrödinger equation.
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
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.
Drag forces on aquatic plants in nonlinear random waves plus current
NASA Astrophysics Data System (ADS)
Henry, Pierre-Yves; Myrhaug, Dag; Aberle, Jochen
2015-11-01
Plant-flow interactions are characterised by an assemblage of processes acting at different temporal and spatial scales. In order to mathematically characterise these interactions, such processes have to be parameterised given some simplifications. Typically, drag coefficients are derived from experiments to characterise the plant reconfiguration and wave energy dissipation processes. By reviewing the different plant drag coefficients CD valid in oscillatory flows, this study first highlights the lack of normalisation of the different existing CD formulations and identifies possibilities for a standardisation of the formulations for oscillatory and steady flows. Then, by taking into account the wave crest height distribution of a sea state condition, this study further develops a stochastic method to compute the expected wave induced forces on a plant in linear/nonlinear random waves plus current based on two different CD formulations for waves alone and waves plus current. This method improves the characterisation of the stochastic plant-flow interactions by allowing the calculation of expected values under different random wave plus currents conditions. Results are compared to a classic deterministic approach and some differences are identified, calling for further investigations against experimental datasets. Based on the appropriate CD formulations, this study finally revealed that wave nonlinearities have a significant effect on expected wave forces for a higher wave activity, and that in presence of an increasing current, the effect of wave nonlinearities decreases while the expected wave forces increase.
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.
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.
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. PMID:25314566
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.
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.
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
Exact finite difference schemes for the non-linear unidirectional wave equation
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1985-01-01
Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.
Nonlinear interaction of fast particles with Alfven waves in toroidal plasmas
Candy, J.; Borba, D.; Huysmans, G.T.A.; Kerner, W.; Berk, H.L.
1996-12-17
A numerical algorithm to study the nonlinear, resonant interaction of fast particles with Alfven waves in tokamak geometry has been developed. The scope of the formalism is wide enough to describe the nonlinear evolution of fishbone modes, toroidicity-induced Alfven eigenmodes and ellipticity-induced Alfven eigenmodes, driven by both passing and trapped fast ions. When the instability is sufficiently weak, it is known that the wave-particle trapping nonlinearity will lead to mode saturation before wave-wave nonlinearities are appreciable. The spectrum of linear modes can thus be calculated using a magnetohydrodynamic normal-mode code, then nonlinearly evolved in time in an efficient way according to a two-time-scale Lagrangian dynamical wave model. The fast particle kinetic equation, including the effect of orbit nonlinearity arising from the mode perturbation, is simultaneously solved of the deviation, {delta}f = f {minus} f{sub 0}, from an initial analytic distribution f{sub 0}. High statistical resolution allows linear growth rates, frequency shifts, resonance broadening effects, and nonlinear saturation to be calculated quickly and precisely. The results have been applied to an ITER instability scenario. Results show that weakly-damped core-localized modes alone cause negligible alpha transport in ITER-like plasmas--even with growth rates one order of magnitude higher than expected values. However, the possibility of significant transport in reactor-type plasmas due to weakly unstable global modes remains an open question.
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. PMID:24156928
NASA Astrophysics Data System (ADS)
Sharma, Vivek Kumar; Goyal, Amit
2016-05-01
We explore the modulational instability and existence of dark, bright solitary wave solutions in negative index-materials (NIMs) modeled by generalized nonlinear Schrödinger equation with competing cubic-quintic and higher-order nonlinearities with dispersive permittivity and permeability. Parameter domains are delineated in which these ultrashort pulses exist in NIMs. Unlike the ordinary materials, these novel excitations occur for different signs of dispersion, Kerr and non-Kerr nonlinearities.
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 astrophysical Alfven waves - Onset and outcome of the modulational instability
NASA Technical Reports Server (NTRS)
Spangler, S. R.
1985-01-01
The nonlinear development of Alfven waves is numerically studied, with applications to Alfven waves in astrophysical plasmas. It is found that amplitude-modulated Alfven wave packets undergo a collapse instability in which the wave packets become more intense and of smaller spatial extent. The wave packet steepening is eventually halted in a process most aptly described as soliton formation. A simple analytic model based on the method of characteristics can account for many of the results of the numerical calculations. The instability probably cannot prevent particle pitch angle isotropization due to self-generated Alfven waves. Nonlinear effects of the collapse may modify the process by which energetic electrons are reaccelerated by plasma turbulence. The model calculations can semiquantitatively account for properties of shock-associated Alfven waves in the solar system.
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
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
The evolution of nonlinear internal waves in Massachusetts Bay: observations and model results.
NASA Astrophysics Data System (ADS)
Scotti, A. D.
2004-05-01
Nonlinear internal waves are a common feature in many coastal areas. In Massachusetts Bay, trains of high-frequency and short-wavelength internal waves are generated by the semidiurnal barotropic tide flowing over Stellwagen Bank, and propagate shoreward. In this talk, we present observational and modeling results that have been accumulated over the past 6 years. We will consider in particular the strongly nonlinear interaction with the bottom that occurs when the waves propagate along the incline leading to the shallow (25 m) area just off the coast south of Boston. Contrary to what was previously thought, only part of the baroclinic energy is dissipated locally. The remaining energy propagates in the shallow area to the west of the incline, creating highly nonlinear and very steep waves of elevation that we were able to observe in great detail. The evidence accumulated so far suggest that these waves depart strongly from the hydrostatic equilibrium. The consequences for modeling will be discussed.
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. PMID:17931024
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 Schroedinger 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.
Critical-layer nonlinearity in the resonance growth of three-dimensional waves in boundary layers
NASA Technical Reports Server (NTRS)
Mankbadi, Reda R.
1990-01-01
The nonlinear interactions of a triad of initially linear stability waves are addressed. The triad consisted of a single two-dimensional mode at a given frequency and two oblique modes with equal and opposite spanwise wave numbers. The oblique waves were at half the frequency and streamwise wave number of the two-dimensional mode. Attention was focused on the boundary-layer transition at low frequencies and high Reynolds numbers. A five-zoned structure and low-frequency scaling were used to derive the nonlinear-interaction equations. The initial nonlinear development of the waves was analyzed; the results indicated that the two-dimensional wave behaves according to linear theory. Nonlinear interactions caused exponential-of-an-exponential growth of the oblique modes. This resonant amplification of the subharmonic depended on the initial amplitude of the two-dimensional wave and on the initial phase angle between the two-dimensional wave and the oblique waves. The resonant growth of the oblique modes was more pronounced at lower frequencies than at higher frequencies. The results are in good agreement with experimental results and offer explanations of the observed process.
On nonlinear Alfvén-cyclotron waves in multi-species plasma
NASA Astrophysics Data System (ADS)
Marsch, Eckart; Verscharen, Daniel
2011-06-01
Large-amplitude Alfvén waves are ubiquitous in space plasmas and a main component of magnetohydrodynamic (MHD) turbulence in the heliosphere. As pump waves, they are prone to parametric instability by which they can generate cyclotron and acoustic daughter waves. Here, we revisit a related process within the framework of the multi-fluid equations for a plasma consisting of many species. The nonlinear coupling of the Alfvén wave to acoustic waves is studied, and a set of compressive and coupled-wave equations for the transverse magnetic field and longitudinal electric field is derived for waves propagating along the mean-field direction. It turns out that slightly compressive Alfvén waves exert, through induced gyro-radius and kinetic-energy modulations, an electromotive force on the particles in association with a longitudinal electric field, which has a potential that is given by the gradient of the transverse kinetic energy of the particles gyrating about the mean field. This in turn drives electric fluctuations (sound and ion-acoustic waves) along the mean magnetic field, which can nonlinearly react back on the transverse magnetic field. Mutually coupled Alfvén-cyclotron-acoustic waves are thus excited, a nonlinear process that can drive a cascade of wave energy in the plasma, and may generate compressive microturbulence. These driven electric fluctuations might have consequences for the dissipation of an MHD turbulence and, thus, for the heating and acceleration of particles in the solar wind.
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.
Propagation of Nonlinear Waves in Waveguides and Application to Nondestructive Stress Measurement
NASA Astrophysics Data System (ADS)
Nucera, Claudio
Propagation of nonlinear waves in waveguides is a field that has received an ever increasing interest in the last few decades. Nonlinear guided waves are excellent candidates for interrogating long waveguide like structures because they combine high sensitivity to structural conditions, typical of nonlinear parameters, with large inspection ranges, characteristic of wave propagation in bounded media. The primary topic of this dissertation is the analysis of ultrasonic waves, including ultrasonic guided waves, propagating in their nonlinear regime and their application to structural health monitoring problems, particularly the measurement of thermal stress in Continuous Welded Rail (CWR). Following an overview of basic physical principles generating nonlinearities in ultrasonic wave propagation, the case of higher-harmonic generation in multi-mode and dispersive guided waves is examined in more detail. A numerical framework is developed in order to predict favorable higher-order generation conditions (i.e. specific guided modes and frequencies) for waveguides of arbitrary cross-sections. This model is applied to various benchmark cases of complex structures. The nonlinear wave propagation model is then applied to the case of a constrained railroad track (CWR) subjected to thermal variations. This study is a direct response to the key need within the railroad transportation community to develop a technique able to measure thermal stresses in CWR, or determine the rail temperature corresponding to a null thermal stress (Neutral Temperature -- NT). The numerical simulation phase concludes with a numerical study performed using ABAQUS commercial finite element package. These analyses were crucial in predicting the evolution of the nonlinear parameter beta with thermal stress level acting in the rail. A novel physical model, based on interatomic potential, was developed to explain the origin of nonlinear wave propagation under constrained thermal expansion. In fact
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. 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.
The soliton transform and a possible application to nonlinear Alfven waves in space
NASA Technical Reports Server (NTRS)
Hada, T.; Hamilton, R. L.; Kennel, C. F.
1993-01-01
The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.
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.
Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.
Kourakis, I; Shukla, P K
2005-07-01
We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained. PMID:16090126
Nonlinear theory of unstable fluid mixing driven by shock wave
NASA Astrophysics Data System (ADS)
Zhang, Qiang; Sohn, Sung-Ik
1997-04-01
A shock driven material interface between two fluids of different density is unstable. This instability is known as Richtmyer-Meshkov (RM) instability. In this paper, we present a quantitative nonlinear theory of compressible Richtmyer-Meshkov instability in two dimensions. Our nonlinear theory contains no free parameter and provides analytical predictions for the overall growth rate, as well as the growth rates of the bubble and spike, from early to later times for fluids of all density ratios. The theory also includes a general formulation of perturbative nonlinear solutions for incompressible fluids (evaluated explicitly through the fourth order). Our theory shows that the RM unstable system goes through a transition from a compressible and linear one at early times to a nonlinear and incompressible one at later times. Our theoretical predictions are in excellent agreement with the results of full numerical simulations from linear to nonlinear regimes.
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.
Nonlinear Drift-Kinetic Equation in the Presence of a Circularly Polarized Wave
NASA Technical Reports Server (NTRS)
Khazanov, G. V.; Krivorutsky, E. N.; Whitaker, Ann F. (Technical Monitor)
2001-01-01
Equations of the single particle motion and nonlinear kinetic equation for plasma in the presence of a circularly polarized wave of arbitrary frequency in the drift approximation are presented. The nonstationarity and inhomogeneity of the plasma-wave system are taken into account.
Nonlinear Drift-Kinetic Equation in the Presence of a Circularly Polarized Wave
NASA Technical Reports Server (NTRS)
Khazanov, G. V.; Krivorutsky, E. N.; Six, N. Frank (Technical Monitor)
2002-01-01
Equations of the single particle motion and nonlinear kinetic equation for plasma in the presence of a circularly polarized wave of arbitrary frequency in the drift approximation are presented. The nonstationarity and inhomogeneity of the plasma-wave system are taken into account. The time dependent part of the ponderomotive force is discussed.
Nonlinearities of waves propagating over a mild-slope beach: laboratory and numerical results
NASA Astrophysics Data System (ADS)
Rocha, Mariana V. L.; Michallet, Hervé; Silva, Paulo A.; Cienfuegos, Rodrigo
2014-05-01
As surface gravity waves propagate from deeper waters to the shore, their shape changes, primarily due to nonlinear wave interactions and further on due to breaking. The nonlinear effects amplify the higher harmonics and cause the oscillatory flow to transform from nearly sinusoidal in deep water, through velocity-skewed in the shoaling zone, to velocity asymmetric in the inner-surf and swash zones. In addition to short-wave nonlinearities, the presence of long waves and wave groups also results in a supplementary wave-induced velocity and influences the short-waves. Further, long waves can themselves contribute to velocity skewness and asymmetry at low frequencies, particularly for very dissipative mild-slope beach profiles, where long wave shoaling and breaking can also occur. The Hydralab-IV GLOBEX experiments were performed in a 110-m-long flume, with a 1/80 rigid-bottom slope and allowed the acquisition of high-resolution free-surface elevation and velocity data, obtained during 90-min long simulations of random and bichromatic wave conditions, and also of a monochromatic long wave (Ruessink et al., Proc. Coastal Dynamics, 2013). The measurements are compared to numerical results obtained with the SERR-1D Boussinesq-type model, which is designed to reproduce the complex dynamics of high-frequency wave propagation, including the energy transfer mechanisms that enhance infragravity-wave generation. The evolution of skewness and asymmetry along the beach profile until the swash zone is analyzed, relatively to that of the wave groupiness and long wave propagation. Some particularities of bichromatic wave groups are further investigated, such as partially-standing long-wave patterns and short-wave reformation after the first breakpoint, which is seen to influence particularly the skewness trends. Decreased spectral width (for random waves) and increased modulation (for bichromatic wave groups) are shown to enhance energy transfers between super- and sub
Nonlinear wave growth theory of coherent hiss emissions in the plasmasphere
NASA Astrophysics Data System (ADS)
Omura, Yoshiharu; Nakamura, Satoko; Kletzing, Craig A.; Summers, Danny; Hikishima, Mitsuru
2015-09-01
Recent observations of plasmaspheric hiss emissions by the Van Allen Probes show that broadband hiss emissions in the plasmasphere comprise short-time coherent elements with rising and falling tone frequencies. Based on nonlinear wave growth theory of whistler mode chorus emissions, we have examined the applicability of the nonlinear theory to the coherent hiss emissions. We have generalized the derivation of the optimum wave amplitude for triggering rising tone chorus emissions to the cases of both rising and falling tone hiss elements. The amplitude profiles of the hiss emissions are well approximated by the optimum wave amplitudes for triggering rising or falling tones. Through the formation of electron holes for rising tones and electron hills for falling tones, the coherent waves evolve to attain the optimum amplitudes. An electromagnetic particle simulation confirms the nonlinear wave growth mechanism as the initial phase of the hiss generation process. We find very good agreement between the theoretical optimum amplitudes and the observed amplitudes as a function of instantaneous frequency. We calculate nonlinear growth rates at the equator and find that nonlinear growth rates for rising tone emissions are much larger than the linear growth rates. The time scales of observed hiss emissions also agree with those predicted by the nonlinear theory. Based on the theory, we can infer properties of energetic electrons generating hiss emissions in the equatorial region of the plasmasphere.
Acceleration of soliton by nonlinear Landau damping of dust-helical waves
Ehsan, Zahida; Tsintsadze, Nodar L.; Vranjes, J.; Poedts, S.
2009-05-15
The problem of nonlinear Landau damping of helicon waves in dusty plasma in particular emphasis to the acceleration of soliton is presented here. This in the framework of a collisionless, anisotropic homogeneous dusty plasma in one dimension, can be well described by two coupled dynamical equations of the generalized Zakharov type, with one extra nonlocal term coming from Landau damping. Nonlinear-nonlocal term gives rise to essential contributions relative to the local term. Then under different conditions, kinetic nonlinear Schroedinger equation is constructed and nonlinear decrement is obtained for two cases. It is noticed that the time dependant term in the ponderomotive force plays a significant role for this kind of damping. Additionally, it is shown that nonlinear Landau damping leads to the amplitude modulation of dust helicon waves, further modulational instability, and maximal growth rate is obtained when the group velocity of the helicon wave reaches the dust-acoustic speed. It is demonstrated that how the nonlinear Landau damping leads to the acceleration of soliton, which is eventually slowed down after transferring some of its energy to the wave. Emission of dust-acoustic wave by accelerated soliton is discussed briefly.
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
On the dispersion relation of nonlinear wave current interaction by means of the HAM
NASA Astrophysics Data System (ADS)
Liu, Zeng; Lin, Zhiliang; Liao, Shijun
2012-09-01
The influence of exponentially sheared currents on unidirectional bichromatic waves in deep water is investigated by the HAM. The governing equations contain four coupled PDEs, including a nonlinear vorticity transport equation and two nonlinear free-surface conditions on the unknown wave elevation. No constrain is made for the primary wave amplitudes, and the current owns a exponential type profile along the vertical line. Convergent solutions are obtained with the help of convergence-control parameter. It is found that a critical characteristic current profile slope exists for each parts of phase velocity caused by nonlinear interaction, under/above which the mean flow vorticity increases/decreases the corresponding part of phase velocity. This work indicates that the HAM is a powerful tool for complicated coupled nonlinear PDEs, which deserves more attention for further development.
On strongly nonlinear vortex/wave interactions in boundary-layer transition
NASA Technical Reports Server (NTRS)
Hall, Philip; Smith, Frank T.
1989-01-01
The interactions between longitudinal vortices and accompanying waves considered are strongly nonlinear, in the sense that the mean-flow profile throughout the boundary layer is completely altered from its original undisturbed state. Nonlinear interactions between vortex flow and Tollmien-Schlichting waves are addressed first, and some analytical and computational properties are described. These include the possibility in the spatial-development case of a finite-distance break-up, inducing a singularity in the displacement thickness. Second, vortex/Rayleigh wave nonlinear interactions are considered for the compressible boundary-layer, along with certain special cases of interest and some possible solution properties. Both types, vortex/Tollmien-Schlichting and vortex/Rayleigh, are short-scale/long-scale interactions and they have potential applications to many flows at high Reynolds numbers. The strongly nonlinear nature is believed to make them very relevant to fully fledged transition to turbulence.
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.
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.
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.
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.
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.
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.
Gauss' law and nonlinear plane waves for Yang-Mills theory
NASA Astrophysics Data System (ADS)
Tsapalis, A.; Politis, E. P.; Maintas, X. N.; Diakonos, F. K.
2016-04-01
We investigate nonlinear plane-wave solutions of the classical Minkowskian Yang-Mills (YM) equations of motion. By imposing a suitable ansatz which solves Gauss' law for the SU(3) theory, we derive solutions which consist of Jacobi elliptic functions depending on an enumerable set of elliptic modulus values. The solutions represent periodic anharmonic plane waves which possess arbitrary nonzero mass and are exact extrema of the nonlinear YM action. Among them, a unique harmonic plane wave with a nontrivial pattern in phase, spin, and color is identified. Similar solutions are present in the SU(4) case, while they are absent from the SU(2) theory.
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 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 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
Atom laser based on four-wave mixing with Bose-Einstein condensates in nonlinear lattices
NASA Astrophysics Data System (ADS)
Wasak, T.; Konotop, V. V.; Trippenbach, M.
2013-12-01
Optical lattices are typically used to modify the dispersion relation of the matter wave, in particular, to ensure resonant conditions for multiwave interactions. Here we propose an alternative mechanism of wave interactions. It can be implemented using a nonlinear lattice and modifies the momentum conservation law of the interacting atoms, leaving the energy conservation unchanged. We propose to apply this phenomenon to construct an atom laser via a resonant four-wave mixing process.
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
NASA Astrophysics Data System (ADS)
Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan
2016-05-01
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
Construction of rogue wave and lump solutions for nonlinear evolution equations
NASA Astrophysics Data System (ADS)
Lü, Zhuosheng; Chen, Yinnan
2015-07-01
Based on symbolic computation and an ansatz, we present a constructive algorithm to seek rogue wave and lump solutions for nonlinear evolution equations. As illustrative examples, we consider the potential-YTSF equation and a variable coefficient KP equation, and obtain nonsingular rational solutions of the two equations. The solutions can be rogue wave or lump solutions under different parameter conditions. We also present graphic illustration of some special solutions which would help better understand the evolution of solution waves.
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.
Non-linear Frequency Shifts, Mode Couplings, and Decay Instability of Plasma Waves
NASA Astrophysics Data System (ADS)
Affolter, Mathew; Anderegg, F.; Driscoll, C. F.; Valentini, F.
2015-11-01
We present experiments and theory for non-linear plasma wave decay to longer wavelengths, in both the oscillatory coupling and exponential decay regimes. The experiments are conducted on non-neutral plasmas in cylindrical Penning-Malmberg traps, θ-symmetric standing plasma waves have near acoustic dispersion ω (kz) ~kz - αkz2 , discretized by kz =mz (π /Lp) . Large amplitude waves exhibit non-linear frequency shifts δf / f ~A2 and Fourier harmonic content, both of which are increased as the plasma dispersion is reduced. Non-linear coupling rates are measured between large amplitude mz = 2 waves and small amplitude mz = 1 waves, which have a small detuning Δω = 2ω1 -ω2 . At small excitation amplitudes, this detuning causes the mz = 1 mode amplitude to ``bounce'' at rate Δω , with amplitude excursions ΔA1 ~ δn2 /n0 consistent with cold fluid theory and Vlasov simulations. At larger excitation amplitudes, where the non-linear coupling exceeds the dispersion, phase-locked exponential growth of the mz = 1 mode is observed, in qualitative agreement with simple 3-wave instability theory. However, significant variations are observed experimentally, and N-wave theory gives stunningly divergent predictions that depend sensitively on the dispersion-moderated harmonic content. Measurements on higher temperature Langmuir waves and the unusual ``EAW'' (KEEN) waves are being conducted to investigate the effects of wave-particle kinetics on the non-linear coupling rates. Department of Energy Grants DE-SC0002451and DE-SC0008693.
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.
Noncontact Evaluation of Surface-Wave Nonlinearity for Creep Damage in Cr-Mo-V Steel
NASA Astrophysics Data System (ADS)
Ohtani, Toshihiro; Ogi, Hirotsugu; Hirao, Masahiko
2009-07-01
A nonlinear acoustic measurement is studied for creep damage evaluation. An electromagnetic acoustic transducer (EMAT) magnetostrictively couples to a surface-shear-wave resonance along the circumference of a cylindrical specimen during the creep of Cr-Mo-V steels. The excitation of the EMAT at half of the resonance frequency caused a standing wave to contain only the second-harmonic component, which was received by the same EMAT for determining the second-harmonic amplitude. This measured surface-wave nonlinearity showed a peak at 30% and a minimum at 50% of the total life. We interpreted these phenomena in terms of dislocation mobility and restructuring, with support from scanning electron microscope (SEM) and transmission electron microscope (TEM) observations. This noncontact resonance-EMAT measurement can monitor the evolution of surface-shear-wave nonlinearity throughout creep life and has a potential to assess damage advance and predict the creep life of metals.
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 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.
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.
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
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. PMID:26647962
Nonlinear Generation of Electromagnetic Waves through Induced Scattering by Thermal Plasma
NASA Astrophysics Data System (ADS)
Tejero, E. M.; Crabtree, C.; Blackwell, D. D.; Amatucci, W. E.; Mithaiwala, M.; Ganguli, G.; Rudakov, L.
2015-12-01
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.
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. PMID:26552636
Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory
NASA Astrophysics Data System (ADS)
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.
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. PMID:27078341
NASA Astrophysics Data System (ADS)
Fahlen, Jay Edward
The generation and propagation of nonlinear plasma waves is studied using particle-in-cell (PIC) simulations. We concentrate on regimes of interest to inertial fusion and space physics in which wave-particle interactions are important. Experiments soon to be performed at the National Ignition Facility require the understanding and control of stimulated Raman scattering (SRS) for their success. The SRS instability occurs when an incident laser decays into a backscattered light wave and an electron plasma wave. Recent computer simulations of SRS indicate that the daughter plasma waves have finite longitudinal and transverse extent and that they reach large amplitudes. The nonlinear behavior of such waves determines the growth, saturation, and recurrence of SRS. However, little attention has been paid to the behavior of plasma waves having these properties, and their study in SRS simulations is complicated by the large-amplitude light waves associated with the instability. Most theory and simulation work on SRS and its daughter plasma waves has been limited to infinite plane waves, often in the one-dimension limit. This thesis therefore studies isolated electron plasma waves over a wide range of parameters in one and multiple dimensions using PIC simulations. The simulations are performed with the goal of understanding the wave's behavior for parameters relevant to SRS, but the normalized parameters have general applicability to a range of densities and temperatures. Accordingly, an external ponderomotive driver generates traveling waves, driving them either continuously to study their peak amplitude and saturation mechanisms, or impulsively to study their propagation. Several novel effects are identified and characterized, including nonlinear resonance for driven waves, wave packet etching for finite-length waves, and localization and local damping for finite-width waves. Finite-length wave packets are found to erode away at a constant rate due to particle trapping
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.
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.
Fully nonlinear modeling of radiated waves generated by floating flared structures
NASA Astrophysics Data System (ADS)
Zhou, Bin-Zhen; Ning, De-Zhi; Teng, Bin; Zhao, Ming
2014-10-01
The nonlinear radiated waves generated by a structure in forced motion, are simulated numerically based on the potential theory. A fully nonlinear numerical model is developed by using a higher-order boundary element method (HOBEM). In this model, the instantaneous body position and the transient free surface are updated at each time step. A Lagrangian technique is employed as the time marching scheme on the free surface. The mesh regridding and interpolation methods are adopted to deal with the possible numerical instability. Several auxiliary functions are proposed to calculate the wave loads indirectly, instead of directly predicting the temporal derivative of the velocity potential. Numerical experiments are carried out to simulate the heave motions of a submerged sphere in infinite water depth, the heave and pitch motions of a truncated flared cylinder in finite depth. The results are verified against the published numerical results to ensure the effectiveness of the proposed model. Moreover, a series of higher harmonic waves and force components are obtained by the Fourier transformation to investigate the nonlinear effect of oscillation frequency. The difference among fully nonlinear, body-nonlinear and linear results is analyzed. It is found that the nonlinearity due to free surface and body surface has significant influences on the numerical results of the radiated waves and forces.
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.
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.
Spatiotemporal three-dimensional mapping of nonlinear X waves.
Trull, J; Jedrkiewicz, O; Di Trapani, P; Matijosius, A; Varanavicius, A; Valiulis, G; Danielius, R; Kucinskas, E; Piskarskas, A; Trillo, S
2004-02-01
The spatiotemporal intensity profile of a 100-fs wave packet at the output of a X2 crystal, tuned for mismatched second-harmonic generation, is probed via sum-frequency generation with a compressed, 20-fs pulse, revealing the appearance of an X-type wave shape. PMID:14995580
NASA Astrophysics Data System (ADS)
Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Zhe; Qi, Feng-Hua; Guo, Rui
2016-04-01
We present the semirational solution in terms of the determinant form for the derivative nonlinear Schrödinger equation. It describes the nonlinear combinations of breathers and rogue waves (RWs). We show here that the solution appears as a mixture of polynomials with exponential functions. The k-order semirational solution includes k - 1 types of nonlinear superpositions, i.e., the l-order RW and (k-l)-order breather for l = 1 , 2 , … , k - 1 . By adjusting the shift and spectral parameters, we display various patterns of the semirational solutions for describing the interactions among the RWs and breathers. We find that k-order RW can be derived from a l-order RW interacting with 1/2(k - l) (k + l + 1) neighboring elements of a (k - l)-order breather for l = 1 , 2 , … , k - 1 .
Zhang Jiefang; Meng Jianping; Wu Lei; Li Yishen; Malomed, Boris A.
2010-09-15
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.
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)
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.
Solitary waves and stable analysis for the quintic discrete nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Zhang, Jinliang; Liu, Zhiguo; Li, Siwei; Wang, Mingliang
2012-07-01
The quintic discrete nonlinear Schrödinger equation (QDNLS) is an important model for describing the propagation of discrete self-trapped beams in an array of weakly coupled nonlinear optical waveguides. In this paper, the QDNLS is studied and bright solitons, dark solitons, alternating phase solitons, trigonometric function periodic wave solutions and rational wave solutions with arbitrary parameters are obtained using the extended G'/G-expansion method. The linear stability of the bright soliton, the dark soliton and the rational wave solution is analyzed using the perturbation method, and the conditions that stable solitary wave solutions satisfy are presented. The stable solitary wave solutions to the QDNLS are useful in understanding the complicated physical phenomena described by QDNLS.
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 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.
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.
NASA Astrophysics Data System (ADS)
Adcock, T. A. A.; Taylor, P. H.
2016-01-01
The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.
NASA Astrophysics Data System (ADS)
Han, Jiu-Ning; Luo, Jun-Hua; Li, Jun-Xiu
2014-01-01
The nonlinear propagation of ion-acoustic solitary and shock waves in a dissipative, nonplanar quantum plasma comprised of electrons, positrons, and ions are studied. A modified Korteweg-de Vries Burgers equation is derived in the limit of low frequency and long wavelength by taking into account the kinematic viscosity among the plasma constituents. It is shown that this plasma system supports the propagation of both compressive and rarefactive nonlinear waves. The effects of variation of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision of solitary waves are discussed. It is found that these parameters have significant effects on the properties of nonlinear waves in cylindrical and spherical geometries, and these effects for compressive and rarefactive nonlinear waves are obviously different.
NASA Astrophysics Data System (ADS)
Ustinova, I. A.; Cherkasskii, M. A.; Ustinov, A. B.; Kalinikos, B. A.
2015-12-01
The nonlinear phase shift and nonlinear damping of spin-electromagnetic waves were theoretically studied for the first time in sub-terahertz frequency range in infinite homogeneous longitudinal magnetized multiferroics. The research was based on the solution of the Ginzburg-Landau equation. It is shown that the saturation of the phase shift occurs due to the nonlinear damping if the nonlinear damping coefficients exceed v1=108 s-1 and v2=109 s-1.
The Propagation of Nonlinear Pressure Waves Through Regions of Non-Uniform Temperature
NASA Astrophysics Data System (ADS)
Dizinno, Nicholas; Vradis, George; Otugen, Volkan
2006-11-01
A numerical study of wave propagation through gases with non-uniform temperature distributions will be presented. The aim of this study is to determine the impact of temperature gradients on high-intensity pressure waves of various initial wave forms. Emphasis is paid to wave reflection and transmission. Ultimately, the performance of thermal barriers in attenuating nonlinear waves is evaluated. The concept of using regions of hot gas inside an ambient environment has potential in aeroacoustic applications, such as jet screech mitigation. This analysis considers the one-dimensional compressible unsteady Euler's equations with an ideal gas state equation. The domain is composed of two regions with uniform and equal gas properties separated by a third region with higher gas temperature (lower density). Pressure is uniform throughout the domain. We introduce various high-intensity wave forms into this medium. Our investigation studies how the shape and extent of the thermal zone affect transmission and reflection of the wave. This is done for a range of wave and thermal field parameters. A Fourier analysis will study the frequency content of the incident, transmitted and reflected waves. These results will help determine the effectiveness of using thermal barriers for nonlinear wave attenuation.