Strongly Nonlinear Stress Waves in Dissipative Metamaterials
NASA Astrophysics Data System (ADS)
Xu, Yichao; Nesterenko, Vitali
2015-06-01
We present the measurements, numerical simulations, and theoretical analysis of stress wave propagation in a one-dimensional strongly nonlinear dissipative metamaterial composed of steel disks and Nitrile O-rings. A stress wave of bell shape is generated by impactor with different masses. A strongly nonlinear double power-law is used to describe the nonlinear viscoelastic force interaction between the disks due to the compression of rubber O-rings. Numerical modeling including a nonlinear dissipative term is developed to predict the wave shape and propagation speed. The shape of generated stress wave can be dramatically changed by the viscous dissipation, which may prevent the pulse from splitting into trains of solitary waves. This strongly nonlinear dissipative metamaterial has a potential for attenuation of dynamic loading and allows an enhanced tunability of signal speed.
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}.
Solitary and Shock Waves in Strongly Nonlinear Metamaterials
NASA Astrophysics Data System (ADS)
Herbold, E. B.; Nesterenko, V. F.
2007-12-01
Strongly nonlinear laminar metamaterials can be assembled using rigid metal plates interacting through light deformable strongly nonlinear elements placed between them. They may consist of single toroidal polymer o-rings, combinations of o-rings with different stiffness or combinations of hardening and softening nonlinear elements including gaps between them. Solitary waves and shocks are investigated in these metamaterials numerically and experimentally.
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 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 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
Solitary and shock waves in discrete strongly nonlinear double power-law materials
NASA Astrophysics Data System (ADS)
Herbold, E. B.; Nesterenko, V. F.
2007-06-01
A laminar metamaterial supporting strongly nonlinear solitary and shock waves with impact energy mitigating capabilities is presented. It consists of steel plates with intermittent polymer toroidal rings acting as strongly nonlinear springs with large allowable strain. The force-displacement relationship of a compressed o-ring is described by the addition of two power-law relationships resulting in a solitary wave speed and width depending on the amplitude. This double nonlinearity allows splitting of an initial impulse into three separate strongly nonlinear solitary wave trains. Solitary and shock waves are observed experimentally and analyzed numerically in an assembly with Teflon o-rings.
Strongly nonlinear waves in locally resonant granular chains
NASA Astrophysics Data System (ADS)
Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; Vainchtein, Anna
2016-11-01
We explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the existence of two types of configurations: (a) small-amplitude periodic traveling waves and (b) dark-breather solutions, i.e. exponentially localized, time-periodic states mounted on top of a non-vanishing background. A remarkable feature distinguishing our results from other settings where dark breathers are observed is the complete absence of precompression in the system, i.e. the absence of a linear spectral band. We also identify conditions under which the system admits long-lived bright breather solutions. Our results are obtained by means of an asymptotic reduction to a suitably modified version of the so-called discrete p-Schrödinger (DpS) equation, which is established as controllably approximating the solutions of the original system for large but finite times (under suitable assumptions on the solution amplitude and the resonator mass). The findings are also corroborated by detailed numerical computations. Long-lived bright breathers are proved to exist over long but finite times, after which numerical simulations indicate that the breathers disintegrate. In line with these results, we prove that the only exact time-periodic bright breathers consist of trivial linear oscillations, without contact interactions between discrete elements.
Transmission and reflection of strongly nonlinear solitary waves at granular interfaces.
Tichler, A M; Gómez, L R; Upadhyaya, N; Campman, X; Nesterenko, V F; Vitelli, V
2013-07-26
The interaction of a solitary wave with an interface formed by two strongly nonlinear noncohesive granular lattices displays rich behavior, characterized by the breakdown of continuum equations of motion in the vicinity of the interface. By treating the solitary wave as a quasiparticle with an effective mass, we construct an intuitive (energy- and linear-momentum-conserving) discrete model to predict the amplitudes of the transmitted solitary waves generated when an incident solitary-wave front, parallel to the interface, moves from a denser to a lighter granular hexagonal lattice. Our findings are corroborated with simulations. We then successfully extend this model to oblique interfaces, where we find that the angle of refraction and reflection of a solitary wave follows, below a critical value, an analogue of Snell's law in which the solitary-wave speed replaces the speed of sound, which is zero in the sonic vacuum.
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.
NASA Astrophysics Data System (ADS)
Wang, Xiaodan; Wang, Yunliang; Liu, Tielu; Zhang, Fan
2016-06-01
> Two-dimensional nonlinear magnetosonic solitary and shock waves propagating perpendicular to the applied magnetic field are presented in quantum electron-positron-ion plasmas with strongly coupled classical ions and weakly coupled quantum electrons and positrons. The generalized viscoelastic hydrodynamic model is used for the ions and a quantum hydrodynamic model is introduced for the electrons and positrons. In the weakly nonlinear limit, a modified Kadomstev-Petviashvili (KP) equation with a damping term and a KP-Burgers equation have been derived in the kinetic regime and hydrodynamic regime, respectively. The analytical and numerical solutions of the modified KP and KP-Burgers equations are also presented and analysed with the typical parameters of a white dwarf star and pulsar magnetosphere, which show that the quantum plasma beta and the variation of positron number density have remarkable effects on the propagation of magnetosonic solitary and shock waves.
Modeling of strongly-nonlinear wave propagation using the extended Rankine-Hugoniot shock relations
NASA Astrophysics Data System (ADS)
Lee, J.-W.; Ohm, W.-S.; Shim, W.
2015-10-01
This paper presents a computational scheme solely based on the Rankine-Hugoniot shock relations to describe the propagation of strongly-nonlinear waves in fluids, the amplitude of which is so great that second-order approximations such as the weak shock theory and the Burgers equation do not apply. The Rankine-Hugoniot relations are three algebraic equations connecting the flow variables (pressure, density, particle velocity, and energy) across a shock. What is not well known is that the Rankine-Hugoniot relations can be used to compute the nonlinear evolution of the continuous segment of a wave, if the continuous segment can be approximated by a succession of infinitesimal compression shocks [Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover, New York, 2002), pp. 85-86]. We further extend this idea to the other continuous segment that can be discretized into a series of infinitesimal rarefaction shocks. The discretization of a waveform and the subsequent application of the Rankine-Hugoniot relations lead to a Riemann problem that conveniently treats continuous segments and real shocks in the same manner. Our computational scheme distinguishes itself from the conventional Riemann problem in that shocks are treated as particles, which facilitates an enormous saving in computation time. The scheme is verified against the 1-D Riemann solver for the case of strong blast waves.
Nonlinear dust-acoustic solitary waves in strongly coupled dusty plasmas.
Cousens, S E; Sultana, S; Kourakis, I; Yaroshenko, V V; Verheest, F; Hellberg, M A
2012-12-01
Dust-acoustic waves are investigated in a three-component plasma consisting of strongly coupled dust particles and Maxwellian electrons and ions. A fluid model approach is used, with the effects of strong coupling being accounted for by an effective electrostatic "pressure" which is a function of the dust number density and the electrostatic potential. Both linear and weakly nonlinear cases are considered by derivation and analysis of the linear dispersion relation and the Korteweg-de Vries equation, respectively. In contrast to previous studies using this model, this paper presents the results arising from an expansion of the dynamical form of the electrostatic pressure, accounting for the variations in its value in the vicinity of the wave. PMID:23368056
Bubble merger model for the nonlinear Rayleigh-Taylor instability driven by a strong blast wave
Miles, A R
2004-03-18
A bubble merger model is presented for the nonlinear evolution of the Rayleigh-Taylor instability driven by a strong blast wave. Single bubble motion is determined by an extension of previous buoyancy-drag models extended to the blast wave driven case, and a simple bubble merger law in the spirit of the Sharp-Wheeler model allows for the generation of larger scales. The blast wave driven case differs in several respects from the classical case of incompressible fluids in a uniform gravitational field. Because of material decompression in the rarefaction behind the blast front, the asymptotic bubble velocity and the merger time depend on time as well as the transverse scale and the drive. For planar blast waves, this precludes the emergence of a self-similar regime independent of the initial conditions. With higher-dimensional blast waves, divergence restores the properties necessary for the establishment of the self-similar state, but its establishment requires a very high initial characteristic mode number and a high Mach number for the incident blast wave.
NASA Astrophysics Data System (ADS)
Aguiar-González, Borja; Gerkema, Theo
2015-04-01
We derive a new two-fluid layer model consisting of a set of forced rotation-modified Boussinesq equations for studying the generation and evolution of strongly nonlinear weakly nonhydrostatic dispersive interfacial waves in a rotating ocean. The forcing for internal tide generation is due to tide-topography interaction (an oscillating non-flat bottom mimicking a barotropic tidal flow over topography). The resulting model forms a generalization of the Miyata-Choi-Camassa (MCC) equations, to which we add topography, tidal forcing and Coriolis dispersion due to Earth's rotation. Solitons are generated by disintegration of the first-mode of the internal tide. Because of strong non-linearity, they can attain a table-shaped form. Our moving (accelerating) topography is not an inertial frame and, hence, the transformation to a frame at rest is not simply a Galilean transformation. The effect of this transformation is discussed and is shown to be slight for the parameters under consideration. The set of equations is solved numerically using finite-difference methods. Numerical experiments using these equations are a useful tool for exploring and interpreting the conditions under which full nonlinearity becomes important for soliton generation. In particular, this is the case for table-top solitons when approaching the theoretical maximum amplitude and the appearance of nonlinearities when the two-layer system consists of two layers of equal thickness. At the early stage of the strongly nonlinear disintegration of an internal tide into table-top solitons, we observe that the low mode internal tide splits up into two different groups of rank-ordered solitons: a train of depressions on the leading edge and a train of elevations, after the former packet, with initially smaller amplitudes. Evolving in time, the largest elevations reach the smaller depressions in the train ahead, and three leading solitons at the front attain almost equal amplitudes. The table-top soliton
Shahmansouri, M.; Mamun, A. A.
2014-03-15
Linear and nonlinear propagation of dust-acoustic waves in a magnetized strongly coupled dusty plasma is theoretically investigated. The normal mode analysis (reductive perturbation method) is employed to investigate the role of ambient/external magnetic field, obliqueness, and effective electrostatic dust-temperature in modifying the properties of linear (nonlinear) dust-acoustic waves propagating in such a strongly coupled dusty plasma. The effective electrostatic dust-temperature, which arises from strong electrostatic interactions among highly charged dust, is considered as a dynamical variable. The linear dispersion relation (describing the linear propagation characteristics) for the obliquely propagating dust-acoustic waves is derived and analyzed. On the other hand, the Korteweg-de Vries equation describing the nonlinear propagation of the dust-acoustic waves (particularly, propagation of dust-acoustic solitary waves) is derived and solved. It is shown that the combined effects of obliqueness, magnitude of the ambient/external magnetic field, and effective electrostatic dust-temperature significantly modify the basic properties of linear and nonlinear dust-acoustic waves. The results of this work are compared with those observed by some laboratory experiments.
Strong Surface Contribution to the Nonlinear Meissner Effect in d-Wave Superconductors
NASA Astrophysics Data System (ADS)
Zare, A.; Dahm, T.; Schopohl, N.
2010-06-01
We demonstrate that in a d-wave superconductor the bulk nonlinear Meissner effect is dominated by a surface effect due to Andreev bound states at low temperatures. The contribution of this surface effect to the nonlinear response coefficient follows a 1/T3 law with the opposite sign compared to the bulk 1/T behavior. The crossover from bulk dominated behavior to surface dominated behavior occurs at a temperature of T/Tc˜1/κ. We present an approximate analytical calculation, which supports our numerical calculations and provides a qualitative understanding of the effect. The effect can be probed by intermodulation distortion experiments.
Strong surface contribution to the nonlinear Meissner effect in d-wave superconductors.
Zare, A; Dahm, T; Schopohl, N
2010-06-11
We demonstrate that in a d-wave superconductor the bulk nonlinear Meissner effect is dominated by a surface effect due to Andreev bound states at low temperatures. The contribution of this surface effect to the nonlinear response coefficient follows a 1/T3 law with the opposite sign compared to the bulk 1/T behavior. The crossover from bulk dominated behavior to surface dominated behavior occurs at a temperature of T/Tc∼1/square root(κ). We present an approximate analytical calculation, which supports our numerical calculations and provides a qualitative understanding of the effect. The effect can be probed by intermodulation distortion experiments. PMID:20867262
Nonlinear dispersion of resonance extraordinary wave in a plasma with strong magnetic field
Krasovitskiy, V. B.; Turikov, V. A.; Sotnikov, V. I.
2007-09-15
In this paper, the efficiency of electron acceleration by a short, powerful laser pulse propagating across an external magnetic field is investigated. Conditions for the decay of a laser pulse with frequency close to the upper hybrid resonance frequency are analyzed. It is also shown that a laser pulse propagating as an extraordinary wave in cold, magnetized, low-density plasma takes the form of a nonlinear wave with the modulated amplitude (envelope soliton). Finally, simulation results on the interaction of an electromagnetic pulse with a semi-infinite plasma, obtained with the help of an electromagnetic relativistic PIC code, are discussed and a comparison with the obtained theoretical results is presented.
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.
NASA Astrophysics Data System (ADS)
Zhao, Huijiang
2000-04-01
In this paper, we show that a strong planar rarefaction wave is nonlinear stable, namely it is an attractor for the relaxation approximation of the scalar conservation laws in several space dimensions. Compared with former results obtained by T. P. Liu (1987, Comm. Math. Phys.108, 153-175) and T. Luo (1997, J. Differential Equations133, 255-279), our main novelty lies in the fact that the planar rarefaction waves do not need to be small, and in the one-dimensional case, the initial disturbance can also be chosen arbitrarily large.
Nonlinear coda wave analysis of hysteretic elastic behavior in strongly scattering media
NASA Astrophysics Data System (ADS)
Ouarabi, M. Ait; Boubenider, F.; Gliozzi, A. S.; Scalerandi, M.
2016-10-01
Strongly scattering elastic media, such as consolidated granular materials, respond to ultrasonic pulse excitations with a long response signal with peculiar properties. The portion of the signal at late times, termed coda, is due to multiple scattering. It contains information about the elastic properties of the material, and it has been proven to be very sensitive to small variations in the modulus. Here we propose a technique based on a nonlinear analysis of the coda of a signal, which might be applied to quantify the nonlinear elastic response in consolidated granular media exhibiting a hysteretic elastic behavior. The method proposed allows for an intrinsic definition of the reference signal which is normally needed for applying coda-based methods.
Miles, Aaron R.
2004-01-01
In core-collapse supernovae, strong blast waves drive interfaces susceptible to Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) instabilities. In addition, perturbation growth can result from material expansion in large-scale velocity gradients behind the shock front. Laser-driven experiments are designed to produce a strongly shocked interface whose evolution is a scaled version of the unstable hydrogen-helium interface in core-collapse supernovae such as SN 1987A. The ultimate goal of this research is to develop an understanding of the effect of hydrodynamic instabilities and the resulting transition to turbulence on supernovae observables that remain as yet unexplained. In this dissertation, we present a computational study of unstable systems driven by high Mach number shock and blast waves. Using multi-physics radiation hydrodynamics codes and theoretical models, we consider the late nonlinear instability evolution of single mode, few mode, and multimode interfaces. We rely primarily on 2D calculations but present recent 3D results as well. For planar multimode systems, we show that compressibility effects preclude the emergence of a regime of self-similar instability growth independent of the initial conditions (IC's) by allowing for memory of the initial conditions to be retained in the mix-width at all times. The loss of transverse spectral information is demonstrated, however, along with the existence of a quasi-self-similar regime over short time intervals. Aspects of the IC's are shown to have a strong effect on the time to transition to the quasi-self-similar regime. With higher-dimensional blast waves, divergence restores the properties necessary for establishment of the self-similar state, but achieving it requires very high initial characteristic mode number and high Mach number for the incident blast wave. We point to recent stellar calculations that predict IC's we find incompatible with self-similarity, and emphasize the
NASA Technical Reports Server (NTRS)
Bennett, J.; Hall, P.; Smith, F. T.
1988-01-01
Viscous fluid flows with curved streamlines can support both centrifugal and viscous traveling wave instabilities. Here the interaction of these instabilities in the context of the fully developed flow in a curved channel is discussed. The viscous (Tollmein-Schlichting) instability is described asymptotically at high Reynolds numbers and it is found that it can induce a Taylor-Goertler flow even at extremely small amplitudes. In this interaction, the Tollmein-Schlichting wave can drive a vortex state with wavelength either comparable with the channel width or the wavelength of lower branch viscous modes. The nonlinear equations which describe these interactions are solved for nonlinear equilibrium states.
NASA Astrophysics Data System (ADS)
Terletska, Kateryna; Maderich, Vladimir; Talipova, Tatiana; Brovchenko, Igor; Jung, Kyung Tae; Grimshaw, Roger
2014-05-01
Second mode internal waves are widespread in offshore areas, and they frequently follow the first mode internal waves on the oceanic shelf. To study the main properties of interaction of second mode internal waves with a bottom features we consider simple configuration of numerical tank with a bottom step. The tank is filled by symmetricaly stratified three-layer fluid. Depending on the parameter of blocking B (ratio of the lower layer depth over the step to incident wave amplitude [1]) a several regimes can be separated. If B > 4, that means that the lower layer is deep enough in comparison with amplitude of the incident wave, then the second mode internal wave pass the step without significant changes. At the range of 0< B<0.5, that corresponds to the case when amplitude of the incident wave is greater than the depth of the lower layer over the step, incident second mode wave completely transforms into a solitary wave of the first mode and into reflected wave of the second mode. These transformations are opposite to the well-known mechanism of formation of the second mode wave in result of the first mode wave interaction with bottom relief. The most interesting is the transitional regime with the range of blocking parameter 0.5wave amplitude decreases after step whereas first mode wave is radiated in front of the transmitted second mode internal wave. So the first and the second mode internal waves coexist over the step. During this transformation internal wave breathers are generated after the step. Thus in the frame of numerical modeling new mechanism of the breather generation was found: in the case of three-layer stratification internal wave-breather can occur due to interaction of the second mode internal wave with abrupt changes of the bottom topography. The dependencies for transformation coefficients (reflection and transmission) on the parameter of blocking are similar for incident long and intermediate waves
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 density waves in planetary rings
NASA Technical Reports Server (NTRS)
Borderies, Nicole; Goldreich, Peter; Tremaine, Scott
1986-01-01
The steady-state structure of planetary rings in the presence of density waves at the Lindblad resonances of a satellite is indicated. The study is based on the dispersion relation and damping rate for nonlinear density waves, derived by Shu et al. (1985) and by Borderies, Goldreich, and Tremaine (1985). It is shown that strong density waves lead to an enhancement of the background surface density in the wave zone.
Relativistically modulational instability by strong Langmuir waves
Liu, X. L.; Liu, S. Q.; Li, X. Q.
2012-09-15
Based on the set of nonlinear coupling equations, which has considered the relativistic effects of electrons, modulational instability by strong Langmuir waves has been investigated in this paper. Both the characteristic scale and maximum growth rate of the Langmuir field will enhance with the increase in the electron relativistic effect. The numerical results indicate that longitudinal perturbations induce greater instability than transverse perturbations do, which will lead to collapse and formation of the pancake-like structure.
Short-pulse dynamics in strongly nonlinear dissipative granular chains.
Rosas, Alexandre; Romero, Aldo H; Nesterenko, Vitali F; Lindenberg, Katja
2008-11-01
We study the energy decay properties of a pulse propagating in a strongly nonlinear granular chain with damping proportional to the relative velocity of the grains. We observe a wave disturbance that at low viscosities consists of two parts exhibiting two entirely different time scales of dissipation. One part is an attenuating solitary wave, dominated by discreteness and nonlinearity effects as in a dissipationless chain, and has the shorter lifetime. The other is a purely dissipative shocklike structure with a much longer lifetime and exists only in the presence of dissipation. The range of viscosities and initial configurations that lead to this complex wave disturbance are explored.
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.
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.
Nonlinear Landau damping and Alfven wave dissipation
NASA Technical Reports Server (NTRS)
Vinas, Adolfo F.; Miller, James A.
1995-01-01
Nonlinear Landau damping has been often suggested to be the cause of the dissipation of Alfven waves in the solar wind as well as the mechanism for ion heating and selective preacceleration in solar flares. We discuss the viability of these processes in light of our theoretical and numerical results. We present one-dimensional hybrid plasma simulations of the nonlinear Landau damping of parallel Alfven waves. In this scenario, two Alfven waves nonresonantly combine to create second-order magnetic field pressure gradients, which then drive density fluctuations, which in turn drive a second-order longitudinal electric field. Under certain conditions, this electric field strongly interacts with the ambient ions via the Landau resonance which leads to a rapid dissipation of the Alfven wave energy. While there is a net flux of energy from the waves to the ions, one of the Alfven waves will grow if both have the same polarization. We compare damping and growth rates from plasma simulations with those predicted by Lee and Volk (1973), and also discuss the evolution of the ambient ion distribution. We then consider this nonlinear interaction in the presence of a spectrum of Alfven waves, and discuss the spectrum's influence on the growth or damping of a single wave. We also discuss the implications for wave dissipation and ion heating in the solar wind.
NASA Astrophysics Data System (ADS)
Rapoport, Yu G.; Boardman, A. D.; Grimalsky, V. V.; Ivchenko, V. M.; Kalinich, N.
2014-05-01
The idea of nonlinear ‘transformation optics-inspired’ [1-6] electromagnetic cylindrical field concentrators has been taken up in a preliminary manner in a number of conference reports [7-9]. Such a concentrator includes both external linear region with a dielectric constant increased towards the centre and internal region with nonlinearity characterized by constant coefficients. Then, in the process of farther investigations we realized the following factors considered neither in [7-9] nor in the recent paper [10]: saturation of nonlinearity, nonlinear losses, linear gain, numerical convergence, when nonlinear effect becomes very strong and formation of ‘hotspots’ starts. It is clearly demonstrated here that such a strongly nonlinear process starts when the nonlinear amplitude of any incident beam(s) exceeds some ‘threshold’ value. Moreover, it is shown that the formation of hotspots may start as the result of any of the following processes: an increase of the input amplitude, increasing the linear amplification in the central nonlinear region, decreasing the nonlinear losses, a decrease in the saturation of the nonlinearity. Therefore, a tendency to a formation of ‘hotspots’ is a rather universal feature of the strongly nonlinear behaviour of the ‘nonlinear resonator’ system, while at the same time the system is not sensitive to the ‘prehistory’ of approaching nonlinear threshold intensity (amplitude). The new proposed method includes a full-wave nonlinear solution analysis (in the nonlinear region), a new form of complex geometric optics (in the linear inhomogeneous external cylinder), and new boundary conditions, matching both solutions. The observed nonlinear phenomena will have a positive impact upon socially and environmentally important devices of the future. Although a graded-index concentrator is used here, it is a direct outcome of transformation optics. Numerical evaluations show that for known materials these nonlinear effects
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 gravity-capillary water waves
NASA Astrophysics Data System (ADS)
Jiang, Lei
1997-11-01
Two-dimensional gravity-capillary water waves are analyzed using a fully-nonlinear Cauchy-integral method with spectral accuracy. Standing waves are generated in experiments by vertical oscillation and measured by a non-intrusive optical system along with a wave probe. Nonlinear resonance of standing waves with non-wetting contact line effects are discussed in detail. Amplitude- dependent wave frequency and damping in a glass rectangular tank suggest a new contact-line model. A new type of sideband resonance due to modulated forcing is discovered and explained by weakly-nonlinear analysis. This analytical solution is verified by our numerical simulations and physical experiments. New standing waveforms with dimpled or sharp crests are observed in experiments and computations. These new waveforms have strong symmetry breaking in time as a result of nonlinear harmonic interaction. With increasing wave steepness, steep standing waves experience period- tripling with three distinct forms: sharp crest, dimpled or flat crest, and round crest. Significant breaking occurs in the sharp-crest mode and the dimpled-crest mode. Using a complex-demodulation technique, I find that these breaking waves are related to the same 1:2 internal resonance (harmonic interaction) that causes the new steep waveforms. Novel approaches are used to estimate the (breaking and non-breaking) wave dissipation in steep and breaking standing waves. The breaking events (spray, air entrainment, and plunging) approximately double the wave dissipation. Weak capillarity significantly affects the limiting wave height and the form of standing waves, as demonstrated by both computations and small-scale Faraday-wave experiments. Capillary ripple generation on traveling waves is shown to be significant even at moderate wave steepness. The ubiquitous horizontal asymmetry of traveling waves is shown to be critical to capillary ripple generation. Two new asymmetric modes are identified and are shown to have an
Exact propagating nonlinear singular disturbances in strongly coupled dusty plasmas
Das, Amita; Tiwari, Sanat Kumar; Kaw, Predhiman; Sen, Abhijit
2014-08-15
The dynamical response of the strongly coupled dusty plasma medium has recently been described by utilizing the Generalized Hydrodynamic (GHD) model equations. The GHD equations capture the visco-elastic properties of the medium and have been successful in predicting a host of phenomena (e.g., existence of novel transverse shear waves in the fluid medium, modification of longitudinal wave dispersion by elastic effects, etc.) which have found experimental confirmation. In this paper, the nonlinear longitudinal response of the medium governed by GHD equations in strong coupling limit is discussed analytically. The structure of the equations rules out the balance between dispersion and nonlinearity, thereby, forbidding soliton formation. However, a host of new varieties of nonlinear solutions are found to exist, which have singular spatial profiles and yet have conservative properties. For instance, existence of novel conservative shock structures with zero strength is demonstrated, waves whose breaking produces no dissipation in the medium are observed, propagating solutions which produce cusp like singularities can exist and so on. It is suggested that simulations and experiments should look for these novel nonlinear structures in the large amplitude strong coupling limit of longitudinal disturbances in dusty plasmas.
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 Interaction of Waves in Geomaterials
NASA Astrophysics Data System (ADS)
Ostrovsky, L. A.
2009-05-01
Progress of 1990s - 2000s in studying vibroacoustic nonlinearities in geomaterials is largely related to experiments in resonance samples of rock and soils. It is now a common knowledge that many such materials are very strongly nonlinear, and they are characterized by hysteresis in the dependence between the stress and strain tensors, as well as by nonlinear relaxation ("slow time"). Elastic wave propagation in such media has many peculiarities; for example, third harmonic amplitude is a quadratic (not cubic as in classical solids) function of the main harmonic amplitude, and average wave velocity is linearly (not quadratically as usual) dependent on amplitude. The mechanisms of these peculiarities are related to complex structure of a material typically consisting of two phases: a hard matrix and relatively soft inclusions such as microcracks and grain contacts. Although most informative experimental results have been obtained in rock in the form of resonant bars, few theoretical models are yet available to describe and calculate waves interacting in such samples. In this presentation, a brief overview of structural vibroacoustic nonlinearities in rock is given first. Then, a simple but rather general approach to the description of wave interaction in solid resonators is developed based on accounting for resonance nonlinear perturbations which are cumulating from period to period. In particular, the similarity and the differences between traveling waves and counter-propagating waves are analyzed for materials with different stress-strain dependences. These data can be used for solving an inverse problem, i.e. characterizing nonlinear properties of a geomaterial by its measured vibroacoustic parameters. References: 1. L. Ostrovsky and P. Johnson, Riv. Nuovo Chimento, v. 24, 1-46, 2007 (a review); 2. L. Ostrovsky, J. Acoust. Soc. Amer., v. 116, 3348-3353, 2004.
Kummer solitons in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Zhong, Wei-Ping; Belić, Milivoj
2009-01-01
We solve the three-dimensional (3D) time-dependent strongly nonlocal nonlinear Schrödinger equation (NNSE) in spherical coordinates, with the help of Kummer's functions. We obtain analytical solitary solutions, which we term the Kummer solitons. We compare analytical solutions with the numerical solutions of NNSE. We discuss higher-order Kummer spatial solitons, which can exist in various forms, such as the 3D vortex solitons and the multipole solitons.
Nonlinear plasma wave in magnetized plasmas
NASA Astrophysics Data System (ADS)
Bulanov, Sergei V.; Zh. Esirkepov, Timur; Kando, Masaki; Koga, James K.; Hosokai, Tomonao; Zhidkov, Alexei G.; Kodama, Ryosuke
2013-08-01
Nonlinear axisymmetric cylindrical plasma oscillations in magnetized collisionless plasmas are a model for the electron fluid collapse on the axis behind an ultrashort relativisically intense laser pulse exciting a plasma wake wave. We present an analytical description of the strongly nonlinear oscillations showing that the magnetic field prevents closing of the cavity formed behind the laser pulse. This effect is demonstrated with 3D PIC simulations of the laser-plasma interaction. An analysis of the betatron oscillations of fast electrons in the presence of the magnetic field reveals a characteristic "Four-Ray Star" pattern.
Waves in strong centrifugal fields: dissipationless gas
NASA Astrophysics Data System (ADS)
Bogovalov, S. V.; Kislov, V. A.; Tronin, I. V.
2015-04-01
Linear waves are investigated in a rotating gas under the condition of strong centrifugal acceleration of the order 106 g realized in gas centrifuges for separation of uranium isotopes. Sound waves split into three families of the waves under these conditions. Dispersion equations are obtained. The characteristics of the waves strongly differ from the conventional sound waves on polarization, velocity of propagation and distribution of energy of the waves in space for two families having frequencies above and below the frequency of the conventional sound waves. The energy of these waves is localized in rarefied region of the gas. The waves of the third family were not specified before. They propagate exactly along the rotational axis with the conventional sound velocity. These waves are polarized only along the rotational axis. Radial and azimuthal motions are not excited. Energy of the waves is concentrated near the wall of the rotor where the density of the gas is largest.
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.
Scaling of chaos in strongly nonlinear lattices
Mulansky, Mario
2014-06-15
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.
Nonlinear excitations in strongly coupled Fermi-Dirac plasmas
NASA Astrophysics Data System (ADS)
Akbari-Moghanjoughi, M.
2012-04-01
In this paper, we use the conventional quantum hydrodynamics (QHD) model in combination with the Sagdeev pseudopotential method to explore the effects of Thomas-Fermi nonuniform electron distribution, Coulomb interactions, electron exchange, and ion correlation on the large-amplitude nonlinear soliton dynamics in Fermi-Dirac plasmas. It is found that in the presence of strong interactions, significant differences in nonlinear wave dynamics of Fermi-Dirac plasmas in the two distinct regimes of nonrelativistic and relativistic degeneracies exist. Furthermore, it is remarked that first-order corrections due to such interactions (which are proportional to the fine-structure constant) are more significant on soliton characteristics (particularly the amplitude) in the nonrelativistic plasma degeneracy regime rather than the relativistic one. In the relativistic degeneracy regime, however, these effects become less important and the electron quantum-tunneling and Pauli-exclusion dominate the nonlinear wave dynamics. Hence, application of non-interacting Fermi-Dirac QHD model to study the nonlinear wave dynamics in quantum plasmas, such as in compact stars is most appropriate for the relativistic degeneracy regime rather than nonrelativistic one.
Nonlinear MHD Waves in a Prominence Foot
NASA Astrophysics Data System (ADS)
Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.
2015-11-01
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ˜ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5-11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5-14 G. For the typical prominence density the corresponding fast magnetosonic speed is ˜20 km s-1, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
Nonlinear wave dynamics in honeycomb lattices
Bahat-Treidel, Omri; Segev, Mordechai
2011-08-15
We study the nonlinear dynamics of wave packets in honeycomb lattices and show that, in quasi-one-dimensional configurations, the waves propagating in the lattice can be separated into left-moving and right-moving waves, and any wave packet composed of only left (or only right) movers does not change its intensity structure in spite of the nonlinear evolution of its phase. We show that the propagation of a general wave packet can be described, within a good approximation, as a superposition of left- and right-moving self-similar (nonlinear) wave packets. Finally, we find that Klein tunneling is not suppressed by nonlinearity.
Investigation of Nonlinear Whistler Wave Processes in the Laboratory
NASA Astrophysics Data System (ADS)
Tejero, E. M.; Blackwell, D. D.; Amatucci, B.; Crabtree, C. E.; Ganguli, G.; Rudakov, L.
2015-12-01
Nonlinear interactions involving whistler wave turbulence can strongly effect the dynamics of the radiation belts. The building blocks of whistler wave turbulence are currently being studied in the NRL Space Physics Simulation Chamber (SPSC) under scaled magnetospheric conditions. These processes include parametric three-wave decay and a nonlinear wave-particle scattering off of thermal electrons that can substantially change the wave vector direction and energy flux. In the laboratory experiments, both of these processes have been observed and characterized. The results are consistent with theoretical predictions. Results from continuing laboratory experiments demonstrating triggered emissions and chorus-like emissions via nonlinear whistler wave-energetic particle interactions will be discussed. These chirped whistler waves are also observed to exhibit three-wave decay/coalescence and wave-particle scattering.
Yokoyama, Naoto; Takaoka, Masanori
2014-01-01
A weakly nonlinear spectrum and a strongly nonlinear spectrum coexist in a statistically steady state of elastic wave turbulence. The analytical representation of the nonlinear frequency is obtained by evaluating the extended self-nonlinear interactions. The critical wave numbers at which the nonlinear frequencies are comparable with the linear frequencies agree with the separation wave numbers between the weak and strong turbulence spectra. We also confirm the validity of our analytical representation of the separation wave numbers through comparison with the results of direct numerical simulations by changing the material parameters of a vibrating plate. PMID:24580299
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"
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.
Frequency bands of strongly nonlinear homogeneous granular systems.
Lydon, Joseph; Jayaprakash, K R; Ngo, Duc; Starosvetsky, Yuli; Vakakis, Alexander F; Daraio, Chiara
2013-07-01
Recent numerical studies on an infinite number of identical spherical beads in Hertzian contact showed the presence of frequency bands [Jayaprakash, Starosvetsky, Vakakis, Peeters, and Kerschen, Nonlinear Dyn. 63, 359 (2011)]. These bands, denoted here as propagation and attenuation bands (PBs and ABs), are typically present in linear or weakly nonlinear periodic media; however, their counterparts are not intuitive in essentially nonlinear periodic media where there is a complete lack of classical linear acoustics, i.e., in "sonic vacua." Here, we study the effects of PBs and ABs on the forced dynamics of ordered, uncompressed granular systems. Through numerical and experimental techniques, we find that the dynamics of these systems depends critically on the frequency and amplitude of the applied harmonic excitation. For fixed forcing amplitude, at lower frequencies, the oscillations are large in amplitude and governed by strongly nonlinear and nonsmooth dynamics, indicating PB behavior. At higher frequencies the dynamics is weakly nonlinear and smooth, in the form of compressed low-amplitude oscillations, indicating AB behavior. At the boundary between the PB and the AB large-amplitude oscillations due to resonance occur, giving rise to collisions between beads and chaotic dynamics; this renders the forced dynamics sensitive to initial and forcing conditions, and hence unpredictable. Finally, we study asymptotically the near field standing wave dynamics occurring for high frequencies, well inside the AB. PMID:23944453
Compactons of nonlinear Schrödinger lattices under strong nonlinearity management
NASA Astrophysics Data System (ADS)
Salerno, Mario
2016-09-01
We review recent work on compacton matter waves in Bose-Einstein condensates (BEC) trapped in deep optical lattices in the presence of strong and rapid periodic time modulations of the atomic scattering length. In particular, we derive averaged discrete nonlinear Schrödinger equations (DNLSE) and show that compacton solutions of different types can exist as stable excitations. Stability properties are also investigated both by linear analysis and by direct numerical integrations of the DNLSE.
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.
Generation of dispersion in nondispersive nonlinear waves in thermal equilibrium
Lee, Wonjung; Kovačič, Gregor; Cai, David
2013-01-01
In this work, we examine the important theoretical question of whether dispersion relations can arise from purely nonlinear interactions among waves that possess no linear dispersive characteristics. Using two prototypical examples of nondispersive waves, we demonstrate how nonlinear interactions can indeed give rise to effective dispersive-wave–like characteristics in thermal equilibrium. Physically, these example systems correspond to the strong nonlinear coupling limit in the theory of wave turbulence. We derive the form of the corresponding dispersion relation, which describes the effective dispersive structures, using the generalized Langevin equations obtained in the Zwanzig–Mori projection framework. We confirm the validity of this effective dispersion relation in our numerical study using the wavenumber–frequency spectral analysis. Our work may provide insight into an important connection between highly nonlinear turbulent wave systems, possibly with no discernible dispersive properties, and the dispersive nature of the corresponding renormalized waves. PMID:23401526
NASA Astrophysics Data System (ADS)
Sutin, A. M.; Johnson, P. A.
2005-04-01
This paper presents the second part of the review of Nonlinear Elastic Wave Spectroscopy (NEWS) in NDE, and describe two different methods of nonlinear NDE that provide not only damage detection but location as well. Nonlinear Wave Modulation Spectroscopy is based on the application of an ultrasonic probe signal modulated by a low frequency vibration. Damage location can be obtained by application of Impulse Modulation Techniques that exploit the modulation of a short pulse reflected from a damage feature (e.g. crack) by low frequency vibration. Nonlinear Time Reversed Acoustic methods provide the means to focus acoustic energy to any point in a solid. In combination, we are applying the focusing properties of TRA and the nonlinear properties of cracks to locate them.
Measuring Acoustic Nonlinearity by Collinear Mixing Waves
NASA Astrophysics Data System (ADS)
Liu, M.; Tang, G.; Jacobs, L. J.; Qu, J.
2011-06-01
It is well known that the acoustic nonlinearity parameter β is correlated to fatigue damage in metallic materials. Various methods have been developed to measure β. One of the most often used methods is the harmonic generation technique, in which β is obtained by measuring the magnitude of the second order harmonic waves. An inherent weakness of this method is the difficulty in distinguishing material nonlinearity from the nonlinearity of the measurement system. In this paper, we demonstrate the possibility of using collinear mixing waves to measure β. The wave mixing method is based on the interaction between two incident waves in a nonlinear medium. Under certain conditions, such interactions generate a third wave of different frequency. This generated third wave is also called resonant wave, because its amplitude is unbounded if the medium has no attenuation. Such resonant waves are less sensitive to the nonlinearity of the measurement system, and have the potential to identify the source location of the nonlinearity. In this work, we used a longitudinal wave and a shear wave as the incident waves. The resonant shear wave is measured experimentally on samples made of aluminum and steel, respectively. Numerical simulations of the tests were also performed using a finite difference method.
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
Strong electronic correlation effects in coherent multidimensional nonlinear optical spectroscopy.
Karadimitriou, M E; Kavousanaki, E G; Dani, K M; Fromer, N A; Perakis, I E
2011-05-12
We discuss a many-body theory of the coherent ultrafast nonlinear optical response of systems with a strongly correlated electronic ground state that responds unadiabatically to photoexcitation. We introduce a truncation of quantum kinetic density matrix equations of motion that does not rely on an expansion in terms of the interactions and thus applies to strongly correlated systems. For this we expand in terms of the optical field, separate out contributions to the time-evolved many-body state due to correlated and uncorrelated multiple optical transitions, and use "Hubbard operator" density matrices to describe the exact dynamics of the individual contributions within a subspace of strongly coupled states, including "pure dephasing". Our purpose is to develop a quantum mechanical tool capable of exploring how, by coherently photoexciting selected modes, one can trigger nonlinear dynamics of strongly coupled degrees of freedom. Such dynamics could lead to photoinduced phase transitions. We apply our theory to the nonlinear response of a two-dimensional electron gas (2DEG) in a magnetic field. We coherently photoexcite the two lowest Landau level (LL) excitations using three time-delayed optical pulses. We identify some striking temporal and spectral features due to dynamical coupling of the two LLs facilitated by inter-Landau-level magnetoplasmon and magnetoroton excitations and compare to three-pulse four-wave-mixing (FWM) experiments. We show that these features depend sensitively on the dynamics of four-particle correlations between an electron-hole pair and a magnetoplasmon/magnetoroton, reminiscent of exciton-exciton correlations in undoped semiconductors. Our results shed light into unexplored coherent dynamics and relaxation of the quantum Hall system (QHS) and can provide new insight into non-equilibrium co-operative phenomena in strongly correlated systems.
Strongly coupled stress waves in heterogeneous plates.
NASA Technical Reports Server (NTRS)
Wang, A. S. D.; Chou, P. C.; Rose, J. L.
1972-01-01
Consideration of coupled stress waves generated by an impulsive load applied at one end of a semiinfinite plate. For the field equations governing the one-dimensional coupled waves a hyperbolic system of equations is obtained in which a strong coupling in the second derivatives exists. The method of characteristics described by Chou and Mortimer (1967) is extended to cover the case of strong coupling, and a study is made of the transient stress waves in a semiinfinite plate subjected to an initial step input. Coupled discontinuity fronts are found to propagate at different velocities. The normal plate stress and the bending moment at different time regimes are illustrated by graphs.
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.
Electromagnetic waves in a strong Schwarzschild plasma
Daniel, J.; Tajima, T.
1996-11-01
The physics of high frequency electromagnetic waves in a general relativistic plasma with the Schwarzschild metric is studied. Based on the 3 + 1 formalism, we conformalize Maxwell`s equations. The derived dispersion relations for waves in the plasma contain the lapse function in the plasma parameters such as in the plasma frequency and cyclotron frequency, but otherwise look {open_quotes}flat.{close_quotes} Because of this property this formulation is ideal for nonlinear self-consistent particle (PIC) simulation. Some of the physical consequences arising from the general relativistic lapse function as well as from the effects specific to the plasma background distribution (such as density and magnetic field) give rise to nonuniform wave equations and their associated phenomena, such as wave resonance, cutoff, and mode-conversion. These phenomena are expected to characterize the spectroscopy of radiation emitted by the plasma around the black hole. PIC simulation results of electron-positron plasma are also presented.
Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua
2015-08-01
Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping.
Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua
2015-08-01
Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping. PMID:25937493
Nonlinear Alfven waves in high-speed solar wind streams
NASA Technical Reports Server (NTRS)
Abraham-Shrauner, B.; Feldman, W. C.
1977-01-01
A nonlinear proton distribution function that is an exact stationary solution of the nonlinear Vlasov equation and Maxwell's equations and which supports a single nonlinear transverse Alfven (ion cyclotron) wave that is circularly polarized and nondispersive is proposed for most of the observations during high-speed solar wind streams. This nonlinear distribution removes the strong Alfven wave instability, inconsistent with the persistence of the observed proton distribution functions in high-speed streams, found by the linear stability analysis. Model temperature anisotropies and drift velocities of the two spatially inhomogeneous bi-Maxwellian components are consistent with typical proton velocity distributions measured in high-speed streams at 1 AU. Two derived relations for each of the wave number and the phase velocity of the wave are obeyed within experimental uncertainties by two typical proton measurements. Our model also predicts that the alpha particle bulk flow velocity exceeds the proton particle bulk flow velocity, as is observed.
PARTICLE ACCELERATION IN SUPERLUMINAL STRONG WAVES
Teraki, Yuto; Ito, Hirotaka; Nagataki, Shigehiro
2015-06-01
We calculate the electron acceleration in random superluminal strong waves (SLSWs) and radiation from them using numerical methods in the context of the termination shocks of pulsar wind nebulae. We pursue the orbit of electrons by solving the equation of motion in the analytically expressed electromagnetic turbulences. These consist of a primary SLS and isotropically distributed secondary electromagnetic waves. Under the dominance of the secondary waves, all electrons gain nearly equal energy. On the other hand, when the primary wave is dominant, selective acceleration occurs. The phase of the primary wave for electrons moving nearly along the wavevector changes very slowly compared with the oscillation of the wave, which is “phase-locked,” and such electrons are continuously accelerated. This acceleration by SLSWs may play a crucial role in pre-shock acceleration. In general, the radiation from the phase-locked population is different from the synchro-Compton radiation. However, when the amplitude of the secondary waves is not extremely weaker than that of the primary wave, the typical frequency can be estimated from synchro-Compton theory using the secondary waves. The primary wave does not contribute to the radiation because the SLSW accelerates electrons almost linearly. This radiation can be observed as a radio knot at the upstream of the termination shocks of the pulsar wind nebulae without counterparts in higher frequency ranges.
Dislocation nonlinearity and nonlinear wave processes in polycrystals with dislocations
NASA Astrophysics Data System (ADS)
Nazarov, V. E.
2016-09-01
Based on the modification of the linear part of the Granato-Lücke dislocation theory of absorption, the equation of state of polycrystalline solids with dissipative and reactive nonlinearity has been derived. The nonlinear effects of the interaction and self-action of longitudinal elastic waves in such media have been theoretically studied.
Observation of Shock Waves in a Strongly Interacting Fermi Gas
Joseph, J. A.; Thomas, J. E.; Kulkarni, M.; Abanov, A. G.
2011-04-15
We study collisions between two strongly interacting atomic Fermi gas clouds. We observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as the clouds collide and subsequent evolution into a boxlike shape. We model the nonlinear dynamics of these collisions by using quasi-1D hydrodynamic equations. Our simulations of the time-dependent density profiles agree very well with the data and provide clear evidence of shock wave formation in this universal quantum hydrodynamic system.
Observation of shock waves in a strongly interacting Fermi gas.
Joseph, J A; Thomas, J E; Kulkarni, M; Abanov, A G
2011-04-15
We study collisions between two strongly interacting atomic Fermi gas clouds. We observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as the clouds collide and subsequent evolution into a boxlike shape. We model the nonlinear dynamics of these collisions by using quasi-1D hydrodynamic equations. Our simulations of the time-dependent density profiles agree very well with the data and provide clear evidence of shock wave formation in this universal quantum hydrodynamic system.
Linear superposition solutions to nonlinear wave equations
NASA Astrophysics Data System (ADS)
Liu, Yu
2012-11-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed.
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.
Optimization of the dynamic behavior of strongly nonlinear heterogeneous materials
NASA Astrophysics Data System (ADS)
Herbold, Eric B.
New aspects of strongly nonlinear wave and structural phenomena in granular media are developed numerically, theoretically and experimentally. One-dimensional chains of particles and compressed powder composites are the two main types of materials considered here. Typical granular assemblies consist of linearly elastic spheres or layers of masses and effective nonlinear springs in one-dimensional columns for dynamic testing. These materials are highly sensitive to initial and boundary conditions, making them useful for acoustic and shock-mitigating applications. One-dimensional assemblies of spherical particles are examples of strongly nonlinear systems with unique properties. For example, if initially uncompressed, these materials have a sound speed equal to zero (sonic vacuum), supporting strongly nonlinear compression solitary waves with a finite width. Different types of assembled metamaterials will be presented with a discussion of the material's response to static compression. The acoustic diode effect will be presented, which may be useful in shock mitigation applications. Systems with controlled dissipation will also be discussed from an experimental and theoretical standpoint emphasizing the critical viscosity that defines the transition from an oscillatory to monotonous shock profile. The dynamic compression of compressed powder composites may lead to self-organizing mesoscale structures in two and three dimensions. A reactive granular material composed of a compressed mixture of polytetrafluoroethylene (PTFE), tungsten (W) and aluminum (Al) fine-grain powders exhibit this behavior. Quasistatic, Hopkinson bar, and drop-weight experiments show that composite materials with a high porosity and fine metallic particles exhibit a higher strength than less porous mixtures with larger particles, given the same mass fraction of constituents. A two-dimensional Eulerian hydrocode is implemented to investigate the mechanical deformation and failure of the compressed
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
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.
Dispersive shock waves with nonlocal nonlinearity.
Barsi, Christopher; Wan, Wenjie; Sun, Can; Fleischer, Jason W
2007-10-15
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
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.
NASA Astrophysics Data System (ADS)
Kurt, Mehmet; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.
2014-03-01
We consider a linear cantilever beam attached to ground through a strongly nonlinear stiffness at its free boundary, and study its dynamics computationally by the assumed-modes method. The nonlinear stiffness of this system has no linear component, so it is essentially nonlinear and nonlinearizable. We find that the strong nonlinearity mostly affects the lower-frequency bending modes and gives rise to strongly nonlinear beat phenomena. Analysis of these beats proves that they are caused by internal resonance interactions of nonlinear normal modes (NNMs) of the system. These internal resonances are not of the classical type since they occur between bending modes whose linearized natural frequencies are not necessarily related by rational ratios; rather, they are due to the strong energy-dependence of the frequency of oscillation of the corresponding NNMs of the beam (arising from the strong local stiffness nonlinearity) and occur at energy ranges where the frequencies of these NNMs are rationally related. Nonlinear effects start at a different energy level for each mode. Lower modes are influenced at lower energies due to larger modal displacements than higher modes and thus, at certain energy levels, the NNMs become rationally related, which results in internal resonance. The internal resonances of NNMs are studied using a reduced order model of the beam system. Then, a nonlinear system identification method is developed, capable of identifying this type of strongly nonlinear modal interactions. It is based on an adaptive step-by-step application of empirical mode decomposition (EMD) to the measured time series, which makes it valid for multi-frequency beating signals. Our work extends an earlier nonlinear system identification approach developed for nearly mono-frequency (monochromatic) signals. The extended system identification method is applied to the identification of the strongly nonlinear dynamics of the considered cantilever beam with the local strong
Longitudinal nonlinear wave propagation through soft tissue.
Valdez, M; Balachandran, B
2013-04-01
In this paper, wave propagation through soft tissue is investigated. A primary aim of this investigation is to gain a fundamental understanding of the influence of soft tissue nonlinear material properties on the propagation characteristics of stress waves generated by transient loadings. Here, for computational modeling purposes, the soft tissue is modeled as a nonlinear visco-hyperelastic material, the geometry is assumed to be one-dimensional rod geometry, and uniaxial propagation of longitudinal waves is considered. By using the linearized model, a basic understanding of the characteristics of wave propagation is developed through the dispersion relation and in terms of the propagation speed and attenuation. In addition, it is illustrated as to how the linear system can be used to predict brain tissue material parameters through the use of available experimental ultrasonic attenuation curves. Furthermore, frequency thresholds for wave propagation along internal structures, such as axons in the white matter of the brain, are obtained through the linear analysis. With the nonlinear material model, the authors analyze cases in which one of the ends of the rods is fixed and the other end is subjected to a loading. Two variants of the nonlinear model are analyzed and the associated predictions are compared with the predictions of the corresponding linear model. The numerical results illustrate that one of the imprints of the nonlinearity on the wave propagation phenomenon is the steepening of the wave front, leading to jump-like variations in the stress wave profiles. This phenomenon is a consequence of the dependence of the local wave speed on the local deformation of the material. As per the predictions of the nonlinear material model, compressive waves in the structure travel faster than tensile waves. Furthermore, it is found that wave pulses with large amplitudes and small elapsed times are attenuated over shorter spans. This feature is due to the elevated
Interactive Workshop Discusses Nonlinear Waves and Chaos
NASA Astrophysics Data System (ADS)
Tsurutani, Bruce; Morales, George; Passot, Thierry
2010-07-01
Eighth International Nonlinear Wave Workshop; La Jolla, California, 1-5 March 2010; Nonlinear waves and chaos were the focus of a weeklong series of informal and interactive discussions at the Eighth International Nonlinear Wave Workshop (NWW8), held in California. The workshop gathered nonlinear plasma and water wave experts from the United States, France, Czech Republic, Germany, Greece, Holland, India, and Japan. Attendees were from the fields of space, laboratory, and fusion plasma physics, astrophysics, and applied mathematics. Special focus was placed on nonlinear waves and turbulence in the terrestrial environment as well as in the interstellar medium from observational, laboratory, and theoretical perspectives. Discussions covered temperature anisotropies and related instabilities, the properties and origin of the so-called dissipation range, and various coherent structures of electromagnetic as well as electrostatic nature. Reconnection and shocks were also topics of discussion, as were properties of magnetospheric whistler and chorus waves. Examples and analysis techniques for superdiffusion and subdiffusion were identified. On this last topic, a good exchange of ideas and results occurred between a water wave expert and a plasma expert, with the rest of the audience listening intently.
Quantification and prediction of rare events in nonlinear waves
NASA Astrophysics Data System (ADS)
Sapsis, Themistoklis; Cousins, Will; Mohamad, Mustafa
2014-11-01
The scope of this work is the quantification and prediction of rare events characterized by extreme intensity, in nonlinear dispersive models that simulate water waves. In particular we are interested for the understanding and the short-term prediction of rogue waves in the ocean and to this end, we consider 1-dimensional nonlinear models of the NLS type. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A stochastic analysis of the Gabor coefficients reveals i) the low-dimensionality of the intermittent structures, ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as iii) the critical scales (or Gabor coefficients) where a critical energy can trigger the formation of an extreme event. The unstable character of these critical localized modes is analysed directly through the system equation and it is shown that it is defined as the result of the system nonlinearity and the wave dissipation (that mimics wave breaking). These unstable modes are randomly triggered through the dispersive ``heat bath'' of random waves that propagate in the nonlinear medium. Using these properties we formulate low-dimensional functionals of these Gabor coefficients that allow for the prediction of extreme event well before the strongly nonlinear interactions begin to occur. The prediction window is further enhanced by the combination of the developed scheme with traditional filtering schemes.
Nonlinear growth of strongly unstable tearing modes
Waelbroeck, F.L.
1993-11-01
Rutherford`s theory of the tearing instability is extended to cases where current nonlinearities are important, such as long wavelength modes in current slabs and the m = 1 instability in tokamaks with moderately large aspect-ratios. Of particular interest is the possibility that the associated magnetic islands, as a result of secondary instabilities, have a singular response to the Ohmic diffusion of the current. A family of islands is used to test this possibility; it is found that the response remains bounded.
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.
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.
Nonlinear compressional waves in marine sediments
NASA Astrophysics Data System (ADS)
McDonald, B. Edward
2005-09-01
A theory for nonlinear waves in marine sediments must account for the presence of a granular frame filled with water and possibly gas bubbles. When grains are in full contact, the stress-strain relation for the sediment contains a contribution varying as strain to the power 3/2, referred to as the Hertz force. The quadratic nonlinearity parameter derived from the second pressure derivative with respect to density thus diverges in the limit of small strain. We present a simple nonlinear wave equation model (a variant of the NPE) for compressional waves in marine sediments that avoids Taylor expansion and the problem of diverging nonlinearity parameter. An equation of state for partially consolidated sediments is derived from consolidation test results. Pressure is found to increase with overdensity to the power 5/2, indicating an increase in the number of contacts per grain as density increases. Numerical results for nonlinear compressional waves show agreement with analytic self-similar profiles derived from the nonlinear wave equation. [Work supported by the ONR.
Nonlinear Talbot effect of rogue waves.
Zhang, Yiqi; Belić, Milivoj R; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Song, Jianping; Zhang, Yanpeng
2014-03-01
Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.
Compact waves in microscopic nonlinear diffusion.
Hurtado, P I; Krapivsky, P L
2012-06-01
We analyze the spread of a localized peak of energy into vacuum for nonlinear diffusive processes. In contrast with standard diffusion, the nonlinearity results in a compact wave with a sharp front separating the perturbed region from vacuum. In d spatial dimensions, the front advances as t^{1/(2+da)} according to hydrodynamics, with a the nonlinearity exponent. We show that fluctuations in the front position grow as ∼t^{μ}η, where μ<1/2+da is an exponent that we measure and η is a random variable whose distribution we characterize. Fluctuating corrections to hydrodynamic profiles give rise to an excess penetration into vacuum, revealing scaling behaviors and robust features. We also examine the discharge of a nonlinear rarefaction wave into vacuum. Our results suggest the existence of universal scaling behaviors at the fluctuating level in nonlinear diffusion.
Narrow-band nonlinear sea waves
NASA Technical Reports Server (NTRS)
Tayfun, M. A.
1980-01-01
Probabilistic description of nonlinear waves with a narrow-band spectrum is simplified to a form in which each realization of the surface displacement becomes an amplitude-modulated Stokes wave with a mean frequency and random phase. Under appropriate conditions this simplification provides a convenient yet rigorous means of describing nonlinear effects on sea surface properties in a semiclosed or closed form. In particular, it is shown that surface displacements are non-Gaussian and skewed, as was previously predicted by the Gram-Charlier approximation; that wave heights are Rayleigh distributed, just as in the linear case; and that crests are non-Rayleigh.
Nonlinear sharpening during superposition of surface waves
NASA Astrophysics Data System (ADS)
Chalikov, Dmitry; Babanin, Alexander V.
2016-08-01
Two-dimensional direct wave model is used for demonstration of the role of reversible interactions which probably is the main process leading to breaking. One-dimensional model was used for performing of thousands of exact short-term simulations of evolution of two superposed wave trains with different steepness, and wavenumbers were performed to investigate the effect of wave crests merging. Nonlinear sharpening of the merging crests is demonstrated. It is suggested that such effect may be responsible for appearance of the typical sharp crests of surface waves, as well as for wave breaking.
Nonlinear extraordinary wave in dense plasma
Krasovitskiy, V. B.; Turikov, V. A.
2013-10-15
Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. The possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.
Shock waves in strongly coupled plasmas
Khlebnikov, Sergei; Kruczenski, Martin; Michalogiorgakis, Georgios
2010-12-15
Shock waves are supersonic disturbances propagating in a fluid and giving rise to dissipation and drag. Weak shocks, i.e., those of small amplitude, can be well described within the hydrodynamic approximation. On the other hand, strong shocks are discontinuous within hydrodynamics and therefore probe the microscopics of the theory. In this paper, we consider the case of the strongly coupled N=4 plasma whose microscopic description, applicable for scales smaller than the inverse temperature, is given in terms of gravity in an asymptotically AdS{sub 5} space. In the gravity approximation, weak and strong shocks should be described by smooth metrics with no discontinuities. For weak shocks, we find the dual metric in a derivative expansion, and for strong shocks we use linearized gravity to find the exponential tail that determines the width of the shock. In particular, we find that, when the velocity of the fluid relative to the shock approaches the speed of light v{yields}1 the penetration depth l scales as l{approx}(1-v{sup 2}){sup 1/4}. We compare the results with second-order hydrodynamics and the Israel-Stewart approximation. Although they all agree in the hydrodynamic regime of weak shocks, we show that there is not even qualitative agreement for strong shocks. For the gravity side, the existence of shock waves implies that there are disturbances of constant shape propagating on the horizon of the dual black holes.
Steady-state solutions for relativistically strong electromagnetic waves in plasmas.
NASA Technical Reports Server (NTRS)
Max, C. E.
1973-01-01
New steady-state solutions are derived which describe electromagnetic waves strong enough to make plasma ions and electrons relativistic. A two-fluid model is used throughout. The following solutions are studied: (1) linearly polarized waves with phase velocity much greater than c; (2) arbitrarily polarized waves with phase velocity near c, in a cold uniform plasma; (3) circularly polarized waves in a uniform plasma characterized by a scalar pressure tensor. All of these waves are capable of propagating in normally overdense plasmas, due to nonlinearities introduced by relativistic effects. The propagation of relativistically strong waves in a density gradient is examined, for the example of a circularly polarized wave strong enough to make electrons but not ions relativistic. It is shown that such a wave propagates at constant energy flux despite the nonlinearity of the system.
Laboratory investigation of nonlinear whistler wave processes
NASA Astrophysics Data System (ADS)
Amatucci, Bill; Tejero, Erik; Crabtree, Chris; Enloe, Lon; Blackwell, Dave; Ganguli, Guru
2015-11-01
Nonlinear interactions involving whistler wave turbulence result from processes such as wave-particle interactions in the radiation belts and instability generation in sharp magnetospheric boundary layers. Nonlinear scattering of large amplitude waves off thermal electrons substantially changes the wave vector direction and energy flux, while inducing a small frequency shift [Crabtree, Phys. Plasmas 19, 032903 (2012)]. This nonlinear scattering of primarily electrostatic lower hybrid waves into electromagnetic whistler modes is being investigated in the NRL Space Chamber under conditions scaled to match the respective environments. Lower hybrid waves are generated directly by antennas or self-consistently from sheared cross-magnetic field flows with scale length less than an ion gyroradius via the Electron-Ion Hybrid Instability [Ganguli, Phys. Fluids 31, 2753 (1988)), Amatucci, Phys. Plasmas 10, 1963 (2003)]. Sufficiently large amplitude lower hybrid waves have been observed to convert into whistler modes by scattering from thermal electrons. The plasma response as a function of transmitted lower hybrid wave amplitude is monitored with magnetic loop antennas. Details of the observed wave spectra and mode characteristics will be presented. This work supported by the NRL Base Program.
Nonlinear noise waves in soft biological tissues
NASA Astrophysics Data System (ADS)
Rudenko, O. V.; Gurbatov, S. N.; Demin, I. Yu.
2013-09-01
The study of intense waves in soft biological tissues is necessary both for diagnostics and therapeutic aims. Tissue represents an inherited medium with frequency-dependent dissipative properties, in which waves are described by nonlinear integro-differential equations. The equations for such waves are well known. Their group analysis has been performed, and a number of exact solutions have been found. However, statistical problems for nonlinear waves in tissues have hardly been studied. As well, for medical applications, both intense noise waves and waves with fluctuating parameters can be used. In addition, statistical solutions are simpler in structure than regular solutions; they are useful for understanding the physics of processes. Below a general approach is described for solving nonlinear statistical problems applied to the considered mathematical models of biological tissues. We have calculated the dependences of the intensities of the narrowband noise harmonics on distance. For wideband noise, we have calculated the dependence of the spectral integral intensity on distance. In all cases, wave attenuation is determined both by the specific dissipative properties of the tissue and the nonlinearity of the medium.
Boosted X Waves in Nonlinear Optical Systems
Arevalo, Edward
2010-01-15
X waves are spatiotemporal optical waves with intriguing superluminal and subluminal characteristics. Here we theoretically show that for a given initial carrier frequency of the system localized waves with genuine superluminal or subluminal group velocity can emerge from initial X waves in nonlinear optical systems with normal group velocity dispersion. Moreover, we show that this temporal behavior depends on the wave detuning from the carrier frequency of the system and not on the particular X-wave biconical form. A spatial counterpart of this behavior is also found when initial X waves are boosted in the plane transverse to the direction of propagation, so a fully spatiotemporal motion of localized waves can be observed.
Boosted X waves in nonlinear optical systems.
Arévalo, Edward
2010-01-15
X waves are spatiotemporal optical waves with intriguing superluminal and subluminal characteristics. Here we theoretically show that for a given initial carrier frequency of the system localized waves with genuine superluminal or subluminal group velocity can emerge from initial X waves in nonlinear optical systems with normal group velocity dispersion. Moreover, we show that this temporal behavior depends on the wave detuning from the carrier frequency of the system and not on the particular X-wave biconical form. A spatial counterpart of this behavior is also found when initial X waves are boosted in the plane transverse to the direction of propagation, so a fully spatiotemporal motion of localized waves can be observed.
A Numerical Study of Nonlinear Wave Interactions
NASA Astrophysics Data System (ADS)
de Bakker, A.; Tissier, M.; Ruessink, G.
2014-12-01
Nonlinear triad interactions redistribute energy among a wave field, which transforms the shape of the incident short waves (f = 0.05 - 2 Hz) and generates energy at infragravity frequencies (f = 0.005-0.05 Hz). Recently, it has been suggested that infragravity energy may dissipate by energy transfers from infragravity frequencies to either the (former) short-wave spectral peak, or through infragravity-infragravity self-interactions that cause the infragravity waves to steepen and to eventually break. To investigate these infragravity dissipation mechanisms, we use the non-hydrostatic SWASH model. In this study, we first validate the model with the high-resolution GLOBEX laboratory data set and then explore the dependence of the energy transfers, with a focus on infragravity frequencies, on beach slope. Consistent with previous studies we find that SWASH is able to reproduce the transformation and corresponding nonlinear energy transfers of shoreward propagating waves to great detail. Bispectral analysis is used to study the coupling between wave frequencies; nonlinear energy transfers are then quantified using the Boussinesq coupling coefficient. To obtain more detailed insight we divide the nonlinear interactions in four categories based on triads including 1) infragravity frequencies only, 2) two infragravity frequencies and one short-wave frequency, 3) one infragravity frequency and two short-wave frequencies and 4) short-wave frequencies only. Preliminary results suggest that interactions are rather weak on gently beach slopes (1:80) and, in the innermost part of the surf zone, are dominated by infragravity-infragravity interactions. On steeper slopes (1:20), interactions are stronger, but entirely dominated by those involving short-wave frequencies only. The dependence of the transfers on offshore wave conditions and beach shape will be explored too. Funded by NWO.
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming
2014-04-15
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.
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.
Nonplanar dust acoustic solitary waves in a strongly coupled dusty plasma with superthermal ions
El-Labany, S. K. Zedan, N. A.; El-Taibany, W. F. E-mail: eltaibany@du.edu.eg; El-Shamy, E. F.
2014-12-15
The nonplanar amplitude modulation of dust acoustic (DA) envelope solitary waves in a strongly coupled dusty plasma (SCDP) has been investigated. By using a reductive perturbation technique, a modified nonlinear Schrödinger equation (NLSE) including the effects of geometry, polarization, and ion superthermality is derived. The modulational instability (MI) of the nonlinear DA wave envelopes is investigated in both planar and nonplanar geometries. There are two stable regions for the DA wave propagation strongly affected by polarization and ion superthermality. Moreover, it is found that the nonlinear DA waves in spherical geometry are the more structurally stable. The larger growth rate of the nonlinear DA MI is observed in the cylindrical geometry. The salient characteristics of the MI in the nonplanar geometries cannot be found in the planar one. The DA wave propagation and the NLSE solutions are investigated both analytically and numerically.
Nonlinear neutrino-photon interactions inside strong laser pulses
NASA Astrophysics Data System (ADS)
Meuren, Sebastian; Keitel, Christoph H.; Di Piazza, Antonino
2015-06-01
Even though neutrinos are neutral particles and interact only via the exchange of weak gauge bosons, charged leptons and quarks can mediate a coupling to the photon field beyond tree level. Inside a relativistically strong laser field nonlinear effects in the laser amplitude can play an important role, as electrons and positrons interact nonperturbatively with the coherent part of the photon field. Here, we calculate for the first time the leading-order contribution to the axial-vector-vector current-coupling tensor inside an arbitrary plane-wave laser field (which is taken into account exactly by employing the Furry picture). The current-coupling tensor appears in the calculation of various electroweak processes inside strong laser fields like photon emission or trident electron-positron pair production by a neutrino. Moreover, as we will see below, the axial-vector-vector current-coupling tensor contains the Adler-Bell-Jackiw (ABJ) anomaly. This occurrence renders the current-coupling tensor also interesting from a fundamental point of view, as it is the simplest Feynman diagram in an external field featuring this kind of anomaly.
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
Laboratory investigation of nonlinear whistler wave processes
NASA Astrophysics Data System (ADS)
Amatucci, B.; Tejero, E.; Cothran, C.; Ganguli, G.; Crabtree, C.; Mithiawala, M.; Sotnikov, V.
2012-10-01
Nonlinear interactions involving whistler wave turbulence result from processes, including wave-particle interactions and instabilities in sharp boundary layers. Given sufficient whistler energy density, nonlinear scattering off thermal electrons substantially changes the wave vector direction and energy flux, while inducing a small frequency shift.footnotetextCrabtree et al., Phys. Plasmas, 19, Art. No. 032903 (2012). In the magnetosphere, boundary layers often have highly sheared plasma flows and lower hybrid turbulence. Such nonlinear processes are being investigated in the NRL Space Chamber in conditions scaled to match the respective environments. By creating boundary layers with controllable density gradient and transverse electric fields and scale length much smaller than an ion gyroradius, lower hybrid waves consistent with the Electron-Ion Hybrid InstabilityfootnotetextGanguli et al., Phys. Fluids, 31, 2753 (1988). have been observed. Sufficiently large amplitude lower hybrid waves have been observed to scatter into whistler modes by scattering from thermal electrons. The plasma response as a function of transmitted lower hybrid wave amplitude is monitored with magnetic antennas. Details of the observed wave spectra and mode characteristics will be presented.
Nonlinear parallel momentum transport in strong electrostatic turbulence
NASA Astrophysics Data System (ADS)
Wang, Lu; Wen, Tiliang; Diamond, P. H.
2015-05-01
Most existing theoretical studies of momentum transport focus on calculating the Reynolds stress based on quasilinear theory, without considering the nonlinear momentum flux- ⟨ v ˜ r n ˜ u ˜ ∥ ⟩ . However, a recent experiment on TORPEX found that the nonlinear toroidal momentum flux induced by blobs makes a significant contribution as compared to the Reynolds stress [Labit et al., Phys. Plasmas 18, 032308 (2011)]. In this work, the nonlinear parallel momentum flux in strong electrostatic turbulence is calculated by using a three dimensional Hasegawa-Mima equation, which is relevant for tokamak edge turbulence. It is shown that the nonlinear diffusivity is smaller than the quasilinear diffusivity from Reynolds stress. However, the leading order nonlinear residual stress can be comparable to the quasilinear residual stress, and so may be important to intrinsic rotation in tokamak edge plasmas. A key difference from the quasilinear residual stress is that parallel fluctuation spectrum asymmetry is not required for nonlinear residual stress.
Nonlinear Internal Waves - Evolution and Energy Dissipation
NASA Astrophysics Data System (ADS)
Orr, M.; Mignerey, P.
2003-04-01
Nonlinear internal waves have been observed propagating up the slope of the South China Sea during the recent ONR Asian Seas International Acoustics Experiment. Energy dissipation rates have been extracted. The location of the initiation of the depression to elevation conversion has been identified. Scaling parameters have been extracted and used to initialize a two-layer evolution equation model simulation. Mode1, 2 linear and nonlinear internal waves and instabilities have been observed near the shelf break of the United States of America New Jersey Shelf. Acoustic flow visualization records will be presented. Work supported by the Office of Naval Research (ONR) Ocean Acoustics Program and ONR's NRL base funding.
Nonlinear excited waves on the interventricular septum
NASA Astrophysics Data System (ADS)
Bekki, Naoaki; Harada, Yoshifumi; Kanai, Hiroshi
2012-11-01
Using a novel ultrasonic noninvasive imaging method, we observe some phase singularities in propagating excited waves on a human cardiac interventricular septum (IVS) for a healthy young male. We present a possible physical model explaining one-dimensional dynamics of phase singularities in nonlinearly excited waves on the IVS. We show that at least one of the observed phase singularities in the excited waves on the IVS can be explained by the Bekki-Nozaki hole solution of the complex Ginzburg-Landau equation without any adjustable parameters. We conclude that the complex Ginzburg-Landau equation is such a suitable model for one-dimensional dynamics of cardiac phase singularities in nonlinearly excited waves on the IVS.
Optics in a nonlinear gravitational plane wave
NASA Astrophysics Data System (ADS)
Harte, Abraham I.
2015-09-01
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. At least for freely falling sources and observers, it is shown that the commonly-used predictions of linear perturbation theory can be generically overshadowed by nonlinear effects; even for very weak gravitational waves, higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected when considering observations of sufficiently distant sources. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.
Nonlinear whistler wave scattering in space plasmas
Yukhimuk, V.; Roussel-Dupre, R.
1997-04-01
In this paper the evolution of nonlinear scattering of whistler mode waves by kinetic Alfven waves (KAW) in time and two spatial dimensions is studied analytically. The authors suggest this nonlinear process as a mechanism of kinetic Alfven wave generation in space plasmas. This mechanism can explain the dependence of Alfven wave generation on whistler waves observed in magnetospheric and ionospheric plasmas. The observational data show a dependence for the generation of long periodic pulsations Pc5 on whistler wave excitation in the auroral and subauroral zone of the magnetosphere. This dependence was first observed by Ondoh T.I. For 79 cases of VLF wave excitation registered by Ondoh at College Observatory (L=64.6 N), 52 of them were followed by Pc5 geomagnetic pulsation generation. Similar results were obtained at the Loparskaia Observatory (L=64 N) for auroral and subauroral zone of the magnetosphere. Thus, in 95% of the cases when VLF wave excitation occurred the generation of long periodic geomagnetic pulsations Pc5 were observed. The observations also show that geomagnetic pulsations Pc5 are excited simultaneously or insignificantly later than VLF waves. In fact these two phenomena are associated genetically: the excitation of VLF waves leads to the generation of geomagnetic pulsations Pc5. The observations show intensive generation of geomagnetic pulsations during thunderstorms. Using an electromagnetic noise monitoring system covering the ULF range (0.01-10 Hz) A.S. Fraser-Smith observed intensive ULF electromagnetic wave during a large thunderstorm near the San-Francisco Bay area on September 23, 1990. According to this data the most significant amplification in ULF wave activity was observed for waves with a frequency of 0.01 Hz and it is entirely possible that stronger enhancements would have been measured at lower frequencies.
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.
Incompressible magnetohydrodynamic surface waves - Nonlinear aspects
NASA Technical Reports Server (NTRS)
Hollweg, Joseph V.
1987-01-01
The nonlinear properties of MHD surface waves in the solar atmosphere are investigated analytically, assuming that the fluid is incompressible and that the waves are confined to a single surface, with semiinfinite regions on both sides. The governing equations are derived in detail, and qualitative results are presented in a graph. For propagating waves, second-order terms in the wave amplitude are found to lead to wave steepening at leading or trailing edges, the steepening rate becoming very large as the threshold for the linear Kelvin-Helmholtz instability is approached. Second-order effects on standing waves include crest and trough sharpening (increasing with time), a current independent of distance on the surface but decreasing exponentially with distance from the surface, and pressure-field fluctuations of infinite extent. It is suggested that these effects could account for a large fraction of solar-atmosphere heating.
Collision of strong gravitational and electromagnetic waves in the expanding universe
NASA Astrophysics Data System (ADS)
Alekseev, G. A.
2016-03-01
An exact analytical model of the process of collision and nonlinear interaction of gravitational and/or electromagnetic soliton waves and strong nonsoliton electromagnetic traveling waves of arbitrary profile propagating in the expanding universe (the symmetric Kasner spacetime) is presented. In contrast to intuitive expectations that rather strong traveling waves can destroy the soliton, it occurs that the soliton survives during its interaction with electromagnetic waves of arbitrary amplitude and profile, but its parameters begin to evolve under the influence of this interaction. If a traveling electromagnetic wave possesses a finite duration, the soliton parameters after interaction take constant values again, but these values in general are different from those before the interaction. Based on exact solutions of the Einstein-Maxwell equations, our model demonstrates a series of nonlinear phenomena, such as (a) creation of gravitational waves in the collision of two electromagnetic waves, (b) creation of electromagnetic soliton waves in the collision of a gravitational soliton with traveling electromagnetic waves, (c) scattering of a part of a soliton wave in the direction of propagation of a traveling electromagnetic wave, and (d) quasiperiodic oscillating character of fields in the wave interaction region and multiple mutual transformations of gravitational and electromagnetic waves in this region. The figures illustrate these features of nonlinear wave interactions in general relativity.
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.
Nonlinear random optical waves: Integrable turbulence, rogue waves and intermittency
NASA Astrophysics Data System (ADS)
Randoux, Stéphane; Walczak, Pierre; Onorato, Miguel; Suret, Pierre
2016-10-01
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we specifically focus on optical fiber systems accurately described by the integrable one-dimensional nonlinear Schrödinger equation. We consider random complex fields having a Gaussian statistics and an infinite extension at initial stage. We use numerical simulations with periodic boundary conditions and optical fiber experiments to investigate spectral and statistical changes experienced by nonlinear waves in focusing and in defocusing propagation regimes. As a result of nonlinear propagation, the power spectrum of the random wave broadens and takes exponential wings both in focusing and in defocusing regimes. Heavy-tailed deviations from Gaussian statistics are observed in focusing regime while low-tailed deviations from Gaussian statistics are observed in defocusing regime. After some transient evolution, the wave system is found to exhibit a statistically stationary state in which neither the probability density function of the wave field nor the spectrum changes with the evolution variable. Separating fluctuations of small scale from fluctuations of large scale both in focusing and defocusing regimes, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian.
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 acoustic/seismic waves in earthquake processes
NASA Astrophysics Data System (ADS)
Johnson, Paul A.
2012-09-01
Nonlinear dynamics induced by seismic sources and seismic waves are common in Earth. Observations range from seismic strong ground motion (the most damaging aspect of earthquakes), intense near-source effects, and distant nonlinear effects from the source that have important consequences. The distant effects include dynamic earthquake triggering—one of the most fascinating topics in seismology today—which may be elastically nonlinearly driven. Dynamic earthquake triggering is the phenomenon whereby seismic waves generated from one earthquake trigger slip events on a nearby or distant fault. Dynamic triggering may take place at distances thousands of kilometers from the triggering earthquake, and includes triggering of the entire spectrum of slip behaviors currently identified. These include triggered earthquakes and triggered slow, silent-slip during which little seismic energy is radiated. It appears that the elasticity of the fault gouge—the granular material located between the fault blocks—is key to the triggering phenomenon.
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
Strong curvature effects in Neumann wave problems
Willatzen, M.; Pors, A.; Gravesen, J.
2012-08-15
Waveguide phenomena play a major role in basic sciences and engineering. The Helmholtz equation is the governing equation for the electric field in electromagnetic wave propagation and the acoustic pressure in the study of pressure dynamics. The Schroedinger equation simplifies to the Helmholtz equation for a quantum-mechanical particle confined by infinite barriers relevant in semiconductor physics. With this in mind and the interest to tailor waveguides towards a desired spectrum and modal pattern structure in classical structures and nanostructures, it becomes increasingly important to understand the influence of curvature effects in waveguides. In this work, we demonstrate analytically strong curvature effects for the eigenvalue spectrum of the Helmholtz equation with Neumann boundary conditions in cases where the waveguide cross section is a circular sector. It is found that the linear-in-curvature contribution originates from parity symmetry breaking of eigenstates in circular-sector tori and hence vanishes in a torus with a complete circular cross section. The same strong curvature effect is not present in waveguides subject to Dirichlet boundary conditions where curvature contributions contribute to second-order in the curvature only. We demonstrate this finding by considering wave propagation in a circular-sector torus corresponding to Neumann and Dirichlet boundary conditions, respectively. Results for relative eigenfrequency shifts and modes are determined and compared with three-dimensional finite element method results. Good agreement is found between the present analytical method using a combination of differential geometry with perturbation theory and finite element results for a large range of curvature ratios.
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.
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.
Nonlinear analysis of helix traveling wave tubes
Freund, H.P.; Zaidman, E.G.; Mankofsky, A.; Vanderplaats, N.R.; Kodis, M.A.
1995-10-01
A time-dependent nonlinear formulation of the interaction in the helix traveling wave tube is presented for a configuration in which an electron beam propagates through a sheath helix surrounded by a conducting wall. In order to describe both the variation in the wave dispersion and in the transverse inhomogeneity of the electromagnetic field with wave number, the field is represented as a superposition of waves in a vacuum sheath helix. An overall explicit sinusoidal variation of the form exp({ital ikz}{minus}{ital i}{omega}{ital t}) is assumed (where {omega} denotes the angular frequency corresponding to the wave number {ital k} in the vacuum sheath helix), and the polarization and radial variation of each wave is determined by the boundary conditions in a vacuum sheath helix. Thus, while the field is three-dimensional in nature, it is azimuthally symmetric. The propagation of each wave {ital in} {ital vacuo} as well as the interaction of each wave with the electron beam is included by allowing the amplitudes of the waves to vary in {ital z} and {ital t}. A dynamical equation for the field amplitudes is derived analogously to Poynting`s equation, and solved in conjunction with the three-dimensional Lorentz force equations for an ensemble of electrons. Numerical examples are presented corresponding to both single- and multiwave interactions. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Nonlinear 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 guided wave propagation in prestressed plates.
Pau, Annamaria; Lanza di Scalea, Francesco
2015-03-01
The measurement of stress in a structure presents considerable interest in many fields of engineering. In this paper, the diagnostic potential of nonlinear elastic guided waves in a prestressed plate is investigated. To do so, an analytical model is formulated accounting for different aspects involved in the phenomenon. The fact that the initial strains can be finite is considered using the Green Lagrange strain tensor, and initial and final configurations are not merged, as it would be assumed in the infinitesimal strain theory. Moreover, an appropriate third-order expression of the strain energy of the hyperelastic body is adopted to account for the material nonlinearities. The model obtained enables to investigate both the linearized case, which gives the variation of phase and group velocity as a function of the initial stress, and the nonlinear case, involving second-harmonic generation as a function of the initial state of stress. The analysis is limited to Rayleigh-Lamb waves propagating in a plate. Three cases of initial prestress are considered, including prestress in the direction of the wave propagation, prestress orthogonal to the direction of wave propagation, and plane isotropic stress.
Nonlinear guided wave propagation in prestressed plates.
Pau, Annamaria; Lanza di Scalea, Francesco
2015-03-01
The measurement of stress in a structure presents considerable interest in many fields of engineering. In this paper, the diagnostic potential of nonlinear elastic guided waves in a prestressed plate is investigated. To do so, an analytical model is formulated accounting for different aspects involved in the phenomenon. The fact that the initial strains can be finite is considered using the Green Lagrange strain tensor, and initial and final configurations are not merged, as it would be assumed in the infinitesimal strain theory. Moreover, an appropriate third-order expression of the strain energy of the hyperelastic body is adopted to account for the material nonlinearities. The model obtained enables to investigate both the linearized case, which gives the variation of phase and group velocity as a function of the initial stress, and the nonlinear case, involving second-harmonic generation as a function of the initial state of stress. The analysis is limited to Rayleigh-Lamb waves propagating in a plate. Three cases of initial prestress are considered, including prestress in the direction of the wave propagation, prestress orthogonal to the direction of wave propagation, and plane isotropic stress. PMID:25786963
Nonlinear acoustic wave propagation in atmosphere
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1985-01-01
A model problem that simulates an atmospheric acoustic wave propagation situation that is nonlinear is considered. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.
Nonlinear acoustic wave propagation in atmosphere
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1986-01-01
In this paper a model problem is considered that simulates an atmospheric acoustic wave propagation situation that is nonlinear. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well-posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.
Strong nonlinear current–voltage behaviour in iron oxyborate
Song, Yuanjun; Xu, Yingying; Song, Yujun; Li, Jianqi; Wang, Rongming
2014-11-15
Strong nonlinear resistance has been found in the charge ordered ferroelectric iron oxyborate (Fe{sub 2}OBO{sub 3}) with a high dielectric constant and giant converse magnetoelectric effect. In low temperature range the I-V nonlinearity increases quickly with decreasing temperature. Transport measurements on polycrystalline and single crystal Fe{sub 2}OBO{sub 3} indicate that the nonlinearity is not induced by grain boundaries. The nonlinear I-V behavior is intrinsically correlated with the charge order phase melting in Fe{sub 2}OBO{sub 3} by detailed in-situ TEM investigations. These results provide an insight into structure-activity relationship of resistance switching effects at atomic and electric scales, which is essential for its potential application as varistors and storage media.
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
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.
Developments in strong shock wave position tracking
NASA Astrophysics Data System (ADS)
Rae, Philip; Glover, Brain; Perry, Lee; WX-6; WX-7 Team
2011-06-01
This poster will highlight several modified techniques to allow the position vs. time to be tracked in strong shock situations (such as detonation). Each is a modification or improvement of existing ideas either making use of advances in specialist materials availability or recent advances in electronics.) Shorting embedded mini-coaxial cable with a standing microwave pattern. This technique is a modified version of an old LANL method of shock position tracking making use of a traveling short imposed in an embedded coaxial cable. A high frequency standing wave (3-8GHz) is present in the cable and the moving short position can be tracked by monitoring the output voltage envelope as a function of time. A diode detector is used to allow the envelope voltage to be monitored on a regular low frequency digitizer significantly reducing the cost. The small and cheap high frequency voltage generators now available allow much greater spatial resolution than possible previously. 2) Very thin shorting resistance track gauges. Parallel tracks of constantan resistance material are etched on a thin dielectric substrate. The gauges are less than 0.2 mm thick. The ionized gas present in a detonation front sweeps up the tracks lowering the measured resistance. A potential divider circuit allows the shock position vs. time to be monitored on a regular digitizer after easy calibration. The novel feature is the thin section of the gauge producing minimal perturbation in the detonation front.
Variational modelling of nonlinear water waves
NASA Astrophysics Data System (ADS)
Kalogirou, Anna; Bokhove, Onno
2015-11-01
Mathematical modelling of water waves is demonstrated by investigating variational methods. A potential flow water wave model is derived using variational techniques and extented to include explicit time-dependence, leading to non-autonomous dynamics. As a first example, we consider the problem of a soliton splash in a long wave channel with a contraction at its end, resulting after a sluice gate is removed at a finite time. The removal of the sluice gate is included in the variational principle through a time-dependent gravitational potential. A second example involving non-autonomous dynamics concerns the motion of a free surface in a vertical Hele-Shaw cell. Explicit time-dependence now enters the model through a linear damping term due to the effect of wall friction and a term representing the motion of an artificially driven wave pump. In both cases, the model is solved numerically using a Galerkin FEM and the numerical results are compared to wave structures observed in experiments. The water wave model is also adapted to accommodate nonlinear ship dynamics. The novelty is this case is the coupling between the water wave dynamics, the ship dynamics and water line dynamics on the ship. For simplicity, we consider a simple ship structure consisting of V-shaped cross-sections.
Nonlinear parallel momentum transport in strong electrostatic turbulence
Wang, Lu Wen, Tiliang; Diamond, P. H.
2015-05-15
Most existing theoretical studies of momentum transport focus on calculating the Reynolds stress based on quasilinear theory, without considering the nonlinear momentum flux-〈v{sup ~}{sub r}n{sup ~}u{sup ~}{sub ∥}〉. However, a recent experiment on TORPEX found that the nonlinear toroidal momentum flux induced by blobs makes a significant contribution as compared to the Reynolds stress [Labit et al., Phys. Plasmas 18, 032308 (2011)]. In this work, the nonlinear parallel momentum flux in strong electrostatic turbulence is calculated by using a three dimensional Hasegawa-Mima equation, which is relevant for tokamak edge turbulence. It is shown that the nonlinear diffusivity is smaller than the quasilinear diffusivity from Reynolds stress. However, the leading order nonlinear residual stress can be comparable to the quasilinear residual stress, and so may be important to intrinsic rotation in tokamak edge plasmas. A key difference from the quasilinear residual stress is that parallel fluctuation spectrum asymmetry is not required for nonlinear residual stress.
The rapidly convergent solutions of strongly nonlinear oscillators.
Alam, M S; Abdur Razzak, Md; Alal Hosen, Md; Riaz Parvez, Md
2016-01-01
Based on the harmonic balance method (HBM), an approximate solution is determined from the integral expression (i.e., first order differential equation) of some strongly nonlinear oscillators. Usually such an approximate solution is obtained from second order differential equation. The advantage of the new approach is that the solution converges significantly faster than that obtained by the usual HBM as well as other analytical methods. By choosing some well known nonlinear oscillators, it has been verified that an n-th (n ≥ 2) approximate solution (concern of this article) is very close to (2n - 1)-th approximations obtained by usual HBM. PMID:27536541
Probing Acoustic Nonlinearity by Mixing Surface Acoustic Waves
Hurley, David Howard; Telschow, Kenneth Louis
2000-07-01
Measurement methods aimed at determining material properties through nonlinear wave propagation are sensitive to artifacts caused by background nonlinearities inherent in the ultrasonic generation and detection methods. The focus of this paper is to describe our investigation of nonlinear mixing of surface acoustic waves (SAWs) as a means to decrease sensitivity to background nonlinearity and increase spatial sensitivity to acoustic nonlinearity induced by material microstructure.
Electron wind in strong wave guide fields
Krienen, F.
1985-03-01
The x-ray activity observed near highly powered wave guide structures is usually caused by local electric discharges originating from discontinuities such as couplers, tuners or bends. In traveling waves electrons are shown to move in the direction of the power flow. Seed electrons can multipactor in a traveling wave, the moving charge pattern is different from the multipactor in a resonant structure and is self-extinguishing. Given sufficient primary sources, the charge density in the wave guide will modify impedance and propagation constant of the wave guide. An estimate is made of the radiation level inside the output wave guide of the SLAC, 50 MW, S-band, klystron. Possible contributions of radiation to window failure are discussed.
Viscous Fluid Conduits as a Prototypical Nonlinear Dispersive Wave Platform
NASA Astrophysics Data System (ADS)
Lowman, Nicholas K.
This thesis is devoted to the comprehensive characterization of slowly modulated, nonlinear waves in dispersive media for physically-relevant systems using a threefold approach: analytical, long-time asymptotics, careful numerical simulations, and quantitative laboratory experiments. In particular, we use this interdisciplinary approach to establish a two-fluid, interfacial fluid flow setting known as viscous fluid conduits as an ideal platform for the experimental study of truly one dimensional, unidirectional solitary waves and dispersively regularized shock waves (DSWs). Starting from the full set of fluid equations for mass and linear momentum conservation, we use a multiple-scales, perturbation approach to derive a scalar, nonlinear, dispersive wave equation for the leading order interfacial dynamics of the system. Using a generalized form of the approximate model equation, we use numerical simulations and an analytical, nonlinear wave averaging technique, Whitham-El modulation theory, to derive the key physical features of interacting large amplitude solitary waves and DSWs. We then present the results of quantitative, experimental investigations into large amplitude solitary wave interactions and DSWs. Overtaking interactions of large amplitude solitary waves are shown to exhibit nearly elastic collisions and universal interaction geometries according to the Lax categories for KdV solitons, and to be in excellent agreement with the dynamics described by the approximate asymptotic model. The dispersive shock wave experiments presented here represent the most extensive comparison to date between theory and data of the key wavetrain parameters predicted by modulation theory. We observe strong agreement. Based on the work in this thesis, viscous fluid conduits provide a well-understood, controlled, table-top environment in which to study universal properties of dispersive hydrodynamics. Motivated by the study of wave propagation in the conduit system, we
Nonlinear waves with negative phase velocity.
Huang, Xiaoqing; Liao, Xuhong; Cui, Xiaohua; Zhang, Hong; Hu, Gang
2009-09-01
Recently, waves propagating with negative phase velocity [simply called antiwaves (AWs)] have attracted great attention in the area of nonlinear oscillatory systems. In the present work we investigate the parameter conditions for AWs. So far AWs have been revealed from systems slightly beyond Hopf bifurcation or some other instabilities, and from some wave sources with certain restricted frequencies. Here we study general oscillatory media (including generalized complex Ginzburg-Landau systems and Brusselator model) and specify the parameter conditions of AWs by certain characteristic behaviors of the dispersion relation of the systems. Moreover, we predict that AWs and NWs (normal waves with positive phase velocity) can be realized at a same intrinsic parameter values but different pacing frequencies in parameter regions where the dispersion relation exhibits a maximum or minimum. All numerical simulations are perfectly consistent with these theoretical predictions where the oscillatory systems are driven by external periodic pacings with 1:1 frequency locking responses. PMID:19905204
Nonlinear waves with negative phase velocity
NASA Astrophysics Data System (ADS)
Huang, Xiaoqing; Liao, Xuhong; Cui, Xiaohua; Zhang, Hong; Hu, Gang
2009-09-01
Recently, waves propagating with negative phase velocity [simply called antiwaves (AWs)] have attracted great attention in the area of nonlinear oscillatory systems. In the present work we investigate the parameter conditions for AWs. So far AWs have been revealed from systems slightly beyond Hopf bifurcation or some other instabilities, and from some wave sources with certain restricted frequencies. Here we study general oscillatory media (including generalized complex Ginzburg-Landau systems and Brusselator model) and specify the parameter conditions of AWs by certain characteristic behaviors of the dispersion relation of the systems. Moreover, we predict that AWs and NWs (normal waves with positive phase velocity) can be realized at a same intrinsic parameter values but different pacing frequencies in parameter regions where the dispersion relation exhibits a maximum or minimum. All numerical simulations are perfectly consistent with these theoretical predictions where the oscillatory systems are driven by external periodic pacings with 1:1 frequency locking responses.
Linear and Nonlinear Electrostatic Waves in Unmagnetized Dusty Plasmas
Mamun, A. A.; Shukla, P. K.
2010-12-14
A rigorous and systematic theoretical study has been made of linear and nonlinear electrostatic waves propagating in unmagnetized dusty plasmas. The basic features of linear and nonlinear electrostatic waves (particularly, dust-ion-acoustic and dust-acoustic waves) for different space and laboratory dusty plasma conditions are described. The experimental observations of such linear and nonlinear features of dust-ion-acoustic and dust-acoustic waves are briefly discussed.
Dynamic deformation of strongly nonlinear toroidal rubber elements
NASA Astrophysics Data System (ADS)
Lee, Chien-Wei; Nesterenko, Vitali F.
2013-08-01
Dynamic deformation of rubber toroidal elements (o-rings) was investigated under dynamic loading conditions at strain rates 102 s-1. The forces acting on o-rings were simultaneously monitored using an accelerometer and strain gauges, while global engineering strains were independently determined by a synchronized high speed camera. Dynamic non-linear stress-strain relation was compared with empirical relation obtained from static loading of o-rings. The paper presents first experimental results and analysis of dissipative properties of o-rings during dynamic compression and unloading. The strongly nonlinear force-strain and strain-rate dependent behavior was described using nonlinear viscoelastic relation with only one adjustable parameter.
Coexistence of weak and strong wave turbulence in incompressible Hall MHD
NASA Astrophysics Data System (ADS)
Meyrand, Romain; Kiyani, Khurom; Galtier, Sebastien
2016-04-01
We report a numerical investigation of 3D Hall Magnetohydrodynamic turbulence with a strong mean magnetic field. By using a helicity decomposition and a cross-bicoherence analysis, we observe that the nonlinear 3-wave coupling is substantial among ion cyclotron and whistler waves. By studying in detail the degree of nonlinearity of these two populations we show that ion cyclotron and whistler turbulent fluctuations belong respectively to strong and weak wave turbulence. The non trivial blending of these two regime give rise to anomalous anisotropy and scaling properties. The separation of the weak random wave and strong coherent turbulence component can however be effectively done using simultaneous space and time Fourier transforms. Using this techniques we show that it is possible to recover some statistical prediction of weak turbulent theory.
Detecting plastic strain distribution by a nonlinear wave mixing method
NASA Astrophysics Data System (ADS)
Tang, Guangxin; Liu, Minghe; Jacobs, Laurence J.; Qu, Jianmin
2013-01-01
A nonlinear wave mixing method is used to measure the plastic strain distribution in polycrystalline materials. A pair of collinear longitudinal and shear waves is generated. Under the phase matching condition, a resonant shear wave with a difference frequency is generated and propagates towards the shear wave transducer. The amplitude of this resonant shear wave is proportional to the acoustic nonlinearity parameter β, which is known to be related to plastic deformation. By adjusting the two primary waves so that they mix at different locations, the distribution of β can be obtained. This study demonstrates the feasibility of detecting plastic strain distribution in polycrystalline materials by the nonlinear wave mixing technique.
Attenuation of short stress pulses in strongly nonlinear dissipative metamaterial
NASA Astrophysics Data System (ADS)
Xu, Yichao; Nesterenko, Vitali F.
2015-03-01
Attenuation of short stress pulses under different levels of precompression was investigated in a one-dimensional strongly nonlinear discrete metamaterial assembled using alternating steel disks and toroidal Nitrile O-rings. The results were compared with the numerical modeling. A double power-law is used to describe the nonlinear interaction between the disks due to the compression of rubber O-rings. The dispersion behavior caused by the periodic arrangement of elements is contributing to the attenuation of pulse, but could not explain the experimental observations. It was explained by taking into account the nonlinear viscous behavior of O-rings. The numerical simulations were able to predict the dependence of the signal speed on the precompression force, a significant decrease of the pulse width with the precompression and the attenuation of the leading positive pulse, the latter of major significance in the protection against impact. This strongly nonlinear dissipative metamaterial has a potential for attenuation of dynamic loading and allows an enhanced tunability of signal speed and degree of attenuation.
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°.
Nonlinear traveling wave solution for the MJO skeleton model
NASA Astrophysics Data System (ADS)
Chen, S.; Stechmann, S. N.
2014-12-01
Recently, a minimal dynamical model is presented for capturing MJO's fundamental features. The model is a nonlinear oscillator model for the MJO skeleton and it involves interactions between convection, moisture and circulation. I will present the exact nonlinear traveling wave solutions for the model based on its energy conservation. The exact nonlinear solution provides for an explicit comparison of features between linear and nonlinear waves such as dispersion relations and traveling wave speeds. Moreover, the nonlinear solutions, compared with the linear ones, produce a narrow region of active convection and a wider region of suppressed convection. These predictions offer nonlinear MJO features that could potentially be targets of observational investigations.
Nonlinear effects associated with kinetic Alfvén wave
NASA Astrophysics Data System (ADS)
Gaur, Nidhi; Sharma, R. P.
2015-04-01
The nonlinear phenomena are of striking importance in understanding the particle acceleration, heating, and turbulence in the interplanetary space. Kinetic Alfvén wave (KAW) is one of the strong candidates responsible for accelerating the solar wind and powering the solar wind turbulence. Therefore, the nonlinear properties of KAW are attracting a good attention. In the present work, we have investigated the nonlinear effects associated with KAW in the solar wind plasma at around 1 A.U. The ponderomotive force of (relatively high frequency, high power) pump KAW may be used to excite the low-frequency KAW (LKAW). For this purpose, we have derived the dynamical equations to analyze the nonlinear dynamics of relatively high frequency pump KAW in the presence of LKAW perturbation. The numerical solution has been carried out for the coupled system of equations by using the pseudospectral method for space integration and finite difference method along with the predictor corrector scheme for the evolution in time. The coupled system of nonlinear dynamical equations has been analyzed to study the nonlinear effects associated with pump KAW and the resulting turbulent spectra at 1 A.U.
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium.
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-01-01
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium.
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-01-01
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066
Nonlinear ion acoustic waves scattered by vortexes
NASA Astrophysics Data System (ADS)
Ohno, Yuji; Yoshida, Zensho
2016-09-01
The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.
Rotation-induced nonlinear wavepackets in internal waves
Whitfield, A. J. Johnson, E. R.
2014-05-15
The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets. It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.
Nonlinear scattering of acoustic waves by vibrating obstacles
NASA Astrophysics Data System (ADS)
Piquette, J. C.
1983-06-01
The problem of the generation of sum- and difference-frequency waves produced via the scattering of an acoustic wave by an obstacle whose surface vibrates harmonically was studied both theoretically and experimentally. The theoretical approach involved solving the nonlinear wave equation, subject to appropriate boundary conditions, by the use of a perturbation expansion of the fields and a Green's function method. In addition to ordinary rigid-body scattering, Censor predicted nongrowing waves at frequencies equal to the sum and to the difference of the frequencies of the primary waves. The solution to the nonlinear wave equation also yields scattered waves at the sum and difference frequencies. However, the nonlinearity of the medium causes these waves to grow with increasing distance from the scatter's surface and, after a very small distance, dominate those predicted by Censor. The simple-source formulation of the second-order nonlinear wave equation for a lossless fluid medium has been derived for arbitrary primary wave fields. This equation was used to solve the problem of nonlinear scattering of acoustic waves by a vibrating obstacle for three geometries: (1) a plane-wave scattering by a vibrating plane, (2) cylindrical-wave scattering by a vibrating cylinder, and (3) plane-wave scattering by a vibrating cylinder. Successful experimental validation of the theory was inhibited by previously unexpected levels of nonlinearity in the hydrophones used. Such high levels of hydrophone nonlinearity appeared in hydrophones that, by their geometry of construction, were expected to be fairly linear.
Nonlinear shallow ocean-wave soliton interactions on flat beaches.
Ablowitz, Mark J; Baldwin, Douglas E
2012-09-01
Ocean waves are complex and often turbulent. While most ocean-wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these shallow-water nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. Here we report that such nonlinear interactions occur every day, close to low tide, on two flat beaches that are about 2000 km apart. These interactions are closely related to the analytic, soliton solutions of a widely studied multidimensional nonlinear wave equation. On a much larger scale, tsunami waves can merge in similar ways.
Electromagnetic shock wave in nonlinear vacuum: exact solution.
Kovachev, Lubomir M; Georgieva, Daniela A; Kovachev, Kamen L
2012-10-01
An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. An exact solution with its own angular momentum in the form of a shock wave is obtained.
Nonlinear Dispersion of Magnetostatic Surface Waves on Ferromagnetic Films
NASA Astrophysics Data System (ADS)
A, D. Boardman; Bao, Jiashan; Wang, Qi; Cai, Yingshi; S, A. Nikitov
1991-11-01
The wave equation of nonlinear magnetostatic surface waves (MSSW) on ferromagnetic films is derived and its solution is found. The nonlinear dispersion relation of MSSW is discussed. Our result shows that the wave power has a little effect to the frequency shift of MSSW with lower frequency, but has a considerably larger effect to that with higher frequency within the band.
Group velocity and nonlinear dispersive wave propagation.
NASA Technical Reports Server (NTRS)
Hayes, W. D.
1973-01-01
By the use of a Hamiltonian formulation, a basic group velocity is defined as the derivative of frequency with respect to wavenumber keeping action density constant, and is shown to represent an incremental action velocity in the general nonlinear case. The stability treatment of Whitham and Lighthill is extended to several dimensions. The water-wave analysis of Whitham (1967) is extended to two space dimensions, and is shown to predict oblique-mode instabilities for kh smaller than 1.36. A treatment of Lighthill's (1965) solution in the one-dimensional elliptic case resolves the problem of the energy distribution in the solution past the critical time.
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.
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
Nonlinear chorus wave effects on energetic electrons reexamined
NASA Astrophysics Data System (ADS)
Zheng, Q.; Fok, M. H.; Zheng, Y.; Lui, A.
2012-12-01
Electron energy transport due to nonlinear plasma wave particle interactions are carried out by wave and particles resonating with each other. Many nonlinear wave studies conducted in the past have only considered the main resonance between wave and electrons. However, we have found through test particle simulations that although independent, separate contributions from higher order resonances can be small, but they can have a rather significant impact on the main-order contribution hence the total nonlinear wave effects. Contribution from different orders can interfere with each other hence the overall nonlinear wave effect is significantly different from that of just the major resonance. Therefore in the nonlinear wave particle interaction regime, contribution from different resonant orders is inseparable and contributions from higher order wave-particle resonances should be all included. For the same token, banded plasma waves should be used in nonlinear wave studies instead of assumed monochromatic waves. By including all the essential factors mentioned above, the overall electron transport due to the nonlinear plasma wave effects take the form of diffusion-like rather than advection, which was reported in many previous studies. It is also found that chorus wave induced electron transport is one important mechanism for the formation of electron butterfly pitch angle distribution.
Strongly nonlinear dynamics of electrolytes in large ac voltages.
Højgaard Olesen, Laurits; Bazant, Martin Z; Bruus, Henrik
2010-07-01
We study the response of a model microelectrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two features--significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasiequilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination" since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute-solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids, and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.
Nonlinear ship waves and computational fluid dynamics
MIYATA, Hideaki; ORIHARA, Hideo; SATO, Yohei
2014-01-01
Research works undertaken in the first author’s laboratory at the University of Tokyo over the past 30 years are highlighted. Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design. Based on these findings, a multitude of the Computational Fluid Dynamic (CFD) techniques have been developed over this period, and are highlighted in this paper. The TUMMAC code has been developed for wave problems, based on a rectangular grid system, while the WISDAM code treats both wave and viscous flow problems in the framework of a boundary-fitted grid system. These two techniques are able to cope with almost all fluid dynamical problems relating to ships, including the resistance, ship’s motion and ride-comfort issues. Consequently, the two codes have contributed significantly to the progress in the technology of ship design, and now form an integral part of the ship-designing process. PMID:25311139
Nonlinear ship waves and computational fluid dynamics.
Miyata, Hideaki; Orihara, Hideo; Sato, Yohei
2014-01-01
Research works undertaken in the first author's laboratory at the University of Tokyo over the past 30 years are highlighted. Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design. Based on these findings, a multitude of the Computational Fluid Dynamic (CFD) techniques have been developed over this period, and are highlighted in this paper. The TUMMAC code has been developed for wave problems, based on a rectangular grid system, while the WISDAM code treats both wave and viscous flow problems in the framework of a boundary-fitted grid system. These two techniques are able to cope with almost all fluid dynamical problems relating to ships, including the resistance, ship's motion and ride-comfort issues. Consequently, the two codes have contributed significantly to the progress in the technology of ship design, and now form an integral part of the ship-designing process.
Interaction of Oblique Instability Waves with a Nonlinear Plane Wave
NASA Technical Reports Server (NTRS)
Wundrow, David W.; Hultgren, Lennart S.; Goldstein, M. E.
1994-01-01
This paper is concerned with the downstream evolution of a resonant triad of initially non-interacting linear Instability waves in a boundary layer with a weak adverse pressure gradient. The triad consists of a two-dimensional fundamental mode and a pair of equal-amplitude oblique modes that form a subharmonic standing wave in the spanwise direction. The growth rates are small and there is a well-defined common critical layer for these waves. As in Goldstein & Lee (1992), the wave interaction takes place entirely within this critical layer and is initially of the parametric-resonance type. This enhances the spatial growth rate of the subharmonic but does not affect that of the fundamental. However, in contrast to Goldstein & Lee (1992), the initial subharmonic amplitude is assumed to be small enough so that the fundamental can become nonlinear within its own critical layer before it is affected by the subharmonic. The subharmonic evolution is then dominated by the parametric-resonance effects and occurs on a much shorter streamwise scale than that of the fundamental. The subharmonic amplitude continues to increase during this parametric-resonance stage - even as the growth rate of the fundamental approaches zero - and the subharmonic eventually becomes large enough to influence the fundamental which causes both waves to evolve on the same shorter streamwise scale.
Nonlinear 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.
Strong and moderate nonlinear El Niño regimes
NASA Astrophysics Data System (ADS)
Takahashi, Ken; Dewitte, Boris
2016-03-01
It has been previously proposed that two El Niño (EN) regimes, strong and moderate, exist but the historical observational record is too short to establish this conclusively. Here, 1200 years of simulations with the GFDL CM2.1 model allowed us to demonstrate their existence in this model and, by showing that the relevant dynamics are also evident in observations, we present a stronger case for their existence in nature. In CM2.1, the robust bimodal probability distribution of equatorial Pacific sea surface temperature (SST) indices during EN peaks provides evidence for the existence of the regimes, which is also supported by a cluster analysis of these same indices. The observations agree with this distribution, with the EN of 1982-1983 and 1997-1998 corresponding to the strong EN regime and all the other observed EN to the moderate regime. The temporal evolution of various indices during the observed strong EN agrees very well with the events in CM2.1, providing further validation of this model as a proxy for nature. The two regimes differ strongly in the magnitude of the eastern Pacific warming but not much in the central Pacific. Observations and model agree in the existence of a finite positive threshold in the SST anomaly above which the zonal wind response to warming is strongly enhanced. Such nonlinearity in the Bjerknes feedback, which increases the growth rate of EN events if they reach sufficiently large amplitude, is very likely the essential mechanism that gives rise to the existence of the two EN regimes. Oceanic nonlinear advection does not appear essential for the onset of strong EN. The threshold nonlinearity could make the EN regimes very sensitive to stochastic forcing. Observations and model agree that the westerly wind stress anomaly in the central equatorial Pacific in late boreal summer has a substantial role determining the EN regime in the following winter and it is suggested that a stochastic component at this time was key for the
Electrostatic waves and the strong diffusion of magnetospheric electrons
NASA Technical Reports Server (NTRS)
Kennel, C. F.; Ashour-Abdalla, M.
1982-01-01
A comprehensive review of electron pitch angle scattering in the magnetosphere and the plasma waves responsible for it is presented, emphasizing the strong diffusion of diffuse auroral electrons by electrostatic electron cyclotron harmonic waves. The weak diffusion of energetic radiation belt electrons within the plasmasphere is reviewed briefly. Several new suggestions concerning the quasilinear diffusion from and saturation of electrostatic waves are included.
On shallow water rogue wave formation in strongly inhomogeneous channels
NASA Astrophysics Data System (ADS)
Didenkulova, Ira; Pelinovsky, Efim
2016-05-01
Rogue wave formation in shallow water is often governed by dispersive focusing and wave-bottom interaction. In this study we try to combine these mechanisms by considering dispersive nonreflecting wave propagation in shallow strongly inhomogeneous channels. Nonreflecting wave propagation provides extreme wave amplification and the transfer of wave energy over large distances, while dispersive effects allow formation of a short-lived wave of extreme height (rogue wave). We found several types of water channels, where this mechanism can be realized, including (i) channels with a monotonically decreasing cross-section (normal dispersion), (ii) an inland basin described by a half of elliptic paraboloid (abnormal dispersion) and (iii) an underwater hill described by a half of hyperbolic paraboloid (normal dispersion). Conditions for variations of local frequency in the wave train providing optimal focusing of the wave train are also found.
NASA Astrophysics Data System (ADS)
Wan, W. M. V.; Lee, H. C.; Hui, P. M.; Yu, K. W.
1996-08-01
The effective response of random media consisting of two different kinds of strongly nonlinear materials with strong power-law nonlinearity is studied. Each component satisfies current density and electric-field relation of the form J=χ\\|E\\|βE. A simple self-consistent mean-field theory, which leads to a simple way in determining the average local electric field in each constituent, is introduced. Each component is assumed to have a conductivity depending on the averaged local electric field. The averaged local electric field is then determined self-consistently. Numerical simulations of the system are carried out on random nonlinear resistor networks. Theoretical results are compared with simulation data, and excellent agreements are found. Results are also compared with the Hashin-Shtrikman lower bound proposed by Ponte Castaneda et al. [Phys. Rev. B 46, 4387 (1992)]. It is found that the present theory, at small contrasts of χ between the two components, gives a result identical to that of Ponte Castaneda et al. up to second order of the contrast. The crossover and scaling behavior of the effective response near the percolation threshold as suggested by the present theory are discussed and demonstrated.
Response of MDOF strongly nonlinear systems to fractional Gaussian noises.
Deng, Mao-Lin; Zhu, Wei-Qiu
2016-08-01
In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems. PMID:27586630
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.
Pulsatile instability in rapid directional solidification - Strongly-nonlinear analysis
NASA Technical Reports Server (NTRS)
Merchant, G. J.; Braun, R. J.; Brattkus, K.; Davis, S. H.
1992-01-01
In the rapid directional solidification of a dilute binary alloy, analysis reveals that, in addition to the cellular mode of Mullins and Sekerka (1964), there is an oscillatory instability. For the model analyzed by Merchant and Davis (1990), the preferred wavenumber is zero; the mode is one of pulsation. Two strongly nonlinear analyses are performed that describe this pulsatile mode. In the first case, nonequilibrium effects that alter solute rejection at the interface are taken asymptotically small. A nonlinear oscillator equation governs the position of the solid-liquid interface at leading order, and amplitude and phase evolution equations are derived for the uniformly pulsating interface. The analysis provides a uniform description of both subcritical and supercritical bifurcation and the transition between the two. In the second case, nonequilibrium effects that alter solute rejection are taken asymptotically large, and a different nonlinear oscillator equation governs the location of the interface to leading order. A similar analysis allows for the derivation of an amplitude evolution equation for the uniformly pulsating interface. In this case, the bifurcation is always supercritical. The results are used to make predictions about the characteristics of solute bands that would be frozen into the solid.
On tidal variability induced by nonlinear interaction with planetary waves
Teitelbaum, H.; Vial, F. )
1991-08-01
Short-time variability of the atmospheric tides is frequently observed in the meteor region but is not yet fully explained in terms of production mechanisms. This is probably due to the existence of several such mechanisms acting together or separately. In this paper the authors show that many observations can be explained by nonlinear interactions between tides and planetary waves having periods corresponding to those of the observed tidal amplitude modulations. These nonlinear interactions generate two secondary waves whose frequencies are the sum and difference of frequencies of the primary waves. These two waves beat with the tide, modulating its amplitude with the planetary wave period. A numerical model is used to demonstrate that with primary waves of reasonable amplitudes the nonlinear interactions can be quite large. This is because the importance of nonlinearity depends essentially on the amplitude of the induced fluid velocity in the direction of wave propagation compared to the wave propagation velocity. When two waves propagate simultaneously, the fluid velocity can have a large component in the direction of propagation of one of the waves, and advective (nonlinear) terms can be large. This point is further illustrated in the case of two gravity waves interacting together. Finally, some observational campaigns carried out above Garchy (45{degree}N) are analyzed using a nonparametric method. The results indicate that nonlinear interactions between tides and planetary waves really take place in the upper mesosphere and lower thermosphere.
Strongly nonlinear dynamics of electrolytes in large ac voltages
NASA Astrophysics Data System (ADS)
Højgaard Olesen, Laurits; Bazant, Martin Z.; Bruus, Henrik
2010-07-01
We study the response of a model microelectrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two features—significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasiequilibrium structure of the double layers. The former leads to the prediction of “ac capacitive desalination” since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute-solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids, and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.
Compactification of nonlinear patterns and waves.
Rosenau, Philip; Kashdan, Eugene
2008-12-31
We present a nonlinear mechanism(s) which may be an alternative to a missing wave speed: it induces patterns with a compact support and sharp fronts which propagate with a finite speed. Though such mechanism may emerge in a variety of physical contexts, its mathematical characterization is universal, very simple, and given via a sublinear substrate (site) force. Its utility is shown studying a Klein-Gordon -u(tt) + [phi/(u(x)]x = P'(u) equation, where phi'(sigma) = sigma + beta sigma3 and endowed with a subquadratic site potential P(u) approximately /1-u2/(alpha+1), 0 < or = alpha < 1, and the Schrödinger iZt + inverted delta2 Z = G(/Z/)Z equation in a plane with G(A) = gammaA(-delta) - sigmaA2, 0 < delta < or = 1.
NASA Astrophysics Data System (ADS)
Selim, M. M.; El-Depsy, A.; El-Shamy, E. F.
2015-12-01
Properties of nonlinear ion-acoustic travelling waves propagating in a three-dimensional multicomponent magnetoplasma system composed of positive ions, negative ions and superthermal electrons are considered. Using the reductive perturbation technique (RPT), the Zkharov-Kuznetsov (ZK) equation is derived. The bifurcation theory of planar dynamical systems is applied to investigate the existence of the solitary wave solutions and the periodic travelling wave solutions of the resulting ZK equation. It is found that both compressive and rarefactive nonlinear ion-acoustic travelling waves strongly depend on the external magnetic field, the unperturbed positive-to-negative ions density ratio, the direction cosine of the wave propagation vector with the Cartesian coordinates, as well as the superthermal electron parameter. The present model may be useful for describing the formation of nonlinear ion-acoustic travelling wave in certain astrophysical scenarios, such as the D and F-regions of the Earth's ionosphere.
Nonlinear 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.
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.
Application of nonlinear wave modulation spectroscopy to discern material damage
Johnson, P.A.; Sutin, A.; Abeele, K.E.A. van den
1999-04-01
Materials containing structural damage have a far greater nonlinear elastic response than materials with no structural damage. This is the basis for nonlinear wave diagnostics of damage, methods which are remarkably sensitive to the detection and progression of damage in materials. Here the authors describe one nonlinear method, the application of harmonics and sum and difference frequency to discern damage in materials. The method is termed Nonlinear Wave Modulation Spectroscopy (NWMS). It consists of exciting a sample with continuous waves of two separate frequencies simultaneously, and inspecting the harmonics of the two waves, and their sum and difference frequencies (sidebands). Undamaged materials are essentially linear in their response to the two waves, while the same material, when damaged, becomes highly nonlinear, manifested by harmonics and sideband generation. The authors illustrate the method by experiments on uncracked and cracked plexiglass and sandstone samples, and by applying it to intact and damaged engine components.
Nonlinear analysis of helix traveling wave tubes
Freund, H.P.; Zaidman, E.G.; Vanderplaats, N.R.; Kodis, M.A.
1994-12-31
A nonlinear formulation of the interaction in a helix traveling wave tube (TWT) is presented. The formulation is intended to treat a wide class of helix TWTs including both emission-gated and multi-tone operation. The essential feature of each of these configurations is that multiple waves must be included in the formulation. As a result, a fully time-dependent analysis is required. The numerical procedure for this in a helix TWT is complicated by the fact that the radial profile of the field varies with frequency. This contrasts, for example, with the case of a smooth bore waveguide in which the radial profile for each TE{sub ln} or TM{sub ln} mode is invariant in frequency. Because of this, a complete self-consistent particle-in-cell (PIC) formulation must be three-dimensional. In order to circumvent the computational expense of a 3D PIC formulation, the authors adopt an approach in which the electromagnetic field is represented as a superposition of azimuthally symmetric modes in a vacuum sheath helix. The specific electron distributions are chosen to model either a continuous beam for the multi-tone TWT and a pulsed beam for the emission-gated TWT. Numerical results of the simulation for examples of interest to an emission-gated TWT experiment at NRL will be presented.
Linear and nonlinear electrostatic modes in a strongly coupled quantum plasma
Ghosh, Samiran; Chakrabarti, Nikhil
2012-07-15
The properties of linear and nonlinear electrostatic waves in a strongly coupled electron-ion quantum plasma are investigated. In this study, the inertialess electrons are degenerate, while non-degenerate inertial ions are strongly correlated. The ion dynamics is governed by the continuity and the generalized viscoelastic momentum equations. The quantum forces associated with the quantum statistical pressure and the quantum recoil effect act on the degenerate electron fluid, whereas strong ion correlation effects are embedded in generalized viscoelastic momentum equation through the viscoelastic relaxation of ion correlations and ion fluid shear viscosities. Hence, the spectra of linear electrostatic modes are significantly affected by the strong ion coupling effect. In the weakly nonlinear limit, due to ion-ion correlations, the quantum plasma supports a dispersive shock wave, the dynamics of which is governed by the Korteweg-de Vries Burgers' equation. For a particular value of the quantum recoil effect, only monotonic shock structure is observed. Possible applications of our investigation are briefly mentioned.
Linear and nonlinear electrostatic modes in a strongly coupled quantum plasma
NASA Astrophysics Data System (ADS)
Ghosh, Samiran; Chakrabarti, Nikhil; Shukla, P. K.
2012-07-01
The properties of linear and nonlinear electrostatic waves in a strongly coupled electron-ion quantum plasma are investigated. In this study, the inertialess electrons are degenerate, while non-degenerate inertial ions are strongly correlated. The ion dynamics is governed by the continuity and the generalized viscoelastic momentum equations. The quantum forces associated with the quantum statistical pressure and the quantum recoil effect act on the degenerate electron fluid, whereas strong ion correlation effects are embedded in generalized viscoelastic momentum equation through the viscoelastic relaxation of ion correlations and ion fluid shear viscosities. Hence, the spectra of linear electrostatic modes are significantly affected by the strong ion coupling effect. In the weakly nonlinear limit, due to ion-ion correlations, the quantum plasma supports a dispersive shock wave, the dynamics of which is governed by the Korteweg-de Vries Burgers' equation. For a particular value of the quantum recoil effect, only monotonic shock structure is observed. Possible applications of our investigation are briefly mentioned.
Nonlinear airglow signatures of ducted gravity waves in the mesosphere and lower thermosphere
NASA Astrophysics Data System (ADS)
Snively, J. B.; Hickey, M. P.; Taylor, M. J.
2010-12-01
Signatures of short-period gravity waves are detected frequently in airglow data, revealing typical horizontal wavelengths of ˜15-35 km and periods of ˜4-8 minutes [e.g., Simkhada et al., Ann. Geophys., 27, 3213, 2009]. Many of such waves are ducted within the mesosphere and lower thermosphere (MLT) region [e.g., Walterscheid and Hickey, 114, D19109, 2009], and typical airglow intensity perturbations suggest amplitudes on the order of a few to tens of Kelvin within the airglow layers. At these amplitudes, trapped small-scale waves may be intermittently subject to nonlinear dissipation, potentially contributing to the local small-scale dynamics and variability of the lower thermosphere. For exceptionally strong small-scale waves, nonlinear behavior may become detectable in airglow data, including examples of wave breakdown [e.g., Yamada et al., GRL, 28(11), 2153, 2001], or apparent bore formation [e.g., Smith et al., JGR, 108(A2), 1083, 2003]. For moderately strong gravity waves with principally-linear propagation characteristics, however, airglow signatures may also exhibit nonlinearity in the form of harmonics, due to strong perturbations of reacting minor species at steep gradients of density [Huang et al., JGR, 108(A5), 1173, 2003; Snively et al., JGR, In Press, 2010]. Two scenarios are investigated numerically, using a nonlinear photochemical-dynamical model to simulate ducted gravity wave perturbations to the hydroxyl airglow layer. First, signatures of ducted waves are considered that exhibit nonlinearity associated with the wave perturbations to minor species participating in the emission processes. In this case, the nonlinear signatures are not indicative of changes in the wave packet spectrum. Second, we consider signatures of ducted waves at sufficient amplitudes to exhibit nonlinear propagation as they approach dissipation. In this second case, observable nonlinearity in the airglow signatures arise simultaneously from the overall wave perturbation and
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-06-23
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.
Introduction to Wave Propagation in Nonlinear Fluids and Solids
NASA Astrophysics Data System (ADS)
Drumheller, Douglas S.
1998-02-01
Waves occur widely in nature and have innumerable commercial uses. Waves are responsible for the sound of speech, meteors igniting the atmosphere, radio and television broadcasting, medical diagnosis using ultrasound. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models for a variety of gases, liquids, and solids. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Students at an advanced undergraduate/graduate level will find this text a clear and comprehensive introduction to the study of nonlinear wave phenomena, and it will also be valuable as a professional reference in engineering and applied physics.
Nonlinear interference and unidirectional wave mixing in metamaterials.
Rose, Alec; Huang, Da; Smith, David R
2013-02-01
When both electric and magnetic mechanisms contribute to a particular nonlinear optical process, there exists the possibility for nonlinear interference, often characterized by constructive or destructive interference in the radiation pattern of harmonics and mix waves. However, observation of a significant effect from nonlinear interference requires careful balancing of the various contributions. For this purpose, we propose an artificial metamaterial, using the formalism of nonlinear magnetoelectric coupling to simultaneously engineer the nonlinear polarization and magnetization. We confirm our predictions of nonlinear interference with both simulations and experiment, demonstrating unidirectional wave mixing in two microwave metamaterials. Our results point toward an ever wider range of nonlinear properties, in which nonlinear interference is just one of many potential applications.
Strongly interacting photons in a quantum nonlinear medium
NASA Astrophysics Data System (ADS)
Peyronel, Thibault
2014-05-01
Photons are fast and robust carriers of information but their lack of mutual interactions hinders their use in quantum information protocols. Interactions can be mediated by nonlinear media, and optical nonlinearities at the single photon level are a long-standing goal of quantum optical science. By coherently coupling slowly propagating photons to Rydberg states in a dense cold atomic gas, we create a single-pass medium with large photon-photon interactions. We first demonstrate that combining electromagnetically induced transparency techniques with the Rydberg blockade effect leads to strong dissipative interactions between individual photons. As a result, the simultaneous propagation of photons is suppressed in an otherwise transparent medium, and coherent laser pulses are converted into single photons. We subsequently explore the regime of coherent interactions, where simultaneously propagating photons acquire a large conditional phase-shift and become entangled. In this regime, the photons behave as massive particles exerting an attractive force onto each other and their evolution is governed by the existence of a photonic bound-state. This work paves the way for cavity-free deterministic optical quantum gates and quantum many-body physics with light.
Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics
NASA Technical Reports Server (NTRS)
Zhu, Yanqui; Cohn, Stephen E.; Todling, Ricardo
1999-01-01
The Kalman filter is the optimal filter in the presence of known gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions. Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz model as well as more realistic models of the means and atmosphere. A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter situations to allow for correct update of the ensemble members. The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to be quite puzzling in that results state estimates are worse than for their filter analogue. In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use the Lorenz model to test and compare the behavior of a variety of implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.
El-Labany, S. K. Zedan, N. A.; El-Taibany, W. F. E-mail: eltaibany@du.edu.eg
2015-07-15
Cylindrical and spherical amplitude modulations of dust acoustic (DA) solitary wave envelopes in a strongly coupled dusty plasma containing nonthermal distributed ions are studied. Employing a reductive perturbation technique, a modified nonlinear Schrödinger equation including the geometrical effect is derived. The influences of nonthermal ions, polarization force, and the geometries on the modulational instability conditions are analyzed and the possible rogue wave structures are discussed in detail. It is found that the spherical DA waves are more structurally stable to perturbations than the cylindrical ones. Possible applications of these theoretical findings are briefly discussed.
Acoustic field distribution of sawtooth wave with nonlinear SBE model
Liu, Xiaozhou Zhang, Lue; Wang, Xiangda; Gong, Xiufen
2015-10-28
For precise prediction of the acoustic field distribution of extracorporeal shock wave lithotripsy with an ellipsoid transducer, the nonlinear spheroidal beam equations (SBE) are employed to model acoustic wave propagation in medium. To solve the SBE model with frequency domain algorithm, boundary conditions are obtained for monochromatic and sawtooth waves based on the phase compensation. In numerical analysis, the influence of sinusoidal wave and sawtooth wave on axial pressure distributions are investigated.
Nonlinear physics of shear Alfvén waves
NASA Astrophysics Data System (ADS)
Zonca, Fulvio; Chen, Liu
2014-02-01
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These "nonlinear equilibria" or "phase-space zonal structures" dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
Nonlinear physics of shear Alfvén waves
Zonca, Fulvio; Chen, Liu
2014-02-12
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These 'nonlinear equilibria' or 'phase-space zonal structures' dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
Nonlinear wave interactions in bubble layers
NASA Astrophysics Data System (ADS)
Karpov, S.; Prosperetti, A.; Ostrovsky, L.
2003-03-01
Due to the large compressibility of gas bubbles, layers of a bubbly liquid surrounded by pure liquid exhibit many resonances that can give rise to a strongly nonlinear behavior even for relatively low-level excitation. In an earlier paper [Druzhinin et al., J. Acoust. Soc. Am. 100, 3570 (1996)] it was pointed out that, by exciting the bubbly layer in correspondence of two resonant modes, so chosen that the difference frequency also corresponds to a resonant mode, it might be possible to achieve an efficient parametric generation of a low-frequency signal. The earlier work made use of a simplified model for the bubbly liquid that ignored the dissipation and dispersion introduced by the bubbles. Here a more realistic description of the bubble behavior is used to study the nonlinear oscillations of a bubble layer under both single- and dual-frequency excitation. It is found that a difference-frequency power of the order of 1% can be generated with incident pressure amplitudes of the order of 50 kPa or so. It appears that similar phenomena would occur in other systems, such as porous waterlike or rubberlike media.
NASA Astrophysics Data System (ADS)
Ranjbar, Monireh; Bahari, Ali
2016-09-01
Four-wave mixing in propagation of cylindrical waves in a homogeneous nonlinear optical media has been investigated theoretically. An explicit analytical expression which contains all the main nonlinear optical effects, including third harmonic generation, sum and difference frequency generation has been obtained. A comparison between sum frequency efficiency for exact and approximation expression in a homogeneous nonlinear medium has been done. The effect of increasing the nonlinear optical coefficient (χeff(3)) and increasing the frequency difference between two adjacent waves (Δ ω) , on the efficiency of sum frequency generation in homogeneous media has been investigated.
Amplitude-dependent Lamb wave dispersion in nonlinear plates.
Packo, Pawel; Uhl, Tadeusz; Staszewski, Wieslaw J; Leamy, Michael J
2016-08-01
The paper presents a perturbation approach for calculating amplitude-dependent Lamb wave dispersion in nonlinear plates. Nonlinear dispersion relationships are derived in closed form using a hyperelastic stress-strain constitutive relationship, the Green-Lagrange strain measure, and the partial wave technique integrated with a Lindstedt-Poincaré perturbation approach. Solvability conditions are derived using an operator formalism with inner product projections applied against solutions to the adjoint problem. When applied to the first- and second-order problems, these solvability conditions lead to amplitude-dependent, nonlinear dispersion corrections for frequency as a function of wavenumber. Numerical simulations verify the predicted dispersion shifts for an example nonlinear plate. The analysis and identification of amplitude-dependent, nonlinear Lamb wave dispersion complements recent research focusing on higher harmonic generation and internally resonant waves, which require precise dispersion relationships for frequency-wavenumber matching. PMID:27586758
Book review: Nonlinear ocean waves and the inverse scattering transform
Geist, Eric L.
2011-01-01
Nonlinear Ocean Waves and the Inverse Scattering Transform is a comprehensive examination of ocean waves built upon the theory of nonlinear Fourier analysis. The renowned author, Alfred R. Osborne, is perhaps best known for the discovery of internal solitons in the Andaman Sea during the 1970s. In this book, he provides an extensive treatment of nonlinear water waves based on a nonlinear spectral theory known as the inverse scattering transform. The writing is exceptional throughout the book, which is particularly useful in explaining some of the more difficult mathematical concepts. Review info: Nonlinear Ocean Waves and the Inverse Scattering Transform. By Alfred R. Osborne, 2010. ISBN: 978-125286299, 917 pp.
Superposed nonlinear waves in coherently coupled Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Babu Mareeswaran, R.; Kanna, T.
2016-09-01
We study the dynamics of superposed nonlinear waves in coherently coupled Gross-Pitaevskii (CCGP) equations with constant (autonomous system) and time varying (non-autonomous system) nonlinearity coefficients. By employing a linear transformation, the autonomous CCGP system is converted into two separate scalar nonlinear Schrödinger equations and we show that linear superposition of different nonlinear wave solutions of these scalar equations results into several kinds of nonlinear coherent structures namely, coexisting rogue wave-Ma breather, Akhmediev-Ma breathers, collision and bound states of Ma breathers and solitons. Next, the non-autonomous CCGP system is converted into an autonomous CCGP system with a similarity transformation. We show an interesting possibility of soliton compression and appearance of creeping solitons for kink-like and periodically modulated nonlinearity coefficient.
NASA Astrophysics Data System (ADS)
Tchinang Tchameu, J. D.; Togueu Motcheyo, A. B.; Tchawoua, C.
2016-09-01
The discrete multi-rogue waves (DMRW) as solution of the discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearities is studied numerically. These biological rogue waves represent the complex probability amplitude of finding an amide-I vibrational quantum at a site. We observe that the growth in the higher order saturable nonlinearity implies the formation of DMRW including an increase in the short-living DMRW and a decrease in amplitude of the long-living DMRW.
Experimental characterization of nonlinear processes of whistler branch waves
NASA Astrophysics Data System (ADS)
Tejero, E. M.; Crabtree, C.; Blackwell, D. D.; Amatucci, W. E.; Ganguli, G.; Rudakov, L.
2016-05-01
Experiments in the Space Physics Simulation Chamber at the Naval Research Laboratory isolated and characterized important nonlinear wave-wave and wave-particle interactions that can occur in the Earth's Van Allen radiation belts by launching predominantly electrostatic waves in the intermediate frequency range with wave normal angle greater than 85 ° and measuring the nonlinearly generated electromagnetic scattered waves. The scattered waves have a perpendicular wavelength that is nearly an order of magnitude larger than that of the pump wave. Calculations of scattering efficiency from experimental measurements demonstrate that the scattering efficiency is inversely proportional to the damping rate and trends towards unity as the damping rate approaches zero. Signatures of both wave-wave and wave-particle scatterings are also observed in the triggered emission process in which a launched wave resonant with a counter-propagating electron beam generates a large amplitude chirped whistler wave. The possibility of nonlinear scattering or three wave decay as a saturation mechanism for the triggered emission is suggested. The laboratory experiment has inspired the search for scattering signatures in the in situ data of chorus emission in the radiation belts.
Nonlinear time reversal of classical waves: experiment and model.
Frazier, Matthew; Taddese, Biniyam; Xiao, Bo; Antonsen, Thomas; Ott, Edward; Anlage, Steven M
2013-12-01
We consider time reversal of electromagnetic waves in a closed, wave-chaotic system containing a discrete, passive, harmonic-generating nonlinearity. An experimental system is constructed as a time-reversal mirror, in which excitations generated by the nonlinearity are gathered, time-reversed, transmitted, and directed exclusively to the location of the nonlinearity. Here we show that such nonlinear objects can be purely passive (as opposed to the active nonlinearities used in previous work), and we develop a higher data rate exclusive communication system based on nonlinear time reversal. A model of the experimental system is developed, using a star-graph network of transmission lines, with one of the lines terminated by a model diode. The model simulates time reversal of linear and nonlinear signals, demonstrates features seen in the experimental system, and supports our interpretation of the experimental results.
The Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics
NASA Technical Reports Server (NTRS)
Zhu, Yanqiu; Cohn, Stephen E.; Todling, Ricardo
1999-01-01
The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.
Self-organization in nonlinear wave turbulence
Jordan, Richard; Josserand, Christophe
2000-02-01
We present a statistical equilibrium model of self-organization in a class of focusing, nonintegrable nonlinear Schroedinger (NLS) equations. The theory predicts that the asymptotic-time behavior of the NLS system is characterized by the formation and persistence of a large-scale coherent solitary wave, which minimizes the Hamiltonian given the conserved particle number (L{sup 2}-norm squared), coupled with small-scale random fluctuations, or radiation. The fluctuations account for the difference between the conserved value of the Hamiltonian and the Hamiltonian of the coherent state. The predictions of the statistical theory are tested against the results of direct numerical simulations of NLS, and excellent qualitative and quantitative agreement is demonstrated. In addition, a careful inspection of the numerical simulations reveals interesting features of the transitory dynamics leading up to the long-time statistical equilibrium state starting from a given initial condition. As time increases, the system investigates smaller and smaller scales, and it appears that at a given intermediate time after the coalescense of the soliton structures has ended, the system is nearly in statistical equilibrium over the modes that it has investigated up to that time. (c) 2000 The American Physical Society.
Nonlinear time reversal in a wave chaotic system.
Frazier, Matthew; Taddese, Biniyam; Antonsen, Thomas; Anlage, Steven M
2013-02-01
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems and is embodied in the time-reversal mirror. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We demonstrate that the time-reversed nonlinear excitations reconstruct exclusively upon the source of the nonlinearity. As an example of its utility, we demonstrate a new form of secure communication and point out other applications.
Lower hybrid wave propagation in tokamaks in weak and strong absorption regimes
NASA Astrophysics Data System (ADS)
Wright, J. C.; Bonoli, P. T.; Harvey, R. W.; Schmidt, A. E.; Wallace, G. W.; Valeo, E. J.; Phillips, C. K.
2011-12-01
Lower hybrid (LH) waves have the attractive property of damping strongly via electron Landau resonance on relatively fast tail electrons at (2.5-3)×vte, where vte = (2Te/me)1/2. The velocity at which damping occurs depends on the non-linear balance between quasilinear diffusion and collisions. For high efficiency current drive, a low parallel index of refraction, n∥, corresponding to a high phase velocity, is chosen. Depending on the plasma electron temperature this may put the wave propagation in a multi-pass regime. In cases of low parallel refractive index, ray tracing with no SOL has been shown to have differences with experiment [1] and collision effects in the scrape off layer may be important [2]. Using a coupled model of the full wave code, TORLH[3], and the Fokker-Planck code, CQL3D[4], the importance of full wave effects in weak and strong absorption regimes are studied.
Nonlinear waves in nonplanar and nonuniform dusty plasmas
Xue Jukui; Zhang Liping
2006-02-15
The nonlinear properties of the dust acoustic solitary wave and shock wave in inhomogeneous nonplanar dusty plasmas are considered theoretically and numerically. The effects of nonthermally distributed ions, nonadiabatic dust charge fluctuation, and the inhomogeneity caused by nonuniform equilibrium particle density, nonuniform equilibrium charging, and nonplanar geometry on waves are presented. When {tau}{sub ch}/{tau}{sub d} is small but finite, where {tau}{sub ch} is the charging time scale and {tau}{sub d} is the hydrodynamical time scale, a variable coefficients nonplanar Korteweg-de Vries (KdV) Burgers equation governing the nonlinear waves is derived by the perturbation method. The analytical expressions for the evolution of soliton and shock wave (both oscillatory and monotone shock) are obtained and the theoretical results are confirmed by the numerical solution of the nonlinear wave equation.
Effect of Forcing Function on Nonlinear Acoustic Standing Waves
NASA Technical Reports Server (NTRS)
Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce
2003-01-01
Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.
Signatures of Nonlinear Waves in Coronal Plumes and Holes
NASA Technical Reports Server (NTRS)
Ofman, Leon
1999-01-01
In recent Ultraviolet Coronagraph Spectrometer/Solar and Heliospheric Observatory (UVCS/SOHO) White Light Channel (WLC) observations we found quasi-periodic variations in the polarized brightness (pB) in the polar coronal holes at heliocentric distances of 1.9-2.45 solar radii. The motivation for the observation is the 2.5D Magnetohydrodynamics (MHD) model of solar wind acceleration by nonlinear waves, that predicts compressive fluctuations in coronal holes. To help identify the waves observed with the UVCS/WLC we model the propagation and dissipation of slow magnetosonic waves in polar plumes using 1D MHD code in spherical geometry, We find that the slow waves nonlinearly steepen in the gravitationally stratified plumes. The nonlinear steepening of the waves leads to enhanced dissipation due to compressive viscosity at the wave-fronts.
Nonlinear hyperbolic theory of thermal waves in metals
NASA Technical Reports Server (NTRS)
Wilhelm, H. E.; Choi, S. H.
1975-01-01
A closed-form solution for cylindrical thermal waves in metals is given based on the nonlinear hyperbolic system of energy-conservation and heat-flux relaxation equations. It is shown that heat released from a line source propagates radially outward with finite speed in the form of a thermal wave which exhibits a discontinuous wave front. Unique nonlinear thermal-wave solutions exist up to a critical amount of driving energy, i.e., for larger energy releases, the thermal flow becomes multivalued (occurrence of shock waves). By comparison, it is demonstrated that the parabolic thermal-wave theory gives, in general, a misleading picture of the profile and propagation of thermal waves and leads to physical (infinite speed of heat propagation) and mathematical (divergent energy integrals) difficulties. Attention is drawn to the importance of temporal heat-flux relaxation for the physical understanding of fast transient processes such as thermal waves and more general explosions and implosions.
Observation of ShockWaves in a Strongly Interacting Fermi Gas
Kulkarni, M.; Joseph, J.A.; Thomas, J.E.; Abanov, A.G.
2011-04-11
We study collisions between two strongly interacting atomic Fermi gas clouds. We observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as the clouds collide and subsequent evolution into a boxlike shape. We model the nonlinear dynamics of these collisions by using quasi-1D hydrodynamic equations. Our simulations of the time-dependent density profiles agree very well with the data and provide clear evidence of shock wave formation in this universal quantum hydrodynamic system.
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time. PMID:26986334
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.
Variational principle for nonlinear wave propagation in dissipative systems
NASA Astrophysics Data System (ADS)
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.
Nonlinear spin wave coupling in adjacent magnonic crystals
NASA Astrophysics Data System (ADS)
Sadovnikov, A. V.; Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E.; Nikitov, S. A.
2016-07-01
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
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.
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.
Kim, Kihong; Phung, D K; Rotermund, F; Lim, H
2008-01-21
We develop a generalized version of the invariant imbedding method, which allows us to solve the electromagnetic wave equations in arbitrarily inhomogeneous stratified media where both the dielectric permittivity and magnetic permeability depend on the strengths of the electric and magnetic fields, in a numerically accurate and efficient manner. We apply our method to a uniform nonlinear slab and find that in the presence of strong external radiation, an initially uniform medium of positive refractive index can spontaneously change into a highly inhomogeneous medium where regions of positive or negative refractive index as well as metallic regions appear. We also study the wave transmission properties of periodic nonlinear media and the influence of nonlinearity on the mode conversion phenomena in inhomogeneous plasmas. We argue that our theory is very useful in the study of the optical properties of a variety of nonlinear media including nonlinear negative index media fabricated using wires and split-ring resonators.
Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas
NASA Technical Reports Server (NTRS)
Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.
1997-01-01
We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.
Highly nonlinear Bragg quasisolitons in the dynamics of water waves.
Ruban, V P
2008-05-01
Finite-amplitude gravity water waves in Bragg resonance with a periodic one-dimensional topography are studied numerically using exact equations of motion for ideal potential free-surface flows. Spontaneous formation of highly nonlinear localized structures is observed in the numerical experiments. These coherent structures consisting of several nearly standing extreme waves are similar in many aspects to the Bragg solitons previously known in nonlinear optics. PMID:18643128
Ionizing gas breakdown waves in strong electric fields.
NASA Technical Reports Server (NTRS)
Klingbeil, R.; Tidman, D. A.; Fernsler, R. F.
1972-01-01
A previous analysis by Albright and Tidman (1972) of the structure of an ionizing potential wave driven through a dense gas by a strong electric field is extended to include atomic structure details of the background atoms and radiative effects, especially, photoionization. It is found that photoionization plays an important role in avalanche propagation. Velocities, electron densities, and temperatures are presented as a function of electric field for both negative and positive breakdown waves in nitrogen.
Three-dimensional strong Langmuir turbulence and wave collapse
NASA Technical Reports Server (NTRS)
Robinson, P. A.; Newman, D. L.; Goldman, M. V.
1988-01-01
Results from the first fully three-dimensional simulations of driven damped strong Langmuir turbulence and wave collapse are presented. Key results are that turbulence is maintained at least in part by nucleation, the cores of most collapsing objects are pancake shaped in form, and the power spectrum falls off approximately as the product of a power law and an exponential at large wave number.
Engineering Strong Interactions Between mm-wave and Optical Photons
NASA Astrophysics Data System (ADS)
Stone, Mark; Suleymanzade, Aziza; Estes, Jeremy; Eustice, Scott; Schuster, David; Simon, Jonathan
2016-05-01
We propose an atomic interface of Rydberg atoms as a means of engineering effective strong interactions between single mm-wave and optical photons. The atomic sample resides at the intersection of a high-finesse optical cavity and a superconducting mm-wave cavity, where it can coherently interact with photons of both regimes. The use of mm-wave (100 GHz) frequencies allows strong coupling at higher temperatures and with less sensitivity to stray electric fields. A hybrid cryogenic vacuum chamber at 4 Kelvin enables access to superconductivity as well as a UHV environment with optical access necessary for cold atom experiments. Strong interactions between these separate quantum degrees of freedom has important applications in quantum computing as well as simulation of many-body interacting systems.
Simulation of the nonlinear evolution of electron plasma waves
NASA Technical Reports Server (NTRS)
Nishikawa, K.-I.; Cairns, I. H.
1991-01-01
Electrostatic waves driven by an electron beam in an ambient magnetized plasma were studied using a quasi-1D PIC simulation of electron plasma waves (i.e., Langmuir waves). The results disclose the presence of a process for moving wave energy from frequencies and wavenumbers predicted by linear theory to the Langmuir-like frequencies during saturation of the instability. A decay process for producing backward propagating Langmuir-like waves, along with low-frequency waves, is observed. The simulation results, however, indicate that the backscattering process is not the conventional Langmuir wave decay. Electrostatic waves near multiples of the electron plasma frequency are generated by wave-wave coupling during the nonlinear stage of the simulations, confirming the suggestion of Klimas (1983).
Chromospheric alfvenic waves strong enough to power the solar wind.
De Pontieu, B; McIntosh, S W; Carlsson, M; Hansteen, V H; Tarbell, T D; Schrijver, C J; Title, A M; Shine, R A; Tsuneta, S; Katsukawa, Y; Ichimoto, K; Suematsu, Y; Shimizu, T; Nagata, S
2007-12-01
Alfvén waves have been invoked as a possible mechanism for the heating of the Sun's outer atmosphere, or corona, to millions of degrees and for the acceleration of the solar wind to hundreds of kilometers per second. However, Alfvén waves of sufficient strength have not been unambiguously observed in the solar atmosphere. We used images of high temporal and spatial resolution obtained with the Solar Optical Telescope onboard the Japanese Hinode satellite to reveal that the chromosphere, the region sandwiched between the solar surface and the corona, is permeated by Alfvén waves with strong amplitudes on the order of 10 to 25 kilometers per second and periods of 100 to 500 seconds. Estimates of the energy flux carried by these waves and comparisons with advanced radiative magnetohydrodynamic simulations indicate that such Alfvén waves are energetic enough to accelerate the solar wind and possibly to heat the quiet corona. PMID:18063784
Chromospheric alfvenic waves strong enough to power the solar wind.
De Pontieu, B; McIntosh, S W; Carlsson, M; Hansteen, V H; Tarbell, T D; Schrijver, C J; Title, A M; Shine, R A; Tsuneta, S; Katsukawa, Y; Ichimoto, K; Suematsu, Y; Shimizu, T; Nagata, S
2007-12-01
Alfvén waves have been invoked as a possible mechanism for the heating of the Sun's outer atmosphere, or corona, to millions of degrees and for the acceleration of the solar wind to hundreds of kilometers per second. However, Alfvén waves of sufficient strength have not been unambiguously observed in the solar atmosphere. We used images of high temporal and spatial resolution obtained with the Solar Optical Telescope onboard the Japanese Hinode satellite to reveal that the chromosphere, the region sandwiched between the solar surface and the corona, is permeated by Alfvén waves with strong amplitudes on the order of 10 to 25 kilometers per second and periods of 100 to 500 seconds. Estimates of the energy flux carried by these waves and comparisons with advanced radiative magnetohydrodynamic simulations indicate that such Alfvén waves are energetic enough to accelerate the solar wind and possibly to heat the quiet corona.
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.
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.
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.
Yu, X.; Hsu, T.-J.; Hanes, D.M.
2010-01-01
Sediment transport under nonlinear waves in a predominately sheet flow condition is investigated using a two-phase model. Specifically, we study the relative importance between the nonlinear waveshape and nonlinear boundary layer streaming on cross-shore sand transport. Terms in the governing equations because of the nonlinear boundary layer process are included in this one-dimensional vertical (1DV) model by simplifying the two-dimensional vertical (2DV) ensemble-averaged two-phase equations with the assumption that waves propagate without changing their form. The model is first driven by measured time series of near-bed flow velocity because of a wave group during the SISTEX99 large wave flume experiment and validated with the measured sand concentration in the sheet flow layer. Additional studies are then carried out by including and excluding the nonlinear boundary layer terms. It is found that for the grain diameter (0.24 mm) and high-velocity skewness wave condition considered here, nonlinear waveshape (e.g., skewness) is the dominant mechanism causing net onshore transport and nonlinear boundary layer streaming effect only causes an additional 36% onshore transport. However, for conditions of relatively low-wave skewness and a stronger offshore directed current, nonlinear boundary layer streaming plays a more critical role in determining the net transport. Numerical experiments further suggest that the nonlinear boundary layer streaming effect becomes increasingly important for finer grain. When the numerical model is driven by measured near-bed flow velocity in a more realistic surf zone setting, model results suggest nonlinear boundary layer processes may nearly double the onshore transport purely because of nonlinear waveshape. Copyright 2010 by the American Geophysical Union.
Advanced data assimilation in strongly nonlinear dynamical systems
NASA Technical Reports Server (NTRS)
Miller, Robert N.; Ghil, Michael; Gauthiez, Francois
1994-01-01
Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.
Optical surface wave in a crystal with diffusion photorefractive nonlinearity
Chetkin, S A; Akhmedzhanov, I M
2011-11-30
We consider a steady-state nonlinear photorefractive surface wave (PR SW) with TE or TM polarisation when the refractive index of the photorefractive crystal (PRC) depends on the strength of the diffusion crystal electric field emerging upon the wave propagation. We have determined the phase trajectory and transverse structure of the PR SW intensity distribution for different values of the diffusion photorefractive nonlinearity. We have investigated a photorefractive diffraction grating, which arises in the surface PRC layer during propagation of the nonlinear PR SW.
Nonlinear volume holography for wave-front engineering.
Hong, Xu-Hao; Yang, Bo; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan
2014-10-17
The concept of volume holography is applied to the design of an optical superlattice for the nonlinear harmonic generation. The generated harmonic wave can be considered as a holographic image caused by the incident fundamental wave. Compared with the conventional quasi-phase-matching method, this new method has significant advantages when applied to complicated nonlinear processes such as the nonlinear generation of special beams. As an example, we experimentally realized a second-harmonic Airy beam, and the results are found to agree well with numerical simulations.
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.
Strong motion from surface waves in deep sedimentary basins
Joyner, W.B.
2000-01-01
It is widely recognized that long-period surface waves generated by conversion of body waves at the boundaries of deep sedimentary basins make an important contribution to strong ground motion. The factors controlling the amplitude of such motion, however, are not widely understood. A study of pseudovelocity response spectra of strong-motion records from the Los Angeles Basin shows that late-arriving surface waves with group velocities of about 1 km/sec dominate the ground motion for periods of 3 sec and longer. The rate of amplitude decay for these waves is less than for the body waves and depends significantly on period, with smaller decay for longer periods. The amplitude can be modeled by the equation log y = f(M, RE) + c + bRB where y is the pseudovelocity response, f(M, RE) is an attenuation relation based on a general strong-motion data set, M is moment magnitude, RE is the distance from the source to the edge of the basin, RB is the distance from the edge of the basin to the recording site, and b and c are parameters fit to the data. The equation gives values larger by as much as a factor of 3 than given by the attenuation relationships based on general strong-motion data sets for the same source-site distance. It is clear that surface waves need to be taken into account in the design of long-period structures in deep sedimentary basins. The ground-motion levels specified by the earthquake provisions of current building codes, in California at least, accommodate the long-period ground motions from basin-edge-generated surface waves for periods of 5 sec and less and earthquakes with moment magnitudes of 7.5 or less located more than 20 km outside the basin. There may be problems at longer periods and for earthquakes located closer to the basin edge. The results of this study suggest that anelastic attenuation may need to be included in attempts to model long-period motion in deep sedimentary basins. To obtain better data on surface waves in the future
Stochastic acceleration of charged particle in nonlinear wave field
NASA Astrophysics Data System (ADS)
He, Kaifen
2003-04-01
Possibility of stochastic acceleration of charged particle by nonlinear waves is investigated. Spatially regular (SR) and spatiotemporal chaotic (STC) wave solutions evolving from saddle steady wave are tested as the fields. In the non-steady SR field the particle is finally trapped by the wave and averagely gains its group velocity, while in the STC field the particle motion displays trapped-free phases with its averaged velocity larger or smaller than the group velocity depending on the charge sign. A simplified model is established to investigate the acceleration mechanism. By analogy with motor protein, it is found that the virtual pattern of saddle steady wave plays a role of asymmetric potential, which and the nonlinear varying perturbation wave are the two sufficient ingredients for the acceleration in our case.
Time-reversed wave mixing in nonlinear optics.
Zheng, Yuanlin; Ren, Huaijin; Wan, Wenjie; Chen, Xianfeng
2013-11-19
Time-reversal symmetry is important to optics. Optical processes can run in a forward or backward direction through time when such symmetry is preserved. In linear optics, a time-reversed process of laser emission can enable total absorption of coherent light fields inside an optical cavity of loss by time-reversing the original gain medium. Nonlinearity, however, can often destroy such symmetry in nonlinear optics, making it difficult to study time-reversal symmetry with nonlinear optical wave mixings. Here we demonstrate time-reversed wave mixings for optical second harmonic generation (SHG) and optical parametric amplification (OPA) by exploring this well-known but underappreciated symmetry in nonlinear optics. This allows us to observe the annihilation of coherent beams. Our study offers new avenues for flexible control in nonlinear optics and has potential applications in efficient wavelength conversion, all-optical computing.
Nonlinear waves in PT -symmetric systems
NASA Astrophysics Data System (ADS)
Konotop, Vladimir V.; Yang, Jianke; Zezyulin, Dmitry A.
2016-07-01
Recent progress on nonlinear properties of parity-time (PT )-symmetric systems is comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying PT symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a PT -symmetric system. The natural inclusion of nonlinearity into these PT systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above PT -symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear PT -symmetric systems arising from various physical disciplines are presented, nonlinear properties of these systems are thoroughly elucidated, and relevant experimental results are described. In addition, emerging applications of PT symmetry are pointed out.
Nonlinear Self-Similar Beams of Electromagnetic Waves in Vacuum
NASA Astrophysics Data System (ADS)
Vlasov, S. N.
2015-12-01
We study nonlinear beams of electromagnetic waves in vacuum. Within the lowest approximation, their structure is determined by the cubic self-focusing nonlinearity, which manifests itself with the maximum intensity in the presence of counterpropagating waves. It is shown that the fields in the beams have no singularities if their power is less than the critical power of the self-focusing. The dependences of the eigenfrequencies of the modes of the quasioptical resonator on the beam power are found. The structure of the fields of these modes corresponds to self-similar wave beams.
Nonlinear ring waves in a two-layer fluid
NASA Astrophysics Data System (ADS)
Khusnutdinova, Karima R.; Zhang, Xizheng
2016-10-01
Surface and interfacial weakly-nonlinear ring waves in a two-layer fluid are modelled numerically, within the framework of the recently derived 2 + 1-dimensional cKdV-type equation. In a case study, we consider concentric waves from a localised initial condition and waves in a 2D version of the dam-break problem, as well as discussing the effect of a piecewise-constant shear flow. The modelling shows, in particular, the formation of 2D dispersive shock waves and oscillatory wave trains.
Relativistic nonlinear plasma waves in a magnetic field
NASA Technical Reports Server (NTRS)
Kennel, C. F.; Pellat, R.
1976-01-01
An investigation is conducted of five relativistic plane nonlinear waves, taking into account circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. It is found that a large-amplitude superluminous wave determines the average plasma properties, and not vice versa. Attention is given to the implications of the obtained results for the acceleration of cosmic rays in pulsar magnetospheres.
Relativistic nonlinear plasma waves in a magnetic field
NASA Technical Reports Server (NTRS)
Kennel, C. F.; Pellat, R.
1975-01-01
Five relativistic plane nonlinear waves were investigated: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. When the ions are driven relativistic, they behave like electrons, and the assumption of an 'electron-positron' plasma leads to equations which have the form of a one-dimensional potential well. The solutions indicate that a large-amplitude superluminous wave determines the average plasma properties.
Localized Nonlinear Waves in Systems with Time- and Space-Modulated Nonlinearities
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Konotop, Vladimir V.
2008-04-25
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schroedinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.
Exact and explicit solitary wave solutions to some nonlinear equations
Jiefang Zhang
1996-08-01
Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative {Phi}{sup 4}-model equation, the generalized Fisher equation, and the elastic-medium wave equation.
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.
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.
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.
Gravitational waves from a very strong electroweak phase transition
NASA Astrophysics Data System (ADS)
Leitao, Leonardo; Mégevand, Ariel
2016-05-01
We investigate the production of a stochastic background of gravitational waves in the electroweak phase transition. We consider extensions of the Standard Model which can give very strongly first-order phase transitions, such that the transition fronts either propagate as detonations or run away. To compute the bubble wall velocity, we estimate the friction with the plasma and take into account the hydrodynamics. We track the development of the phase transition up to the percolation time, and we calculate the gravitational wave spectrum generated by bubble collisions, magnetohydrodynamic turbulence, and sound waves. For the kinds of models we consider, we find parameter regions for which the gravitational waves are potentially observable at the planned space-based interferometer eLISA. In such cases, the signal from sound waves is generally dominant, while that from bubble collisions is the least significant of them. Since the sound waves and turbulence mechanisms are diminished for runaway walls, the models with the best prospects of detection at eLISA are those which do not have such solutions. In particular, we find that heavy extra bosons provide stronger gravitational wave signals than tree-level terms.
Modeling of Shock Wave Generated from a Strong Focused Ultrasound Transducer
NASA Astrophysics Data System (ADS)
Chen, Tao; Qiu, Yuan-Yuan; Fan, Ting-Bo; Zhang, Dong
2013-07-01
A combined time and frequency domain method is developed for the calculation of a shock wave induced by a strong focused ultrasound transducer in the oblate spheroidal coordinate system. The spheroidal beam equation (SBE) is utilized to describe the nonlinear sound propagation; the diffraction and attenuation effects are calculated in the frequency-domain, while the nonlinear effect is calculated in the time-domain. Compared with the traditional frequency-domain method, this method could calculate the shock wave effectively without oscillation at the shock front and with less computation time. When the harmonic number is 200, the computation time by this method is about 1/16 of that used by the traditional frequency-domain method.
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
Nonlinear Pressure Wave Analysis by Concentrated Mass Model
NASA Astrophysics Data System (ADS)
Ishikawa, Satoshi; Kondou, Takahiro; Matsuzaki, Kenichiro
A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effect of fluid. Analyzing this phenomenon by the finite difference method requires high computational cost. To lessen the computational cost, a concentrated mass model is proposed. This model consists of masses, connecting nonlinear springs, connecting dampers, and base support dampers. The characteristic of a connecting nonlinear spring is derived from the adiabatic change of fluid, and the equivalent mass and equivalent damping coefficient of the base support damper are derived from the equation of motion of fluid in a cylindrical tube. Pressure waves generated in a hydraulic oil tube, a sound tube and a plane-wave tube are analyzed numerically by the proposed model to confirm the validity of the model. All numerical computational results agree very well with the experimental results carried out by Okamura, Saenger and Kamakura. Especially, the numerical analysis reproduces the phenomena that a pressure wave with large amplitude propagating in a sound tube or in a plane tube changes to a shock wave. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem.
Wave-vortex interactions in the nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Guo, Yuan; Bühler, Oliver
2014-02-01
This is a theoretical study of wave-vortex interaction effects in the two-dimensional nonlinear Schrödinger equation, which is a useful conceptual model for the limiting dynamics of superfluid quantum condensates at zero temperature. The particular wave-vortex interaction effects are associated with the scattering and refraction of small-scale linear waves by the straining flows induced by quantized point vortices and, crucially, with the concomitant nonlinear back-reaction, the remote recoil, that these scattered waves exert on the vortices. Our detailed model is a narrow, slowly varying wavetrain of small-amplitude waves refracted by one or two vortices. Weak interactions are studied using a suitable perturbation method in which the nonlinear recoil force on the vortex then arises at second order in wave amplitude, and is computed in terms of a Magnus-type force expression for both finite and infinite wavetrains. In the case of an infinite wavetrain, an explicit asymptotic formula for the scattering angle is also derived and cross-checked against numerical ray tracing. Finally, under suitable conditions a wavetrain can be so strongly refracted that it collapses all the way onto a zero-size point vortex. This is a strong wave-vortex interaction by definition. The conditions for such a collapse are derived and the validity of ray tracing theory during the singular collapse is investigated.
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.
Nonlinear waves in second order conformal hydrodynamics
NASA Astrophysics Data System (ADS)
Fogaça, D. A.; Marrochio, H.; Navarra, F. S.; Noronha, J.
2015-02-01
In this work we study wave propagation in dissipative relativistic fluids described by a simplified set of the 2nd order viscous conformal hydrodynamic equations corresponding to Israel-Stewart theory. Small amplitude waves are studied within the linearization approximation while waves with large amplitude are investigated using the reductive perturbation method, which is generalized to the case of 2nd order relativistic hydrodynamics. Our results indicate the presence of a "soliton-like" wave solution in Israel-Stewart hydrodynamics despite the presence of dissipation and relaxation effects.
Nonlinear dynamics of trapped waves on jet currents and rogue waves.
Shrira, V I; Slunyaev, A V
2014-04-01
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrow band in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonlinear theory based on the modal approach of Shrira and Slunyaev [J. Fluid. Mech. 738, 65 (2014)] leads to the one-dimensional modified nonlinear Schrödinger equation of self-focusing type for a single mode. Its solutions such as envelope solitons and breathers are considered to be prototypes of rogue waves; these solutions, in contrast to waves in the absence of currents, are robust with respect to transverse perturbations, which suggests a potentially higher probability of rogue waves. Robustness of the long-lived analytical solutions describing modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations. PMID:24827178
Nonlinear dynamics of trapped waves on jet currents and rogue waves.
Shrira, V I; Slunyaev, A V
2014-04-01
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrow band in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonlinear theory based on the modal approach of Shrira and Slunyaev [J. Fluid. Mech. 738, 65 (2014)] leads to the one-dimensional modified nonlinear Schrödinger equation of self-focusing type for a single mode. Its solutions such as envelope solitons and breathers are considered to be prototypes of rogue waves; these solutions, in contrast to waves in the absence of currents, are robust with respect to transverse perturbations, which suggests a potentially higher probability of rogue waves. Robustness of the long-lived analytical solutions describing modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations.
Behavior of a Moist Kelvin Wave Packet with Nonlinear Heating.
NASA Astrophysics Data System (ADS)
Wang, Bin; Xue, Yan
1992-04-01
The effects of nonlinear (positive only or conditional) heating on moist Kelvin waves are examined with a simple equatorial zonal-plane model describing the gravest baroclinic mode.The unstable perturbation subject to nonlinear beating emerges as a wave packet. A typical amplifying, eastward-moving wave packet is characterized by an asymmetric structure: 1) the ascending branch (wet region) is much narrower than the two descending ones (dry regions); and 2) the circulation cell to the east of the wet region center is smaller and stronger than its counterpart to the west of the center. The wet-dry asymmetry is primarily caused by the nonlinear beating effect, while the east-west asymmetry is a result of the movement of the wave packet relative to mean flow. The existence of Newtonian cooling and Rayleigh friction enhances the structural asymmetries.The unstable wave packet is characterized by two zonal length scales: the ascending branch length (ABL) and total circulation extent (TCE). For a given basic state, the growth rate of a wave packet increases with decreasing ABL or TCE. However, up to a moderate growth rate (order of day1) the energy spectra of all wave packets are dominated by zonal wavenumber one regardless of ABL size. In particular, the slowly growing (low frequency) wave packets normally exhibit TCEs of planetary scale and ABLs of synoptic scale.Observed equatorial intraseasonal disturbances often display a narrow convection region in between two much broader dry regions and a total circulation of planetary scale. These structure and scale characteristics are caused by the effects of nonlinear heating and the cyclic geometry of the equator. It is argued that the unstable disturbance found in numerical experiments (e.g., Lau and Peng; Hayashi and Sumi) is a manifestation of the nonlinear wave packet.
The Role of Wave Nonlinearity on Sediment Motion and Transport
NASA Astrophysics Data System (ADS)
Foster, D. L.; Kaihatu, J. M.; Frank, D. P.
2014-12-01
It has long been assumed that higher moments of velocity and acceleration affect the motion and transport of mobile sediment beds. The goal of this effect is to identify the influence of wave shape on sediment motion and mobile layer thickness. Theoretic predictions of neared velocity and horizontal pressure gradient will be approximated with Dean's 1965 stream function theory for representing nonlinear waves. The formulation also allows for the inclusion of mean flow. Wave nonlinearity is characterized with skewness and asymmetry of the wave shape. An incipient motion criterion that resolves the fluid forcing due to both the bed shear stress and the horizontal pressure gradients is applied to a slab of sediment. The resulting formulation provides a measure of sediment transport vulnerability to commonly available wave parameters (wave height, wave period, water depth, skewness, and asymmetry). The formulation is compared with several available data sets with a range of forcing and sediment conditions. Particle image velocimetry observations of velocity and sediment motion and acoustic Doppler observations of the three-dimensional velocity field provide high resolution of the near bed dynamics. The wave shape is characterized with mid water column pressure sensors and wave gages. As the wave nonlinearities increase, the role of the horizontal pressure gradient also increases. The influence of the pressure gradient also is shown to be particularly sensitive to a decrease in the wave period and an increase in the wave asymmetry. The influence of the bed shear is shown to be particularly sensitive to wave skewness. The analysis demonstrates the potential for improving the larger scale predictions of sediment transport in our nearshore and coastal waters.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
Tataronis, J. A.
2004-06-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfvkn continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named “accumulation continuum” and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory.
A direct Vlasov simulation of nonlinear plasma waves
NASA Astrophysics Data System (ADS)
Hara, Kentaro; Boyd, Iain; Kaganovich, Igor
2013-10-01
A direct Vlasov simulation, which solves the collisionless Vlasov equation directly on a discretized phase space, achieves good resolution of velocity distribution functions in comparison to particle methods. In this presentation, nonlinear electron plasma waves (EPWs) and ion acoustic waves (IAWs) are investigated with a fully-kinetic one-dimensional Vlasov simulation. A parallelized Vlasov simulation is employed since grid resolution of the discretized phase space is required to be fine enough in order to capture the nonlinear waves with higher harmonic modes. The primary goal is benchmarking our simulation with results obtained from another Vlasov code and verification with the nonlinear theories [R. L. Berger et al., Phys. Plasmas 20, 032107 (2013)]. The frequency shift of nonlinear plasma waves is investigated by applying an initial density perturbation or an external driver potential. It has been observed that the plasma frequency decreases for EPWs and increases for IAWs for Te /Ti = 10 , which agrees with Berger's simulation and theories. A further investigation varying the generation of the nonlinear wave such as driver amplitude and duration time will be performed and discussed. Supported by the U.S. Department of Energy Office of Science, Fusion Energy Sciences Program, Grant # DE-SC0001939, and the Air Force Research Laboratory Grant # F9550-09-1-0695.
Self-similar rogue waves and nonlinear tunneling effects in inhomogeneous nonlinear fiber optics
NASA Astrophysics Data System (ADS)
Wang, Lei; Zhu, Yu-Jie; Jiang, Dong-Yang
2016-04-01
Analytical first- and second-order rogue wave solutions of the inhomogeneous modified nonlinear Schrödinger equation are presented by using similarity transformation. Then, by the proper choices of the inhomogeneous coefficients and free parameters, the controllable behaviors of the optical rogue waves are graphically discussed in the nonlinear fiber optics context. It is found that the width of the rogue wave can be tuned by adjusting the parameter ? and the locations of the rogue waves are linearly controlled by the parameter ?. The intensities of the rogue waves are influenced by the inhomogeneous linear gain/loss coefficient ? and parameter ?. The dispersion management function ? has effects on the periods and trajectories of the rogue waves and can induce maintenance (or annihilation) along ? direction. Interestingly, the composite rogue waves are revealed, the location of which is manipulated through changing the dispersion management function ?. Additionally, the nonlinear tunneling of those rogue waves is investigated as they propagate through a dispersion barrier (or well) and nonlinear barrier (or well).
Acoustic waves in gases with strong pressure gradients
NASA Technical Reports Server (NTRS)
Zorumski, William E.
1989-01-01
The effect of strong pressure gradients on the acoustic modes (standing waves) of a rectangular cavity is investigated analytically. When the cavity response is represented by a sum of modes, each mode is found to have two resonant frequencies. The lower frequency is near the Viaesaela-Brundt frequency, which characterizes the buoyant effect, and the higher frequency is above the ordinary acoustic resonance frequency. This finding shows that the propagation velocity of the acoustic waves is increased due to the pressure gradient effect.
Emergent geometries and nonlinear-wave dynamics in photon fluids.
Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D
2016-03-22
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.
Emergent geometries and nonlinear-wave dynamics in photon fluids
Marino, F.; Maitland, C.; Vocke, D.; Ortolan, A.; Faccio, D.
2016-01-01
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level. PMID:27001128
Emergent geometries and nonlinear-wave dynamics in photon fluids.
Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D
2016-01-01
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level. PMID:27001128
Self-sustained nonlinear waves in traffic flow
NASA Astrophysics Data System (ADS)
Flynn, M. R.; Kasimov, A. R.; Nave, J.-C.; Rosales, R. R.; Seibold, B.
2009-05-01
In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions to the hyperbolic (“inviscid”) continuum traffic equations. Generic existence criteria are examined in the context of the Lax entropy conditions. Our analysis naturally precludes traveling wave solutions for which the shocks travel downstream more rapidly than individual vehicles. Consistent with recent experimental observations from a periodic roadway [Y. Sugiyama , N. J. Phys. 10, 033001 (2008)], our numerical calculations show that nonlinear traveling waves are attracting solutions, with the time evolution of the system converging toward a wave-dominated configuration. Theoretical principles are elucidated by considering examples of traffic flow on open and closed roadways.
Langmuir wave harmonics due to driven nonlinear currents
NASA Astrophysics Data System (ADS)
Malaspina, David M.; Graham, Daniel B.; Ergun, Robert E.; Cairns, Iver H.
2013-11-01
The conversion of Langmuir waves into electromagnetic radiation near the local plasma frequency (fpe) and twice the local plasma frequency (2fpe) occurs in diverse heliospheric environments including along the path of type III radio bursts, at interplanetary shocks, and in planetary foreshocks. This radiation has the potential to act as a probe of remote plasma conditions, provided that the conversion mechanism is well understood. One candidate conversion mechanism is the antenna radiation of localized Langmuir waves. Antenna radiation near 2fpe requires the presence of nonlinear currents at 2fpe. In this work, properties of these currents are predicted from theory and compared with observations of Langmuir wave electric fields made using the WAVES instrument on the STEREO spacecraft. It is found that the observed frequency structure, polarization, and wave number ratio are consistent with nonlinear current predictions, once electric fields near 2fpeconsistent with sheath effects are taken into account.
Effect of strong coupling on dust acoustic waves and instabilities
Rosenberg, M.; Kalman, G.
1998-10-21
The presence of charged dust in a plasma can lead to very low frequency dust acoustic waves and instabilities. In certain laboratory plasmas the dust is strongly coupled, as characterized by the condition {gamma}{sub d}=Q{sub d}{sup 2} exp(-d/{lambda}{sub D})/dT{sub d}{>=}1, where Q{sub d} is the dust charge, d is the intergrain spacing, T{sub d} is the dust thermal energy, and {lambda}{sub D} is the plasma screening length. When the dust is strongly coupled, the spatial correlation of the grains can affect the dispersion relation of these waves. We review our recent work [1] on the dispersion properties of dust acoustic waves in the strongly coupled (liquid) phase in a dusty plasma, including also the effects of dust-neutral collisions. We then discuss a preliminary analysis of the effect of strong dust coupling on an ion dust two-stream instability in a collisional dusty plasma. Applications to laboratory dusty plasmas are discussed.
Effect of strong coupling on dust acoustic waves and instabilities
Rosenberg, M. Kalman, G.
1998-10-01
The presence of charged dust in a plasma can lead to very low frequency dust acoustic waves and instabilities. In certain laboratory plasmas the dust is strongly coupled, as characterized by the condition {Gamma}{sub d}=Q{sub d}{sup 2} exp({minus}d/{lambda}{sub D})/dT{sub d}{ge}1, where Q{sub d} is the dust charge, {ital d} is the intergrain spacing, T{sub d} is the dust thermal energy, and {lambda}{sub D} is the plasma screening length. When the dust is strongly coupled, the spatial correlation of the grains can affect the dispersion relation of these waves. We review our recent work [1] on the dispersion properties of dust acoustic waves in the strongly coupled (liquid) phase in a dusty plasma, including also the effects of dust-neutral collisions. We then discuss a preliminary analysis of the effect of strong dust coupling on an ion dust two-stream instability in a collisional dusty plasma. Applications to laboratory dusty plasmas are discussed. {copyright} {ital 1998 American Institute of Physics.}
Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water
NASA Astrophysics Data System (ADS)
Jiménez, N.; Romero-García, V.; Picó, R.; Garcia-Raffi, L. M.; Staliunas, K.
2015-11-01
We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10-4). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.
Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water
Jiménez, N.; Picó, R.; Romero-García, V.; Garcia-Raffi, L. M.
2015-11-16
We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10{sup −4}). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.
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.
Dynamical Nonlinear Interactions of Solids with Strong Terahertz Pulses
NASA Astrophysics Data System (ADS)
Hirori, Hideki; Tanaka, Koichiro
2016-08-01
Table-top high-power terahertz (THz) pulse sources based on the femtosecond lasers are able to reveal fascinating nonlinear transport phenomena in materials and coherently drive low-energy transitions into the nonperturbative nonlinear regime. This article summarizes recent studies on THz nonlinear interactions with solid materials as follows. The tilted-pump-intensity-front scheme uses a LiNbO3 crystal to generate high-field single-cycle THz pulses with a 1 MV/cm amplitude. Such a high amplitude pulse can cause impact ionization in GaAs that excites electrons from the valence band to the conduction band, leading to exciton luminescence. A narrow-bandwidth THz pulse can be generated by using a chirped-pulse-beating method; this scheme has been used to show that resonant intraexcitonic excitation in GaAs induces a large Autler-Townes splitting. Moreover, nonlinear dynamics of magnetism can be studied by using a metallic split ring resonator to enhance the THz magnetic field.
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.
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.
Nonparaxial elliptic waves and solitary waves in coupled nonlinear Helmholtz equations
NASA Astrophysics Data System (ADS)
Tamilselvan, K.; Kanna, T.; Khare, Avinash
2016-10-01
We obtain a class of elliptic wave solutions of coupled nonlinear Helmholtz (CNLH) equations describing nonparaxial ultra-broad beam propagation in nonlinear Kerr-like media, in terms of the Jacobi elliptic functions and also discuss their limiting forms (hyperbolic solutions). Especially, we show the existence of non-trivial solitary wave profiles in the CNLH system. The effect of nonparaxiality on speed, pulse width and amplitude of the nonlinear waves is analyzed in detail. Particularly, a mechanism for tuning the speed by altering the nonparaxial parameter is proposed. We also identify a novel phase-unlocking behavior due to the presence of nonparaxial parameter.
Nonlinear development of strong current-driven instabilities and selective acceleration of ^3He ions
NASA Astrophysics Data System (ADS)
Toida, Mieko; Okumura, Hayato
2003-10-01
In some solar flares, the abundance of high-energy ^3He ions is extremely increased. As a mechanism for these ^3He rich events, current-driven instabilities are believed to be important. Nonlinear development of the strong current-driven instabilities and associated energy transfer to ^3He ions are studied theoretically and numerically [1]. First, by means of a two-dimensional, electrostatic, particle simulation code, it is demonstrated that ^3He ions are selectively accelerated by fundamental H cyclotron waves with frequencies ω ≃ 2Ω_3He (Ω_3He is the cyclotron frequency of ^3He). Then, from the analysis of the dispersion relation of these waves, it is found that the ω ≃ 2 Ω_ 3He waves have the greatest growth rate, if Te > 10 T_H. Energies of the ^3He ions are also discussed. Theoretical expression for the maximum ^3He energy is presented, which is in good agreement with the simulation results. Based on this theory, it is shown that when the initial electron drift energy is of the order of 10 keV, many ^3He ions can be accelerated to energies of the order of MeV/n. [1] M. Toida and H. Okumura, J. Phys. Soc. Jpn. 72,1098 (2003)
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.
Effect of dilute strongly pinning impurities on charge density waves
NASA Astrophysics Data System (ADS)
Okamoto, Jun-ichi; Millis, Andrew J.
2015-05-01
We study theoretically the effects of strong pinning centers on a charge density wave in the limit that the charge density wave coherence length is shorter than the average interimpurity distance. An analysis based on a Ginzburg-Landau model shows that long-range forces arising from the elastic response of the charge density wave induce a kind of collective pinning which suppresses impurity-induced phase fluctuations, leading to a long-range ordered ground state. The correlations induced by impurities are characterized by a length scale parametrically longer than the average interimpurity distance. Long-wavelength fluctuations are found to be gapped, implying the stability of the ground state. We also present Monte Carlo simulations that confirm the basic features of the analytical results.
Nonlinear transient waves in coupled phase oscillators with inertia
NASA Astrophysics Data System (ADS)
Jörg, David J.
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
Nonlinear wave particle interaction in the Earth's foreshock
NASA Technical Reports Server (NTRS)
Mazelle, C.; LeQueau, D.; Meziane, K.; Lin, R. P.; Parks, G.; Reme, H.; Sanderson, T.; Lepping, R. P.
1997-01-01
The possibility that ion beams could provide a free energy source for driving an ion/ion instability responsible for the ULF wave occurrence is investigated. For this, the wave dispersion relation with the observed parameters is solved. Secondly, it is shown that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered around a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions with the observations are compared.
Nonlinear absorption of Alfven wave in dissipative plasma
Taiurskii, A. A. Gavrikov, M. B.
2015-10-28
We propose a method for studying absorption of Alfven wave propagation in a homogeneous non-isothermal plasma along a constant magnetic field, and relaxation of electron and ion temperatures in the A-wave. The absorption of a A-wave by the plasma arises due to dissipative effects - magnetic and hydrodynamic viscosities of electrons and ions and their elastic interaction. The method is based on the exact solution of two-fluid electromagnetic hydrodynamics of the plasma, which for A-wave, as shown in the work, are reduced to a nonlinear system of ordinary differential equations.
Nonlinear transient waves in coupled phase oscillators with inertia.
Jörg, David J
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
Nonlinear acoustic wave equations with fractional loss operators.
Prieur, Fabrice; Holm, Sverre
2011-09-01
Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations.
Kinetic equation for nonlinear resonant wave-particle interaction
NASA Astrophysics Data System (ADS)
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
Nonlinear waves propagating in the electrical transmission line
NASA Astrophysics Data System (ADS)
Duan, W.-S.
2004-04-01
A coupled Zakharov-Kuznetsov (ZK) equation is derived for a nonlinear transmission line in which the nonlinear capacitance C is of a general form C = C0(1 + k1V + k2V2 + ...). For a solitary-wave solution of the ZK equation, there is an instability region which is given numerically in this paper. It is in agreement with the analytical results for special cases.
FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations
NASA Astrophysics Data System (ADS)
Ibragimov, N. H.; Torrisi, M.; Tracinà, R.
2010-11-01
In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
NASA Astrophysics Data System (ADS)
Alka, W.; Goyal, Amit; Nagaraja Kumar, C.
2011-01-01
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Parametric instability of a relativistically strong electromagnetic wave.
NASA Technical Reports Server (NTRS)
Max, C. E.
1973-01-01
The stability of a circularly polarized electromagnetic wave that is strong enough to make plasma electrons, but not ions, relativistic is studied. Small perturbations are considered which propagate parallel to the large-amplitude driver. A relativistically strong wave can be unstable on time scales as short as twice its own oscillation period, and decays into a forward-going plasma oscillation and either one or two electromagnetic waves. Ion motion introduces an additional instability which can be important at short perturbation wavelengths, where the driver would otherwise be stable. The unstable ion and electron modes both have potential for producing anomalously large acceleration of relativistic particles, as well as significant amounts of backscattered light. These effects may be important in two applications: (1) the use of intense lasers to heat or compress plasma, and (2) the plasma surrounding a pulsar, if the pulsar is losing energy by radiation of electromagnetic waves at its rotation frequency. Instability persists in the nonrelativistic regime, reducing to stimulated Raman scattering as a special case.
NASA Astrophysics Data System (ADS)
Galiev, Sh. U.
2003-08-01
A non-linear theory of transresonant wave phenomena based on consideration of perturbed wave equations is presented. In particular, the waves in a surface layer of a porous compressible viscoelastoplastic material are considered. For such layers the 3-D equations of deformable media are reduced to 1-D or 2-D perturbed wave equations. A set of approximate, closed-form, general solutions of these equations are presented, which take into account non-linear, dissipative, dispersive, topographic and boundary effects. Then resonant, site and liquefaction effects are analysed. Resonance is considered as a global parameter. Transresonant evolution of the equations is studied. Within the resonant band, utt~a20∇2u and the perturbed wave equations transform into non-linear diffusion equations, either to a basic highly non-linear ordinary differential equation or to the basic algebraic equation for travelling waves. Resonances can destroy predictability and wave reversibility. Surface topography (valleys, islands, etc.) is considered as a series of earthquake-induced resonators. A non-linear transresonant evolution of smooth seismic waves into shock-, jet- and mushroom-like waves and vortices is studied. The amplitude of the resonant waves may be of the order of the square or cube root of the exciting amplitude. Therefore, seismic waves with a moderate amplitude can be amplified very strongly in natural resonators, whereas strong seismic waves can be attenuated. Reports of the 1835 February 20 Chilean earthquake given by Charles Darwin are qualitatively examined using the non-linear theory. The theory qualitatively describes the `shivering' of islands and ridges, volcano spouts and generation of tsunami-like waves and supports Darwin's opinion that these events were part of a single phenomenon. Same-day earthquake/eruption events and catastrophic amplification of seismic waves near the edge of sediment layers are discussed. At the same time the theory can account for recent
Effect of nonlinear wave collapse on line shapes in a plasma
NASA Astrophysics Data System (ADS)
Hannachi, I.; Stamm, R.; Rosato, J.; Marandet, Y.
2016-04-01
The nonlinear interaction of waves can change the structural and radiative properties of plasmas. We describe the main features of a fully ionized unmagnetized plasma affected by strong Langmuir turbulence characterized by nonlinear wave collapse, and propose a simple model for evaluating the changes expected on a hydrogen line shape affected by such conditions. Our model is based on a stochastic renewal model using an exponential waiting time distribution and a half-normal probability density function for the electric-field magnitude of the turbulent wave packet. The first results obtained with a simulation calculation of the hydrogen \\text{L}α line show that strong Langmuir turbulence can provide an additional broadening to a Stark profile.
Shear waves in an inhomogeneous strongly coupled dusty plasma
Janaki, M. S.; Banerjee, D.; Chakrabarti, N.
2011-09-15
The properties of electrostatic transverse shear waves propagating in a strongly coupled dusty plasma with an equilibrium density gradient are examined using the generalized hydrodynamic (GH) equation. In the usual kinetic limit, the resulting equation has similarity to zero energy Schrodinger's equation. This has helped in obtaining some exact eigenmode solutions in both Cartesian and cylindrical geometries for certain nontrivial density profiles. The corresponding velocity profiles and the discrete eigenfrequencies are obtained for several interesting situations and their physics discussed.
NASA Astrophysics Data System (ADS)
Wang, Yunliang; Guo, Xiaoyan; Lu, Yanzhen; Wang, Xiaodan
2016-01-01
The combined effects of nonadiabatic dust charge fluctuation and strongly coupled dust particles on the nonlinear propagation of dust acoustic (DA) waves in dusty plasma consisting of nonthermal electrons and trapped ions with vortex-like distribution are presented here. We use generalized viscoelastic hydrodynamic model for dust particles. In the weak nonlinearity limit, a modified Korteweg-de Vries (KdV) equation with a damping term and a KdV-Burger equation have been derived in the kinetic regime and hydrodynamic regime, respectively. The approximate analytical solitary solution of modified KdV equation is derived in the weak nonadiabatic dust charge variation limit, which shows that the amplitude of DA solitary waves decreases with time. The presence of viscosity due to strong coupling stands for the formation of DA shock waves in the hydrodynamic regime. The results show that the DA shock waves will be oscillating one for weak viscosity and will become monotonic ones for large viscosity.
Sasanpour, Pezhman; Shahmansouri, Afsaneh; Rashidian, Bizhan
2010-11-01
Third order nonlinear effects and its enhancement in gold nanostructures has been numerically studied. Analysis method is based on computationally solving nonlinear Maxwell's equations, considering dispersion behavior of permittivity described by Drude model and third order nonlinear susceptibility. Simulation is done by method of nonlinear finite difference time domain method, in which nonlinear equations of electric field are solved by Newton-Raphshon method. As the main outcomes of third order nonlinear susceptibility, four wave mixing and third harmonic generation terms are produced around gold nanostructures. Results of analysis on different geometries and structures show that third order nonlinearity products are more enhanced in places where electric field enhancement is occurred due to surface plasmons. Results indicates that enhancement of nonlinearities is strongly occurred in structures whose interface is dielectric. According to analysis results, nonlinear effects are highly concentrated in the vicinity of nanostructures. Hence this approach can be used in applications where localized ultraviolet light is required.
Strong nonlinear photonic responses from microbiologically synthesized tellurium nanocomposites
Liao, K.-S.; Wang, Jingyuan; Dias, S.; Dewald, J.; Alley, N.J.; Baesman, S.M.; Oremland, R.S.; Blau, W.J.; Curran, S.A.
2010-01-01
A new class of nanomaterials, namely microbiologically-formed nanorods composed of elemental tellurium [Te(0)] that forms unusual nanocomposites when combined with poly(m-phenylenevinylene-co-2,5-dioctoxy-phenylenevinylene) (PmPV) is described. These bio-nanocomposites exhibit excellent broadband optical limiting at 532 and 1064 nm. Nonlinear scattering, originating from the laser induced solvent bubbles and microplasmas, is responsible for this nonlinear behavior. The use of bacterially-formed Te(0) when combined with an organic chemical host (e.g., PmPV) is a new green method of nanoparticle syntheses. This opens the possibilities of using unique, biologically synthesized materials to advance future nanoelectronic and nanophotonic applications. ?? 2009 Elsevier B.V. All rights reserved.
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.
Light steering in a strongly nonlocal nonlinear medium
Ouyang Shigen; Hu Wei; Guo Qi
2007-11-15
With a strongly nonlocal model, we present an analytical solution of the coherent interaction of two Gaussian beams with an arbitrary phase difference and arbitrary incident angles. Numerical simulations show that the analytical solution can describe the interaction of two Gaussian beams very well in the strongly nonlocal case. It is theoretically shown that one can steer lights in strongly nonlocal media by tuning the incident conditions of coherently interacting beams like the phase difference between beams and their relative amplitude.
Nonlinear fast sausage waves in homogeneous magnetic flux tubes
NASA Astrophysics Data System (ADS)
Mikhalyaev, Badma B.; Ruderman, Michael S.
2015-12-01
> We consider fast sausage waves in straight homogeneous magnetic tubes. The plasma motion is described by the ideal magnetohydrodynamic equations in the cold plasma approximation. We derive the nonlinear Schrödinger equation describing the nonlinear evolution of an envelope of a carrier wave. The coefficients of this equation are expressed in terms Bessel and modified Bessel functions. They are calculated numerically for various values of parameters. In particular, we show that the criterion for the onset of the modulational or Benjamin-Fair instability is satisfied. The implication of the obtained results for solar physics is discussed.
Selection rules for the nonlinear interaction of internal gravity waves.
Jiang, Chung-Hsiang; Marcus, Philip S
2009-03-27
Two intersecting beams of internal gravity waves will generically create two wave packets by nonlinear interaction. The frequency of one packet will be the sum and that of the other packet will be the difference of the frequencies of the intersecting beams. In principle, each packet should form an "X" pattern, or "St. Andrew's cross" consisting of four beams outgoing from the point of intersection. Here we derive selection rules and show that most of the expected nonlinear beams are forbidden. These rules can also be applied to the reflection of a beam from a boundary.
Oblique propagation of nonlinear electrostatic waves in dense astrophysical magnetoplasmas
Masood, W.; Siddiq, M.; Rizvi, H.
2011-10-15
Nonlinear quantum ion-acoustic waves in dense dissipative as well as non-dissipative magnetized plasmas are investigated employing the quantum hydrodynamic model. In this regard, Zakharov Kuznetsov Burgers equation is derived in quantum plasmas, for the first time, using the small amplitude perturbation expansion method. The unique features of nonlinear electrostatic structures in pure electron-ion quantum magnetoplasma are highlighted and the parametric domain of the applicability of the model is unequivocally expressed. The present study may be useful to understand the nonlinear propagation characteristics of electrostatic shock and solitary structures in dense astrophysical systems where the quantum effects are expected to dominate.
Oblique propagation of nonlinear electrostatic waves in dense astrophysical magnetoplasmas
NASA Astrophysics Data System (ADS)
Masood, W.; Rizvi, H.; Siddiq, M.
2011-10-01
Nonlinear quantum ion-acoustic waves in dense dissipative as well as non-dissipative magnetized plasmas are investigated employing the quantum hydrodynamic model. In this regard, Zakharov Kuznetsov Burgers equation is derived in quantum plasmas, for the first time, using the small amplitude perturbation expansion method. The unique features of nonlinear electrostatic structures in pure electron-ion quantum magnetoplasma are highlighted and the parametric domain of the applicability of the model is unequivocally expressed. The present study may be useful to understand the nonlinear propagation characteristics of electrostatic shock and solitary structures in dense astrophysical systems where the quantum effects are expected to dominate.
Nonlinear evolution of Alfven waves in a finite beta plasma
Som, B.K. ); Dasgupta, B.; Patel, V.L. ); Gupta, M.R. )
1989-12-01
A general form of the derivative nonlinear Schroedinger (DNLS) equation, describing the nonlinear evolution of Alfven waves propagating parallel to the magnetic field, is derived by using two-fluid equations with electron and ion pressure tensors obtained from Braginskii (in {ital Reviews} {ital of} {ital Plasma Physics} (Consultants Bureau, New York, 1965), Vol. 1, p. 218). This equation is a mixed version of the nonlinear Schroedinger (NLS) equation and the DNLS, as it contains an additional cubic nonlinear term that is of the same order as the derivative of the nonlinear terms, a term containing the product of a quadratic term, and a first-order derivative. It incorporates the effects of finite beta, which is an important characteristic of space and laboratory plasmas.
Nonlinear waves in a fluid-filled thin viscoelastic tube
NASA Astrophysics Data System (ADS)
Zhang, Shan-Yuan; Zhang, Tao
2010-11-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incompressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin—Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the propagation of nonlinear pressure wave in the solid—liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the exponent α of the perturbation parameter in Gardner—Morikawa transformation according to the order of viscous coefficient η, three kinds of evolution equations with soliton solution, i.e. Korteweg—de Vries (KdV)—Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
Time-reversal of nonlinear waves: Applicability and limitations
NASA Astrophysics Data System (ADS)
Ducrozet, G.; Fink, M.; Chabchoub, A.
2016-09-01
Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.
Reverberation clutter induced by nonlinear internal waves in shallow water.
Henyey, Frank S; Tang, Dajun
2013-10-01
Clutter is related to false alarms for active sonar. It is demonstrated that, in shallow water, target-like clutter in reverberation signals can be caused by nonlinear internal waves. A nonlinear internal wave is modeled using measured stratification on the New Jersey shelf. Reverberation in the presence of the internal wave is modeled numerically. Calculations show that acoustic energy propagating near a sound speed minimum is deflected as a high intensity, higher angle beam into the bottom, where it is backscattered along the reciprocal path. The interaction of sound with the internal wave is isolated in space, hence resulting in a target-like clutter, which is found to be greater than 10 dB above the mean reverberation level. PMID:24116532
Nonlinear particle simulation of ion cyclotron waves in toroidal geometry
Kuley, A. Lin, Z.; Bao, J.; Wei, X. S.; Xiao, Y.
2015-12-10
Global particle simulation model has been developed in this work to provide a first-principles tool for studying the nonlinear interactions of radio frequency (RF) waves with plasmas in tokamak. In this model, ions are considered as fully kinetic particles using the Vlasov equation and electrons are treated as guiding centers using the drift kinetic equation with realistic electron-to-ion mass ratio. Boris push scheme for the ion motion has been developed in the toroidal geometry using magnetic coordinates and successfully verified for the ion cyclotron and ion Bernstein waves in global gyrokinetic toroidal code (GTC). The nonlinear simulation capability is applied to study the parametric decay instability of a pump wave into an ion Bernstein wave side band and a low frequency ion cyclotron quasi mode.
Effect of nonlinear instability on gravity-wave momentum transport
NASA Technical Reports Server (NTRS)
Dunkerton, Timothy J.
1987-01-01
This paper investigates the nonlinear instability of internal gravity waves and the effects of their nonlinear interaction on momentum flux, using simple theoretical and numerical models. From the result of an analysis of parametric instability of a two-dimensional internal gravity wave as discussed by Yeh and Liu (1981) and Klostermeyer (1982), a group trajectory length scale for a gravity wave packet was determined, expressed in terms of the dominant vertical wavelenght and the degree of convective saturation. It is shown that this analysis justifies the Eikonal saturation method for relatively transient packets, that are well below the saturation amplitude, propagating in a slowly varying mean flow. Conversely, linear theory fails for persistent disturbances and trasient wave packets near convective saturation.
On the nature of kinetic electrostatic electron nonlinear (KEEN) waves
Dodin, I. Y.; Fisch, N. J.
2014-03-15
An analytical theory is proposed for the kinetic electrostatic electron nonlinear (KEEN) waves originally found in simulations by Afeyan et al. [arXiv:1210.8105]. We suggest that KEEN waves represent saturated states of the negative mass instability (NMI) reported recently by Dodin et al. [Phys. Rev. Lett. 110, 215006 (2013)]. Due to the NMI, trapped electrons form macroparticles that produce field oscillations at harmonics of the bounce frequency. At large enough amplitudes, these harmonics can phase-lock to the main wave and form stable nonlinear dissipationless structures that are nonstationary but otherwise similar to Bernstein-Greene-Kruskal modes. The theory explains why the formation of KEEN modes is sensitive to the excitation scenario and yields estimates that agree with the numerical results of Afeyan et al. A new type of KEEN wave may be possible at even larger amplitudes of the driving field than those used in simulations so far.
Doppler effect of nonlinear waves and superspirals in oscillatory media.
Brusch, Lutz; Torcini, Alessandro; Bär, Markus
2003-09-01
Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example in which waves originate from a source exhibiting a back-and-forth movement in a radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves ("superspiral"). Using direct simulations as well as numerical nonlinear analysis within the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonic growth or decay as well as saturation of these modulations depending on the perturbation frequency. Our findings elucidate recent experimental observations concerning superspirals and their decay to spatiotemporal chaos.
Reverberation clutter induced by nonlinear internal waves in shallow water.
Henyey, Frank S; Tang, Dajun
2013-10-01
Clutter is related to false alarms for active sonar. It is demonstrated that, in shallow water, target-like clutter in reverberation signals can be caused by nonlinear internal waves. A nonlinear internal wave is modeled using measured stratification on the New Jersey shelf. Reverberation in the presence of the internal wave is modeled numerically. Calculations show that acoustic energy propagating near a sound speed minimum is deflected as a high intensity, higher angle beam into the bottom, where it is backscattered along the reciprocal path. The interaction of sound with the internal wave is isolated in space, hence resulting in a target-like clutter, which is found to be greater than 10 dB above the mean reverberation level.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
ERIC Educational Resources Information Center
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Nonlinear reflection of internal gravity wave onto a slope
NASA Astrophysics Data System (ADS)
Raja, Keshav; Sommeria, Joel; Staquet, Chantal; Leclair, Matthieu; Grisouard, Nicolas; Gostiaux, Louis
2016-04-01
The interaction of internal waves on sloping topography is one of the processes that cause mixing and transport in oceans. The mixing caused by internal waves is considered to be an important source of energy that is needed to bring back deep, dense water from the abyss to the surface of the ocean, across constant density surfaces. Apart from the vertical transport of heat (downwards) and mass (upwards), internal waves are also observed to irreversibly induce a mean horizontal flow. Mixing and wave induced mean flow may be considered as the processes that transfer wave induced energy to smaller and larger scales respectively. The process of mixing has been a subject of intense research lately. However, the process of wave induced mean flow and their dynamic impact await thorough study. The present study involves this wave induced mean flow, its generation and energetics. The nonlinear subcritical reflection of internal waves from a sloping boundary is studied using laboratory experiments carried out on the Coriolis Platform at Grenoble and, 2D and 3D numerical simulations done using a non-hydrostatic code. In the experiment, a plane wave is produced using a wave generator and is made to reflect normally on a sloping bottom in a uniformly stratified fluid. We consider both rotating and non-rotating cases. The numerical simulation mimicks the laboratory setup with an initial condition of an analytical plane wave solution in a vertical plane limited by a smooth envelope to simulate the finite wave generator. The interaction of the incident and reflected waves produce, apart from higher harmonics, an irreversible wave induced mean flow which grows in time and is localised in the interacting region. The finite extent of the wave generator allows the mean flow to recirculate in the horizontal plane, resulting in a dipolar potential vorticity field. Moreover, the generation of mean flow and higher harmonics, along with dissipative effects, diminishes the amplitude of
Optical vortex interaction and generation via nonlinear wave mixing
Lenzini, F.; Residori, S.; Bortolozzo, U.; Arecchi, F. T.
2011-12-15
Optical vortex beams are made to interact via degenerate two-wave mixing in a Kerr-like nonlinear medium. Vortex mixing is shown to occur inside the medium, leading to exchange of topological charge and cascaded generation of vortex beams. A mean-field model is developed and is shown to account for the selection rules of the topological charges observed after the wave-mixing process. Fractional charges are demonstrated to follow the same rules as for integer charges.
Nonlinear Guided Wave Mixing for Localized Material State Characterization
NASA Astrophysics Data System (ADS)
Lissenden, Cliff J.; Liu, Yang; Chillara, Vamshi K.; Choi, Gloria; Cho, Hwanjeong
Material state characterization methods sensitive to incipient damage provide new opportunities for managing the life cycle of structures. Finite element simulations of ultrasonic guided waves show the potential of nonlinear wave mixing to detect localized degradation invisible to both linear elastic stress-strain response and the eye. Correlation of material degradation to the generation of higher harmonics or combinational harmonics makes estimation of remaining life possible from material state data early in the service life.
Coda wave interferometry for estimating nonlinear behavior in seismic velocity.
Snieder, Roel; Grêt, Alexandre; Douma, Huub; Scales, John
2002-03-22
In coda wave interferometry, one records multiply scattered waves at a limited number of receivers to infer changes in the medium over time. With this technique, we have determined the nonlinear dependence of the seismic velocity in granite on temperature and the associated acoustic emissions. This technique can be used in warning mode, to detect the presence of temporal changes in the medium, or in diagnostic mode, where the temporal change in the medium is quantified.
Warm wavebreaking of nonlinear plasma waves with arbitrary phasevelocities
Schroeder, C.B.; Esarey, E.; Shadwick, B.A.
2004-11-12
A warm, relativistic fluid theory of a nonequilibrium, collisionless plasma is developed to analyze nonlinear plasma waves excited by intense drive beams. The maximum amplitude and wavelength are calculated for nonrelativistic plasma temperatures and arbitrary plasma wave phase velocities. The maximum amplitude is shown to increase in the presence of a laser field. These results set a limit to the achievable gradient in plasma-based accelerators.
On the pressure field of nonlinear standing water waves
NASA Technical Reports Server (NTRS)
Schwartz, L. W.
1980-01-01
The pressure field produced by two dimensional nonlinear time and space periodic standing waves was calculated as a series expansion in the wave height. The high order series was summed by the use of Pade approximants. Calculations included the pressure variation at great depth, which was considered to be a likely cause of microseismic activity, and the pressure distribution on a vertical barrier or breakwater.
Self-Assembled Organic Nanocrystals with Strong Nonlinear Optical Response.
Rosenne, Shaked; Grinvald, Eran; Shirman, Elijah; Neeman, Lior; Dutta, Sounak; Bar-Elli, Omri; Ben-Zvi, Regev; Oksenberg, Eitan; Milko, Petr; Kalchenko, Vyacheslav; Weissman, Haim; Oron, Dan; Rybtchinski, Boris
2015-11-11
Facile molecular self-assembly affords a new family of organic nanocrystals that, unintuitively, exhibit a significant nonlinear optical response (second harmonic generation, SHG) despite the relatively small molecular dipole moment of the constituent molecules. The nanocrystals are self-assembled in aqueous media from simple monosubstituted perylenediimide (PDI) molecular building blocks. Control over the crystal dimensions can be achieved via modification of the assembly conditions. The combination of a simple fabrication process with the ability to generate soluble SHG nanocrystals with tunable sizes may open new avenues in the area of organic SHG materials.
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.
Gusev, Vitalyi
2002-01-01
A particular form of the energy potential (cubic in strains) is proposed, which leads to the bow-tie behavior of the nonlinear modulus in an isotropic material with hysteresis of quadratic nonlinearity. The nonlinear scattering of a weak probe wave in the field of a strong pump wave is analyzed. It is demonstrated that collinear interactions of the shear waves are allowed in materials with nonlinearity hysteresis. Both in collinear and non-collinear frequency-mixing processes the combination frequency is composed of the probe wave frequency and one of the even harmonics of the pump wave. In general, the developed theory predicts that in the presence of the hysteretic nonlinearity the number of possible resonant scattering processes increases. In particular, if frequency-mixing processes are forbidden in the material with the elastic quadratic nonlinearity (for a fixed ratio of primary frequencies), they may be allowed in the materials with hysteretic quadratic nonlinearity. Moreover, in materials with hysteresis of the nonlinearity the resonant frequency mixing for a fixed ratio of primary frequencies may be allowed for multiple mutual orientations of the primary wave vectors. PMID:11831826
NASA Astrophysics Data System (ADS)
Ema, S. A.; Hossen, M. R.; Mamun, A. A.
2016-04-01
The nonlinear propagation of ion-acoustic (IA) waves in a strongly coupled plasma system containing Maxwellian electrons and nonthermal ions has been theoretically and numerically investigated. The well-known reductive perturbation technique is used to derive both the Burgers and Korteweg-de Vries (KdV) equations. Their shock and solitary wave solutions have also been numerically analyzed in understanding localized electrostatic disturbances. It has been observed that the basic features (viz. polarity, amplitude, width, etc.) of IA waves are significantly modified by the effect of polarization force and other plasma parameters (e.g., the electron-to-ion number density ratio and ion-to-electron temperature ratio). This is a unique finding among all theoretical investigations made before, whose probable implications are discussed in this investigation. The implications of the results obtained from this investigation may be useful in understanding the wave propagation in both space and laboratory plasmas.
NASA Astrophysics Data System (ADS)
Hasan, Md Arif
In this dissertation, we aim to analyze the strongly nonlinear dynamics of coupled ordered granular media and investigate interesting response regimes such as, passive wave redirection / redistribution and targeted energy transfer (TET). These studies are performed using numerical computations, analytical calculations, and experimental tests. In particular, we consider weakly coupled granular chains with or without on-site potentials, as well as two-dimensional granular networks with regularly placed intruders that act as effective coupling elements. Unlike previous studies of weakly coupled oscillatory chains, the dynamical systems considered herein incorporate both non-smooth effects due to possible separations between interacting neighboring beads (granules), as well as strongly nonlinear inter-particle Hertzian interactions. We show that these systems exhibit very rich and complex dynamics that, however, can be completely captured by our analytical approximations. For the case of weakly interacting granular networks, three independent mechanisms of efficient transport of energy from one chain to another are found. The first mechanism is a simple exchange of energy between the weakly interacting granular chains providing equi-partition of Nesterenko solitary waves through the chains. The second mechanism is a complete and recurrent exchange of energy (beating phenomenon) between the propagating breathers through the weakly coupled granular chains laying on a strong elastic foundation. The last mechanism is the most intriguing one and demonstrates targeted (irreversible) energy transfer between coupled granular chains due to appropriate stratification of their elastic foundations, in a macroscopic analogue of the well-known Landau-Zener Quantum effect in space. The aforementioned mechanisms of energy transfer and redirection in highly nonlinear granular chains are conceptually new and were presented for the first time. Analytical and computational studies of
Nonlinear interaction of dispersive Alfven waves and magnetosonic waves in space plasma
Sharma, R. P.; Kumar, Sanjay; Singh, H. D.
2009-03-15
This paper presents the model equations governing the nonlinear interaction between dispersive Alfven wave (DAW) and magnetosonic wave in the low-{beta} plasmas ({beta}<
Stochastic electron acceleration during turbulent reconnection in strong shock waves
NASA Astrophysics Data System (ADS)
Matsumoto, Yosuke
2016-04-01
Acceleration of charged particles is a fundamental topic in astrophysical, space and laboratory plasmas. Very high energy particles are commonly found in the astrophysical and planetary shocks, and in the energy releases of solar flares and terrestrial substorms. Evidence for relativistic particle production during such phenomena has attracted much attention concerning collisionless shock waves and magnetic reconnection, respectively, as ultimate plasma energization mechanisms. While the energy conversion proceeds macroscopically, and therefore the energy mostly flows to ions, plasma kinetic instabilities excited in a localized region have been considered to be the main electron heating and acceleration mechanisms. We present that efficient electron energization can occur in a much larger area during turbulent magnetic reconnection from the intrinsic nature of a strong collisionless shock wave. Supercomputer simulations have revealed a multiscale shock structure comprising current sheets created via an ion-scale Weibel instability and resulting energy dissipation through magnetic reconnection. A part of the upstream electrons undergoes first-order Fermi acceleration by colliding with reconnection jets and magnetic islands, giving rise to a nonthermal relativistic population downstream. The dynamics has shed new light on magnetic reconnection as an agent of energy dissipation and particle acceleration in strong shock waves.
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
Interaction of relativistically strong electromagnetic waves with a layer of overdense plasma
Korzhimanov, A. V.; Eremin, V. I. Kim, A. V.; Tushentsov, M. R.
2007-10-15
Plasma-field structures that arise under the interaction between a relativistically strong electromagnetic wave and a layer of overdense plasma are considered within a quasistationary approximation. It is shown that, together with known solutions, which are nonlinear generalizations of skin-layer solutions, multilayer structures containing cavitation regions with completely removed electrons (ion layers) can be excited when the amplitude of the incident field exceeds a certain threshold value. Under symmetric irradiation, these cavitation regions, which play the role of self-consistent resonators, may amplify the field and accumulate electromagnetic energy.
Corrigendum and addendum. Modeling weakly nonlinear acoustic wave propagation
Christov, Ivan; Christov, C. I.; Jordan, P. M.
2014-12-18
This article presents errors, corrections, and additions to the research outlined in the following citation: Christov, I., Christov, C. I., & Jordan, P. M. (2007). Modeling weakly nonlinear acoustic wave propagation. The Quarterly Journal of Mechanics and Applied Mathematics, 60(4), 473-495.
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
A k-space method for moderately nonlinear wave propagation.
Jing, Yun; Wang, Tianren; Clement, Greg T
2012-08-01
A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant-Friedrichs-Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation.
A k-Space Method for Moderately Nonlinear Wave Propagation
Jing, Yun; Wang, Tianren; Clement, Greg T.
2013-01-01
A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant–Friedrichs–Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation. PMID:22899114
Non-linear Langmuir waves in a warm quantum plasma
Dubinov, Alexander E. Kitaev, Ilya N.
2014-10-15
A non-linear differential equation describing the Langmuir waves in a warm quantum electron-ion plasma has been derived. Its numerical solutions of the equation show that ordinary electronic oscillations, similar to the classical oscillations, occur along with small-scale quantum Langmuir oscillations induced by the Bohm quantum force.
Nonlinear Weibel Instability and Turbulence in Strong Collisionless Shocks
Medvedev, Mikhail M.
2008-08-31
This research project was devoted to studies of collisionless shocks, their properties, microphysics and plasma physics of underlying phenomena, such as Weibel instability and generation of small-scale fields at shocks, particle acceleration and transport in the generated random fields, radiation mechanisms from these fields in application to astrophysical phenomena and laboratory experiments (e.g., laser-plasma and beam-plasma interactions, the fast ignition and inertial confinement, etc.). Thus, this study is highly relevant to astrophysical sciences, the inertial confinement program and, in particular, the Fast Ignition concept, etc. It makes valuable contributions to the shock physics, nonlinear plasma theory, as well as to the basic plasma science, in general.
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 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
NASA Astrophysics Data System (ADS)
Garai, S.; Janaki, M. S.; Chakrabarti, N.
2016-09-01
The nonlinear propagation of low frequency waves, in a collisionless, strongly coupled dusty plasma (SCDP) with a density dependent viscosity, has been studied with a proper Galilean invariant generalized hydrodynamic (GH) model. The well known reductive perturbation technique (RPT) has been employed in obtaining the solutions of the longitudinal and transverse perturbations. It has been found that the nonlinear propagation of the acoustic perturbations govern with the modified Korteweg-de Vries (KdV) equation and are decoupled from the sheared fluctuations. In the regions, where transversal gradients of the flow exists, coupling between the longitudinal and transverse perturbations occurs due to convective nonlinearity which is true for the homogeneous case also. The results, obtained here, can have relative significance to astrophysical context as well as in laboratory plasmas.
Evolution of Nonlinear Internal Waves in China Seas
NASA Technical Reports Server (NTRS)
Liu, Antony K.; Hsu, Ming-K.; Liang, Nai K.
1997-01-01
Synthetic Aperture Radar (SAR) images from ERS-I have been used to study the characteristics of internal waves of Taiwan in the East China Sea, and east of Hainan Island in the South China Sea. Rank-ordered packets of internal solitons propagating shoreward from the edge of the continental shelf were observed in the SAR images. Based on the assumption of a semidiurnal tidal origin, the wave speed can be estimated and is consistent with the internal wave theory. By using the SAR images and hydrographic data, internal waves of elevation have been identified in shallow water due to a thicker mixed layer as compared with the bottom layer on the continental shelf. The generation mechanism includes the influences of the tide and the Kuroshio intrusion across the continental shelf for the formations of elevation internal waves. The effects of water depth on the evolution of solitons and wave packets are modeled by nonlinear Kortweg-deVries (KdV) type equation and linked to satellite image observations. The numerical calculations of internal wave evolution on the continental shelf have been performed and compared with the SAR observations. For a case of depression waves in deep water, the solitons first disintegrate into dispersive wave trains and then evolve to a packet of elevation waves in the shallow water area after they pass through a turning point of approximately equal layer depths has been observed in the SAR image and simulated by numerical model.
Nonlinear dynamic behaviors of a floating structure in focused waves
NASA Astrophysics Data System (ADS)
Cao, Fei-feng; Zhao, Xi-zeng
2015-12-01
Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house CFD code is developed to investigate the accurate prediction of nonlinear dynamic behaviors of a two-dimensional (2-D) box-shaped floating structure in focused waves. Computations are performed by an enhanced Constrained Interpolation Profile (CIP)-based Cartesian grid model, in which a more accurate VOF (Volume of Fluid) method, the THINC/SW scheme (THINC: tangent of hyperbola for interface capturing; SW: Slope Weighting), is used for interface capturing. A focusing wave theory is used for the focused wave generation. The wave component of constant steepness is chosen. Comparisons between predictions and physical measurements show good agreement including body motions and free surface profiles. Although the overall agreement is good, some discrepancies are observed for impact pressure on the superstructure due to water on deck. The effect of grid resolution on the results is checked. With a fine grid, no obvious improvement is seen in the global body motions and impact pressures due to water on deck. It is concluded that highly nonlinear phenomena, such as distorted free surface, large-amplitude body motions, and violent impact flow, have been predicted successfully.
NONLINEAR GRAVITATIONAL-WAVE MEMORY FROM BINARY BLACK HOLE MERGERS
Favata, Marc
2009-05-10
Some astrophysical sources of gravitational waves can produce a 'memory effect', which causes a permanent displacement of the test masses in a freely falling gravitational-wave detector. The Christodoulou memory is a particularly interesting nonlinear form of memory that arises from the gravitational-wave stress-energy tensor's contribution to the distant gravitational-wave field. This nonlinear memory contributes a nonoscillatory component to the gravitational-wave signal at leading (Newtonian-quadrupole) order in the waveform amplitude. Previous computations of the memory and its detectability considered only the inspiral phase of binary black hole coalescence. Using an 'effective-one-body' (EOB) approach calibrated to numerical relativity simulations, as well as a simple fully analytic model, the Christodoulou memory is computed for the inspiral, merger, and ringdown. The memory will be very difficult to detect with ground-based interferometers, but is likely to be observable in supermassive black hole mergers with LISA out to redshifts z {approx}< 2. Detection of the nonlinear memory could serve as an experimental test of the ability of gravity to 'gravitate'.
Negative-mass Instability in Nonlinear Plasma Waves
Dodin, I. Y.; Schmit, P. F.; Rocks, J.; Fisch, N. J.
2013-01-30
The negative-mass instability (NMI), previously found in ion traps, appears as a distinct regime of the sideband instability in nonlinear plasma waves with trapped particles. As the bounce frequency of these particles decreases with the bounce action, bunching can occur if the action distribution is inverted in trapping islands. In contrast to existing theories that also infer instabilities from the anharmonicity of bounce oscillations, spatial periodicity of the islands turns out to be unimportant, and the particle distribution can be unstable even if it is at at the resonance. An analytical model is proposed which describes both single traps and periodic nonlinear waves and concisely generalizes the conventional description of the sideband instability in plasma waves. The theoretical results are supported by particle-in-cell simulations carried out for a regime accentuating the NMI effect.
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.
Exact solutions for two nonlinear wave equations with nonlinear terms of any order
NASA Astrophysics Data System (ADS)
Chen, Yong; Li, Biao; Zhang, Hongqing
2005-03-01
In this paper, based on a variable-coefficient balancing-act method, by means of an appropriate transformation and with the help of Mathematica, we obtain some new types of solitary-wave solutions to the generalized Benjamin-Bona-Mahony (BBM) equation and the generalized Burgers-Fisher (BF) equation with nonlinear terms of any order. These solutions fully cover the various solitary waves of BBM equation and BF equation previously reported.
Liu, Chang; Dodin, Ilya Y.
2015-08-15
The nonlinear frequency shift is derived in a transparent asymptotic form for intense Langmuir waves in general collisionless plasma. The formula describes both fluid and kinetic effects simultaneously. The fluid nonlinearity is expressed, for the first time, through the plasma dielectric function, and the kinetic nonlinearity accounts for both smooth distributions and trapped-particle beams. Various known limiting scalings are reproduced as special cases. The calculation avoids differential equations and can be extended straightforwardly to other nonlinear plasma waves.
Dust acoustic waves in strongly coupled dusty plasmas
Rosenberg, M. Kalman, G.
1997-12-01
Dust grains, or solid particles of {mu}m to sub-{mu}m sizes, are observed in various low-temperature laboratory plasmas such as process plasmas and dust plasma crystals. The massive dust grains are generally highly charged, and it has been shown within the context of standard plasma theory that their presence can lead to new low-frequency modes such as dust acoustic waves. In certain laboratory plasmas, however, the dust may be strongly coupled, as characterized by the condition {Gamma}{sub d}=Q{sub d}{sup 2}exp({minus}d/{lambda}{sub D})/dT{sub d}{ge}1, where Q{sub d} is the dust charge, d is the intergrain spacing, T{sub d} is the dust thermal energy, and {lambda}{sub D} is the plasma screening length. This paper investigates the dispersion relation for dust acoustic waves in a strongly coupled dusty plasma comprised of strongly coupled negatively charged dust grains, and weakly correlated classical ions and electrons. The dust grains are assumed to interact via a (screened Coulomb) Yukawa potential. The strongly coupled gas phase (liquid phase) is considered, and a quasilocalized charge approximation scheme is used, generalized to take into account electron and/or ion screening of the dust grains. The scheme relates the small-k dispersion to the total correlation energy of the system, which is obtained from the results of published numerical simulations. Some effects of collisions of charged particles with neutrals are taken into account. Applications to laboratory dusty plasmas are discussed. {copyright} {ital 1997} {ital The American Physical Society}
Polarization dependence of nonlinear wave mixing of spinor polaritons in semiconductor microcavities
NASA Astrophysics Data System (ADS)
Lewandowski, Przemyslaw; Lafont, Ombline; Baudin, Emmanuel; Chan, Chris K. P.; Leung, P. T.; Luk, Samuel M. H.; Galopin, Elisabeth; Lemaître, Aristide; Bloch, Jacqueline; Tignon, Jerome; Roussignol, Philippe; Kwong, N. H.; Binder, Rolf; Schumacher, Stefan
2016-07-01
The pseudospin dynamics of propagating exciton-polaritons in semiconductor microcavities are known to be strongly influenced by TE-TM splitting. As a vivid consequence, in the Rayleigh scattering regime, the TE-TM splitting gives rise to the optical spin Hall effect (OSHE). Much less is known about its role in the nonlinear optical regime in which four-wave mixing, for example, allows the formation of spatial patterns in the polariton density, such that hexagons and two-spot patterns are observable in the far field. Here we present a detailed analysis of spin-dependent four-wave mixing processes, by combining the (linear) physics of TE-TM splitting with spin-dependent nonlinear processes, i.e., exciton-exciton interaction and fermionic phase-space filling. Our combined theoretical and experimental study elucidates the complex physics of the four-wave mixing processes that govern polarization and orientation of off-axis modes.
Nonlinear theory of electron neutralization waves in ions beams with dissipation
NASA Technical Reports Server (NTRS)
Wilhelm, H. E.
1974-01-01
An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions, while diffusion in the pressure gradient is disregarded (zero-temperature approximation). The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave, which exhibits a periodic field structure (incomplete neutralization). This periodic wave structure is damped out by intercomponent momentum transfer - i.e., after a few relaxation lengths a quasi-neutral plasma results.
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.
Marchiano, Régis; Thomas, Jean-Louis; Coulouvrat, François
2003-10-31
An accelerating supersonic aircraft produces noisy superboom due to acoustical shock wave focusing at a fold caustic. This phenomenon is modeled by the mixed-type nonlinear Tricomi equation. An innovative experimental simulation in a water tank has been carried out, with perfect similitude to sonic boom in air. In the linear regime, the canonical Airy function is reproduced using the inverse filter technique. In the nonlinear regime (weak shock waves), the experiment demonstrates the key role of nonlinear effects: they limit the field amplitude, distort the sonic line, and strongly alter the phase of the signal, in agreement with numerical simulations. PMID:14611285
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.
NASA Technical Reports Server (NTRS)
Liepmann, H. W.; Torczynski, J. R.
1983-01-01
Second sound techniques were used to study superfluid helium. Second sound shock waves produced relative velocities in the bulk fluid. Maximum counterflow velocities produced in this way are found to follow the Langer-Fischer prediction for the fundamental critical velocity in its functional dependence on temperature and pressure. Comparison of successive shock and rotating experiments provides strong evidence that breakdown results in vorticity production in the flow behind the shock. Schlieren pictures have verified the planar nature of second sound shocks even after multiple reflections. The nonlinear theory of second sound was repeatedly verified in its prediction of double shocks and other nonlinear phenomena.
Excitation of nonlinear ion acoustic waves in CH plasmas
NASA Astrophysics Data System (ADS)
Feng, Q. S.; Zheng, C. Y.; Liu, Z. J.; Xiao, C. Z.; Wang, Q.; He, X. T.
2016-08-01
Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number k λ D e increases, the linear Landau damping of the fast mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of T i / T e < 0.2 in which the fast mode is weakly damped mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with k λ D e increasing. When k λ D e is not large, such as k λ D e = 0.1 , 0.3 , 0.5 , the nonlinear IAW can be excited by the driver with the linear frequency of the modes. However, when k λ D e is large, such as k λ D e = 0.7 , the linear frequency cannot be applied to exciting the nonlinear IAW, while the frequency calculated by the dispersion relation with no damping can be applied to exciting the nonlinear IAW.
Nonlinear behavior of acoustic waves in combustion chambers
NASA Technical Reports Server (NTRS)
Culick, F. E. C.
1975-01-01
The nonlinear growth and limiting amplitude of acoustic waves in a combustion chamber are considered. A formal framework is provided within which practical problems can be treated with a minimum of effort and expense. The general conservation equations were expanded in two small parameters, one characterizing the mean flow field and one measuring the amplitude of oscillations, and then combined to yield a nonlinear inhomogeneous wave equation. The unsteady pressure and velocity fields were expressed as syntheses of the normal modes of the chamber, but with unknown time-varying amplitudes. This procedure yielded a representation of a general unsteady field as a system of coupled nonlinear oscillators. The system of nonlinear equations was treated by the method of averaging to produce a set of coupled nonlinear first order differential equations for the amplitudes and phases of the modes. The analysis is applicable to any combustion chamber. The most interesting applications are probably to solid rockets, liquid rockets, or thrust augmentors on jet engines.
Relativistic warm plasma theory of nonlinear laser-driven electron plasma waves.
Schroeder, C B; Esarey, E
2010-05-01
A relativistic, warm fluid model of a nonequilibrium, collisionless plasma is developed and applied to examine nonlinear Langmuir waves excited by relativistically intense, short-pulse lasers. Closure of the covariant fluid theory is obtained via an asymptotic expansion assuming a nonrelativistic plasma temperature. The momentum spread is calculated in the presence of an intense laser field and shown to be intrinsically anisotropic. Coupling between the transverse and longitudinal momentum variances is enabled by the laser field. A generalized dispersion relation is derived for Langmuir waves in a thermal plasma in the presence of an intense laser field. Including thermal fluctuations in three-velocity-space dimensions, the properties of the nonlinear electron plasma wave, such as the plasma temperature evolution and nonlinear wavelength, are examined and the maximum amplitude of the nonlinear oscillation is derived. The presence of a relativistically intense laser pulse is shown to strongly influence the maximum plasma wave amplitude for nonrelativistic phase velocities owing to the coupling between the longitudinal and transverse momentum variances.
Relativistic warm plasma theory of nonlinear laser-driven electron plasma waves
Schroeder, Carl B.; Esarey, Eric
2010-06-30
A relativistic, warm fluid model of a nonequilibrium, collisionless plasma is developed and applied to examine nonlinear Langmuir waves excited by relativistically-intense, short-pulse lasers. Closure of the covariant fluid theory is obtained via an asymptotic expansion assuming a non-relativistic plasma temperature. The momentum spread is calculated in the presence of an intense laser field and shown to be intrinsically anisotropic. Coupling between the transverse and longitudinal momentum variances is enabled by the laser field. A generalized dispersion relation is derived for langmuir waves in a thermal plasma in the presence of an intense laser field. Including thermal fluctuations in three velocity-space dimensions, the properties of the nonlinear electron plasma wave, such as the plasma temperature evolution and nonlinear wavelength, are examined, and the maximum amplitude of the nonlinear oscillation is derived. The presence of a relativistically intense laser pulse is shown to strongly influence the maximum plasma wave amplitude for non-relativistic phase velocities owing to the coupling between the longitudinal and transverse momentum variances.
Xiao, Jianyuan; Liu, Jian; Qin, Hong; Yu, Zhi; Xiang, Nong
2015-09-15
In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. It is illustrated that nonlinear effects significantly modify the physics of the radio-frequency injection in magnetized plasmas. The evolutions of the radio-frequency wave reflectivity and the energy deposition are observed, as well as the self-interaction of the Bernstein waves and mode excitations. Even for waves with small magnitude, nonlinear effects can also become important after continuous wave injections, which are common in the realistic radio-frequency wave heating and current drive experiments.
Nonlinear waves in deforming porous media with the finite difference method
NASA Astrophysics Data System (ADS)
Räss, Ludovic; Duretz, Thibault; Podladchikov, Yuri
2016-04-01
The actual trend in computational geodynamics tends toward the development of coupled multi-physics models. The resulting models involve various types of nonlinear processes such as non-Newtonian rheologies and multi-physics coupling. One of the main challenge is to treat these nonlinearities in order to preserve the predictive power of these forward models. In this framework, we designed two dimensional (2D) finite difference models using both implicit and explicit discretisations. We apply the models to study the initiation and the propagation of nonlinear waves in deforming porous media (porosity waves). A strong coupling of a Stokes solver to a nonlinear Darcy flow is required to describe the complex evolution of permeability and porosity in space and in time. In our models, we also take into account porosity-dependant permeability and rheologies that are representative of major reservoir rock type (i.e. tight shales). We conduct numerical simulations and show that both implicit and explicit approaches capture the channeling instabilities and the development of focused flow. We perform quantitative comparison of the two methods and discuss the treatment of multi-physics coupling and rheological nonlinearities. We show that implicit and explicit discretisations converge to similar solutions only if the nonlinearities are accurately resolved. Explicit numerical algorithms can therefore be attractive because they are very comprehensible and well suited for HPC while implicit models are performing well on desktop computations.
SCALAR AND VECTOR NONLINEAR DECAYS OF LOW-FREQUENCY ALFVÉN WAVES
Zhao, J. S.; Wu, D. J.; Voitenko, Y.; De Keyser, J.
2015-02-01
We found several efficient nonlinear decays for Alfvén waves in the solar wind conditions. Depending on the wavelength, the dominant decay is controlled by the nonlinearities proportional to either scalar or vector products of wavevectors. The two-mode decays of the pump MHD Alfvén wave into co- and counter-propagating product Alfvén and slow waves are controlled by the scalar nonlinearities at long wavelengths ρ{sub i}{sup 2}k{sub 0⊥}{sup 2}<ω{sub 0}/ω{sub ci} (k {sub 0} is wavenumber perpendicular to the background magnetic field, ω{sub 0} is frequency of the pump Alfvén wave, ρ {sub i} is ion gyroradius, and ω {sub ci} is ion-cyclotron frequency). The scalar decays exhibit both local and nonlocal properties and can generate not only MHD-scale but also kinetic-scale Alfvén and slow waves, which can strongly accelerate spectral transport. All waves in the scalar decays propagate in the same plane, hence these decays are two-dimensional. At shorter wavelengths, ρ{sub i}{sup 2}k{sub 0⊥}{sup 2}>ω{sub 0}/ω{sub ci}, three-dimensional vector decays dominate generating out-of-plane product waves. The two-mode decays dominate from MHD up to ion scales ρ {sub i} k {sub 0} ≅ 0.3; at shorter scales the one-mode vector decays become stronger and generate only Alfvén product waves. In the solar wind the two-mode decays have high growth rates >0.1ω{sub 0} and can explain the origin of slow waves observed at kinetic scales.
Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation
Jing, Yun; Tao, Molei; Clement, Greg T.
2011-01-01
A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green’s function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed. PMID:21302985
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.
NASA Astrophysics Data System (ADS)
Savel'ev, Sergey; Yampol'skii, V. A.; Rakhmanov, A. L.; Nori, Franco
2010-02-01
The recent growing interest in terahertz (THz) and sub-THz science and technology is due to its many important applications in physics, astronomy, chemistry, biology and medicine, including THz imaging, spectroscopy, tomography, medical diagnosis, health monitoring, environmental control, as well as chemical and biological identification. We review the problem of linear and nonlinear THz and sub-THz Josephson plasma waves in layered superconductors and their excitations produced by moving Josephson vortices. We start by discussing the coupled sine-Gordon equations for the gauge-invariant phase difference of the order parameter in the junctions, taking into account the effect of breaking the charge neutrality, and deriving the spectrum of Josephson plasma waves. We also review surface and waveguide Josephson plasma waves. The spectrum of these waves is presented, and their excitation is discussed. We review the propagation of weakly nonlinear Josephson plasma waves below the plasma frequency, ωJ, which is very unusual for plasma-like excitations. In close analogy to nonlinear optics, these waves exhibit numerous remarkable features, including a self-focusing effect and the pumping of weaker waves by a stronger one. In addition, an unusual stop-light phenomenon, when ∂ω/∂k ≈ 0, caused by both nonlinearity and dissipation, can be observed in the Josephson plasma waves. At frequencies above ωJ, the current-phase nonlinearity can be used for transforming continuous sub-THz radiation into short, strongly amplified, pulses. We also present quantum effects in layered superconductors, specifically, the problem of quantum tunneling of fluxons through stacks of Josephson junctions. Moreover, the nonlocal sine-Gordon equation for Josephson vortices is reviewed. We discuss the Cherenkov and transition radiations of the Josephson plasma waves produced by moving Josephson vortices, either in a single Josephson junction or in layered superconductors. Furthermore, the
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.
Sustained strong fluctuations in a nonlinear chain at acoustic vacuum: beyond equilibrium.
Ávalos, Edgar; Sun, Diankang; Doney, Robert L; Sen, Surajit
2011-10-01
Here we consider dynamical problems as in linear response theory but for purely nonlinear systems where acoustic propagation is prohibited by the potential, e.g., the case of an alignment of elastic grains confined between walls. Our simulations suggest that in the absence of acoustic propagation, the system relaxes using only solitary waves and the eventual state does not resemble an equilibrium state. Further, the studies reveal that multiple perturbations could give rise to hot and cold spots in these systems. We first use particle dynamics based simulations to understand how one of the two unequal colliding solitary waves in the chain can gain energy. Specifically, we find that for head-on collisions the smaller wave gains energy, whereas when a more energetic wave overtakes a less energetic wave, the latter gains energy. The balance between the rate at which the solitary waves break down and the rate at which they grow eventually makes it possible for the system to reach a peculiar equilibriumlike phase that is characteristic of these purely nonlinear systems. The study of the features and the robustness of the fluctuations in time has been addressed next. A particular characteristic of this equilibriumlike or quasiequilibrium phase is that very large energy fluctuations are possible--and by very large, we mean that the energy can vary between zero and several times the average energy per grain. We argue that the magnitude of the fluctuations depend on the nature of the nonlinearity in the potential energy function and the feature that any energy must eventually travel as a compact solitary wave in these systems where the solitary wave energies may vary widely. In closing we address whether these fluctuations are peculiar to one dimension or can exist in higher dimensions. The study hence raises the following intriguing possibility. Are there physical or biological systems where these kinds of nonlinear forces exist, and if so, can such large fluctuations
Fast numerical treatment of nonlinear wave equations by spectral methods
Skjaeraasen, Olaf; Robinson, P. A.; Newman, D. L.
2011-02-15
A method is presented that accelerates spectral methods for numerical solution of a broad class of nonlinear partial differential wave equations that are first order in time and that arise in plasma wave theory. The approach involves exact analytical treatment of the linear part of the wave evolution including growth and damping as well as dispersion. After introducing the method for general scalar and vector equations, we discuss and illustrate it in more detail in the context of the coupling of high- and low-frequency plasma wave modes, as modeled by the electrostatic and electromagnetic Zakharov equations in multiple dimensions. For computational efficiency, the method uses eigenvector decomposition, which is particularly advantageous when the wave damping is mode-dependent and anisotropic in wavenumber space. In this context, it is shown that the method can significantly speed up numerical integration relative to standard spectral or finite difference methods by allowing much longer time steps, especially in the limit in which the nonlinear Schroedinger equation applies.
A nonlinear wave equation in nonadiabatic flame propagation
Booty, M.R.; Matalon, M.; Matkowsky, B.J.
1988-06-01
The authors derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time.
Nonlinear interaction of drift waves with driven plasma currents
Brandt, Christian; Grulke, Olaf; Klinger, Thomas
2010-03-15
In a cylindrical magnetized plasma, coherent drift wave modes are synchronized by a mode selective drive of plasma currents. Nonlinear effects of the synchronization are investigated in detail. Frequency pulling is observed over a certain frequency range. The dependence of the width of this synchronization range on the amplitude of the driven plasma currents forms Arnold tongues. The transition between complete and incomplete synchronization is indicated by the onset of periodic pulling and phase slippage. Synchronization is observed for driven current amplitudes, which are some percent of the typical value of parallel currents generated by drift waves.
Nonlinear generation of magnetostatic fluctuations by drift waves
NASA Astrophysics Data System (ADS)
Shukla, P. K.; Kaw, P. K.
1984-10-01
A self-consistent analysis of nonlinear coupling between drift waves and magnetostatic modes in tokomak discharges is presented. It is shown that an instability arises in the magnetostatic modes when they couple back to the drift waves. The disturbances are modeled with a parallel electron momentum equation and, in the case of a hydrogen plasma, have a growth rate close to 100 msec. The growth rate could, however, accelerate with higher electron densities, which may be a problem in current cold plasma toroidal devices which have a 5 msec confinement time.
Collapse of nonlinear electron plasma waves in a plasma layer
NASA Astrophysics Data System (ADS)
Grimalsky, V.; Koshevaya, S.; Rapoport, Yu; Kotsarenko, A.
2016-10-01
The excitation of nonlinear electron plasma waves in the plasma layer is investigated theoretically. This excitation is realized by means of initial oscillatory perturbations of the volume electron concentration or by initial oscillatory distributions of the longitudinal electron velocity. The amplitudes of the initial perturbations are small and the manifestation of the volume nonlinearity is absent. When the amplitudes of the initial perturbations exceed some thresholds, the values of the electron concentration near the plasma boundary increase catastrophically. The maxima of the electron concentration reach extremely high magnitudes, and sharp peaks in the electron concentration occur, which are localized both in the longitudinal and transverse directions. This effect is interpreted as wave collapse near the plasma boundary.
Nonlinear waves in coherently coupled Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Congy, T.; Kamchatnov, A. M.; Pavloff, N.
2016-04-01
We consider a quasi-one-dimensional two-component Bose-Einstein condensate subject to a coherent coupling between its components, such as realized in spin-orbit coupled condensates. We study how nonlinearity modifies the dynamics of the elementary excitations. The spectrum has two branches, which are affected in different ways. The upper branch experiences a modulational instability, which is stabilized by a long-wave-short-wave resonance with the lower branch. The lower branch is stable. In the limit of weak nonlinearity and small dispersion it is described by a Korteweg-de Vries equation or by the Gardner equation, depending on the value of the parameters of the system.
Discrete Element Method Simulation of Nonlinear Viscoelastic Stress Wave Problems
NASA Astrophysics Data System (ADS)
Tang, Zhiping; Horie, Y.; Wang, Wenqiang
2002-07-01
A DEM(Discrete Element Method) simulation of nonlinear viscoelastic stress wave problems is carried out. The interaction forces among elements are described using a model in which neighbor elements are linked by a nonlinear spring and a certain number of Maxwell components in parallel. By making use of exponential relaxation moduli, it is shown that numerical computation of the convolution integral does not require storing and repeatedly calculating strain history, so that the computational cost is dramatically reduced. To validate the viscoelastic DM2 code1, stress wave propagation in a Maxwell rod with one end subjected to a constant stress loading is simulated. Results excellently fit those from the characteristics calculation. The code is then used to investigate the problem of meso-scale damage in a plastic-bonded explosive under shock loading. Results not only show "compression damage", but also reveal a complex damage evolution. They demonstrate a unique capability of DEM in modeling heterogeneous materials.
Nonlinear compressional waves in a two-dimensional Yukawa lattice.
Avinash, K; Zhu, P; Nosenko, V; Goree, J
2003-10-01
A modified Korteweg-de Vries (KdV) equation is obtained for studying the propagation of nonlinear compressional waves and pulses in a chain of particles including the effect of damping. Suitably altering the linear phase velocity makes this equation useful also for the problem of phonon propagation in a two-dimensional (2D) lattice. Assuming a Yukawa potential, we use this method to model compressional wave propagation in a 2D plasma crystal, as in a recent experiment. By integrating the modified KdV equation the pulse is allowed to evolve, and good agreement with the experiment is found. It is shown that the speed of a compressional pulse increases with its amplitude, while the speed of a rarefactive pulse decreases. It is further discussed how the drag due to the background gas has a crucial role in weakening nonlinear effects and preventing the emergence of a soliton. PMID:14683049
Charge density waves in strongly correlated electron systems.
Chen, Chih-Wei; Choe, Jesse; Morosan, E
2016-08-01
Strong electron correlations are at the heart of many physical phenomena of current interest to the condensed matter community. Here we present a survey of the mechanisms underlying such correlations in charge density wave (CDW) systems, including the current theoretical understanding and experimental evidence for CDW transitions. The focus is on emergent phenomena that result as CDWs interact with other charge or spin states, such as magnetism and superconductivity. In addition to reviewing the CDW mechanisms in 1D, 2D, and 3D systems, we pay particular attention to the prevalence of this state in two particular classes of compounds, the high temperature superconductors (cuprates) and the layered transition metal dichalcogenides. The possibilities for quantum criticality resulting from the competition between magnetic fluctuations and electronic instabilities (CDW, unconventional superconductivity) are also discussed. PMID:27376547
Charge density waves in strongly correlated electron systems
NASA Astrophysics Data System (ADS)
Chen, Chih-Wei; Choe, Jesse; Morosan, E.
2016-08-01
Strong electron correlations are at the heart of many physical phenomena of current interest to the condensed matter community. Here we present a survey of the mechanisms underlying such correlations in charge density wave (CDW) systems, including the current theoretical understanding and experimental evidence for CDW transitions. The focus is on emergent phenomena that result as CDWs interact with other charge or spin states, such as magnetism and superconductivity. In addition to reviewing the CDW mechanisms in 1D, 2D, and 3D systems, we pay particular attention to the prevalence of this state in two particular classes of compounds, the high temperature superconductors (cuprates) and the layered transition metal dichalcogenides. The possibilities for quantum criticality resulting from the competition between magnetic fluctuations and electronic instabilities (CDW, unconventional superconductivity) are also discussed.
Head-on-collision of modulated dust acoustic waves in strongly coupled dusty plasma
El-Labany, S. K.; El-Depsy, A.; Zedan, N. A.; El-Taibany, W. F.; El-Shamy, E. F.
2012-10-15
The derivative expansion perturbation method is applied to a strongly coupled dusty plasma system consisting of negatively charged dust grains, electrons, and ions. The basic equations are reduced to a nonlinear Schroedinger type equation appropriate for describing the modulated dust acoustic (DA) waves. We have examined the modulation (in) stability and the dependence of the system physical parameters (angular frequency and group velocity) on the polarization force variation. Finally, the extended Poincare-Lighthill-Kuo technique is employed to investigate the head-on collision (HoC) between two DA dark solitons. The analytical phase shifts and the trajectories of these dark solitons after the collision are derived. The numerical illustrations show that the polarization effect has strong influence on the nature of the phase shifts and the trajectories of the two DA dark solitons after collision.
Lattice Boltzmann model for generalized nonlinear wave equations
NASA Astrophysics Data System (ADS)
Lai, Huilin; Ma, Changfeng
2011-10-01
In this paper, a lattice Boltzmann model is developed to solve a class of the nonlinear wave equations. Through selecting equilibrium distribution function and an amending function properly, the governing evolution equation can be recovered correctly according to our proposed scheme, in which the Chapman-Enskog expansion is employed. We validate the algorithm on some problems where analytic solutions are available, including the second-order telegraph equation, the nonlinear Klein-Gordon equation, and the damped, driven sine-Gordon equation. It is found that the numerical results agree well with the analytic solutions, which indicates that the present algorithm is very effective and can be used to solve more general nonlinear problems.
NASA Technical Reports Server (NTRS)
Matsuda, Y.
1974-01-01
A low-noise plasma simulation model is developed and applied to a series of linear and nonlinear problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. It is demonstrated that use of the hybrid simulation model allows economical studies to be carried out in both the linear and nonlinear regimes with better quantitative results, for comparable computing time, than can be obtained by conventional particle simulation models, or direct solution of the Vlasov equation. The characteristics of the hybrid simulation model itself are first investigated, and it is shown to be capable of verifying the theoretical linear dispersion relation at wave energy levels as low as .000001 of the plasma thermal energy. Having established the validity of the hybrid simulation model, it is then used to study the nonlinear dynamics of monochromatic wave, sideband instability due to trapped particles, and satellite growth.
Fast neural solution of a nonlinear wave equation
NASA Technical Reports Server (NTRS)
Toomarian, Nikzad; Barhen, Jacob
1992-01-01
A neural algorithm for rapidly simulating a certain class of nonlinear wave phenomena using analog VLSI neural hardware is presented and applied to the Korteweg-de Vries partial differential equation. The corresponding neural architecture is obtained from a pseudospectral representation of the spatial dependence, along with a leap-frog scheme for the temporal evolution. Numerical simulations demonstrated the robustness of the proposed approach.
Fast Neural Solution Of A Nonlinear Wave Equation
NASA Technical Reports Server (NTRS)
Barhen, Jacob; Toomarian, Nikzad
1996-01-01
Neural algorithm for simulation of class of nonlinear wave phenomena devised. Numerically solves special one-dimensional case of Korteweg-deVries equation. Intended to be executed rapidly by neural network implemented as charge-coupled-device/charge-injection device, very-large-scale integrated-circuit analog data processor of type described in "CCD/CID Processors Would Offer Greater Precision" (NPO-18972).
Nonlinear Interactions between Gravity Waves in Water of Constant Depth
NASA Astrophysics Data System (ADS)
Szmidt, Kazimierz; Hedzielski, Benedykt
2015-06-01
The paper deals with interactions between water waves propagating in fluid of constant depth. In formulation of this problem, a nonlinear character of these interactions is taken into account. In particular, in order to simplify a solution to nonlinear boundary conditions at the free surface, a system of material coordinates is employed as independent variables in the description of the phenomenon. The main attention is focused on the transient solutions corresponding to fluid motion starting from rest. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in a finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of equations describing nonlinear waves, an approximate formulation is considered, which is based on a power series expansion of dependent variables with respect to a small parameter. Such a solution is assumed to be accurate in describing the main features of the phenomenon. Numerical experiments are conducted to illustrate the approximate formulation developed in this paper.
Quantum corrections to nonlinear ion acoustic wave with Landau damping
Mukherjee, Abhik; Janaki, M. S.; Bose, Anirban
2014-07-15
Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.
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.
Strong Evidence for Stochastic Growth of Langmuir-Like Waves in Earth's Foreshock
NASA Technical Reports Server (NTRS)
Cairns, Iver H.; Robinson, P. A.
1999-01-01
Bursty Langmuir-like waves driven by electron beams in Earth's foreshock have properties which are inconsistent with the standard plasma physics paradigm of uniform exponential growth saturated by nonlinear processes. Here it is demonstrated for a specific period that stochastic growth theory (SGT) quantitatively describes these waves throughout a large fraction of the foreshock. The statistical wave properties are inconsistent with nonlinear processes or self-organized criticality being important. SGT's success in explaining the foreshock waves and type III solar bursts suggests that SGT is widely applicable to wave growth in space, astrophysical, and laboratory plasmas.
MJO: Asymptotically-Nondivergent Nonlinear Wave?: A Review
NASA Astrophysics Data System (ADS)
Yano, J. I.
2014-12-01
MJO is often considered a convectively-coupled wave. The present talk is going to argue that it is best understood primarily as a nonlinear solitary wave dominated by vorticity. Role of convection is secondary,though likely catalytic. According to Charney's (1963) scale analysis, the large-scale tropical circulations are nondivergent to the leading order, i.e., dominated by rotational flows. Yano et al (2009) demonstrate indeed that is the case for a period dominated by three MJO events. The scale analysis of Yano and Bonazzola (2009, JAS) demonstrates such an asymptotically nondivergent regime is a viable alternative to the traditionally-believed equatorial-wave regime. Wedi and Smolarkiewicz (2010, JAS) in turn, show by numerical computations of a dry system that a MJO-like oscillation for a similar period can indeed be generated by free solitary nonlinear equatorial Rossby-wave dynamicswithout any convective forcing to a system. Unfortunately, this perspective is slow to be accepted with people's mind so much fixed on the role of convection. This situation may be compared to a slow historical process of acceptance of Eady and Charney's baroclinicinstability simply because it does not invoke any convection Ironically, once the nonlinear free-wave view for MJO is accepted, interpretations can more easily be developed for a recent series of numerical model experiments under a global channel configuration overthe tropics with a high-resolution of 5-50 km with or without convection parameterization. All those experiments tend to reproduce observed large-scale circulations associated with MJO rather well, though most of time, they fail to reproduce convective coherency associated with MJO.These large-scale circulations appear to be generated by lateral forcing imposed at the latitudinal walls. These lateral boundaries are reasonably far enough (30NS) to induce any direct influence to the tropics. There is no linear dry equatorial wave that supports this period either
Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity.
Shao, Sihong; Quintero, Niurka R; Mertens, Franz G; Cooper, Fred; Khare, Avinash; Saxena, Avadh
2014-09-01
We consider the nonlinear Dirac equation in 1 + 1 dimension with scalar-scalar self interaction g(2)/κ+1(̅ΨΨ)(κ+1) and with mass m. Using the exact analytic form for rest frame solitary waves of the form Ψ(x,t)=ψ(x)e(-iωt) for arbitrary κ, we discuss the validity of various approaches to understanding stability that were successful for the nonlinear Schrödinger equation. In particular we study the validity of a version of Derrick's theorem and the criterion of Bogolubsky as well as the Vakhitov-Kolokolov criterion, and find that these criteria yield inconsistent results. Therefore, we study the stability by numerical simulations using a recently developed fourth-order operator splitting integration method. For different ranges of κ we map out the stability regimes in ω. We find that all stable nonlinear Dirac solitary waves have a one-hump profile, but not all one-hump waves are stable, while all waves with two humps are unstable. We also find that the time t(c), it takes for the instability to set in, is an exponentially increasing function of ω and t(c) decreases monotonically with increasing κ. PMID:25314512
Long-wave model for strongly anisotropic growth of a crystal step.
Khenner, Mikhail
2013-08-01
A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the "one-sided" model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed the nonlinear dynamics. Linear stability depends on whether the stiffness is minimum or maximum in the direction of the step growth. It also depends nontrivially on the combination of the anisotropy strength parameter and the atomic flux from the terrace to the step. Computations show formation and coarsening of a hill-and-valley structure superimposed onto a long-wavelength profile, which independently coarsens. Coarsening laws for the hill-and-valley structure are computed for two principal orientations of a maximum step stiffness, the increasing anisotropy strength, and the varying atomic flux. PMID:24032844
Non-linear solitary sound waves in lipid membranes and their possible role in biological signaling
NASA Astrophysics Data System (ADS)
Shrivastava, Shamit
Biological macromolecules self-assemble under entropic forces to form a dynamic 2D interfacial medium where the elastic properties arise from the curvature of the entropic potential of the interface. Elastic interfaces should be capable of propagating localized perturbations analogous to sound waves. However, (1) the existence and (2) the possible role of such waves in affecting biological functions remain unexplored. Both these aspects of "sound" as a signaling mechanism in biology are explored experimentally on mixed monolayers of lipids-fluorophores-proteins at the air/water interface as a model biological interface. This study shows - for the first time - that the nonlinear susceptibility near a thermodynamic transition in a lipid monolayer results in nonlinear solitary sound waves that are of 'all or none' nature. The state dependence of the nonlinear propagation is characterized by studying the velocity-amplitude relationship and results on distance dependence, effect of geometry and collision of solitary waves are presented. Given that the lipid bilayers and real biological membranes have such nonlinearities in their susceptibility diagrams, similar solitary phenomenon should be expected in biological membranes. In fact the observed characteristics of solitary sound waves such as, their all or none nature, a biphasic pulse shape with a long tail and optp-mechano-electro-thermal coupling etc. are strikingly similar to the phenomenon of nerve pulse propagation as observed in single nerve fibers. Finally given the strong correlation between the activity of membrane bound enzymes and the susceptibility and the fact that the later varies within a single solitary pulse, a new thermodynamic basis for biological signaling is proposed. The state of the interface controls both the nature of sound propagation and its impact on incorporated enzymes and proteins. The proof of concept is demonstrated for acetylcholine esterase embedded in a lipid monolayer, where the
Nonlinear Dirac equation solitary waves in external fields.
Mertens, Franz G; Quintero, Niurka R; Cooper, Fred; Khare, Avinash; Saxena, Avadh
2012-10-01
We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2/κ+1(Ψ[over ¯]Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP(t)/dq[over ̇](t)<0. Here P(t) is the momentum of the solitary wave, and q[over ̇] is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials that we always have dP(t)/dq[over ̇](t)>0, so, when instabilities do occur, they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that, when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations. We found that the time evolution of the collective coordinates of the solitary wave in our numerical simulations, namely the position of the average charge density and the momentum of the solitary wave, provide good indicators for when the solitary wave first becomes unstable. When these variables stop being smooth functions of time (t), then the solitary wave starts to distort
Nonlinear Dirac equation solitary waves in external fields.
Mertens, Franz G; Quintero, Niurka R; Cooper, Fred; Khare, Avinash; Saxena, Avadh
2012-10-01
We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2/κ+1(Ψ[over ¯]Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP(t)/dq[over ̇](t)<0. Here P(t) is the momentum of the solitary wave, and q[over ̇] is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials that we always have dP(t)/dq[over ̇](t)>0, so, when instabilities do occur, they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that, when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations. We found that the time evolution of the collective coordinates of the solitary wave in our numerical simulations, namely the position of the average charge density and the momentum of the solitary wave, provide good indicators for when the solitary wave first becomes unstable. When these variables stop being smooth functions of time (t), then the solitary wave starts to distort
Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
NASA Astrophysics Data System (ADS)
Kim, E.; Li, F.; Chong, C.; Theocharis, G.; Yang, J.; Kevrekidis, P. G.
2015-03-01
In the present work, we experimentally implement, numerically compute with, and theoretically analyze a configuration in the form of a single column woodpile periodic structure. Our main finding is that a Hertzian, locally resonant, woodpile lattice offers a test bed for the formation of genuinely traveling waves composed of a strongly localized solitary wave on top of a small amplitude oscillatory tail. This type of wave, called a nanopteron, is not only motivated theoretically and numerically, but is also visualized experimentally by means of a laser Doppler vibrometer. This system can also be useful for manipulating stress waves at will, for example, to achieve strong attenuation and modulation of high-amplitude impacts without relying on damping in the system.
D'Ambroise, J.; Salerno, M.; Kevrekidis, P. G.; Abdullaev, F. Kh.
2015-11-19
The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined.more » We also found that other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. Finally, the possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.« less
D'Ambroise, J.; Salerno, M.; Kevrekidis, P. G.; Abdullaev, F. Kh.
2015-11-19
The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined. We also found that other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. Finally, the possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.
NASA Astrophysics Data System (ADS)
D'Ambroise, J.; Salerno, M.; Kevrekidis, P. G.; Abdullaev, F. Kh.
2015-11-01
The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined. Other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. The possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.
Weakly nonlinear ion waves in striated electron temperatures.
Guio, P; Pécseli, H L
2016-04-01
The existence of low-frequency waveguide modes of electrostatic ion acoustic waves is demonstrated in magnetized plasmas for cases where the electron temperature is striated along magnetic field lines. For low frequencies, the temperature striation acts as waveguide that supports a trapped mode. For conditions where the ion cyclotron frequency is below the ion plasma frequency we find a dispersion relation having also a radiative frequency band, where waves can escape from the striation. Arguments for the formation and propagation of an equivalent of electrostatic shocks are presented and demonstrated numerically for these conditions. The shock represents here a balance between an external energy input maintained by ion injection and a dissipation mechanism in the form of energy leakage of the harmonics generated by nonlinear wave steepening. This is a reversible form for energy loss that can replace the time-irreversible losses in a standard Burgers equation. PMID:27176415
Nonlinear time-dependent simulation of helix traveling wave tubes
NASA Astrophysics Data System (ADS)
Peng, Wei-Feng; Yang, Zhong-Hai; Hu, Yu-Lu; Li, Jian-Qing; Lu, Qi-Ru; Li, Bin
2011-07-01
A one-dimensional nonlinear time-dependent theory for helix traveling wave tubes is studied. A generalized electromagnetic field is applied to the expression of the radio frequency field. To simulate the variations of the high frequency structure, such as the pitch taper and the effect of harmonics, the spatial average over a wavelength is substituted by a time average over a wave period in the equation of the radio frequency field. Under this assumption, the space charge field of the electron beam can be treated by a space charge wave model along with the space charge coefficient. The effects of the radio frequency and the space charge fields on the electrons are presented by the equations of the electron energy and the electron phase. The time-dependent simulation is compared with the frequency-domain simulation for a helix TWT, which validates the availability of this theory.
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Lepri, Stefano; Pikovsky, Arkady
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
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.
New approximate solutions for the strongly nonlinear cubic-quintic duffing oscillators
NASA Astrophysics Data System (ADS)
Karahan, M. M. Fatih; Pakdemirli, Mehmet
2016-06-01
Strongly nonlinear cubic-quintic Duffing oscillator is considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.
Strong nonlinearity of mesoscopic vibrational modes induced by electron-phonon coupling
NASA Astrophysics Data System (ADS)
Moskovtsev, Kirill; Dykman, M. I.
We show that the electron-phonon coupling can lead to a strong nonlinearity of vibrational modes in semiconductor nano- and micro-resonators. For typical mode frequencies, the electron distribution adiabatically follows lattice strain. Therefore strain leads to redistribution of the electron density over the valleys of the conduction band. It also leads to the onset of a spatial charge. The parameter that controls the distribution is the ratio of the deformation potential to the electron chemical potential or temperature. It is ~102 for many semiconductors of interest even when they are heavily doped. Therefore the change of the electron distribution is strongly nonlinear in the strain. As a consequence, the stress induced by the electron-phonon coupling is also strongly nonlinear. We have found the vibration nonlinearity parameters for n-doped Si and calculated the amplitude dependence of the frequencies of several low-lying Si resonator modes with account taken of their spatial structure. The results are compared with the recent experimental data that shows strong effect of doping on the vibration nonlinearity.
Observations of nonlinear internal waves at a persistent coastal upwelling front
NASA Astrophysics Data System (ADS)
Walter, Ryan K.; Stastna, Marek; Woodson, C. Brock; Monismith, Stephen G.
2016-04-01
We collected high-resolution observations of nonlinear internal waves (NLIWs) at a persistent upwelling front in the shallow coastal environment (~20 m) of northern Monterey Bay, CA. The coastal upwelling front forms between recently upwelled waters and warmer stratified waters that are trapped in the bay (upwelling shadow). The front propagates up and down the coast in the along-shore direction as a buoyant plume front due to modulation by strong diurnal wind forcing. The evolution of the coastal upwelling front, and the subsequent modulation of background environmental conditions, is examined using both individual events and composite day averages. We demonstrate that regional-scale upwelling and local diurnal wind forcing are key components controlling local stratification and the formation of internal wave guides that allow for high-frequency internal wave activity. Finally, we discuss the ability of theoretical models to describe particularly large-amplitude internal waves that exist in the presence of a strong background shear and test a fully nonlinear model (i.e., the Dubreil-Jacotin-Long equation).
Probing Strong-field General Relativity with Gravitational Waves
NASA Astrophysics Data System (ADS)
Pretorius, Frans
We are on the verge of a new era in astrophysics as a world-wide effort to observe the universe with gravitational waves takes hold---ground based laser interferometers (Hz to kHz), pulsar timing (micro to nano Hz), measurements of polarization of the cosmic microwave background (sub-nano Hz), and the planned NASA/ESA mission LISA (.1 mHz to .1 Hz). This project will study the theoretical nature of gravitational waves (GWs) emitted by two sources in the LISA band, namely supermassive-black-hole (SMBH) binary mergers, and extreme-mass-ratio-inspirals (EMRI's)---the merger of a stellar mass black hole, neutron star, or white dwarf with a SMBH. The primary goal will be to ascertain how well LISA, by observing these sources, could answer the following related questions about the fundamental nature of strong-field gravity: Does Einstein's theory of general relativity (GR) describe the geometry of black holes in the universe? What constraints can GW observations of SMBH mergers and EMRIs place on alternative theories of gravity? If there are deviations from GR, are there statistics that could give indications of a deviation if sources are detected using a search strategy based solely on GR waveforms? The primary reasons for focusing on LISA sources to answer these questions are (a) binary SMBH mergers could be detected by LISA with exquisitely high signal-to- noise, allowing enough parameters of the system to be accurately extracted to perform consistency checks of the underlying theory, (b) EMRIs will spend numerous orbits close to the central black hole, and thus will be quite sensitive to even small near-horizon deviations from GR. One approach to develop the requisite knowledge and tools to answer these questions is to study a concrete, theoretically viable alternative to GR. We will focus on the dynamical variant of Chern-Simons modified gravity (CSMG), which is interesting for several reasons, chief among which are (1) that CSMG generically arises in both string
Radiative polarization of electrons in a strong laser wave
NASA Astrophysics Data System (ADS)
Karlovets, Dmitry V.
2011-12-01
We reanalyze the problem of radiative polarization of electrons brought into collision with a circularly polarized strong plane wave. We present an independent analytical verification of formulas for the cross section given by Ivanov [Eur. Phys. J. CEPCFFB1434-604410.1140/epjc/s2004-01861-x 36, 127 (2004)]. By choosing the exact electron's helicity as the spin quantum number we show that the self-polarization effect exists only for the moderately relativistic electrons with energy γ=E/mc2≲10 and only for a non-head-on collision geometry. In these conditions polarization degree may achieve values up to 65%, but the effective polarization time is found to be larger than 1 s even for a high-power optical or infrared laser with intensity parameter ξ=|E|mc2/Ecℏω˜0.1 (Ec=m2c3/eℏ). This makes such a polarization practically unrealizable. We also compare these results with the ones of some papers where the high degree of polarization was predicted for ultrarelativistic case. We argue that this apparent contradiction arises due to the different choice of the spin quantum numbers. In particular, the quantum numbers that provide the high degree of polarization represent neither helicity nor transverse polarization, which makes the use of them inconvenient in practice.
Radiative polarization of electrons in a strong laser wave
Karlovets, Dmitry V.
2011-12-15
We reanalyze the problem of radiative polarization of electrons brought into collision with a circularly polarized strong plane wave. We present an independent analytical verification of formulas for the cross section given by Ivanov et al.[Eur. Phys. J. C 36, 127 (2004)]. By choosing the exact electron's helicity as the spin quantum number we show that the self-polarization effect exists only for the moderately relativistic electrons with energy {gamma}=E/mc{sup 2} < or approx. 10 and only for a non-head-on collision geometry. In these conditions polarization degree may achieve values up to 65%, but the effective polarization time is found to be larger than 1 s even for a high-power optical or infrared laser with intensity parameter {xi}=|E|mc{sup 2}/E{sub c}({Dirac_h}/2{pi}){omega}{approx}0.1 (E{sub c}=m{sup 2}c{sup 3}/e({Dirac_h}/2{pi})). This makes such a polarization practically unrealizable. We also compare these results with the ones of some papers where the high degree of polarization was predicted for ultrarelativistic case. We argue that this apparent contradiction arises due to the different choice of the spin quantum numbers. In particular, the quantum numbers that provide the high degree of polarization represent neither helicity nor transverse polarization, which makes the use of them inconvenient in practice.
Nonlinear Wave-particle Interaction and Particle Trapping in Large Amplitude Dust Acoustic Waves
Chang, Mei-Chu; Teng, Lee-Wen; Lin, I.
2011-11-29
Large amplitude dust acoustic wave can be self-excited by the strong downward ion flow in a dusty plasma liquid formed by negatively charged dusts suspended in a weakly ionized low pressure discharge. In this work, we investigate experimentally the wave-particle phase space dynamics of the large amplitude dust acoustic wave by connecting the Lagrangian and Eulerian views, through directly tracking particle motion and measuring local dust density fluctuations. The microscopic pictures of wave steepening and breaking, resonant particle-wave crest trapping, and the absence of trough trapping observed in our experiment are constructed.
Nonlinear interaction of kinetic Alfven wave with fast magnetosonic wave and turbulent spectrum
Modi, K. V.; Sharma, R. P.
2013-03-15
In the present paper, authors have investigated nonlinear interaction of kinetic Alfven wave (KAW) and fast magnetosonic wave for intermediate {beta}-plasma (m{sub e}/m{sub i} Much-Less-Than {beta} Much-Less-Than 1). Authors have developed the set of dimensionless equations in the presence of ponderomotive nonlinearity due to KAW in the dynamics of fast magnetosonic wave. Numerical simulation has been carried out to study the effect of nonlinear coupling and resulting turbulent/power spectrum for the different angles of propagation of fast magnetosonic wave applicable to solar wind at 1 AU. The localization of KAW has been found which becomes more complex as the angle of propagation of fast magnetosonic wave decreases. Results also reveal the steepening of power spectrum as the angle of propagation decreases which can be responsible for heating and acceleration of plasma particles in solar wind. Relevance of the obtained result is pointed out with observation received by Cluster spacecraft for the solar wind 1 AU.
Local computational strategies for predicting wave propagation in nonlinear media
NASA Astrophysics Data System (ADS)
Leamy, Michael J.; Autrusson, Thibaut B.; Staszewski, Wieslaw J.; Uhl, Tadeusz; Packo, Pawel
2014-03-01
Two local computational strategies for modeling elastic wave propagation, namely the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE), are compared and contrasted in analyzing bulk waves in two-dimensional nonlinear media. Each strategy formulates the problem from the perspective of a cell and its local interactions with other cells, leading to robust treatments of anisotropy, heterogeneity, and nonlinearity. The local approach also enables straight-forward parallelization on high performance computing clusters. While the two share a common local perspective, they differ in two major respects. The first is that CAFE employs both rectangular and triangular cells, while LISA considers only rectangular. The second is that LISA appeared much earlier than CAFE (early 1990's versus late 2000's), and as such has been developed to a much greater degree with a multitude of material models, cell-to-cell interactions, loading possibilities, and boundary treatments. A hybrid approach which combines the two is of great interest since the non-uniform mesh capability of the CAFE triangular cell can be readily coupled to LISA's rectangular grids, taking advantage of the built-in LISA features on the uniform portion of the domain. For linear material domains, the hybrid implementation appears straight-forward since both methods have been shown to recover the same equations in the rectangular case. For nonlinear material domains, the formulations cannot be put into a one-to-one correspondence, and hybrid implementation may be more problematic. This paper addresses these differences by first presenting the underlying formulations, and then computing results for growth of a second harmonic in an introduced bulk pressure wave. Rectangular cells are used in both LISA and CAFE. Results from both approaches are compared to an approximate, analytical solution based on a two-scale field representation. Differences in the LISA and CAFE computed
Nonlinear single Compton scattering of an electron wave packet
NASA Astrophysics Data System (ADS)
Angioi, A.; Mackenroth, F.; Di Piazza, A.
2016-05-01
Nonlinear single Compton scattering has been thoroughly investigated in the literature under the assumption that the electron initially has a definite momentum. Here, we study a more general initial state and consider the electron as a wave packet. In particular, we investigate the energy spectrum of the emitted radiation and show that, in typical experimental situations, some features of the spectra shown in previous works are almost completely washed out. Moreover, we show that, at comparable relative uncertainties, the one in the momentum of the incoming electron has a larger impact on the photon spectra at a fixed observation direction than the one on the laser frequency.
Subwavelength position sensing using nonlinear feedback and wave chaos.
Cohen, Seth D; Cavalcante, Hugo L D de S; Gauthier, Daniel J
2011-12-16
We demonstrate a position-sensing technique that relies on the inherent sensitivity of chaos, where we illuminate a subwavelength object with a complex structured radio-frequency field generated using wave chaos and nonlinear feedback. We operate the system in a quasiperiodic state and analyze changes in the frequency content of the scalar voltage signal in the feedback loop. This allows us to extract the object's position with a one-dimensional resolution of ~λ/10,000 and a two-dimensional resolution of ~λ/300, where λ is the shortest wavelength of the illuminating source.
Poloidal rotation driven by nonlinear momentum transport in strong electrostatic turbulence
NASA Astrophysics Data System (ADS)
Wang, Lu; Wen, Tiliang; Diamond, P. H.
2016-10-01
Virtually, all existing theoretical works on turbulent poloidal momentum transport are based on quasilinear theory. Nonlinear poloidal momentum flux—< {{\\tilde{v}}r}\\tilde{n}{{\\tilde{v}}θ}> is universally neglected. However, in the strong turbulence regime where relative fluctuation amplitude is no longer small, quasilinear theory is invalid. This is true at the all-important plasma edge. In this work, nonlinear poloidal momentum flux < {{\\tilde{v}}r}\\tilde{n}{{\\tilde{v}}θ}> in strong electrostatic turbulence is calculated using the Hasegawa-Mima equation, and is compared with quasilinear poloidal Reynolds stress. A novel property is that symmetry breaking in fluctuation spectrum is not necessary for a nonlinear poloidal momentum flux. This is fundamentally different from the quasilinear Reynold stress. Furthermore, the comparison implies that the poloidal rotation drive from the radial gradient of nonlinear momentum flux is comparable to that from the quasilinear Reynolds force. Nonlinear poloidal momentum transport in strong electrostatic turbulence is thus not negligible for poloidal rotation drive, and so may be significant to transport barrier formation.
Nonlinear interaction of long dispersive Kelvin waves in deep natural basins
NASA Astrophysics Data System (ADS)
Budnev, Nikolay M.; Lovtsov, Sergey V.; Portyanskaya, Inna A.; Rastegin, Alexey E.; Rubtsov, Valeriy Yu.
2010-05-01
solitons in two-liquid systems are certainly assigned by deformation convex into thicker layer. This is another reason for studies of nonlinear Kelvin waves in strongly stratified fluids. At the same time, the developed method may be useful beyond and outside the described processes in natural reservoirs. In our analysis, we have used the variant of technique known as derivative expansion method. All the dependent and independent variables are reduced to dimensionless form. The principal moment of our approach consists in consideration of boundary with vertical wall with model dispersion term introduced in dynamic equation immediately. This simplifies analysis in comparison with the original equations with generally unknown coast slope on shelf. Even if this slope is approximated by analytical expression then mathematical transformations remain enough difficult. On the other hand, the final dimensionless equations should contain only contribution of first order from dispersion caused by boundary effects. So, as initial step we merely introduce a dispersive term of proper form that is provided by similarity reasons. In zero order with respect to small parameter, the standard relations of linear theory of Kelvin waves are obtained. In order to build those expansions those are uniformly valid for all times, we reduced a certain terms to zero. So the system of nonlinear KdV-like equations is arisen as condition that all the secular terms have been removed in the first order. We also discuss possible approaches to solution of obtained equations in regimes of one- and two excited vertical modes of oscillations.
Nonlinear wave propagation in discrete and continuous systems
NASA Astrophysics Data System (ADS)
Rothos, V. M.
2016-09-01
In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.
Cascading nonlinearities in optical four-wave mixing
NASA Astrophysics Data System (ADS)
Zgonik, M.; Günter, P.
1996-03-01
In a crystal without inversion symmetry there exist two-step indirect contributions to third-order nonlinear optical processes (cascading). Contributions to optical four-wave mixing occur through optical rectification and linear electro-optic effects. In contrast to cascading by second-harmonic generation, which has to satisfy strict phase-matching conditions, optical rectification is always allowed. In polar KNbO3 crystals we measured four-wave mixing in several geometries to evaluate the direct contribution of the third-order polarizabilities and the cascaded contribution. We present a theoretical model and show experimentally that the cascading effect is large and that contributing polarization gratings must be transversely polarized.
Quantifying wave-breaking dissipation using nonlinear phase-resolved wave-field simulations
NASA Astrophysics Data System (ADS)
Qi, Y.; Xiao, W.; Yue, D. K. P.
2014-12-01
We propose to understand and quantify wave-breaking dissipation in the evolution of general irregular short-crested wave-fields using direct nonlinear phase-resolved simulations based on a High-Order Spectral (HOS) method (Dommermuth & Yue 1987). We implement a robust phenomenological-based energy dissipation model in HOS to capture the effect of wave-breaking dissipation on the overall wave-field evolution (Xiao et al 2013). The efficacy of this model is confirmed by direct comparisons against measurements for the energy loss in 2D and 3D breaking events. By comparing simulated wave-fields with and without the dissipation model in HOS, we obtain the dissipation field δ(x,y,t), which provides the times, locations and intensity of wave breaking events (δ>δc). This is validated by comparison of HOS simulations with Airborne Terrain Mapper (ATM) measurements in the recent ONR Hi-Res field experiment. Figure (a) shows one frame of simulated wave-field (with dissipation model). Figure (b) is the corresponding measurement from ATM, where a large wave breaking event was captured. Figure (c) is the 3D view of the simulated wave-field with the colored region representing dissipation with δ>δc. The HOS predicted high-dissipation area is found to agree well with the measured breaking area. Based on HOS predicted high-dissipation area (δ>δc), we calculate Λ(c) (Phillips 1985), the distribution of total length of breaking wave front per unit surface area per unit increment of breaking velocity c. Figure (d) shows the distribution Λ(c) calculated from HOS. For breaking speeds c greater than 5m/s, the simulated Λ(c) is in qualitative agreement with Phillips theoretical power-law of Λ(c)~c-6. From δ(x,y,t), we further quantify wave breaking by calculating the whitecap coverage rate Wr(t) and energy dissipation rate ΔE'(t), and study the evolution of Wr and ΔE' to understand the role of wave breaking in nonlinear wave-field evolution. We obtain HOS simulations
Nonlinear wave evolution in pressure-driven stratified flow of Newtonian and Herschel-Bulkley fluids
NASA Astrophysics Data System (ADS)
Valluri, Prashant; Sahu, Kirti; Ding, Hang; Spelt, Peter; Matar, Omar; Lawrence, Chris
2007-11-01
Pressure-driven stratified channel flow of a Newtonian fluid flowing over a Herschel-Bulkley (HB) fluid is considered. The effects of yield stress and shear-thinning rheology on the nonlinear wave evolution are studied using numerical simulations; the HB rheology is regularized at low shear rates using a bi-viscosity formulation. Two different numerical methods were used to carry out the computations: a level-set method (based on that by Spelt, J. Comput. Phys. 2005) and a diffuse-interface method (based on that by Ding et al., J. Comput. Phys., in press). The simulations, which account for fluid inertia, surface tension and gravity are validated against linear theory predictions at early times. The results at later times show the spatio-temporal evolution into the nonlinear regime wherein waves are strongly deformed, leading to the onset of drop entrainment. It is shown that the apparent viscosity in the region of the HB fluid directly involved in the onset of entrainment is almost constant; unyielded regions are confined to wave troughs at late stages of the nonlinear evolution.
NASA Astrophysics Data System (ADS)
Lieberman, M. A.; Lichtenberg, A. J.; Kawamura, Emi; Marakhtanov, A. M.
2015-09-01
It is well known that standing waves having radially center-high rf voltage profiles exist in high frequency capacitive discharges. It is also known that in radially uniform discharges, the capacitive sheath nonlinearities excite strong nonlinear series resonance harmonics that enhance the electron power deposition. In this work, we consider the coupling of the series resonance-enhanced harmonics to the standing waves. A one-dimensional, asymmetric radial transmission line model is developed incorporating the wave and nonlinear sheath physics and a self-consistent dc potential. The resulting coupled pde equation set is solved numerically to determine the discharge voltages and currents. A 10 mT argon base case is chosen with plasma density 2 ×1016 m-3, gap width 2 cm and conducting electrode radius 15 cm, driven by a high frequency 500 V source with source resistance 0.5 ohms. We find that nearby resonances lead to an enhanced ratio of 4.5 of the electron power per unit area on axis, compared to the average. The radial dependence of electron power with frequency shows significant variations, with the central enhancement and sharpness of the spatial resonances depending in a complicated way on the harmonic structure. Work supported by DOE Fusion Energy Science Contract DE-SC000193 and by a gift from the Lam Research Corporation.
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.
Nonlinear electron acceleration by oblique whistler waves: Landau resonance vs. cyclotron resonance
Artemyev, A. V.; Agapitov, O. V.; Krasnoselskikh, V. V.; Mourenas, D.
2013-12-15
This paper is devoted to the study of the nonlinear interaction of relativistic electrons and high amplitude strongly oblique whistler waves in the Earth's radiation belts. We consider electron trapping into Landau and fundamental cyclotron resonances in a simplified model of dipolar magnetic field. Trapping into the Landau resonance corresponds to a decrease of electron equatorial pitch-angles, while trapping into the first cyclotron resonance increases electron equatorial pitch-angles. For 100 keV electrons, the energy gained due to trapping is similar for both resonances. For electrons with smaller energy, acceleration is more effective when considering the Landau resonance. Moreover, trapping into the Landau resonance is accessible for a wider range of initial pitch-angles and initial energies in comparison with the fundamental resonance. Thus, we can conclude that for intense and strongly oblique waves propagating in the quasi-electrostatic mode, the Landau resonance is generally more important than the fundamental one.
Zhao, J. S.; Wu, D. J.; Voitenko, Y.; De Keyser, J.
2014-04-20
We study the nonlocal nonlinear coupling and generation of kinetic Alfvén waves (KAWs) and kinetic slow waves (KSWs) by magnetohydrodynamic Alfvén waves (MHD AWs) in conditions typical for the solar wind in the inner heliosphere. This cross-scale process provides an alternative to the turbulent energy cascade passing through many intermediate scales. The nonlinearities we study are proportional to the scalar products of wave vectors and hence are called 'scalar' ones. Despite the strong Landau damping of kinetic waves, we found fast growing KAWs and KSWs at perpendicular wavelengths close to the ion gyroradius. Using the parametric decay formalism, we investigate two independent decay channels for the pump AW: forward decay (involving co-propagating product waves) and backward decay (involving counter-propagating product waves). The growth rate of the forward decay is typically 0.05 but can exceed 0.1 of the pump wave frequency. The resulting spectral transport is nonlocal and anisotropic, sharply increasing perpendicular wavenumbers but not parallel ones. AWs and KAWs propagating against the pump AW grow with about the same rate and contribute to the sunward wave flux in the solar wind. Our results suggest that the nonlocal decay of MHD AWs into KAWs and KSWs is a robust mechanism for the cross-scale spectral transport of the wave energy from MHD to dissipative kinetic scales in the solar wind and similar media.
Linear and nonlinear effects in detonation wave structure formation
NASA Astrophysics Data System (ADS)
Borisov, S. P.; Kudryavtsev, A. N.
2016-06-01
The role of linear and nonlinear effects in the process of formation of detonation wave structure is investigated using linear stability analysis and direct numerical simulation. A simple model with a one-step irreversible chemical reaction is considered. For linear stability computations, both the local iterative shooting procedure and the global Chebyshev pseudospectral method are employed. Numerical simulations of 1D pulsating instability are performed using a shock fitting approach based on a 5th order upwind-biased compact-difference discretization and a shock acceleration equation deduced from the Rankine-Hugoniot conditions. A shock capturing WENO scheme of the 5th order is used to simulate propagation of detonation wave in a plane channel. It is shown that the linear analysis predicts correctly the mode dominating on early stages of flow evolution and the size of detonation cells which emerge during these stages. Later, however, when a developed self-reproducing cellular structure forms, the cell size is approximately doubled due to nonlinear effects.
Nonlinear focusing of acoustic shock waves at a caustic cusp.
Marchiano, Régis; Coulouvrat, François; Thomas, Jean-Louis
2005-02-01
The present study investigates the focusing of acoustical weak shock waves incoming on a cusped caustic. The theoretical model is based on the Khokhlov-Zabolotskaya equation and its specific boundary conditions. Based on the so-called Guiraud's similitude law for a step shock, a new explanation about the wavefront unfolding due to nonlinear self-refraction is proposed. This effect is shown to be associated not only to nonlinearities, as expected by previous authors, but also to the nonlocal geometry of the wavefront. Numerical simulations confirm the sensitivity of the process to wavefront geometry. Theoretical modeling and numerical simulations are substantiated by an original experiment. This one is carried out in two steps. First, the canonical Pearcey function is synthesized in linear regime by the inverse filter technique. In the second step, the same wavefront is emitted but with a high amplitude to generate shock waves during the propagation. The experimental results are compared with remarkable agreement to the numerical ones. Finally, applications to sonic boom are briefly discussed. PMID:15759678
Solitary waves and nonlinear dynamic coherent structures in magnetic metamaterials
NASA Astrophysics Data System (ADS)
Tankeyev, A. P.; Smagin, V. V.; Borich, M. A.; Zhuravlev, A. S.
2009-03-01
Within the framework of the extended nonlinear Schrödinger equation (ENSE), two types of nonlinear states of magnetization in a ferromagnet-dielectric-metal metamagnetic structure have been obtained and investigated. These states have an internal structure; e.g., a periodic sequence of compound solitons is formed by kink-antikink pairs (shock waves), and coherent periodic breather structures are formed by “bright” quasi-solitons. Conditions have been found under which the envelope of these states is described by a modified Korteweg-de Vries (mKdV) equation. It is shown that the compound solitons are described by an mKdV equation with repulsion, and the breather structures, by an mKdV equation with attraction. It is shown also that the characteristic properties of the solutions are determined by the sign of the group-velocity dispersion rather than by the sign of the group velocity itself. The results obtained can be used for searching new nonlinear dynamic coherent structures, e.g., compound solitons and breathers in high-dispersion magnetic metamaterials.
The Wave Processes in the Media Having Inelastic Hysteresis with Saturation of The Nonlinear Loss
NASA Astrophysics Data System (ADS)
Nazarov, V. E.; Kiyashko, S. B.
2016-07-01
We study theoretically the nonlinear wave processes during excitation of a longitudinal harmonic wave in an unbounded medium and the rod resonator with inelastic hysteresis and saturation of the amplitude-dependent loss. The nonlinear-wave characteristics in such systems, namely, the amplitude-dependent loss, variation in the wave-propagation velocity, the resonant-frequency shift, and the higher-harmonic amplitudes are determined. The results of the theoretical and experimental studies of nonlinear effects in the rod resonator of annealed polycrystalline copper are compared. The effective parameters of the hysteretic nonlinearity of this metal are evaluated.
2D wave-front shaping in optical superlattices using nonlinear volume holography.
Yang, Bo; Hong, Xu-Hao; Lu, Rong-Er; Yue, Yang-Yang; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan
2016-07-01
Nonlinear volume holography is employed to realize arbitrary wave-front shaping during nonlinear processes with properly designed 2D optical superlattices. The concept of a nonlinear polarization wave in nonlinear volume holography is investigated. The holographic imaging of irregular patterns was performed using 2D LiTaO_{3} crystals with fundamental wave propagating along the spontaneous polarization direction, and the results agree well with the theoretical predictions. This Letter not only extends the application area of optical superlattices, but also offers an efficient method for wave-front shaping technology.
High-informative version of nonlinear transformation of Langmuir waves to electromagnetic waves
NASA Astrophysics Data System (ADS)
Erofeev, Vasily I.; Erofeev
2014-04-01
The concept of informativeness of nonlinear plasma physical scenario is discussed. Basic principles for heightening the informativeness of plasma kinetic models are explained. Former high-informative correlation analysis of plasma kinetics (Erofeev, V. 2011 High-Informative Plasma Theory, Saarbrücken: LAP) is generalized for studies of weakly turbulent plasmas that contain fields of solenoidal plasma waves apart from former potential ones. Respective machinery of plasma kinetic modeling is applied to an analysis of fusion of Langmuir waves with transformation to electromagnetic waves. It is shown that the customary version of this phenomenon (Terashima, Y. and Yajima, N. 1963 Prog. Theor. Phys. 30, 443; Akhiezer, I. A., Danelia, I. A. and Tsintsadze, N. L. 1964 Sov. Phys. JETP 19, 208; Al'tshul', L. M. and Karpman, V. I. 1965 Sov. Phys. JETP 20, 1043) substantially distorts the picture of merging of Langmuir waves with long wavelengths (λ >~ c/ωpe ).
NASA Technical Reports Server (NTRS)
Matda, Y.; Crawford, F. W.
1974-01-01
An economical low noise plasma simulation model is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation, to establish the low noise features and to verify the theoretical linear dispersion relation at wave energy levels as low as 0.000,001 of the plasma thermal energy. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories. The additional phenomena of sideband instability and satellite growth, stimulated by large amplitude wave propagation and the resulting particle trapping, are described.
Strong Tidal Modulation of Estuarine Surface Wind Waves
NASA Astrophysics Data System (ADS)
Geiman, J.; Qin, W.; Nayak, M.; Kirby, J.; Badiey, M.
2006-05-01
The surface wave field in Delaware Bay, on the Mid-Atlantic coast of the USA, is often dominated by locally generated fetch and duration limited waves due to a somewhat restricted opening to the ocean. Measurements of wave conditions in the Bay have been conducted only sporadically and for short periods. In several of those periods, we have noticed an apparent modulation of rms wave height which appears to be related to tidal activity, and which is not recovered using SWAN (without current input) and measured wind input. Wave records are too short to allow for reliable Fourier analysis of the wave height signal aimed at demonstrating the dependence on tidal period. In May, 2005, a short experiment collected waverider data for a 5 day period in mid Delaware Bay. During this period, there was a stretch of nearly constant wind speed and direction lasting for almost 2 days, with a speed of 9 to 10 m/s and a direction from nearly due North, which is about 30 degrees oblique to the principal orientation of the Bay. This data record, while not longer than earlier efforts, clearly indicates the role played by tidal currents in modulating the locally generated wave conditions, since this modulation is the only significant variation in environmental conditions involved. About 3.5 cycles of the tidal modulation under constant forcing conditions are exhibited in the data. The principal modulation of wave peak period and rms wave height is explained using a simple process model that examines fetch limited wave growth on an oscillatory current. We utilize the empirical model of Young and Verhagen (1996), but use current information to determine wind speed relative to the moving water column. Subsequently, we interpret the resulting predicted peak frequency as being relative to the moving water column, and use a Doppler shift to convert to absolute frequency in the stationary frame of the waverider. Both extensions to the usual theory play comparable roles in determining the
Turbulent Magnetic Field Amplification behind Strong Shock Waves in GRB and SNR
NASA Astrophysics Data System (ADS)
Inoue, Tsuyoshi
2012-09-01
Using three-dimensional (special relativistic) magnetohydrodynamics simulations, the amplification of magnetic field behind strong shock wave is studied. In supernova remnants and gamma-ray bursts, strong shock waves propagate through an inhomogeneous density field. When the shock wave hit a density bump or density dent, the Richtmyer-Meshkov instability is induced that cause a deformation of the shock front. The deformed shock leaves vorticity behind the shock wave that amplifies the magnetic field due to the stretching of field lines.
NASA Astrophysics Data System (ADS)
Kapuria, S.; Yaqoob Yasin, M.
2013-05-01
In this work, we present an electromechanically coupled efficient layerwise finite element model for the static response of piezoelectric laminated composite and sandwich plates, considering the nonlinear behavior of piezoelectric materials under strong electric field. The nonlinear model is developed consistently using a variational principle, considering a rotationally invariant second order nonlinear constitutive relationship, and full electromechanical coupling. In the piezoelectric layer, the electric potential is approximated to have a quadratic variation across the thickness, as observed from exact three dimensional solutions, and the equipotential condition of electroded piezoelectric surfaces is modeled using the novel concept of an electric node. The results predicted by the nonlinear model compare very well with the experimental data available in the literature. The effect of the piezoelectric nonlinearity on the static response and deflection/stress control is studied for piezoelectric bimorph as well as hybrid laminated plates with isotropic, angle-ply composite and sandwich substrates. For high electric fields, the difference between the nonlinear and linear predictions is large, and cannot be neglected. The error in the prediction of the smeared counterpart of the present theory with the same number of primary displacement unknowns is also examined.
NASA Astrophysics Data System (ADS)
Sleep, Norman H.; Nakata, Nori
2015-07-01
Strong seismic waves bring rock into frictional failure at the uppermost few hundred meters. Numerous small fractures slip with the cumulative effect of anelastic strain and nonlinear attenuation; these fractures should not distinguish between remote sources of stress. Still, frictional failure criteria are not evident especially when seismic waves change the normal traction on fractures. We identify three earthquakes as examples where consideration of interaction among dynamic stresses from different wave types and ambient tectonic stress provides theoretical predictions of nonlinear attenuation that are potentially testable with single station seismograms. For example, because Rayleigh waves produce shallow horizontal dynamic tension and compression, frictional failure should preferentially occur on the tensile half-cycle if no shallow tectonic stress is present and on the compressional half-cycle if the tectonic stress is already near thrust-faulting failure. We observed neither effect on records from the 2011 Mw 9.0 Great Tohoku earthquake. However, Rayleigh waves from this event appear to have brought rock beneath MYGH05 station into frictional failure at ˜10 m depth and thus suppressed high-frequency S waves. The tensile half-cycle of high-frequency P waves reduced normal traction on horizontal planes beneath station IWTH25 during the 2008 Mw 6.9 Iwate-Miyagi earthquake, weakening the rock in shear and suppressing high-frequency S waves. The near-field velocity pulse from the 1992 Mw 7.3 Landers earthquake brought the uppermost few hundred meters of granite beneath Lucerne station into frictional failure, suppressing high-frequency S waves. These moderately positive examples support the reality of nonlinear wave interaction, warranting study future strong ground motions.
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)
Chou, Chung-Pin; Lee, T. K.; Ho, Chang-Ming
2009-03-01
We examine the strong correlation effects of the d-wave superconducting state by including the Gutzwiller projection for no electron double occupancy at each lattice site. The spectral weights (SW's) for adding and removing an electon on the projected superconducting state, the ground state of the 2-dimensional t-t'-t"-J model with moderate doped holes describing the high Tc cuprates, are studied numerically on finite lattices and compared with the observation made by low-temperature tunneling (particle asymmetry of tunneling conductance) and angle-resolved photoemission (SW transfer from the projected Fermi liquid tate) spectoscopies. The contast with the dwave case without projection is alo presented.
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.
Threshold for electron trapping nonlinearity in Langmuir waves
Strozzi, D. J.; Williams, E. A.; Hinkel, D. E.; Langdon, A. B.; Banks, J. W.; Rose, H. A.
2012-11-15
We assess when electron trapping nonlinearity is expected to be important in Langmuir waves. The basic criterion is that the inverse of the detrapping rate {nu}{sub d} of electrons in the trapping region of velocity space must exceed the bounce period of deeply trapped electrons, {tau}{sub B}{identical_to}(n{sub e}/{delta}n){sup 1/2}2{pi}/{omega}{sub pe}. A unitless figure of merit, the 'bounce number'N{sub B}{identical_to}1/{nu}{sub d}{tau}{sub B}, encapsulates this condition and defines a trapping threshold amplitude for which N{sub B}=1. The detrapping rate is found for convective loss (transverse and longitudinal) out of a spatially finite Langmuir wave. Simulations of driven waves with a finite transverse profile, using the 2D-2V Vlasov code LOKI, show trapping nonlinearity increases continuously with N{sub B} for transverse loss, and is significant for N{sub B} Almost-Equal-To 1. The detrapping rate due to Coulomb collisions (both electron-electron and electron-ion) is also found, with pitch-angle scattering and parallel drag and diffusion treated in a unified manner. A simple way to combine convective and collisional detrapping is given. Application to underdense plasma conditions in inertial confinement fusion targets is presented. The results show that convective transverse loss is usually the most potent detrapping process in a single f/8 laser speckle. For typical plasma and laser conditions on the inner laser cones of the National Ignition Facility, local reflectivities {approx}3% are estimated to produce significant trapping effects.
Suret, Pierre; Picozzi, Antonio; Randoux, Stéphane
2011-08-29
We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a statistically stationary state. The evolution of the power spectrum of the field is characterized by the rapid growth of spectral tails that exhibit damped oscillations, until the whole spectrum ultimately reaches a steady state. The kinetic approach allows us to derive an analytical expression of the damped oscillations, which is found in agreement with the numerical simulations of both the NLS and kinetic equations. We report the experimental observation of this peculiar relaxation process of the integrable NLS equation.
Suret, Pierre; Picozzi, Antonio; Randoux, Stéphane
2011-08-29
We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a statistically stationary state. The evolution of the power spectrum of the field is characterized by the rapid growth of spectral tails that exhibit damped oscillations, until the whole spectrum ultimately reaches a steady state. The kinetic approach allows us to derive an analytical expression of the damped oscillations, which is found in agreement with the numerical simulations of both the NLS and kinetic equations. We report the experimental observation of this peculiar relaxation process of the integrable NLS equation. PMID:21935152
Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves.
Salerno, D; Minardi, S; Trull, J; Varanavicius, A; Tamosauskas, G; Valiulis, G; Dubietis, A; Caironi, D; Trillo, S; Piskarskas, A; Di Trapani, P
2003-10-01
We investigate experimentally the competition between spatial and temporal breakup due to modulational instability in chi((2)) nonlinear mixing. The modulation of the wave packets caused by the energy exchange between fundamental and second-harmonic components is found to be the prevailing trigger mechanism which, according to the relative weight of diffraction and dispersion, leads to the appearance of a multisoliton pattern in the low-dimensional spatial or temporal domain.
Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Auxiliary Equation Method
NASA Astrophysics Data System (ADS)
Kaplan, Melike; Akbulut, Arzu; Bekir, Ahmet
2015-10-01
The auxiliary equation method presents wide applicability to handling nonlinear wave equations. In this article, we establish new exact travelling wave solutions of the nonlinear Zoomeron equation, coupled Higgs equation, and equal width wave equation. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions, and rational functions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Throughout the article, all calculations are made with the aid of the Maple packet program.
NASA Astrophysics Data System (ADS)
Demidov, V. E.; Hansen, U.-F.; Dzyapko, O.; Koulev, N.; Demokritov, S. O.; Slavin, A. N.
2006-09-01
Formation of stationary longitudinal amplitude patterns by propagating nonlinear spin waves has been discovered and studied experimentally by means of space-resolved Brillouin light scattering spectroscopy. The pattern formation is observed for spin waves propagating in narrow, longitudinally magnetized yttrium iron garnet stripes, characterized by attractive nonlinearity in both the longitudinal and transverse directions. A clear crossover of the effective dimensionality describing the propagation of spin waves in the stripe is observed with increase of the wave amplitude.
A flexible genuinely nonlinear approach for nonlinear wave propagation, breaking and run-up
NASA Astrophysics Data System (ADS)
Filippini, A. G.; Kazolea, M.; Ricchiuto, M.
2016-04-01
In this paper we evaluate hybrid strategies for the solution of the Green-Naghdi system of equations for the simulation of fully nonlinear and weakly dispersive free surface waves. We consider a two step solution procedure composed of: a first step where the non-hydrostatic source term is recovered by inverting the elliptic coercive operator associated to the dispersive effects; a second step which involves the solution of the hyperbolic shallow water system with the source term, computed in the previous phase, which accounts for the non-hydrostatic effects. Appropriate numerical methods, that can be also generalized on arbitrary unstructured meshes, are used to discretize the two stages: the standard C0 Galerkin finite element method for the elliptic phase; either third order Finite Volume or third order stabilized Finite Element method for the hyperbolic phase. The discrete dispersion properties of the fully coupled schemes obtained are studied, showing accuracy close to or better than that of a fourth order finite difference method. The hybrid approach of locally reverting to the nonlinear shallow water equations is used to recover energy dissipation in breaking regions. To this scope we evaluate two strategies: simply neglecting the non-hydrostatic contribution in the hyperbolic phase; imposing a tighter coupling of the two phases, with a wave breaking indicator embedded in the elliptic phase to smoothly turn off the dispersive effects. The discrete models obtained are thoroughly tested on benchmarks involving wave dispersion, breaking and run-up, showing a very promising potential for the simulation of complex near shore wave physics in terms of accuracy and robustness.
Dual variational principles for nonlinear traveling waves in multifluid plasmas
Webb, G. M.; McKenzie, J. F.; Mace, R. L.; Ko, C. M.; Zank, G. P.
2007-08-15
A Hamiltonian description of nonlinear, obliquely propagating traveling waves in a charge neutral, electron-proton, multifluid plasma is developed. The governing equations are written as a dual spatial Hamiltonian system. In the first formulation, the Hamiltonian is identified with the longitudinal, x-momentum flux integral P{sub x}=const, in which the energy integral {epsilon}={epsilon}{sub 0} acts as a constraint, and the Hamiltonian evolution operator is d/dx, where x is the position coordinate in the wave frame. In the second Hamiltonian formulation, the Hamiltonian is proportional to the conserved energy integral {epsilon}, in which the momentum integral P{sub x}=const acts as a constraint, and the Hamiltonian evolution operator d/d{tau}=u{sub x}d/dx is the Lagrangian time derivative where u{sub x} is the x component of the electron and proton fluids. The analysis is facilitated by using the de Hoffman-Teller frame of magnetohydrodynamic shock theory to simplify the transverse electron and proton momentum equations. The system is exactly integrable in cases in which the total transverse momentum fluxes of the system are zero in the de Hoffman-Teller frame. The implications of this constraint for the Alfven Mach number of the traveling wave are discussed. The physical conditions for the formation of whistler oscillitons based on the whistler dispersion equation are discussed.
NASA Astrophysics Data System (ADS)
Cao, Wenhua
2016-05-01
Predispersion for reduction of intrachannel nonlinear impairments in quasi-linear strongly dispersion-managed transmission system is analyzed in detail by numerical simulations. We show that for moderate amount of predispersion there is an optimal value at which reduction of the nonlinear impairments can be obtained, which is consistent with previous well-known predictions. However, we found that much better transmission performance than that of the previous predictions can be obtained if predispersion is increased to some extent. For large predispersion, the nonlinear impairments reduce monotonically with increasing predispersion and then they tend to be stabilized when predispersion is further increased. Thus, transmission performance can be efficiently improved by inserting a high-dispersive element, such as a chirped fiber bragg grating (CFBG), at the input end of the transmission link to broaden the signal pulses while, at the output end, using another CFBG with the opposite dispersion to recompress the signal.
Ashwin, J.; Ganesh, R.
2011-08-15
Using classical molecular dynamics (MD) simulations, we report on the development and propagation of a nonlinear heat front in parallel shear flows of a strongly coupled Yukawa liquid. At a given coupling strength, a subsonic shear profile is superposed on an equilibrated Yukawa liquid and Kelvin Helmholtz (KH) instability is observed. Coherent vortices are seen to emerge towards the nonlinear regime of the instability. It is seen that while inverse cascade leads to a continuous transfer of flow energy towards the largest scales, there is also a simultaneous transfer of flow energy into the thermal velocities of grains at the smallest scale. The latter is an effect of velocity shear and thus leads to the generation of a nonlinear heat front. In the linear regime, the heat front is seen to propagate at speed much lesser than the adiabatic sound speed of the liquid. Spatio-temporal growth of this heat front occurs concurrently with the inverse cascade of KH modes.
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.
Experimental study of strong nonlinear-optics effects in liquid crystals
NASA Astrophysics Data System (ADS)
Darbin, S. D.; Arakelyan, S. M.; Cheung, M. M.; Shen, Y. R.
1984-07-01
Nonlinear optical effects that arise in nematic liquid crystals as a result of a change in the index of refraction induced by a laser field are considered. Since the resultant nonlinearity is extremely high, the approximation of perturbation theory cannot be used in calculations. However, the change in refractive index results mainly in phase advance as waves propagate through a thin film of liquid crystal, while the change of intensity is significant. Moreover, if there is no change in polarization of the pumping field, calculations are relatively simple. An investigation is made of the propagation of a cross sectionally bounded laser beam through a homeotropically oriented liquid crystal, giving rise to spatial phase modulation of emission. When the intensity of the laser beam exceeds a certain value, a system of aberation rings is observed in the output radiation. Effects of dynamic self-diffraction accompanying degenerate four-wave mixing when a change in refractive index is induced in a homeotropic liquid crystal film, and optical bistability in a nonlinear Fabry-Perot optical cavity, as well as generation of a self-oscillatory state in such a resonator are discussed.
NASA Astrophysics Data System (ADS)
Hasselmann, Klaus; Hasselmann, Susanne
1991-06-01
. This difficulty is overcome by applying a two-step inversion procedure. In the first step the energy level of the wave spectrum is adjusted, and the wave number plane rotated and rescaled, without altering the shape of the spectrum. Using the resulting globally fitted spectrum as the new first-guess input spectrum, the original inversion method is then applied without further constraints in a second step to obtain a final fine-scale optimized spectrum. The forward mapping relation and inversion algorithms are illustrated for three Seasat cases representing different wave conditions corresponding to weakly, moderately, and strongly nonlinear imaging conditions.
On strongly interacting internal waves in a rotating ocean and coupled Ostrovsky equations.
Alias, A; Grimshaw, R H J; Khusnutdinova, K R
2013-06-01
In the weakly nonlinear limit, oceanic internal solitary waves for a single linear long wave mode are described by the KdV equation, extended to the Ostrovsky equation in the presence of background rotation. In this paper we consider the scenario when two different linear long wave modes have nearly coincident phase speeds and show that the appropriate model is a system of two coupled Ostrovsky equations. These are systematically derived for a density-stratified ocean. Some preliminary numerical simulations are reported which show that, in the generic case, initial solitary-like waves are destroyed and replaced by two coupled nonlinear wave packets, being the counterpart of the same phenomenon in the single Ostrovsky equation. PMID:23822486
On strongly interacting internal waves in a rotating ocean and coupled Ostrovsky equations.
Alias, A; Grimshaw, R H J; Khusnutdinova, K R
2013-06-01
In the weakly nonlinear limit, oceanic internal solitary waves for a single linear long wave mode are described by the KdV equation, extended to the Ostrovsky equation in the presence of background rotation. In this paper we consider the scenario when two different linear long wave modes have nearly coincident phase speeds and show that the appropriate model is a system of two coupled Ostrovsky equations. These are systematically derived for a density-stratified ocean. Some preliminary numerical simulations are reported which show that, in the generic case, initial solitary-like waves are destroyed and replaced by two coupled nonlinear wave packets, being the counterpart of the same phenomenon in the single Ostrovsky equation.
Analysis and modeling of broadband airgun data influenced by nonlinear internal waves.
Frank, Scott D; Badiey, Mohsen; Lynch, James F; Siegmann, William L
2004-12-01
To investigate acoustic effects of nonlinear internal waves, the two southwest tracks of the SWARM 95 experiment are considered. An airgun source produced broadband acoustic signals while a packet of large nonlinear internal waves passed between the source and two vertical linear arrays. The broadband data and its frequency range (10-180 Hz) distinguish this study from previous work. Models are developed for the internal wave environment, the geoacoustic parameters, and the airgun source signature. Parabolic equation simulations demonstrate that observed variations in intensity and wavelet time-frequency plots can be attributed to nonlinear internal waves. Empirical tests are provided of the internal wave-acoustic resonance condition that is the apparent theoretical mechanism responsible for the variations. Peaks of the effective internal wave spectrum are shown to coincide with differences in dominant acoustic wavenumbers comprising the airgun signal. The robustness of these relationships is investigated by simulations for a variety of geoacoustic and nonlinear internal wave model parameters.
A nonlinear model of ionic wave propagation along microtubules.
Satarić, M V; Ilić, D I; Ralević, N; Tuszynski, Jack Adam
2009-06-01
Microtubules (MTs) are important cytoskeletal polymers engaged in a number of specific cellular activities including the traffic of organelles using motor proteins, cellular architecture and motility, cell division and a possible participation in information processing within neuronal functioning. How MTs operate and process electrical information is still largely unknown. In this paper we investigate the conditions enabling MTs to act as electrical transmission lines for ion flows along their lengths. We introduce a model in which each tubulin dimer is viewed as an electric element with a capacitive, inductive and resistive characteristics arising due to polyelectrolyte nature of MTs. Based on Kirchhoff's laws taken in the continuum limit, a nonlinear partial differential equation is derived and analyzed. We demonstrate that it can be used to describe the electrostatic potential coupled to the propagating localized ionic waves. PMID:19259657
Standing waves for supercritical nonlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Dávila, Juan; del Pino, Manuel; Musso, Monica; Wei, Juncheng
Let V(x) be a non-negative, bounded potential in R, N⩾3 and p supercritical, p>{N+2}/{N-2}. We look for positive solutions of the standing-wave nonlinear Schrödinger equation Δu-V(x)u+u=0 in R, with u(x)→0 as |x|→+∞. We prove that if V(x)=o(|) as |x|→+∞, then for N⩾4 and p>{N+1}/{N-3} this problem admits a continuum of solutions. If in addition we have, for instance, V(x)=O(|) with μ>N, then this result still holds provided that N⩾3 and p>{N+2}/{N-2}. Other conditions for solvability, involving behavior of V at ∞, are also provided.
Strong quantum squeezing near the pull-in instability of a nonlinear beam
NASA Astrophysics Data System (ADS)
Passian, Ali; Siopsis, George
2016-08-01
Microscopic silicon-based suspended mechanical oscillators, constituting an extremely sensitive force probe, transducer, and actuator, are being increasingly employed in many developing microscopies, spectroscopies, and emerging optomechanical and chem-bio sensors. We predict a significant squeezing in the quantum state of motion of an oscillator constrained as a beam and subject to an electrically induced nonlinearity. By taking into account the quantum noise, the underlying nonlinear dynamics is investigated in both the transient and stationary regimes of the driving force leading to the finding that strongly squeezed states are accessible in the vicinity of the pull-in instability of the oscillator. We discuss a possible application of this strong quantum squeezing as an optomechanical method for detecting broad-spectrum single or low-count photons, and further suggest other novel sensing actions.
Strong quantum squeezing near the pull-in instability of a nonlinear beam
Passian, Ali; Siopsis, George
2016-08-04
Microscopic silicon-based suspended mechanical oscillators, constituting an extremely sensitive force probe, transducer, and actuator, are being increasingly employed in many developing microscopies, spectroscopies, and emerging optomechanical and chem-bio sensors. Here, we predict a significant squeezing in the quantum state of motion of an oscillator constrained as a beam and subject to an electrically induced nonlinearity. When we take into account the quantum noise, the underlying nonlinear dynamics is investigated in both the transient and stationary regimes of the driving force leading to the finding that strongly squeezed states are accessible in the vicinity of the pull-in instability of the oscillator.more » We discuss a possible application of this strong quantum squeezing as an optomechanical method for detecting broad-spectrum single or low-count photons, and further suggest other novel sensing actions.« less
A stabilised nodal spectral element method for fully nonlinear water waves
NASA Astrophysics Data System (ADS)
Engsig-Karup, A. P.; Eskilsson, C.; Bigoni, D.
2016-08-01
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively removes any aliasing driven instabilities while retaining the high-order accuracy of the numerical scheme. The additional computational cost of the over-integration is found insignificant compared to the cost of solving the Laplace problem. The model is applied to several benchmark cases in two dimensions. The results confirm the high order accuracy of the model (exponential convergence), and demonstrate the potential for accuracy and speedup. The results of numerical experiments are in excellent agreement with both analytical and experimental results for strongly nonlinear and irregular dispersive wave propagation. The benefit of using a high-order - possibly adapted - spatial discretisation for accurate water wave propagation over long times and distances is particularly attractive for marine hydrodynamics applications.
Yao, Yu-Qin; Li, Ji; Han, Wei; Wang, Deng-Shan; Liu, Wu-Ming
2016-01-01
The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning.
Yao, Yu-Qin; Li, Ji; Han, Wei; Wang, Deng-Shan; Liu, Wu-Ming
2016-01-01
The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning. PMID:27403634
Nonlinear mechanisms for drift wave saturation and induced particle transport
Dimits, A.M. . Lab. for Plasma Research); Lee, W.W. . Plasma Physics Lab.)
1989-12-01
A detailed theoretical study of the nonlinear dynamics of gyrokinetic particle simulations of electrostatic collisionless and weakly collisional drift waves is presented. In previous studies it was shown that, in the nonlinearly saturated phase of the evolution, the saturation levels and especially the particle fluxes have an unexpected dependence on collisionality. In this paper, the explanations for these collisionality dependences are found to be as follows: The saturation level is determined by a balance between the electron and ion fluxes. The ion flux is small for levels of the potential below an E {times} B-trapping threshold and increases sharply once this threshold is crossed. Due to the presence of resonant electrons, the electron flux has a much smoother dependence on the potential. In the 2-1/2-dimensional ( pseudo-3D'') geometry, the electrons are accelerated away from the resonance as they diffuse spatially, resulting in an inhibition of their diffusion. Collisions and three-dimensional effects can repopulate the resonance thereby increasing the value of the particle flux. 30 refs., 32 figs., 2 tabs.
New Traveling Wave Solutions for a Class of Nonlinear Evolution Equations
NASA Astrophysics Data System (ADS)
Bai, Cheng-Jie; Zhao, Hong; Xu, Heng-Ying; Zhang, Xia
The deformation mapping method is extended to solve a class of nonlinear evolution equations (NLEEs). Many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, and Jacobian elliptic function solutions, are obtained by a simple algebraic transformation relation between the solutions of the NLEEs and those of the cubic nonlinear Klein-Gordon (NKG) equation.
Jiménez-Sánchez, Arturo; Isunza-Manrique, Itzel; Ramos-Ortiz, Gabriel; Rodríguez-Romero, Jesús; Farfán, Norberto; Santillan, Rosa
2016-06-30
Design parameters derived from structure-property relationships play a very important role in the development of efficient molecular-based functional materials with optical properties. Here, we report on the linear and nonlinear optical properties of a fluorene-derived dipolar system (DS) and its octupolar analogue (OS), in which donor and acceptor groups are connected by a phenylacetylene linkage, as a strategy to increase the number of delocalized electrons in the π-conjugated system. The optical nonlinear response was analyzed in detail by experimental and theoretical methods, showing that, in the octupolar system OS, the dipolar effects induced a strong two-photon absorption process whose magnitude is as large as 2210 GM at infrared wavelengths. Solvatochromism studies were implemented to obtain further insight on the charge transfer process. We found that the triple bond plays a fundamental role in the linear and nonlinear optical responses. The strong solvatochromism behavior in DS and OS was analyzed by using four empirical solvent scales, namely Lippert-Mataga, Kamlet-Taft, Catalán, and the recently proposed scale of Laurence et al., finding consistent results of strong solvent polarizability and viscosity dependence. Finally, the role of the acceptor groups was further studied by synthesizing the analogous compound 2DS, having no acceptor group.
Jiménez-Sánchez, Arturo; Isunza-Manrique, Itzel; Ramos-Ortiz, Gabriel; Rodríguez-Romero, Jesús; Farfán, Norberto; Santillan, Rosa
2016-06-30
Design parameters derived from structure-property relationships play a very important role in the development of efficient molecular-based functional materials with optical properties. Here, we report on the linear and nonlinear optical properties of a fluorene-derived dipolar system (DS) and its octupolar analogue (OS), in which donor and acceptor groups are connected by a phenylacetylene linkage, as a strategy to increase the number of delocalized electrons in the π-conjugated system. The optical nonlinear response was analyzed in detail by experimental and theoretical methods, showing that, in the octupolar system OS, the dipolar effects induced a strong two-photon absorption process whose magnitude is as large as 2210 GM at infrared wavelengths. Solvatochromism studies were implemented to obtain further insight on the charge transfer process. We found that the triple bond plays a fundamental role in the linear and nonlinear optical responses. The strong solvatochromism behavior in DS and OS was analyzed by using four empirical solvent scales, namely Lippert-Mataga, Kamlet-Taft, Catalán, and the recently proposed scale of Laurence et al., finding consistent results of strong solvent polarizability and viscosity dependence. Finally, the role of the acceptor groups was further studied by synthesizing the analogous compound 2DS, having no acceptor group. PMID:27281172
"Photonic" Cat States from Strongly Interacting Matter Waves.
Fischer, Uwe R; Kang, Myung-Kyun
2015-12-31
We consider ultracold quantum gases of scalar bosons residing in a coupling strength-density regime in which they constitute a twofold fragmented condensate trapped in a single well. It is shown that the corresponding quantum states are, in the appropriate Fock space basis, identical to the photon cat states familiar in quantum optics, which correspond to superpositions of coherent states of the light field with a phase difference of π. In marked distinction to photon cat states, however, the very existence of matter-wave cat states crucially depends on the many-body correlations of the constituent bosons. We consequently establish that the quadratures of the effective "photons," expressing the highly nonclassical nature of the macroscopic matter-wave superposition state, can be experimentally accessed by measuring the density-density correlations of the interacting quantum gas. PMID:26764977
"Photonic" Cat States from Strongly Interacting Matter Waves.
Fischer, Uwe R; Kang, Myung-Kyun
2015-12-31
We consider ultracold quantum gases of scalar bosons residing in a coupling strength-density regime in which they constitute a twofold fragmented condensate trapped in a single well. It is shown that the corresponding quantum states are, in the appropriate Fock space basis, identical to the photon cat states familiar in quantum optics, which correspond to superpositions of coherent states of the light field with a phase difference of π. In marked distinction to photon cat states, however, the very existence of matter-wave cat states crucially depends on the many-body correlations of the constituent bosons. We consequently establish that the quadratures of the effective "photons," expressing the highly nonclassical nature of the macroscopic matter-wave superposition state, can be experimentally accessed by measuring the density-density correlations of the interacting quantum gas.
Nonlinear effects related to circularly polarized dispersive Alfvén waves
NASA Astrophysics Data System (ADS)
Sharma, Swati; Gaur, Nidhi; Sharma, R. P.
2016-09-01
In situ measurements of solar wind have strongly implicated its turbulent behavior. The observed power spectra report a breakpoint around length scales of the order of ion scales. As one of the responsible mechanisms for the observed steepening in power spectrum, our approach includes a right circularly polarized dispersive Alfvén wave (DAW) with finite frequency correction which, when subjected to transverse collapse/filamentation instability, may possibly result in steepening of spectrum and progressive transfer of energy from larger scales to smaller scales. We have studied the nonlinear effects associated with coupling of DAW with kinetic Alfvén wave in solar wind at 1 A.U. The formation of localized structures provides a clue about the emergence of turbulence. Numerical simulation is performed to study localization and power spectral density of the field and density fluctuations. The results show steeper spectrum indicating transfer of large scale turbulent energy down to small scales.
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.
Robust energy transfer mechanism via precession resonance in nonlinear turbulent wave systems
NASA Astrophysics Data System (ADS)
Lucas, Dan; Bustamante, Miguel; Quinn, Brenda
2014-11-01
The precise mechanisms by which energy is most efficiently transferred in a turbulent system remain an important open question for the fluid mechanics community. In this talk we present a newly discovered resonance which is found to drive transfers across the spectrum of Fourier modes in a nonlinear wave system. Quadratic nonlinearity results in modes interacting in triads and, by considering the ``truly dynamical degrees of freedom'' (amplitudes and triad phases) and the precessional frequencies of the triads, we show transfers are maximal when the precession resonates with the nonlinear temporal frequencies. This can lead to a collective state of synchronised triads with intense cascades at intermediate nonlinearity; we find greatest transfer between the traditional weak and strong turbulence regimes and discover that this new mechanism is dominant here. We present the effect in a hierarchy of models including a full DNS of the Charney-Hasegawa-Mima equation and confirm analytical predictions. Supported by Science Foundation Ireland (SFI) under Grant Number 12/IP/1491.
NASA Astrophysics Data System (ADS)
Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei
2016-07-01
Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.
Experimental study of nonlinear solitary waves in two-dimensional dusty plasma
Sheridan, T. E.; Nosenko, V.; Goree, J.
2008-07-15
The excitation and propagation of solitary waves is studied experimentally in a two-dimensional strongly coupled dusty (complex) plasma. A single layer with {approx_equal}5000 microspheres (8 {mu}m diam) was suspended in an argon plasma with a neutral gas pressure of 3.0 mTorr. The measured Debye shielding parameter was {kappa}{approx_equal}1.6, where {kappa}=a/{lambda} is the ratio of the lattice constant a to the Debye length {lambda}. Nonlinear, planar longitudinal waves were launched by pushing all the particles in a rectangular region at the center of the crystal in the same direction using an 18 W green laser. Compressive solitary waves with density perturbations {delta}n/n{sub 0} < or approx. 0.8 and widths < or approx. 5a were found to propagate in the forward direction at speeds exceeding the dust acoustic speed. For small amplitude solitary waves, the relations between amplitude, width, and velocity are consistent with those predicted for Korteweg-deVries solitons. Rarefactive perturbations were not observed to evolve into solitary waves. However, oscillatory shocks were seen to move in the backward direction after the laser force was removed.
Experimental study of nonlinear solitary waves in two-dimensional dusty plasma
NASA Astrophysics Data System (ADS)
Sheridan, T. E.; Nosenko, V.; Goree, J.
2008-07-01
The excitation and propagation of solitary waves is studied experimentally in a two-dimensional strongly coupled dusty (complex) plasma. A single layer with ≈5000 microspheres (8μmdiam) was suspended in an argon plasma with a neutral gas pressure of 3.0mTorr. The measured Debye shielding parameter was κ ≈1.6, where κ =a/λ is the ratio of the lattice constant a to the Debye length λ. Nonlinear, planar longitudinal waves were launched by pushing all the particles in a rectangular region at the center of the crystal in the same direction using an 18W green laser. Compressive solitary waves with density perturbations δn /n0≲0.8 and widths ≲5a were found to propagate in the forward direction at speeds exceeding the dust acoustic speed. For small amplitude solitary waves, the relations between amplitude, width, and velocity are consistent with those predicted for Korteweg-deVries solitons. Rarefactive perturbations were not observed to evolve into solitary waves. However, oscillatory shocks were seen to move in the backward direction after the laser force was removed.
Automatic computation of the travelling wave solutions to nonlinear PDEs
NASA Astrophysics Data System (ADS)
Liang, Songxin; Jeffrey, David J.
2008-05-01
Various extensions of the tanh-function method and their implementations for finding explicit travelling wave solutions to nonlinear partial differential equations (PDEs) have been reported in the literature. However, some solutions are often missed by these packages. In this paper, a new algorithm and its implementation called TWS for solving single nonlinear PDEs are presented. TWS is implemented in MAPLE 10. It turns out that, for PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases. Program summaryProgram title:TWS Catalogue identifier:AEAM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAM_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:1250 No. of bytes in distributed program, including test data, etc.:78 101 Distribution format:tar.gz Programming language:Maple 10 Computer:A laptop with 1.6 GHz Pentium CPU Operating system:Windows XP Professional RAM:760 Mbytes Classification:5 Nature of problem:Finding the travelling wave solutions to single nonlinear PDEs. Solution method:Based on tanh-function method. Restrictions:The current version of this package can only deal with single autonomous PDEs or ODEs, not systems of PDEs or ODEs. However, the PDEs can have any finite number of independent space variables in addition to time t. Unusual features:For PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases. Additional comments:It is easy to use. Running time:Less than 20 seconds for most cases, between 20 to 100 seconds for some cases, over 100 seconds for few cases. References: [1] E.S. Cheb-Terrab, K. von
Macrosimulation of nonlinear dynamic systems for wave-shaping applications
NASA Astrophysics Data System (ADS)
Ogrodzki, Jan; Bieńkowski, Piotr
2014-11-01
Macromodeling is a technique widely used in circuits simulation. Macromodels usually describe complex, repetitive parts of large systems. They are often created on the base of original circuits by their simplification, e.g. macromodels of operational amplifiers. Another group of macromodels makes use of the circuit response approximation. This approach is called behavioral macromodeling. Low numerical complexity of behavioral macromodels is especially useful in CAD systems where circuit simulation must be run many times. In this paper the behavioral macromodeling technique has been applied to the whole circuit not to its part. This technique may be understood as shaping of the circuit output response and so belongs to a class of wave-shaping methods. We have used it to nonlinear, dynamic circuits with periodic signals of finite spectra, as e.g. in audio systems. The macromodels shape their frequency and spectral characteristics with a sufficient simplicity to omit unwanted distortions and with a sufficient efficiency to run the simulator in real time. Elaboration of this wave-shaping simulator is based on dynamic circuits identification, Fourier approximation of signals and harmonic balance technique. The obtained macromodel can be run as a software substitute for a hardware audio system.
Slabko, Vitaly V; Popov, Alexander K; Tkachenko, Viktor A; Myslivets, Sergey A
2016-09-01
Three-wave mixing of ordinary and backward electromagnetic waves in a pulsed regime is investigated in the metamaterials that enable the coexistence and phase-matching of such waves. It is shown that the opposite direction of phase velocity and energy flux in backward waves gives rise to extraordinary transient processes due to greatly enhanced optical parametric amplification and frequency up- and down-shifting nonlinear reflectivity. The differences are illustrated through comparison with the counterparts in ordinary, co-propagating settings.
NASA Astrophysics Data System (ADS)
Brühl, Markus; Oumeraci, Hocine
2014-05-01
The interaction of nonlinear waves in shallow water causes nonlinear wave-wave interactions that might significantly modify the observed free surface. For the elementary understanding of the underlying processes in wave propagation and the wave interactions it is essential to separate the underlying wave components and their nonlinear interactions. Since 2008 a KdV-based nonlinear Fourier transform (KdV-NLFT) is implemented and successfully applied at Leichtweiß-Institute (LWI) that solves the Korteweg-deVries equation by application of a cnoidal basis for the spectral decomposition of the original data. Therefore, the KdV-NLFT is adaptive within the cnoidal wave limit and the free surface is decomposed into cnoidal waves that span the whole range of possible wave forms in shallow water from linear over slightly and strongly nonlinear waves up to solitons. The number and type of the components depend on the original data. For linear data the KdV-NLFT provides the same results as the conventional Fourier transform. Furthermore, the nonlinear wave-wave interactions are explicitly separated from the underlying basic cnoidal wave components and can be displayed and analysed separately. The KdV-NLFT is successfully applied to different shallow water problems such as the fission of solitons over submerged reefs, the harmonic generation, the problem of bound and free harmonics and the transformation of long linear waves into asymmetric waves and finally their disintegration into a train of solitons (as shown by Zabusky and Kruskal, 1965). The analysis results show that for some applications the conventional concepts that have been developed based on the results of the linear conventional Fourier transform are not sufficient to explain the ongoing nonlinear processes. In contrast, by application of the KdV-NLFT the observed processes in soliton fission, harmonic generation, bound and free harmonics and the transformation of long waves in shallow water can easily be
Nonlinear microwave photon occupancy of a driven resonator strongly coupled to a transmon qubit
NASA Astrophysics Data System (ADS)
Suri, B.; Keane, Z. K.; Bishop, Lev S.; Novikov, S.; Wellstood, F. C.; Palmer, B. S.
2015-12-01
We measure photon occupancy in a thin-film superconducting lumped element resonator coupled to a transmon qubit at 20 mK and find a nonlinear dependence on the applied microwave power. The transmon-resonator system was operated in the strong dispersive regime, where the ac Stark shift (2 χ ) due to a single microwave photon present in the resonator was larger than the linewidth (Γ ) of the qubit transition. When the resonator was coherently driven at 5.474 325 GHz, the transition spectrum of the transmon at 4.982 GHz revealed well-resolved peaks, each corresponding to an individual photon number-state of the resonator. From the relative peak heights we obtain the occupancy of the photon states and the average photon occupancy n ¯ of the resonator. We observe a nonlinear variation of n ¯ with the applied drive power Prf for n ¯<5 and compare our results to numerical simulations of the system-bath master equation in the steady state, as well as to a semiclassical model for the resonator that includes the Jaynes-Cummings interaction between the transmon and the resonator. We find good quantitative agreement using both models and analysis reveals that the nonlinear behavior is principally due to shifts in the resonant frequency caused by a qubit-induced Jaynes-Cummings nonlinearity.
He, Zhaoguo; Zong, Qiugang Wang, Yongfu; Liu, Siqing; Lin, Ruilin; Shi, Liqin
2014-12-15
Resonant pitch angle scattering by electromagnetic ion cyclotron (EMIC) waves has been suggested to account for the rapid loss of ring current ions and radiation belt electrons. For the rising tone EMIC wave (classified as triggered EMIC emission), its frequency sweep rate strongly affects the efficiency of pitch-angle scattering. Based on the Cluster observations, we analyze three typical cases of rising tone EMIC waves. Two cases locate at the nightside (22.3 and 22.6 magnetic local time (MLT)) equatorial region and one case locates at the duskside (18MLT) higher magnetic latitude (λ = –9.3°) region. For the three cases, the time-dependent wave amplitude, cold electron density, and cold ion density ratio are derived from satellite data; while the ambient magnetic field, thermal proton perpendicular temperature, and the wave spectral can be directly provided by observation. These parameters are input into the nonlinear wave growth model to simulate the time-frequency evolutions of the rising tones. The simulated results show good agreements with the observations of the rising tones, providing further support for the previous finding that the rising tone EMIC wave is excited through the nonlinear wave growth process.
Strong gravitational lensing of gravitational waves in Einstein Telescope
Piórkowska, Aleksandra; Biesiada, Marek; Zhu, Zong-Hong E-mail: marek.biesiada@us.edu.pl
2013-10-01
Gravitational wave experiments have entered a new stage which gets us closer to the opening a new observational window on the Universe. In particular, the Einstein Telescope (ET) is designed to have a fantastic sensitivity that will provide with tens or hundreds of thousand NS-NS inspiral events per year up to the redshift z = 2. Some of such events should be gravitationally lensed by intervening galaxies. We explore the prospects of observing gravitationally lensed inspiral NS-NS events in the Einstein telescope. Being conservative we consider the lens population of elliptical galaxies. It turns out that depending on the local insipral rate ET should detect from one per decade detection in the pessimistic case to a tens of detections per year for the most optimistic case. The detection of gravitationally lensed source in gravitational wave detectors would be an invaluable source of information concerning cosmography, complementary to standard ones (like supernovae or BAO) independent of the local cosmic distance ladder calibrations.
Strong anisotropy in two-dimensional surfaces with generic scale invariance: nonlinear effects.
Vivo, Edoardo; Nicoli, Matteo; Cuerno, Rodolfo
2014-04-01
We expand a previous study [Phys. Rev. E 86, 051611 (2012)] on the conditions for occurrence of strong anisotropy in the scaling properties of two-dimensional surfaces displaying generic scale invariance. In that study, a natural scaling ansatz was proposed for strongly anisotropic systems, which arises naturally when analyzing data from, e.g., thin-film production experiments. The ansatz was tested in Gaussian (linear) models of surface dynamics and in nonlinear models, like the Hwa-Kardar (HK) equation [Phys. Rev. Lett. 62, 1813 (1989)], which are susceptible of accurate approximations through the former. In contrast, here we analyze nonlinear equations for which such approximations fail. Working within generically scale-invariant situations, and as representative case studies, we formulate and study a generalization of the HK equation for conserved dynamics and reconsider well-known systems, such as the conserved and the nonconserved anisotropic Kardar-Parisi-Zhang equations. Through the combined use of dynamic renormalization group analysis and direct numerical simulations, we conclude that the occurrence of strong anisotropy in two-dimensional surfaces requires dynamics to be conserved. We find that, moreover, strong anisotropy is not generic in parameter space but requires, rather, specific forms of the terms appearing in the equation of motion, whose justification needs detailed information on the dynamical process that is being modeled in each particular case. PMID:24827260
Influence of thermal conductivity on a strong shock wave converging toward a symmetry center
NASA Astrophysics Data System (ADS)
Makhmudov, A. A.; Popov, A. P.
1980-03-01
In the motion of a shock wave near the axis of a cylinder or the center of a sphere, there occurs a self-similar flow. This region is of practical importance, since many nonself-similar problems reduce to self-similar ones. In the present paper, the transformation of Guderley's (1942) self-simulating solution to an isothermal wave under the influence of nonlinear heat conductivity is analyzed numerically.
The Effect of Crack Orientation on the Nonlinear Interaction of a P-wave with an S-wave
TenCate, J. A.; Malcolm, A. E.; Feng, X.; Fehler, M. C.
2016-06-06
Cracks, joints, fluids, and other pore-scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore-scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presencemore » and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low-amplitude P wave probe by a high-amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.« less
The effect of crack orientation on the nonlinear interaction of a P wave with an S wave
NASA Astrophysics Data System (ADS)
TenCate, J. A.; Malcolm, A. E.; Feng, X.; Fehler, M. C.
2016-06-01
Cracks, joints, fluids, and other pore-scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore-scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presence and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low-amplitude P wave probe by a high-amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.
Laboratory Study of Nonlinear Trapping of Magnetized Langmuir Waves Inside a Density Depletion
Starodubtsev, Mikhail V.; Nazarov, Vladimir V.; Kostrov, Alexander V.
2007-05-11
The formation of a small-scale plasma density depletion region extended along the ambient magnetic field and caused by the nonlinear interaction of the upper-hybrid plasma waves with a magnetoplasma has been observed under laboratory conditions modeling the ionospheric heating experiments. Plasma waves are trapped inside the depletion due to their specific dispersion properties. The threshold of the nonlinear wave trapping significantly increases in the vicinity of the harmonics of the electron gyrofrequency.
The nonlinear equatorial Kelvin wave. [in coastal currents of El Nino and Gulf of Guinea
NASA Technical Reports Server (NTRS)
Boyd, J. P.
1980-01-01
Using the method of strained coordinates, a uniformly valid approximation to the nonlinear equatorial Kelvin wave is derived. It is shown that nonlinear effects are negligible for the Kelvin waves associated with the Gulf of Guinea upwelling. The Kelvin waves involved in El Nino, however, are significantly distorted both in shape and speed. The leading edge is smoothed and expanded rather than steepened, but the trailing edge will form sharp fronts and eventually break.
Study of Nonlinear Interaction and Turbulence of Alfven Waves in LAPD Experiments
Boldyrev, Stanislav; Perez, Jean Carlos
2013-11-29
The complete project had two major goals — investigate MHD turbulence generated by counterpropagating Alfven modes, and study such processes in the LAPD device. In order to study MHD turbulence in numerical simulations, two codes have been used: full MHD, and reduced MHD developed specialy for this project. Quantitative numerical results are obtained through high-resolution simulations of strong MHD turbulence, performed through the 2010 DOE INCITE allocation. We addressed the questions of the spectrum of turbulence, its universality, and the value of the so-called Kolmogorov constant (the normalization coefficient of the spectrum). In these simulations we measured with unprecedented accuracy the energy spectra of magnetic and velocity fluctuations. We also studied the so-called residual energy, that is, the difference between kinetic and magnetic energies in turbulent fluctuations. In our analytic work we explained generation of residual energy in weak MHD turbulence, in the process of random collisions of counterpropagating Alfven waves. We then generalized these results for the case of strong MHD turbulence. The developed model explained generation of residual energy is strong MHD turbulence, and verified the results in numerical simulations. We then analyzed the imbalanced case, where more Alfven waves propagate in one direction. We found that spectral properties of the residual energy are similar for both balanced and imbalanced cases. We then compared strong MHD turbulence observed in the solar wind with turbulence generated in numerical simulations. Nonlinear interaction of Alfv´en waves has been studied in the upgraded Large Plasma Device (LAPD). We have simulated the collision of the Alfven modes in the settings close to the experiment. We have created a train of wave packets with the apltitudes closed to those observed n the experiment, and allowed them to collide. We then saw the generation of the second harmonic, resembling that observed in the
Propagation of Long Extensional Nonlinear Waves in a Hyper-Elastic Layer
NASA Astrophysics Data System (ADS)
Teymür, Mevlüt
Propagation of small but finite amplitude waves in a nonlinear hyper-elastic plate of uniform thickness is considered. By employing a perturbation expansion, extensional waves are examined under the long wave limit. It is shown that the asymptotic wave field is governed by a Korteweg-DeVries (K-dV) equation. Then the propagation characteristics of the asymptotic waves are discussed via the well known solutions of the K-dV equation.
NASA Technical Reports Server (NTRS)
Koons, H. C.; Roeder, J. L.; Bauer, O. H.; Haerendel, G.; Treumann, R.
1987-01-01
Nonlinear wave decay processes have been detected in the solar wind by the plasma wave experiment aboard the Active Magnetospheric Particle Tracer Explorers (AMPTE) IRM spacecraft. The main process is the generation of ultralow-frequency ion acoustic waves from the decay of Langmuir waves near the electron plasma frequency. Frequently, this is accompanied by an enhancement of emissions near twice the plasma frequency. This enhancement is most likely due to the generation of electromagnetic waves from the coalescence of two Langmuir waves. These processes occur within the electron foreshock in front of the earth's bow shock.
NASA Astrophysics Data System (ADS)
Hu, Tao; Ma, Li
2010-09-01
An internal wave observation experiment was performed near the south of Hai-Nan Island in the South China Sea in July 2004. Three vertical thermistor arrays were moored to estimate internal wave propagation direction and velocity. A nonlinear internal wave packet was observed in this experiment. It appeared at flood tide time of wee hours. Computation indicated that the nonlinear internal wave packet's velocity was 0.54 m/s and its propagation direction was northwest. From its propagation direction, we estimated that the nonlinear internal wave packet was generated near Xi-Sha Islands. The dnoidal model of KdV(Korteweg-deVries) equation was used to simulate the waveform of thid nonlinear internal wave. Measured data shows the crest interval of nonlinear internal waves was shorter when they propagated. In the last section of this paper we simulate a nonlinear internal wave packet's effect on sound propagation and analyzed mode coupling led by the nonlinear internal wave packet.
Guided wave methods and apparatus for nonlinear frequency generation
Durfee, III, Charles G.; Rundquist, Andrew; Kapteyn, Henry C.; Murnane, Margaret M.
2000-01-01
Methods and apparatus are disclosed for the nonlinear generation of sum and difference frequencies of electromagnetic radiation propagating in a nonlinear material. A waveguide having a waveguide cavity contains the nonlinear material. Phase matching of the nonlinear generation is obtained by adjusting a waveguide propagation constant, the refractive index of the nonlinear material, or the waveguide mode in which the radiation propagates. Phase matching can be achieved even in isotropic nonlinear materials. A short-wavelength radiation source uses phase-matched nonlinear generation in a waveguide to produce high harmonics of a pulsed laser.
Experimental investigation of linear and nonlinear wave systems: A quantum chaos approach
NASA Astrophysics Data System (ADS)
Neicu, Toni
2002-09-01
An experimental and numerical study of linear and nonlinear wave systems using methods and ideas developed from quantum chaos is presented. We exploit the analogy of the wave equation for the flexural modes of a thin clover-shaped acoustic plate to the stationary solutions of the Schrodinger wave equation for a quantum clover-shaped billiard, a generic system that has regular and chaotic regions in its phase space. We observed periodic orbits in the spectral properties of the acoustic plate, the first such definitive acoustic experiment. We also solved numerically the linear wave equation of the acoustic plate for the first few hundred eigenmodes. The Fourier transform of the eigenvalues show peaks corresponding to the principal periodic orbits of the classical billiard. The signatures of the periodic orbits in the spectra were unambiguously verified by deforming one edge of the plate and observing that only the peaks corresponding to the orbits that hit this edge changed. The statistical measures of the eigenvalues are intermediate between universal forms for completely integrable and chaotic systems. The density distribution of the eigenfunctions agrees with the Porter-Thomas formula of chaotic systems. The viscosity dependence and effects of nonlinearity on the Faraday surface wave patterns in a stadium geometry were also investigated. The ray dynamics inside the stadium, a paradigm of quantum chaos, is completely chaotic. The majority of the observed patterns of the orbits resemble three eigenstates of the stadium: the bouncing ball, longitudinal, and bowtie patterns. We observed many disordered patterns that increase with the viscosity. The experimental results were analyzed using recent theoretical work that explains the suppression of certain modes. The theory also predicts that the perimeter dissipation is too strong for whispering gallery modes, which contradicts our observations of these modes for a fluid with low viscosity. Novel vortex patterns were
Dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation.
Wen, Shao-Fang; Shen, Yong-Jun; Wang, Xiao-Na; Yang, Shao-Pu; Xing, Hai-Jun
2016-08-01
In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method. The dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation is investigated by the IHB method. Then, the effects of the excitation frequency, fractional order, fractional coefficient, and nonlinear stiffness coefficient on the complex dynamical behaviors are analyzed. At last, the detailed results are summarized and the conclusions are made, which present some useful information to analyze and/or control the dynamical response of this kind of system. PMID:27586626
Dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation
NASA Astrophysics Data System (ADS)
Wen, Shao-Fang; Shen, Yong-Jun; Wang, Xiao-Na; Yang, Shao-Pu; Xing, Hai-Jun
2016-08-01
In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method. The dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation is investigated by the IHB method. Then, the effects of the excitation frequency, fractional order, fractional coefficient, and nonlinear stiffness coefficient on the complex dynamical behaviors are analyzed. At last, the detailed results are summarized and the conclusions are made, which present some useful information to analyze and/or control the dynamical response of this kind of system.
Three-point bounds and other estimates for strongly nonlinear composites
NASA Astrophysics Data System (ADS)
Castañeda, P. Ponte
1998-05-01
A variational procedure due to Ponte Castañeda et al. [Phys. Rev. B 46, 4387 (1992)] is used to determine three-point bounds and other types of estimates for the effective response of strongly nonlinear composites with random microstructures. The variational procedure makes use of estimates for the effective properties of ``linear comparison composites'' to generate corresponding estimates for nonlinear composites. Several equivalent forms of the variational procedure are derived. In particular, it is shown that the mean-field theory of Wan et al. [Phys. Rev. B 54, 3946 (1996)], which also makes use of a linear comparison composite, together with a certain ``decoupling approximation,'' leads to results that are precisely identical to those that can be obtained from the earlier variational procedure. Finally, three-point bounds and other estimates are computed for power-law composites with cell-type microstructures, and the results are compared with random resistor network simulations available from the literature.
NASA Astrophysics Data System (ADS)
Verweij, Martin D.; Demi, Libertario; van Dongen, Koen W. A.
2012-09-01
The Iterative Nonlinear Contrast Source (INCS) method is a full-wave method for the accurate computation of wide-angle, pulsed, nonlinear ultrasound fields appearing in, e.g., medical echoscopy. The method is based on the Westervelt equation and considers the occurring nonlinear term as a distributed contrast source that operates in a linear background medium. This formulation leads to an integral equation, which is solved in an iterative way. The original INCS method uses a Neumann scheme to successively approximate the nonlinear wave field in homogeneous, lossless, nonlinear media. To cope with attenuative and/or inhomogeneous nonlinear media, additional contrast sources may be introduced. Since these deteriorate the convergence rate of the Neumann scheme, more advanced iterative solution schemes like Bi-CGSTAB are required. To overcome the difficulty that such schemes only apply to linear integral equations, the nonlinear contrast source is linearized, at the cost of a significant systematic error in the fourth and higher harmonics. In this paper, a strategy is proposed in which the relevant iterative solution scheme is restarted with an updated version of the linearized contrast source. Results demonstrate the effectiveness of this strategy in eliminating the systematic error. In addition, it is shown that the same approach also improves the convergence rate in case of nonlinear propagation in media with attenuation.
Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves
NASA Technical Reports Server (NTRS)
Fibich, G.; Ilan, B.; Tsynkov, S.
2002-01-01
The critical nonlinear Schrodinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L(sub 2) norm of the initial solution) is sufficiently high, then the NLS model predicts that the beam will self-focus to a point (i.e.. collapse) at a finite propagation distance. Mathematically, this behavior corresponds to the formation of a singularity in the solution of the NLS. A key question which has been open for many years is whether the solution to the NLH, i.e., the 'parent' equation, may nonetheless exist and remain regular everywhere, in particular for those initial conditions (input powers) that lead to blowup in the NLS. In the current study, we address this question by introducing linear damping into both models and subsequently comparing the numerical solutions of the damped NLH (boundary-value problem) with the corresponding solutions of the damped NLS (initial-value problem). Linear damping is introduced in much the same way as done when analyzing the classical constant-coefficient Helmholtz equation using the limiting absorption principle. Numerically, we have found that it provides a very efficient tool for controlling the solutions of both the NLH and NHS. In particular, we have been able to identify initial conditions for which the NLS solution does become singular. whereas the NLH solution still remains regular everywhere. We believe that our finding of a larger domain of existence for the NLH than that for the NLS is accounted for by precisely those mechanisms, that have been neglected when deriving the NLS from the NLH, i.e., nonparaxiality and backscattering.
Eliasson, Bengt; Shukla, P K
2010-07-01
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the modulational instability for long-crested wave trains, which agrees well with recent large-scale experiments in wave basins, where it was found that narrower directional spectra lead to self-focusing of ocean waves and an enhanced probability of extreme events. We find that the modulational instability is nonlinearly saturated by a broadening of the wave spectrum, which leads to the stabilization of the water-wave system. Applications of our results to other fields of physics, such as nonlinear optics and plasma physics, are discussed.
Do nonlinear waves evolve in a universal manner in dusty and other plasma environments?
NASA Astrophysics Data System (ADS)
Bharuthram, R.; Singh, S. V.; Maharaj, S. K.; Moolla, S.; Lazarus, I. J.; Reddy, R. V.; Lakhina, G. S.; Lakhina
2014-12-01
Using a fluid theory approach, this article provides a comparative study on the evolution of nonlinear waves in dusty plasmas, as well as other plasma environments, viz electron-ion, and electron-positron plasmas. Where applicable, relevance to satellite measurements is pointed out. A range of nonlinear waves from low frequency (ion acoustic and ion cyclotron waves), high frequency (electron acoustic and electron cyclotron waves) in electron-ion plasmas, ultra-low frequency (dust acoustic and dust cyclotron waves) in dusty plasmas and in electron-positron plasmas are discussed. Depending upon the plasma parameters, saw-tooth and bipolar structures are shown to evolve.
Rogue waves: from nonlinear Schrödinger breather solutions to sea-keeping test.
Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco
2013-01-01
Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.
Verification of nonlinear particle simulation of radio frequency waves in tokamak
Kuley, A. Lin, Z.; Bao, J.; Wei, X. S.; Xiao, Y.; Zhang, W.; Sun, G. Y.; Fisch, N. J.
2015-10-15
Nonlinear simulation model for radio frequency waves in fusion plasmas has been developed and verified using fully kinetic ion and drift kinetic electron. Ion cyclotron motion in the toroidal geometry is implemented using Boris push in the Boozer coordinates. Linear dispersion relation and nonlinear particle trapping are verified for the lower hybrid wave and ion Bernstein wave (IBW). Parametric decay instability is observed where a large amplitude pump wave decays into an IBW sideband and an ion cyclotron quasimode (ICQM). The ICQM induces an ion perpendicular heating, with a heating rate proportional to the pump wave intensity.