Nonlinear ion acoustic waves scattered by vortexes
Ohno, Yuji; Yoshida, Zensho
2016-09-01
The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.
Nonlinear ion acoustic waves scattered by vortexes
Ohno, Yuji
2015-01-01
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.,...
Nonlinear dynamics of Airy-Vortex 3D wave packets: Emission of vortex light waves
Driben, Rodislav
2014-01-01
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. Due to 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 non-zero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse, especially those having small width.
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.
Optical Vortex Solitons in Parametric Wave Mixing
Alexander, T J; Buryak, A V; Sammut, R A; Alexander, Tristram J.; Kivshar, Yuri S.; Buryak, Alexander V.; Sammut, Rowland A.
2000-01-01
We analyze two-component spatial optical vortex solitons supported by degenerate three- or four-wave mixing in a nonlinear bulk medium. We study two distinct cases of such solitons, namely, parametric vortex solitons due to phase-matched second-harmonic generation in a optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a `halo-vortex', consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a `ring-vortex' soliton which is a vortex in a harmonic field that guides a bright localized ring-like mode of a fundamental frequency field.
Delaying vortex breakdown by waves
Yao, M. F.; Jiang, L. B.; Wu, J. Z.; Ma, H. Y.; Pan, J. Y.
1989-03-01
The effect of spiral waves on delaying vortex breakdown in a tube is studied experimentally and theoretically. When a harmonic oscillation was imposed on one of guiding vanes in the tube, the breakdown was observed to be postponed appreciately. According to the generalized Lagrangian mean theory, proper forcing spiral waves may produce an additional streaming momentum, of which the effect is favorable and similar to an axial suction at downstream end. The delayed breakdown position is further predicted by using nonlinear wave theory. Qualitative agreement between theory and experiment is obtained, and experimental comparison of the effects due to forcing spiral wave and axial suction is made.
Li, Wei; Tang, Yougang; Liu, Liqin; Liu, Shuxiao; Cai, Runbo
2017-04-01
Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model. In fact, in addition to the heave and pitch which are in one plane, the nonlinear unstable motion will also occur in roll. From the results of the experiments, the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch. The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force. The nonlinear coupled equations in heave, roll and pitch are established by considering time-varying wet surface and coupling. The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency. Numerical integration of the motion equations has been performed to verify the first-order perturbation solution. The results are confirmed by model test. There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch. It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value. The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch. The energy transfers from heave to pitch and then transfers from pitch to roll. Due to the influence of the low-frequency vortex-excited force, the response of roll is more complicated than that of pitch.
Generation of nonlinear vortex precursors
Chen, Yue-Yue; Liu, Chengpu
2016-01-01
We numerically study the propagation of a few-cycle pulse carrying orbital angular momentum (OAM) through a dense atomic system. Nonlinear precursors consisting of high-order vortex har- monics are generated in the transmitted field due to ultrafast Bloch oscillation. The nonlinear precursors survive to propagation effects and are well separated with the main pulse, which provide a straightforward way of measuring precursors. By the virtue of carrying high-order OAM, the obtained vortex precursors as information carriers have potential applications in optical informa- tion and communication fields where controllable loss, large information-carrying capacity and high speed communication are required.
Nonlinear interaction of instability waves and vortex-pairing noise in axisymmetric subsonic jets
Yang, Hai-Hua; Zhou, Lin; Zhang, Xing-Chen; Wan, Zhen-Hua; Sun, De-Jun
2016-10-01
A direct simulation with selected inflow forcing is performed for an accurate description of the jet flow field and far-field noise. The effects of the Mach number and heating on the acoustic field are studied in detail. The beam patterns and acoustic intensities are both varied as the change of the Mach number and temperature. The decomposition of the source terms of the Lilley-Goldstein (L-G) equation shows that the momentum and thermodynamic components lead to distinctly different beam patterns. Significant cancellation is found between the momentum and thermodynamic components at low polar angles for the isothermal jet and large polar angles for the hot jet. The cancellation leads to the minimum values of the far-field sound. Based on linear parabolized stability equation solutions, the nonlinear interaction model for sound prediction is built in combination with the L-G equation. The dominant beam patterns and their original locations predicted by the nonlinear model are in good agreement with the direct simulation results, and the predictions of sound pressure level (SPL) by the nonlinear model are relatively reasonable.
Van Gorder, Robert A.
2016-05-01
Very recent experimental work has demonstrated the existence of Kelvin waves along quantized vortex filaments in superfluid helium. The possible configurations and motions of such filaments is of great physical interest, and Svistunov previously obtained a Hamiltonian formulation for the dynamics of quantum vortex filaments in the low-temperature limit under the assumption that the vortex filament is essentially aligned along one axis, resulting in a two-dimensional (2D) problem. It is standard to approximate the dynamics of thin filaments by employing the local induction approximation (LIA), and we show that by putting the two-dimensional LIA into correspondence with the first equation in the integrable Wadati-Konno-Ichikawa-Schimizu (WKIS) hierarchy, we immediately obtain solutions to the two-dimensional LIA, such as helix, planar, and self-similar solutions. These solutions are obtained in a rather direct manner from the WKIS equation and then mapped into the 2D-LIA framework. Furthermore, the approach can be coupled to existing inverse scattering transform results from the literature in order to obtain solitary wave solutions including the analog of the Hasimoto one-soliton for the 2D-LIA. One large benefit of the approach is that the correspondence between the 2D-LIA and the WKIS allows us to systematically obtain vortex filament solutions directly in the Cartesian coordinate frame without the need to solve back from curvature and torsion. Implications of the results for the physics of experimentally studied solitary waves, Kelvin waves, and postvortex reconnection events are mentioned.
Ring vortex solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Briedis, D.; Petersen, D.E.; Edmundson, D.;
2005-01-01
or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction....
Coherent Vortex Evolution in Drift Wave Turbulence
Gatto, R.; Terry, P. W.
1998-11-01
Localized structures in turbulence are subject to loss of coherence by mixing. Phase space structures, such as drift-hole, (P. W. Terry, P. H. Diamond, T. S. Hahm, Phys. Fluids B) 2 9 2048 (1990) possess a self-electric field, which if sufficiently large maintains particle trapping against the tidal deformations of ambient turbulence. We show here that intense vortices in fluid drift wave turbulence avoid mixing by suppressing ambient turbulence with the strong flow shear of the vortex edge. Analysis of turbulence evolution in the vortex edge recovers Rapid Distortion Theory (G. K. Batchelor and I. Proudman, Q. J. Mech. Appl. Math.) 7 83 (1954) as the short time limit and the shear suppression scaling theory (H. Biglari, P. H. Diamond and P. W. Terry, Phys. Fluids B) 2 1 (1990) as the long time limit. Shear suppression leads to an amplitude condition for coherence and delineates the Gaussian core from the non Gaussian tail of the probability distribution function. The amplitude condition of shear suppression is compared with the trapping condition for phase space holes. The possibility of nonlinear vortex growth will be examined by considering electron dynamics in the vortex evolution.
Globally linked vortex clusters in trapped wave fields.
Crasovan, Lucian-Cornel; Molina-Terriza, Gabriel; Torres, Juan P; Torner, Lluis; Pérez-García, Víctor M; Mihalache, Dumitru
2002-09-01
We put forward the existence of a rich variety of fully stationary vortex structures, termed H clusters, made of an increasing number of vortices nested in paraxial wave fields confined by trapping potentials. However, we show that the constituent vortices are globally linked, rather than products of independent vortices. Also, they always feature a monopolar global wave front and exist in nonlinear systems, such as the Bose-Einstein condensates. Clusters with multipolar global wave fronts are nonstationary or, at best, flipping.
Spiral Wave Generation in a Vortex Electric Field
Institute of Scientific and Technical Information of China (English)
YUAN Xiao-Ping; CHEN Jiang-Xing; ZHAO Ye-Hua; LOU Qin; WANG Lu-Lu; SIIEN Qian
2011-01-01
The effect of a vortical electric field on nonlinear patterns in excitable media is studied. When an appropriate vortex electric field is applied, the system exhibits pattern transition from chemical turbulence to spiral waves, which possess the same chtality as the vortex electric field. The underlying mechanism of this is discussed. We also show the meandering behavior of a spiral under the taming of a vortex electric field. The results obtained here may contribute to control strategies of patterns on surface reaction.%The effect of a vortical electric field on nonlinear patterns in excitable media is studied.When an appropriate vortex electric field is applied,the system exhibits pattern transition from chemical turbulence to spiral waves,which possess the same chirality as the vortex electric field.The underlying mechanism of this is discussed.We also show the meandering behavior of a spiral under the taming of a vortex electric field.The results obtained here may contribute to control strategies of patterns on surface reaction.Spiral waves are one of the most common and widely studied patterns in nature.They appear in hydrodynamic systems,chemical reactions and a large variety of biological,chemical and physical systems.[1-5] Much attention has been paid to their rich nonlinear dynamics,as well as potential applications in various biological or physiological systems,since the emergence and instability of spirals usually lead to abnormal states,for example in cardiac arrythmia[6,7] and epilepsy[8].Much research has been carried out in studying pattern formations in catalytic CO oxidation on Pt(110),[9-11] because they provide practical utilization in industry.A rich variety of spatiotemporal patterns,including travelling pulses,standing waves,target patterns,spiral waves and chemical turbulence have been observed in this system.[12-16
Solitons and other waves on a quantum vortex filament
Van Gorder, Robert A
2014-01-01
The quantum form of the local induction approximation (LIA, a model approximating the motion of a thin vortex filament in superfluid) including superfluid friction effects is put into correspondence with a type of cubic complex Ginsburg-Landau equation, in a manner analogous to the Hasimoto map taking the classical LIA into the cubic nonlinear Schr\\"odinger equation. From this formulation, we determine the form and behavior of Stokes waves, 1-solitons, and other traveling wave solutions under normal and binormal friction. The most important of these solutions is the soliton on a quantum vortex filament, which is a natural generalization of the 1-soliton solution constructed mathematically by Hasimoto which motivated subsequent real-world experiments. We also conjecture on the possibility of chaos in such systems, and on the existence more complicated solitons such as breathers.
Nonlinear dynamics of resistive electrostatic drift waves
DEFF Research Database (Denmark)
Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.
1999-01-01
The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... is perturbed by a small amplitude incoherent wave-field. The initial evolution is exponential, following the growth of perturbations predicted by linear stability theory. The fluctuations saturate at relatively high amplitudes, by forming a pair of magnetic field aligned vortex-like structures of opposite...
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Wave–vortex interactions in the nonlinear Schrödinger equation
Energy Technology Data Exchange (ETDEWEB)
Guo, Yuan, E-mail: yuanguo@cims.nyu.edu; Bühler, Oliver [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2014-02-15
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.
MHD waves generated by high-frequency photospheric vortex motions
Directory of Open Access Journals (Sweden)
V. Fedun
2011-06-01
Full Text Available In this paper, we discuss simulations of MHD wave generation and propagation through a three-dimensional open magnetic flux tube in the lower solar atmosphere. By using self-similar analytical solutions for modelling the magnetic field in Cartesian coordinate system, we have constructed a 3-D magnetohydrostatic configuration which is used as the initial condition for non-linear MHD wave simulations. For a driver we have implemented a high-frequency vortex-type motion at the footpoint region of the open magnetic flux tube. It is found that the implemented swirly source is able to excite different types of wave modes, i.e. sausage, kink and torsional Alfvén modes. Analysing these waves by magneto-seismology tools could provide insight into the magnetic structure of the lower solar atmosphere.
Vortex algebra by multiply cascaded four-wave mixing of femtosecond optical beams.
Hansinger, Peter; Maleshkov, Georgi; Garanovich, Ivan L; Skryabin, Dmitry V; Neshev, Dragomir N; Dreischuh, Alexander; Paulus, Gerhard G
2014-05-05
Experiments performed with different vortex pump beams show for the first time the algebra of the vortex topological charge cascade, that evolves in the process of nonlinear wave mixing of optical vortex beams in Kerr media due to competition of four-wave mixing with self-and cross-phase modulation. This leads to the coherent generation of complex singular beams within a spectral bandwidth larger than 200nm. Our experimental results are in good agreement with frequency-domain numerical calculations that describe the newly generated spectral satellites.
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A.; Carvalho, Márcio; Leblond, Hervé; Malomed, Boris A.
2016-11-01
We elaborate a solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water, and optical glasses at sufficiently high intensities. We also show that the tubular, rotating, and specklelike filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A; Leblond, Hervé; Malomed, Boris A
2016-01-01
We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Sound Wave in Vortex with Sink
Basak, S
2003-01-01
Using Komar's definition, we give expressions for the mass and angular momentum of a rotating acoustic black hole. We show that the mass and angular momentum so defined, obey the equilibrium version of the first law of Black Hole thermodynamics. We also show that when a phonon passes by a vortex with a sink, its trajectory is bent. The angle of bending of the sound wave to leading order is quadratic in $A/cb$ and $B/cb$, where $b$ is the impact parameter and $A$ and $B$ are the parameters in the velocity of the fluid flow. The time delay in the propagation of sound wave which to first order depends only on $B/c^2$ and is independent of $A$.
Rossby Wave Instability of Thin Accretion Disks - III. Nonlinear Simulations
Li, H; Wendroff, B; Liska, R
2000-01-01
(abridged) We study the nonlinear evolution of the Rossby wave instability in thin disks using global 2D hydrodynamic simulations. The key questions we are addressing in this paper are: (1) What happens when the instability becomes nonlinear? Specifically, does it lead to vortex formation? (2) What is the detailed behavior of a vortex? (3) Can the instability sustain itself and can the vortex last a long time? Among various initial equilibria that we have examined, we generally find that there are three stages of the disk evolution: (1) The exponential growth of the initial small amplitude perturbations. This is in excellent agreement with the linear theory; (2) The production of large scale vortices and their interactions with the background flow, including shocks. Significant accretion is observed due to these vortices. (3) The coupling of Rossby waves/vortices with global spiral waves, which facilitates further accretion throughout the whole disk. Even after more than 20 revolutions at the radius of vortic...
Kelvin Waves and Dynamic Knots on Perturbative Helical Vortex Lines
Kou, Su-Peng
2016-01-01
Vortex lines are one-dimensional extended objects in three-dimensional superfluids. Vortex lines have many interesting properties, including Kelvin waves, exotic statistics, and possible entanglement. In this paper, an emergent "quantum world" is explored by projecting helical vortex lines. A one-dimensional quantum Fermionic model is developed to effectively describe the local fluctuations of helical vortex lines. The elementary excitations are knots with half winding-number that obey emergent quantum mechanics. The Biot-Savart equation, and its Kelvin wave solutions on helical vortex lines become Schrodinger equation, and the wave functions of probability waves for finding knots, respectively. This work shows an alternative approach to simulating quantum many-body physics based on classical systems.
Optical Rogue Waves in Vortex Turbulence
Gibson, Christopher J; Oppo, Gian-Luca
2015-01-01
We present a spatio-temporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability to phase unbound turbulent states in complex Ginzburg- Landau and Swift-Hohenberg models with external driving. When the pumping is high and the external driving is low, synchronized oscillations are unstable and lead to spatio-temporal turbulence with high excursions in amplitude. Nonlinear amplification leads to rogue waves close to turbulent optical vortices, where the amplitude tends to zero, and to probability distribution functions with long tails typical of extreme optical events.
Stabilization of three-wave vortex beams in the waveguide
Gammal, Arnaldo
2015-01-01
We consider two-dimensional (2D) localized vortical modes in the three-wave system with the quadratic ($\\chi ^{(2)}$) nonlinearity, alias nondegenerate second-harmonic-generating system, guided by the isotropic harmonic-oscillator (HO) (alias parabolic) confining potential. In addition to the straightforward realization in optics, the system models mixed atomic-molecular Bose-Einstein condensates (BECs). The main issue is stability of the vortex modes, which is investigated through computation of instability growth rates for eigenmodes of small perturbations, and by means of direct simulations. The threshold of parametric instability for single-color beams, represented solely by the second harmonic (SH) with zero vorticity, is found in an analytical form with the help of the variational approximation (VA). Trapped states with vorticities $\\left( +1,-1,0\\right) $ in the two fundamental-frequency (FF) components and the SH one [the so-called \\textit{hidden-vorticity} (HV) modes] are completely unstable. Also un...
Three-wave electron vortex lattices for measuring nanofields
Energy Technology Data Exchange (ETDEWEB)
Dwyer, C., E-mail: c.dwyer@fz-juelich.de; Boothroyd, C.B.; Chang, S.L.Y.; Dunin-Borkowski, R.E.
2015-01-15
It is demonstrated how an electron-optical arrangement consisting of two electron biprisms can be used to generate three-wave vortex lattices with effective lattice spacings between 0.1 and 1 nm. The presence of vortices in these lattices was verified by using a third biprism to perform direct phase measurements via off-axis electron holography. The use of three-wave lattices for nanoscale electromagnetic field measurements via vortex interferometry is discussed, including the accuracy of vortex position measurements and the interpretation of three-wave vortex lattices in the presence of partial spatial coherence. - Highlights: • We demonstrate how three-wave electron vortex lattices can be generated using two electron biprisms in the TEM. • The optical setup can be used to measure nanoscale electromagnetic fields via vortex interferometry. • The presence of vortices is verified explicitly by using a third biprism to perform phase measurements. • The accuracy of vortex position measurements and the requirements of spatial coherence are discussed.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...
Nonlinear hyperbolic waves in multidimensions
Prasad, Phoolan
2001-01-01
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...
A Nonlinear Vortex Induced Vibration Model of Marine Risers
Institute of Scientific and Technical Information of China (English)
LIU Juan; HUANG Weiping
2013-01-01
With the exploitation of oil and gas in deep water,the traditional vortex induced vibration (VIV) theory is challenged by the unprecedented flexibility of risers.A nonlinear time-dependent VIV model is developed in this paper based on a VIV lift force model and the Morison equation.Both the inline vibration induced by the flow due to vortex shedding and the fluid-structure interaction in the transverse direction are included in the model.One of the characteristics of the model is the response-dependent lift force with nonlinear damping,which is different from other VIV models.The calculations show that the model can well describe the VIV of deepwater risers with the results agreeing with those calculated by other models.
Spin wave vortex from the scattering on Bloch point solitons
Energy Technology Data Exchange (ETDEWEB)
Carvalho-Santos, V.L., E-mail: vagson.carvalho@usach.cl [Instituto Federal de Educação, Ciência e Tecnologia Baiano - Campus Senhor do Bonfim, Km 04 Estrada da Igara, 48970-000 Senhor do Bonfim, Bahia (Brazil); Departamento de Física, Universidad de Santiago de Chile and CEDENNA, Avda. Ecuador 3493, Santiago (Chile); Elías, R.G., E-mail: gabriel.elias@usach.cl [Departamento de Física, Universidad de Santiago de Chile and CEDENNA, Avda. Ecuador 3493, Santiago (Chile); Nunez, A.S., E-mail: alnunez@dfi.uchile.cl [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago (Chile)
2015-12-15
The interaction of a spin wave with a stationary Bloch point is studied. The topological non-trivial structure of the Bloch point manifests in the propagation of spin waves endowing them with a gauge potential that resembles the one associated with the interaction of a magnetic monopole and an electron. By pursuing this analogy, we are led to the conclusion that the scattering of spin waves and Bloch points is accompanied by the creation of a magnon vortex. Interference between such a vortex and a plane wave leads to dislocations in the interference pattern that can be measurable by means of magnon holography.
Propagation of Vortex Electron Wave Functions in a Magnetic Field
Gallatin, Gregg M
2012-01-01
The physics of coherent beams of photons carrying axial orbital angular momentum (OAM) is well understood and such beams, sometimes known as vortex beams, have found applications in optics and microscopy. Recently electron beams carrying very large values of axial OAM have been generated. In the absence of coupling to an external electromagnetic field the propagation of such vortex electron beams is virtually identical mathematically to that of vortex photon beams propagating in a medium with a homogeneous index of refraction. But when coupled to an external electromagnetic field the propagation of vortex electron beams is distinctly different from photons. Here we use the exact path integral solution to Schrodingers equation to examine the time evolution of an electron wave function carrying axial OAM. Interestingly we find that the nonzero OAM wave function can be obtained from the zero OAM wave function, in the case considered here, simply by multipling it by an appropriate time and position dependent pref...
Nonlinear quantum piston for the controlled generation of vortex rings and soliton trains
Pinsker, Florian
2013-05-29
We propose a simple way to generate nonlinear excitations in a controllable way by managing interactions in Bose-Einstein condensates. Under the action of a quantum analog of a classical piston, the condensed atoms are pushed through the trap, generating vortex rings infully three-dimensional condensates or soliton trains in quasi-one-dimensional scenarios. The vortex rings form due to transverse instability of the shock-wave train, enhanced and supported by the energy transfer between waves. We elucidate in what sense the self-interactions within the atom cloud define the properties of the generated vortex rings and soliton trains. Based on the quantum-piston scheme we study the behavior of two-component Bose-Einstein condensates and analyze how the presence of an additional superfluid influences the generation of vortex rings or solitons in the other component, and vice versa. Finally, we show the dynamical emergence of skyrmions within two-component systems in the immiscible regime. © 2013 American Physical Society.
Properties of Nonlinear Dynamo Waves
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.
Impurity effect on Kramer-Pesch core shrinkage in s-wave vortex and chiral p-wave vortex
Hayashi, Nobuhiko; Kato, Yusuke; Sigrist, Manfred
2005-04-01
The low-temperature shrinking of the vortex core (Kramer-Pesch effect) is studied for an isolated single vortex for chiral p-wave and s-wave superconducting phases. The effect of nonmagnetic impurities on the vortex core radius is numerically investigated in the Born limit by means of a quasiclassical approach. It is shown that in the chiral p-wave phase the Kramer-Pesch effect displays a certain robustness against impurities owing to a specific quantum effect, while the s-wave phase reacts more sensitively to impurity scattering. This suggests chiral p-wave superconductors as promising candidates for the experimental observation of the Kramer-Pesch effect.
Nonlinear wave-wave interactions and wedge waves
Institute of Scientific and Technical Information of China (English)
Ray Q.Lin; Will Perrie
2005-01-01
A tetrad mechanism for exciting long waves,for example edge waves,is described based on nonlinear resonant wave-wave interactions.In this mechanism,resonant interactions pass energy to an edge wave,from the three participating gravity waves.The estimated action flux into the edge wave can be orders of magnitude greater than the transfer fluxes derived from other competing mechanisms,such as triad interactions.Moreover,the numerical results show that the actual transfer rates into the edge wave from the three participating gravity waves are two-to three- orders of magnitude greater than bottom friction.
Vortex tubes in the wave bottom boundary layer
Henriquez, M.; Reniers, A.J.H.M.; Ruessink, B.G.; Stive, M.J.F.
2012-01-01
The cause of sediment suspension events during flow reversal under waves in the nearshore is not well understood. Vortex tubes and horizontal pressure gradients have been suggested to be the cause of the suspension events. A medium sized wave flume experiment has been conducted to give insight in th
Three-dimensional vortex structures under breaking waves
WATANABE Yasunori; Saeki, Hiroshi; Hosking, Roger J.
2005-01-01
The large-scale vortex structures under spilling and plunging breakers are investigated, using a fully three-dimensional large-eddy simulation (LES). When an overturning jet projecting from the crest in a breaking wave rebounds from the water surface ahead, the vorticity becomes unstable in a saddle region of strain between the rebounding jet and a primary spanwise vortex, resulting in spanwise undulations of the vorticity. The undulations are amplified on a braid in this saddle region, leadi...
Scattering of Electromagnetic Waves by Drift Vortex in Plasma
Institute of Scientific and Technical Information of China (English)
WANG Dong; CHEN Yinhua; WANG Ge
2008-01-01
In a quasi-two-dimensional model, the scattering of incident ordinary electromag-netic waves by a dipole-electrostatic drift vortex is studied with first-order Born approximation. The distribution of the scattering cross-section and total cross-section are evaluated analytically in different approximate conditions, and the physical interpretations are discussed. When the wavelength of incident wave is much longer than the vortex radius (kia << 1), it is found that the angle at which the scattering cross-section reaches its maxim depends significantly on the approxi-mation of the parameters of the vortex used. It is also found that the total scattering cross-section has an affinitive relation with the parameters of the plasma, while it is irrelevant to the frequency of the incident wave in a wide range of parameters of the vortex. In a totally different range of parameters when incident wave is in the radar-frequency range (then ki<< 1, the wavelength of incident wave is much shorter than the vortex radius), the numerical procedure is conducted with computer in order to obtain the distribution and the total expression of the scattering cross-section. Then it is found that the total scattering cross-section in the low frequency range is much larger than that in high frequency range, so the scattering is more effective in the low frequency range than in high frequency range.
Pattern formation due to non-linear vortex diffusion
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.
Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.
NONLINEAR DYNAMICS RESPONSE OF CASING PIPE UNDER COMBINED WAVE-CURRENT
Institute of Scientific and Technical Information of China (English)
TANG You-gang; GU Jia-yang; ZUO Jian-li; MIN Jian-qin
2005-01-01
The vortex-induced nonlinear vibration of casing pipes in the deep water was studied considering the loads of current and combined wave-current. The vortex-induced vibration equation of a casing pipe was set up considering the beam mode and Morison's nonlinear fluid loads as well as the vortex-excited loads. The approach of calculating vortex-excited nonlinear vibration by Galerkin's method was proposed. The natural vibration frequencies and modes were obtained, and the response including primary resonance induced by current and the composite resonance under combined wave-current for the 170 m long casing pipe in the 160 m depth of water were investigated. The results show that the dynamics response of casing pipe obviously increases, and the complicated response behaviors of casing pipe are described under combined wave-current.
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.
Scattering of sound waves by a compressible vortex
Colonius, Tim; Lele, Sanjiva K.; Moin, Parviz
1991-01-01
Scattering of plane sound waves by a compressible vortex is investigated by direct computation of the two-dimensional Navier-Stokes equations. Nonreflecting boundary conditions are utilized, and their accuracy is established by comparing results on different sized domains. Scattered waves are directly measured from the computations. The resulting amplitude and directivity pattern of the scattered waves is discussed, and compared to various theoretical predictions. For compact vortices (zero circulation), the scattered waves directly computed are in good agreement with predictions based on an acoustic analogy. Strong scattering at about + or - 30 degrees from the direction of incident wave propagation is observed. Back scattering is an order of magnitude smaller than forward scattering. For vortices with finite circulation refraction of the sound by the mean flow field outside the vortex core is found to be important in determining the amplitude and directivity of the scattered wave field.
New approaches to nonlinear waves
2016-01-01
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the app...
Oscillating nonlinear acoustic shock waves
DEFF Research Database (Denmark)
Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth
2016-01-01
We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... that at resonance a stationary state arise consisting of multiple oscillating shock waves. Off resonance driving leads to a nearly linear oscillating ground state but superimposed by bursts of a fast oscillating shock wave. Based on a travelling wave ansatz for the fluid velocity potential with an added 2'nd order...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....
Cylindrical sound wave generated by shock-vortex interaction
Ribner, H. S.
1985-01-01
The passage of a columnar vortex broadside through a shock is investigated. This has been suggested as a crude, but deterministic, model of the generation of 'shock noise' by the turbulence in supersonic jets. The vortex is decomposed by Fourier transform into plane sinusoidal shear waves disposed with radial symmetry. The plane sound waves produced by each shear wave/shock interaction are recombined in the Fourier integral. The waves possess an envelope that is essentially a growing cylindrical sound wave centered at the transmitted vortex. The pressure jump across the nominal radius R = ct attenuates with time as 1/(square root of R) and varies around the arc in an antisymmetric fashion resembling a quadrupole field. Very good agreement, except near the shock, is found with the antisymmetric component of reported interferometric measurements in a shock tube. Beyond the front r approximately equals R is a precursor of opposite sign, that decays like 1/R, generated by the 1/r potential flow around the vortex core. The present work is essentially an extension and update of an early approximate study at M = 1.25. It covers the range (R/core radius) = 10, 100, 1000, and 10,000 for M = 1.25 and (in part) for M = 1.29 and, for fixed (R/core radius) = 1000, the range M = 1.01 to infinity.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...... in Fourier space and equipartition, the role of inhomogeneities and complex geometry and the importance of coupled systems....
Hopf Bifurcation in a Nonlinear Wave System
Institute of Scientific and Technical Information of China (English)
HE Kai-Fen
2004-01-01
@@ Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point.It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for the further exploring routes to turbulence.
Wave equation with concentrated nonlinearities
Noja, Diego; Posilicano, Andrea
2004-01-01
In this paper we address the problem of wave dynamics in presence of concentrated nonlinearities. Given a vector field $V$ on an open subset of $\\CO^n$ and a discrete set $Y\\subset\\RE^3$ with $n$ elements, we define a nonlinear operator $\\Delta_{V,Y}$ on $L^2(\\RE^3)$ which coincides with the free Laplacian when restricted to regular functions vanishing at $Y$, and which reduces to the usual Laplacian with point interactions placed at $Y$ when $V$ is linear and is represented by an Hermitean m...
Exact solitary wave solutions of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The hyperbolic function method for nonlinear wave equations ispresented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Grbner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.
Vortex induced vibrations of pipe in high waves. Field measurements
Energy Technology Data Exchange (ETDEWEB)
Hansen Ottesen, N.-E.; Pedersen, B.
1999-07-01
Vortex induced vibrations have been measured full scale on an instrumented pipe placed vertically in the crest zone of high and steep waves. The Reynolds numbers were in the range 105 to 106. It was found that the vortex induced vibrations in the wave motion were generated within a reduced velocity range of 4 and 8. The vibrations grew intermittently with the passing waves. The vibrations took place in 2-3 modes simultaneously. One mode, however, dominated over the other. The growths of the VIV using a modal analysis were consistent with a basic correlation length of 3 diameters for a stationary pipe with a linear growth of the correlation length of 10 diameter for each 0.1 diameter amplitude. (au)
WAVE BOTTOM LAYERS DYNAMIC WITH SUSPENDED SEDIMENT OVER VORTEX RIPPLES
Institute of Scientific and Technical Information of China (English)
JIANG Chang-bo; BAI Yu-chuan; ZHAO Zi-dan; ZHANG Hong-wu
2004-01-01
Vortex ripple is widely formed in the coastal region, and the dynamic of vortex is quite important because it is responsible for sediment transport. The flow structure around the vortex ripples can be modeled as 2D flow due to the geometry of the flow boundaries. In this paper, 2D Large-Ed dy-Simulation (LES) method was used to predict the flow structure and the dynamic of vortex in the bottom layers under the action of the wave, the numerical simulation results show a completely process of vortex formation, evolvement and disappearance. Based on the study of flow structure, the suspended sediment transport was modeled in present paper. The simulated sediment concentrations were compared to measurements from the literature. The agreement between the time averaged simulated concentration profiles and measurements is satisfactory. For a high setting velocity, the suspended sediment is confined to the vicinity of the bed, and it is dominated by the local bottom shear stress. For a small setting velocity,the suspension is more dominated by the characteristic of vor tex. There are two suspended sediment transport peaks observed in the cross-section at the trough and crest in the half period, the second peak is due to the separation bubble taking the sediment.
Standing waves for discrete nonlinear Schrodinger equations
Ming Jia
2016-01-01
The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Vortex-based spatiotemporal characterization of nonlinear flows
Byrne, Gregory A.
Although the ubiquity of vortices in nature has been recognized by artists for over seven centuries, it was the work of artist and scientist Leonardo da Vinci that provided the monumental transition from an aesthetic form to a scientific tool. DaVinci used vortices to describe the motions he observed in air currents, flowing water and blood flow in the human heart. Five centuries later, the Navier-Stokes equations allow us to recreate the swirling motions of fluid observed in nature. Computational fluid dynamic (CFD) simulations have provided a lens through which to study the role of vortices in a wide variety of modern day applications. The research summarized below represents an effort to look through this lens and bring into focus the practical use of vortices in describing nonlinear flows. Vortex-based spatiotemporal characterizations are obtained using two specific mathematical tools: vortex core lines (VCL) and proper orthogonal decomposition (POD). By applying these tools, we find that vortices continue to provide new insights in the realm of biofluids, urban flows and the phase space of dynamical systems. The insights we have gained are described in this thesis. Our primary focus is on biofluids. Specifically, we seek to gain new insights into the connection between vortices and vascular diseases in order to provide more effective methods for clinical diagnosis and treatment. We highlight several applications in which VCL and POD are used to characterize the flow conditions in a heart pump, identify stenosis in carotid arteries and validate numerical models against PIV-based experimental data. Next, we quantify the spatial complexity and temporal stability of hemodynamics generated by a database of 210 patient-specific aneurysm geometries. Visual classifications of the hemodynamics are compared to the automated, quantitative classifications. The quantities characterizing the hemodynamics are then compared to clinical data to determine conditions that are
Excitation of knotted vortex lines in matter waves
Maucher, F.; Gardiner, S. A.; Hughes, I. G.
2016-06-01
We study the creation of knotted ultracold matter waves in Bose-Einstein condensates via coherent two-photon Raman transitions with a Λ level configuration. The Raman transition allows an indirect transfer of atoms from the internal state | a> to the target state | b> via an excited state | e> , that would be otherwise dipole-forbidden. This setup enables us to imprint three-dimensional knotted vortex lines embedded in the probe field to the density in the target state. We elaborate on experimental feasibility as well as on subsequent dynamics of the matter wave.
Nonlinear Electron Waves in Strongly Magnetized Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans; Juul Rasmussen, Jens
1980-01-01
dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed.......Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...
Nonlinear Fourier analysis with cnoidal waves
Energy Technology Data Exchange (ETDEWEB)
Osborne, A.R. [Dipt. di Fisica Generale dell`Universita, Torino (Italy)
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.
Reconnection of superfluid vortex bundles.
Alamri, Sultan Z; Youd, Anthony J; Barenghi, Carlo F
2008-11-21
Using the vortex filament model and the Gross-Pitaevskii nonlinear Schroedinger equation, we show that bundles of quantized vortex lines in He II are structurally robust and can reconnect with each other maintaining their identity. We discuss vortex stretching in superfluid turbulence and show that, during the bundle reconnection process, kelvin waves of large amplitude are generated, in agreement with the finding that helicity is produced by nearly singular vortex interactions in classical Euler flows.
Nonlinear evolution of whistler wave modulational instability
DEFF Research Database (Denmark)
Karpman, V.I.; Lynov, Jens-Peter; Michelsen, Poul;
1995-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary different......The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary...
Gajjar, J. S. B.
1995-01-01
We consider the nonlinear stability of a fully three-dimensional boundary layer flow in an incompressible fluid and derive an equation governing the nonlinear development of a stationary cross-flow vortex. The amplitude equation is a novel integro-differential equation which has spatial derivatives of the amplitude occurring in the kernal function. It is shown that the evolution of the cross-flow vortex is strongly coupled to the properties of an unsteady wall layer which is in fact driven by an unknown slip velocity, proportional to the amplitude of the cross-flow vortex. The work is extended to obtain the corresponding equation for rotating disk flow. A number of special cases are examined and the numerical solution for one of cases, and further analysis, demonstrates the existence of finite-distance as well as focussing type singularities. The numerical solutions also indicate the presence of a new type of nonlinear wave solution for a certain set of parameter values.
Standing waves for discrete nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Ming Jia
2016-07-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Solving Nonlinear Wave Equations by Elliptic Equation
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
Nonlinear Dispersion Relation in Wave Transformation
Institute of Scientific and Technical Information of China (English)
李瑞杰; 严以新; 曹宏生
2003-01-01
A nonlinear dispersion relation is presented to model the nonlinear dispersion of waves over the whole range of possible water depths. It reduces the phase speed over-prediction of both Hedges′ modified relation and Kirby and Dalrymple′s modified relation in the region of 1＜kh＜1.5 for small wave steepness and maintains the monotonicity in phase speed variation for large wave steepness. And it has a simple form. By use of the new nonlinear dispersion relation along with the mild slope equation taking into account weak nonlinearity, a mathematical model of wave transformation is developed and applied to laboratory data. The results show that the model with the new dispersion relation can predict wave transformation over complicated bathymetry satisfactorily.
Statistical distribution of nonlinear random wave height
Institute of Scientific and Technical Information of China (English)
HOU; Yijun; GUO; Peifang; SONG; Guiting; SONG; Jinbao; YIN; Baoshu; ZHAO; Xixi
2006-01-01
A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.
Control methods for localization of nonlinear waves
Porubov, Alexey; Andrievsky, Boris
2017-03-01
A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions. This article is part of the themed issue 'Horizons of cybernetical physics'.
Nonlinear wave interactions in quantum magnetoplasmas
Shukla, P K; Marklund, M; Stenflo, L
2006-01-01
Nonlinear interactions involving electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfven waves in quantum magnetoplasmas are considered. For this purpose, the quantum hydrodynamical equations are used to derive the governing equations for nonlinearly coupled UH, IC, LH, and Alfven waves. The equations are then Fourier analyzed to obtain nonlinear dispersion relations, which admit both decay and modulational instabilities of the UH waves at quantum scales. The growth rates of the instabilities are presented. They can be useful in applications of our work to diagnostics in laboratory and astrophysical settings.
Nonlinear vortex-phonon interactions in a Bose-Einstein condensate
Mendonça, J. T.; Haas, F.; Gammal, A.
2016-07-01
We consider the nonlinear coupling between an exact vortex solution in a Bose-Einstein condensate and a spectrum of elementary excitations in the medium. These excitations, or Bogoliubov-de Gennes modes, are indeed a special kind of phonons. We treat the spectrum of elementary excitations in the medium as a gas of quantum particles, sometimes also called bogolons. An exact kinetic equation for the bogolon gas is derived, and an approximate form of this equation, valid in the quasi-classical limit, is also obtained. We study the energy transfer between the vortex and the bogolon gas, and establish conditions for vortex instability and damping.
Strongly nonlinear steepening of long interfacial waves
Directory of Open Access Journals (Sweden)
N. Zahibo
2007-06-01
Full Text Available The transformation of nonlinear long internal waves in a two-layer fluid is studied in the Boussinesq and rigid-lid approximation. Explicit analytic formulation of the evolution equation in terms of the Riemann invariants allows us to obtain analytical results characterizing strongly nonlinear wave steepening, including the spectral evolution. Effects manifesting the action of high nonlinear corrections of the model are highlighted. It is shown, in particular, that the breaking points on the wave profile may shift from the zero-crossing level. The wave steepening happens in a different way if the density jump is placed near the middle of the water bulk: then the wave deformation is almost symmetrical and two phases appear where the wave breaks.
Nonlinear waves in strongly interacting relativistic fluids
Fogaça, D A; Filho, L G Ferreira
2013-01-01
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of hadronic matter but also fluids of quarks and gluons. Part of the physics program of these machines is the observation of waves in this strongly interacting medium. From the theoretical point of view, these waves are often treated with li-nearized hydrodynamics. In this text we review the attempts to go beyond linearization. We show how to use the Reductive Perturbation Method to expand the equations of (ideal and viscous) relativistic hydrodynamics to obtain nonlinear wave equations. These nonlinear wave equations govern the evolution of energy density perturbations (in hot quark gluon plasma) or baryon density perturbations (in cold quark gluon plasma and nuclear matter). Different nonlinear wave equations, such as the breaking wave, Korteweg-de Vries and Burgers equations, are...
Kelvin-wave cascade in the vortex filament model
Baggaley, Andrew W.; Laurie, Jason
2014-01-01
The small-scale energy-transfer mechanism in zero-temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves (KWs) transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting KWs to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with the nonlocal six-wave KW interactions as proposed by L'vov and Nazarenko.
On the polarization of nonlinear gravitational waves
Poplawski, Nikodem J.
2011-01-01
We derive a relation between the two polarization modes of a plane, linear gravitational wave in the second-order approximation. Since these two polarizations are not independent, an initially monochromatic gravitational wave loses its periodic character due to the nonlinearity of the Einstein field equations. Accordingly, real gravitational waves may differ from solutions of the linearized field equations, which are being assumed in gravitational-wave detectors.
Energy Technology Data Exchange (ETDEWEB)
Hau, Jan-Niklas, E-mail: hau@fdy.tu-darmstadt.de; Oberlack, Martin [Chair of Fluid Dynamics, Department of Mechanical Engineering, Technische Universität Darmstadt, Otto-Berndt-Strasse 2, 64287 Darmstadt (Germany); GSC CE, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt (Germany); Chagelishvili, George [Chair of Fluid Dynamics, Department of Mechanical Engineering, Technische Universität Darmstadt, Otto-Berndt-Strasse 2, 64287 Darmstadt (Germany); Abastumani Astrophysical Observatory, Ilia State University, Tbilisi 0160, Georgia (United States); M. Nodia Institute of Geophysics, Tbilisi State University, Tbilisi 0128, Georgia (United States); Khujadze, George [Chair of Fluid Mechanics, Universität Siegen, Paul-Bonatz-Str. 9-11, 57068 Siegen (Germany); Tevzadze, Alexander [Faculty of Exact and Natural Sciences, Tbilisi State University, Tbilisi 0128, Georgia (United States)
2015-12-15
Aerodynamic sound generation in shear flows is investigated in the light of the breakthrough in hydrodynamics stability theory in the 1990s, where generic phenomena of non-normal shear flow systems were understood. By applying the thereby emerged short-time/non-modal approach, the sole linear mechanism of wave generation by vortices in shear flows was captured [G. D. Chagelishvili, A. Tevzadze, G. Bodo, and S. S. Moiseev, “Linear mechanism of wave emergence from vortices in smooth shear flows,” Phys. Rev. Lett. 79, 3178-3181 (1997); B. F. Farrell and P. J. Ioannou, “Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow,” Phys. Fluids 12, 3021-3028 (2000); N. A. Bakas, “Mechanism underlying transient growth of planar perturbations in unbounded compressible shear flow,” J. Fluid Mech. 639, 479-507 (2009); and G. Favraud and V. Pagneux, “Superadiabatic evolution of acoustic and vorticity perturbations in Couette flow,” Phys. Rev. E 89, 033012 (2014)]. Its source is the non-normality induced linear mode-coupling, which becomes efficient at moderate Mach numbers that is defined for each perturbation harmonic as the ratio of the shear rate to its characteristic frequency. Based on the results by the non-modal approach, we investigate a two-dimensional homentropic constant shear flow and focus on the dynamical characteristics in the wavenumber plane. This allows to separate from each other the participants of the dynamical processes — vortex and wave modes — and to estimate the efficacy of the process of linear wave-generation. This process is analyzed and visualized on the example of a packet of vortex modes, localized in both, spectral and physical, planes. Further, by employing direct numerical simulations, the wave generation by chaotically distributed vortex modes is analyzed and the involved linear and nonlinear processes are identified. The generated acoustic field is anisotropic in the wavenumber
Hau, Jan-Niklas; Chagelishvili, George; Khujadze, George; Oberlack, Martin; Tevzadze, Alexander
2015-12-01
Aerodynamic sound generation in shear flows is investigated in the light of the breakthrough in hydrodynamics stability theory in the 1990s, where generic phenomena of non-normal shear flow systems were understood. By applying the thereby emerged short-time/non-modal approach, the sole linear mechanism of wave generation by vortices in shear flows was captured [G. D. Chagelishvili, A. Tevzadze, G. Bodo, and S. S. Moiseev, "Linear mechanism of wave emergence from vortices in smooth shear flows," Phys. Rev. Lett. 79, 3178-3181 (1997); B. F. Farrell and P. J. Ioannou, "Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow," Phys. Fluids 12, 3021-3028 (2000); N. A. Bakas, "Mechanism underlying transient growth of planar perturbations in unbounded compressible shear flow," J. Fluid Mech. 639, 479-507 (2009); and G. Favraud and V. Pagneux, "Superadiabatic evolution of acoustic and vorticity perturbations in Couette flow," Phys. Rev. E 89, 033012 (2014)]. Its source is the non-normality induced linear mode-coupling, which becomes efficient at moderate Mach numbers that is defined for each perturbation harmonic as the ratio of the shear rate to its characteristic frequency. Based on the results by the non-modal approach, we investigate a two-dimensional homentropic constant shear flow and focus on the dynamical characteristics in the wavenumber plane. This allows to separate from each other the participants of the dynamical processes — vortex and wave modes — and to estimate the efficacy of the process of linear wave-generation. This process is analyzed and visualized on the example of a packet of vortex modes, localized in both, spectral and physical, planes. Further, by employing direct numerical simulations, the wave generation by chaotically distributed vortex modes is analyzed and the involved linear and nonlinear processes are identified. The generated acoustic field is anisotropic in the wavenumber plane, which
Evolution Of Nonlinear Waves in Compressing Plasma
Energy Technology Data Exchange (ETDEWEB)
P.F. Schmit, I.Y. Dodin, and N.J. Fisch
2011-05-27
Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size {Delta} during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches {Delta}. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
Dispersive shock waves with nonlocal nonlinearity
Barsi, Christopher; Sun, Can; Fleischer, Jason W
2007-01-01
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.
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 surface waves over topography
Janssen, T.T.
2006-01-01
As ocean surface waves radiate into shallow coastal areas and onto beaches, their lengths shorten, wave heights increase, and the wave shape transforms from nearsinusoidal to the characteristic saw-tooth shapes at the onset of breaking; in the ensuing breaking process the wave energy is cascaded to
Nonlinear Electrostatic Wave Equations for Magnetized Plasmas
DEFF Research Database (Denmark)
Dysthe, K.B.; Mjølhus, E.; Pécseli, Hans
1984-01-01
The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed.......The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed....
A NUMERICAL METHOD FOR NONLINEAR WATER WAVES
Institute of Scientific and Technical Information of China (English)
ZHAO Xi-zeng; SUN Zhao-chen; LIANG Shu-xiu; HU Chang-hong
2009-01-01
This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral (HOS) method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform (FFT) algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.
Solitons and Weakly Nonlinear Waves in Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans
1985-01-01
Theoretical descriptions of solitons and weakly nonlinear waves propagating in plasma media are reviewed, with particular attention to the Korteweg-de Vries (KDV) equation and the Nonlinear Schrödinger equation (NLS). The modifications of these basic equations due to the effects of resonant...
Energy Technology Data Exchange (ETDEWEB)
Gul-e-Ali,; Mirza, Arshad M. [Theoretical Plasma Physics Group, Physics Department, Quaid-i-Azam University, Islamabad 45320 (Pakistan); Masood, W. [COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000 (Pakistan); National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan)
2016-02-15
Coupling of drift vortex and the ion acoustic modes in the linear and nonlinear regimes are investigated with sheared ion flow perpendicular to the ambient magnetic field in a plasma comprising of hot ions and nonthermal population of electrons. In this regard, generation of nonlinear vortex structures in the presence of kappa, Cairns, and q-nonextensive electron distributions are investigated in detail, and comparison with the Maxwellian distribution is also made. The appositeness of the present investigation in the matter of auroral F-region is also pointed out.
Nonlinear surface waves in photonic hypercrystals
Ali, Munazza Zulfiqar
2017-08-01
Photonic crystals and hyperbolic metamaterials are merged to give the concept of photonic hypercrystals. It combines the properties of its two constituents to give rise to novel phenomena. Here the propagation of Transverse Magnetic waves at the interface between a nonlinear dielectric material and a photonic hypercrystal is studied and the corresponding dispersion relation is derived using the uniaxial parallel approximation. Both dielectric and metallic photonic hypercrystals are studied and it is found that nonlinearity limits the infinite divergence of wave vectors of the surface waves. These states exist in the frequency region where the linear surface waves do not exist. It is also shown that the nonlinearity can be used to engineer the group velocity of the resulting surface wave.
Nonlinear water waves with soluble surfactant
Lapham, Gary; Dowling, David; Schultz, William
1998-11-01
The hydrodynamic effects of surfactants have fascinated scientists for generations. This presentation describes an experimental investigation into the influence of a soluble surfactant on nonlinear capillary-gravity waves in the frequency range from 12 to 20 Hz. Waves were generated in a plexiglass wave tank (254 cm long, 30.5 cm wide, and 18 cm deep) with a triangular plunger wave maker. The tank was filled with carbon- and particulate-filtered water into which the soluble surfactant Triton-X-100® was added in known amounts. Wave slope was measured nonintrusively with a digital camera running at 225 fps by monitoring the position of light beams which passed up through the bottom of the tank, out through the wavy surface, and onto a white screen. Wave slope data were reduced to determine wave damping and the frequency content of the wave train. Both were influenced by the presence of the surfactant. Interestingly, a subharmonic wave occurring at one-sixth the paddle-driving frequency was found only when surfactant was present and the paddle was driven at amplitudes high enough to produce nonlinear waves in clean water. Although the origins of this subharmonic wave remain unclear, it appears to be a genuine manifestation of the combined effects of the surfactant and nonlinearity.
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
Explicit Traveling Wave Solutions to Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
Linghai ZHANG
2011-01-01
First of all,some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations,nonlinear dissipative dispersive wave equations,nonlinear convection equations,nonlinear reaction diffusion equations and nonlinear hyperbolic equations,respectively.
Vortex flow in the technology of radiation wave cracking (RWC)
Tsoy, L A; Komarov, A G; Tsoy, A N
2012-01-01
This article examines the theory of vortex flows in relation to the processes occurring in the radiation-wave cracking of crude oil, when the crude oil is sprayed into the gas stream in the form of a mist and then is fed into the reactor, where it is treated by the accelerated electrons and the UHF radiation. The output of this process are the products with the specified parameters (high-octane petroleum products). This process operates at the ambient pressure and temperature, which makes the process safer for industrial purposes. Besides the process itself, the authors described the equipment used in this process, as well as the parameters of the optimal process.
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
EXACT SOLUTIONS TO NONLINEAR WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,we use an invariant set to construct exact solutions to a nonlinear wave equation with a variable wave speed. Moreover,we obtain conditions under which the equation admits a nonclassical symmetry. Several different nonclassical symmetries for equations with different diffusion terms are presented.
Solitary waves on nonlinear elastic rods. I
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1984-01-01
Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...
Nonlinear ship waves and computational fluid dynamics
National Research Council Canada - National Science Library
MIYATA, Hideaki; ORIHARA, Hideo; SATO, Yohei
2014-01-01
.... 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...
Backreaction of excitations on a vortex
Arodz, H; Arodz, Henryk; Hadasz, Leszek
1997-01-01
Excitations of a vortex are usually considered in a linear approximation neglecting their backreaction on the vortex. In the present paper we investigate backreaction of Proca type excitations on a straightlinear vortex in the Abelian Higgs model. We propose exact Ansatz for fields of the excited vortex. From initial set of six nonlinear field equations we obtain (in a limit of weak excitations) two linear wave equations for the backreaction corrections. Their approximate solutions are found in the cases of plane wave and wave packet type excitations. We find that the excited vortex radiates vector field and that the Higgs field has a very broad oscillating component.
Electron vortex magnetic holes: A nonlinear coherent plasma structure
Haynes, C.T.; Burgess, D.; Camporeale, E.; Sundberg, T.
2015-01-01
We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional particle-in-cell simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic
The Nonlinear Talbot Effect of Rogue Waves
Zhang, Yiqi; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Song, Jianping; Zhang, Yanpeng
2014-01-01
Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schr\\"odinger 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 \\pi-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.
Nonlinear Landau damping and Alfven wave dissipation
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.
Nanoscale magnetization of a single vortex in d-wave superconductors
Zakharchuk, I.; Januzaj, A.; Safonchik, M.; Traito, K. B.; Lähderanta, E.
2017-01-01
A finite-size scaling of the nanoscale magnetization m on size averaging R of a single vortex in d-wave bulk superconductor is developed using quasiclassical Eilenberger equations. Nanoscaling is anchoring around the linear London approximation for bulk superconductors. Comparing the results with those obtained in local nonlinear approach demonstrated the importance of the nonlocal contribution. Temperature dependences of two-point correlation function χ(T , R 1 , R 2) = m(T , R 2) / m(0 , R 2) - m(T , R 1) / m(0 , R 1) with R2 > R1 and one-point function χ(T, R1 → ∞, R2) are calculated. It is found that χ(T, R1, R2), R2 > R1, is a nonmonotonous function of temperature and changes sign at high temperatures. This nonmonotonous temperature dependence can be understood as a result of competition between various effects i) Volovik effect and nonlocal corrections to superconducting electron density dominating in low temperature range, and ii) current-induced suppression of the order parameter dominating at high temperatures. The introduced nonmagnetic disorder greatly suppresses the low temperature nonlocal and nonlinear effects, leaving the order parameter effects to prevail in the whole temperature range. Nonlocal pairing and tunneling effects are investigated at the superconductor - normal metal border by considering a d-wave superconducting dot (d-dot) inside a normal diffusive metal. These effects result in a suppression of the supercurrent in the vortex core and are essential in nanodots with relatively small sizes. At sizes larger than a temperature dependent characteristic length the nanoscale physics transforms into bulk solution.
Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows
Matsuoka, C.; Nishihara, K.; Sano, T.
2016-10-01
A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.
Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows
Matsuoka, C.; Nishihara, K.; Sano, T.
2017-04-01
A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.
Pattern dynamics of vortex ripples in sand: Nonlinear modeling and experimental validation
DEFF Research Database (Denmark)
Andersen, Ken Haste; Abel, M.; Krug, J.;
2002-01-01
Vortex ripples in sand are studied experimentally in a one-dimensional setup with periodic boundary conditions. The nonlinear evolution, far from the onset of instability, is analyzed in the framework of a simple model developed for homogeneous patterns. The interaction function describing the mass...
Vortex Nucleation in a Dissipative Variant of the Nonlinear Schroedinger Equation Under Rotation
2014-12-01
Vortices in Nonlinear Fields (Clarendon, UK, 1999). [2] Yu.S. Kivshar and B. Luther -Davies, Physics Reports 298, 81–197 (1998). [3] Y.S. Kivshar, J...Christou, V. Tikhonenko, B. Luther -Davies and L. Pismen, Optics Comm. 152, 198–206 (1998). [4] H.J. Lugt, Vortex Flow in Nature and Technology (John
Superresolution through the topological shaping of sound with an acoustic vortex wave antenna
Guild, Matthew D; Martin, Theodore P; Rohde, Charles A; Orris, Gregory J
2016-01-01
In this paper, we demonstrate far-field acoustic superresolution using shaped acoustic vortices. Compared with previously proposed near-field methods of acoustic superresolution, in this work we describe how far-field superresolution can be obtained using an acoustic vortex wave antenna. This is accomplished by leveraging the recent advances in optical vortices in conjunction with the topological diversity of a leaky wave antenna design. In particular, the use of an acoustic vortex wave antenna eliminates the need for a complicated phased array consisting of multiple active elements, and enables a superresolving aperture to be achieved with a single simple acoustic source and total aperture size less than a wavelength in diameter. A theoretical formulation is presented for the design of an acoustic vortex wave antenna with arbitrary planar arrangement, and explicit expressions are developed for the radiated acoustic pressure field. This geometric versatility enables variously-shaped acoustic vortex patterns t...
Nagai, Yuki; Kato, Yusuke
2010-11-01
We investigate the impurity scattering rates for quasiparticles in vortex cores of sign-reversing s -wave superconductors as a probe to detect the internal phase difference of the order parameters among different Fermi surfaces. The impurity scattering rates and coherence factors are related to quasiparticle interference effect by the scanning tunneling microscopy and spectroscopy technique. With use of the Born and Kramer-Pesch approximations for the Andreev bound states, we show that the sign-reversed forward scatterings are dominant in vortex cores. Owing to the coherence factor in vortex cores of ±s -wave superconductors, the impurity scattering rate of the Andreev bound states has a characteristic distribution on the Fermi surfaces. For comparison, the impurity scattering rates in vortex cores of s -wave and d -wave superconductors are also discussed.
Dynamics of Nonlinear Waves on Bounded Domains
Maliborski, Maciej
2016-01-01
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause the energy to concentrate on smaller scales leading to a turbulent behaviour. Which of these two possibilities occurs depends on a model and the initial conditions. In the quasiperiodic scenario there exist very special time-periodic solutions. They result for a delicate balance between dispersion and nonlinear interaction. The main body of this dissertation is concerned with construction (by means of perturbative and numerical methods) of time-periodic solutions for various nonlinear wave equations on bounded domains. While turbulence is mainly associated with hydrodynamics, recent research in General Relativity has also revealed turbulent phenomena. Numerical studies of a self-gravitating massless scalar field in spherical symmetry gave evidence that anti-de Sitter space ...
Wave modes of collective vortex gyration in dipolar-coupled-dot-array magnonic crystals
Han, Dong-Soo; Vogel, Andreas; Jung, Hyunsung; Lee, Ki-Suk; Weigand, Markus; Stoll, Hermann; Schütz, Gisela; Fischer, Peter; Meier, Guido; Kim, Sang-Koog
2013-07-01
Lattice vibration modes are collective excitations in periodic arrays of atoms or molecules. These modes determine novel transport properties in solid crystals. Analogously, in periodical arrangements of magnetic vortex-state disks, collective vortex motions have been predicted. Here, we experimentally observe wave modes of collective vortex gyration in one-dimensional (1D) periodic arrays of magnetic disks using time-resolved scanning transmission x-ray microscopy. The observed modes are interpreted based on micromagnetic simulation and numerical calculation of coupled Thiele equations. Dispersion of the modes is found to be strongly affected by both vortex polarization and chirality ordering, as revealed by the explicit analytical form of 1D infinite arrays. A thorough understanding thereof is fundamental both for lattice vibrations and vortex dynamics, which we demonstrate for 1D magnonic crystals. Such magnetic disk arrays with vortex-state ordering, referred to as magnetic metastructure, offer potential implementation into information processing devices.
Energy Technology Data Exchange (ETDEWEB)
Artemyev, A. V., E-mail: ante0226@gmail.com; Vasiliev, A. A. [Space Research Institute, RAS, Moscow (Russian Federation); Mourenas, D.; Krasnoselskikh, V. V. [LPC2E/CNRS—University of Orleans, Orleans (France); Agapitov, O. V. [Space Sciences Laboratory, University of California, Berkeley, California 94720 (United States)
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.
Quasi self-adjoint nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Torrisi, M; Tracina, R, E-mail: nib@bth.s, E-mail: torrisi@dmi.unict.i, E-mail: tracina@dmi.unict.i [Dipartimento di Matematica e Informatica, University of Catania (Italy)
2010-11-05
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. (fast track communication)
NEW TYPE OF ELASTIC ROTATIONAL WAVES IN GEO-MEDIUM AND VORTEX GEODYNAMICS
Directory of Open Access Journals (Sweden)
Alexander V. Vikulin
2015-09-01
nonlinear wave mechanics of the geo-medium, admitting rotational movements of blocks. According to М.V. Stovas, V.Е. Khain and other researchers, rotation of the planet around its axis is of critical importance for understating the origin of geodynamic movements.Based on the review of results from the previous comprehensive geological and geophysical studies, a conclusion is made on the torque origin of rotating block geo-medium which is termed as Peive–Sedov–Sadovsky medium. Analyses of migration of earthquake foci and volcanic eruptions and movements of edges of tectonic plates provided grounds to design a principally new model, and this rotational model is described in the present publication. Blocks and plates interacting with each other in the model are interrelated by long-range elastic fields which comprise a uniform planetary geodynamic medium, i.e. ‘self-consistent’ state of the geo-medium. Briefly reviewed are data about vortex geological structures and rotary motions of blocks and plates; such data have been detected and recorded in abundance in a variety of geophysical fields. It is stressed that similar, in principle, vortex movements / flows are solutions of the well known Dirichlet–Dedekind–Riemann problem of rotating and gravitating liquid drop that is the problem of the Earth’s equilibrium shape. According to the proposed rotational model, geodynamic solutions of the rotational model combine geodynamic flows in the solution of the problem of the Earth’s equilibrium shape and geologic-geophysical vortex structures and movements on the Earth’s surface in one and the same class of phenomena. It is proposed to apply such solutions for establishing a new geological paradigm – new torque (and/or wave / vortex geodynamics.
Nonlinear Interaction of Waves in Geomaterials
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.
Explicit solutions of nonlinear wave equation systems
Institute of Scientific and Technical Information of China (English)
Ahmet Bekir; Burcu Ayhan; M.Naci (O)zer
2013-01-01
We apply the (G'/G)-expansion method to solve two systems of nonlinear differential equations and construct traveling wave solutions expressed in terms of hyperbolic functions,trigonometric functions,and rational functions with arbitrary parameters.We highlight the power of the (G'/G)-expansion method in providing generalized solitary wave solutions of different physical structures.It is shown that the (G'/G)-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear differential equation systems in mathematical physics.
Nonlinear dynamics of hydrostatic internal gravity waves
Energy Technology Data Exchange (ETDEWEB)
Stechmann, Samuel N.; Majda, Andrew J. [New York University, Courant Institute of Mathematical Sciences, NY (United States); Khouider, Boualem [University of Victoria, Department of Mathematics and Statistics, Victoria, BC (Canada)
2008-11-15
Stratified hydrostatic fluids have linear internal gravity waves with different phase speeds and vertical profiles. Here a simplified set of partial differential equations (PDE) is derived to represent the nonlinear dynamics of waves with different vertical profiles. The equations are derived by projecting the full nonlinear equations onto the vertical modes of two gravity waves, and the resulting equations are thus referred to here as the two-mode shallow water equations (2MSWE). A key aspect of the nonlinearities of the 2MSWE is that they allow for interactions between a background wind shear and propagating waves. This is important in the tropical atmosphere where horizontally propagating gravity waves interact together with wind shear and have source terms due to convection. It is shown here that the 2MSWE have nonlinear internal bore solutions, and the behavior of the nonlinear waves is investigated for different background wind shears. When a background shear is included, there is an asymmetry between the east- and westward propagating waves. This could be an important effect for the large-scale organization of tropical convection, since the convection is often not isotropic but organized on large scales by waves. An idealized illustration of this asymmetry is given for a background shear from the westerly wind burst phase of the Madden-Julian oscillation; the potential for organized convection is increased to the west of the existing convection by the propagating nonlinear gravity waves, which agrees qualitatively with actual observations. The ideas here should be useful for other physical applications as well. Moreover, the 2MSWE have several interesting mathematical properties: they are a system of nonconservative PDE with a conserved energy, they are conditionally hyperbolic, and they are neither genuinely nonlinear nor linearly degenerate over all of state space. Theory and numerics are developed to illustrate these features, and these features are
Optics in a nonlinear gravitational wave
Harte, Abraham I
2015-01-01
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, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. The commonly-used predictions of linear perturbation theory are shown to be generically overshadowed---even for very weak gravitational waves---by nonlinear effects when considering observations of sufficiently distant sources; higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected. 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.
Optics in a nonlinear gravitational plane wave
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.
Linear and nonlinear dynamics of current-driven waves in dusty plasmas
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Ali [National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Department of Physics, COMSATS Institute of Information Technology (CIIT), Islamabad (Pakistan); Theoretical Plasma Physics Division, PINSTECH, P. O. Nilore, Islamabad (Pakistan); Ali Shan, S.; Haque, Q. [National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Theoretical Plasma Physics Division, PINSTECH, P. O. Nilore, Islamabad (Pakistan); Saleem, H. [National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Department of Physics, COMSATS Institute of Information Technology (CIIT), Islamabad (Pakistan)
2012-09-15
The linear and nonlinear dynamics of a recently proposed plasma mode of dusty plasma is studied using kappa distribution for electrons. This electrostatic wave can propagate in the plasma due to the sheared flow of electrons and ions parallel to the external magnetic field in the presence of stationary dust. The coupling of this wave with the usual drift wave and ion acoustic wave is investigated. D'Angelo's mode is also modified in the presence of superthermal electrons. In the nonlinear regime, the wave can give rise to dipolar vortex structures if the shear in flow is weaker and tripolar vortices if the flow has steeper gradient. The results have been applied to Saturn's magnetosphere corresponding to negatively charged dust grains. But the theoretical model is applicable for positively charged dust as well. This work will be useful for future observations and studies of dusty environments of planets and comets.
Nonlinear random optical waves: Integrable turbulence, rogue waves and intermittency
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.
Solitary waves on nonlinear elastic rods. II
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1987-01-01
In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results...
Nonlinear processes in the strong wave-plasma interaction
Pegoraro, Francesco; Califano, Francesco; Attico, Nicola; Bulanov, Sergei
2000-10-01
Nonlinear interactions in hot laboratory and/or astrophysical plasmas are a very efficient mechanism able to transfer the energy from the large to the small spatial scales of the system. As a result, kinetic processes are excited and play a key role in the plasma dynamics since the typical fluid dissipative length scales (where the nonlinear cascade is stopped) are (much) smaller then the kinetic length scales. Then, the key point is the role of the kinetic effects in the global plasma dynamics, i.e. whether the kinetic effects remains confined to the small scales of the system or whether there is a significant feedback on the large scales. Here we will address this problem by discussing the nonlinear kinetic evolution of the electromagnetic beam plasma instability where phase space vortices, as well as large scale vortex like magnetic structures in the physical space, are generated by wave - particle interactions. The role and influence of kinetic effects on the large scale plasma dynamics will be also discussed by addressing the problem of collisionless magnetic reconection.
Nonlinear Landau damping of Alfven waves.
Hollweg, J. V.
1971-01-01
Demonstration that large-amplitude linearly or elliptically polarized Alfven waves propagating parallel to the average magnetic field can be dissipated by nonlinear Landau damping. The damping is due to the longitudinal electric field associated with the ion sound wave which is driven (in second order) by the Alfven wave. The damping rate can be large even in a cold plasma (beta much less than 1, but not zero), and the mechanism proposed may be the dominant one in many plasmas of astrophysical interest.
Electron vortex magnetic holes: a nonlinear coherent plasma structure
Haynes, Christopher T; Camporeale, Enrico; Sundberg, Torbjorn
2014-01-01
We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional PIC simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic holes (EVMHs), have circular cross-section. The magnetic field depression is associated with a diamagnetic azimuthal current provided by a population of trapped electrons in petal-like orbits. The trapped electron population provides a mean azimuthal velocity and since trapping preferentially selects high pitch angles, a perpendicular temperature anisotropy. The structures arise out of initial perturbations in the course of the turbulent evolution of the plasma, and are stable over at least 100 electron gyroperiods. We have verified the model for the EVMH by carrying out test particle and PIC simulations of isolated structures in a uniform plasma. It is found that (quasi-)stable structures can be formed provided that there is ...
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
Nonlinear interactions between gravity waves and tides
Institute of Scientific and Technical Information of China (English)
LIU Xiao; XU JiYao; MA RuiPing
2007-01-01
In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75-85 km, z =90-110 km and z= 115-130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the horizontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90-110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.
Nonlinear interactions between gravity waves and tides
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75―85 km, z = 90―110 km and z = 115―130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the hori-zontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90—110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.
NONLINEAR MHD WAVES IN A PROMINENCE FOOT
Energy Technology Data Exchange (ETDEWEB)
Ofman, L. [Catholic University of America, Washington, DC 20064 (United States); Knizhnik, K.; Kucera, T. [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States); Schmieder, B. [LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris-Diderot, Sorbonne Paris Cit, 5 place Jules Janssen, F-92195 Meudon (France)
2015-11-10
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ∼ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5–11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5–14 G. For the typical prominence density the corresponding fast magnetosonic speed is ∼20 km s{sup −1}, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
Explosive-driven shock wave and vortex ring interaction with a propane flame
Giannuzzi, P. M.; Hargather, M. J.; Doig, G. C.
2016-11-01
Experiments were performed to analyze the interaction of an explosively driven shock wave and a propane flame. A 30 g explosive charge was detonated at one end of a 3-m-long, 0.6-m-diameter shock tube to produce a shock wave which propagated into the atmosphere. A propane flame source was positioned at various locations outside of the shock tube to investigate the effect of different strength shock waves. High-speed retroreflective shadowgraph imaging visualized the shock wave motion and flame response, while a synchronized color camera imaged the flame directly. The explosively driven shock tube was shown to produce a repeatable shock wave and vortex ring. Digital streak images show the shock wave and vortex ring propagation and expansion. The shadowgrams show that the shock wave extinguishes the propane flame by pushing it off of the fuel source. Even a weak shock wave was found to be capable of extinguishing the flame.
Electron vortex magnetic holes: A nonlinear coherent plasma structure
Haynes, Christopher T.; Burgess, David; Camporeale, Enrico; Sundberg, Torbjorn
2015-01-01
We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional particle-in-cell simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic holes (EVMHs), have circular cross-section. The magnetic field depression is associated with a diamagnetic azimuthal current provided by a population of trapped electrons in petal-like orbits. The trapped electron population provides a mean azimuthal velocity and since trapping preferentially selects high pitch angles, a perpendicular temperature anisotropy. The structures arise out of initial perturbations in the course of the turbulent evolution of the plasma, and are stable over at least 100 electron gyroperiods. We have verified the model for the EVMH by carrying out test particle and PIC simulations of isolated structures in a uniform plasma. It is found that (quasi-)stable structures can be formed provided that there is some initial perpendicular temperature anisotropy at the structure location. The properties of these structures (scale size, trapped population, etc.) are able to explain the observed properties of magnetic holes in the terrestrial plasma sheet. EVMHs may also contribute to turbulence properties, such as intermittency, at short scale lengths in other astrophysical plasmas.
Electron vortex magnetic holes: A nonlinear coherent plasma structure
Energy Technology Data Exchange (ETDEWEB)
Haynes, Christopher T., E-mail: c.t.haynes@qmul.ac.uk; Burgess, David; Sundberg, Torbjorn [School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom); Camporeale, Enrico [Multiscale Dynamics, Centrum Wiskunde and Informatica (CWI), Amsterdam (Netherlands)
2015-01-15
We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional particle-in-cell simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic holes (EVMHs), have circular cross-section. The magnetic field depression is associated with a diamagnetic azimuthal current provided by a population of trapped electrons in petal-like orbits. The trapped electron population provides a mean azimuthal velocity and since trapping preferentially selects high pitch angles, a perpendicular temperature anisotropy. The structures arise out of initial perturbations in the course of the turbulent evolution of the plasma, and are stable over at least 100 electron gyroperiods. We have verified the model for the EVMH by carrying out test particle and PIC simulations of isolated structures in a uniform plasma. It is found that (quasi-)stable structures can be formed provided that there is some initial perpendicular temperature anisotropy at the structure location. The properties of these structures (scale size, trapped population, etc.) are able to explain the observed properties of magnetic holes in the terrestrial plasma sheet. EVMHs may also contribute to turbulence properties, such as intermittency, at short scale lengths in other astrophysical plasmas.
Nonlinear effects in the bounded dust-vortex flow in plasma
Laishram, Modhuchandra; Sharma, Devendra; Chattopdhyay, Prabal K.; Kaw, Predhiman K.
2017-03-01
The vortex structures in a cloud of electrically suspended dust in a streaming plasma constitutes a driven system with a rich nonlinear flow regime. Experimentally recovered toroidal formations of this system have motivated study of its volumetrically driven-dissipative vortex flow dynamics using two-dimensional hydrodynamics in the incompressible Navier-Stokes regime. Nonlinear equilibrium solutions are obtained for this system where a nonuniformly driven two-dimensional dust flow exhibits distinct regions of localized accelerations and strong friction caused by stationary fluids at the confining boundaries resisting the dust flow. In agreement with observations in experiments, it is demonstrated that the nonlinear effects appear in the limit of small viscosity, where the primary vortices form scaling with the most dominant spatial scales of the domain topology and develop separated virtual boundaries along their periphery. This separation is triggered beyond a critical dust viscosity that signifies a structural bifurcation. Emergence of uniform vorticity core and secondary vortices with a newer level of identical dynamics highlights the applicability of the studied dynamics to gigantic vortex flows, such as the Jovian great red spot, to microscopic biophysical intracellular activity.
Nonlinear plasma wave in magnetized plasmas
Energy Technology Data Exchange (ETDEWEB)
Bulanov, Sergei V. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Prokhorov Institute of General Physics, Russian Academy of Sciences, Moscow 119991 (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region 141700 (Russian Federation); Esirkepov, Timur Zh.; Kando, Masaki; Koga, James K. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Hosokai, Tomonao; Zhidkov, Alexei G. [Photon Pioneers Center, Osaka University, 2-8 Yamadaoka, Suita, Osaka 565-0871 (Japan); Japan Science and Technology Agency, CREST, 2-1, Yamadaoka, Suita, Osaka 565-0871 (Japan); Kodama, Ryosuke [Photon Pioneers Center, Osaka University, 2-8 Yamadaoka, Suita, Osaka 565-0871 (Japan); Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871 (Japan)
2013-08-15
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.
Study of Linear and Nonlinear Wave Excitation
Chu, Feng; Berumen, Jorge; Hood, Ryan; Mattingly, Sean; Skiff, Frederick
2013-10-01
We report an experimental study of externally excited low-frequency waves in a cylindrical, magnetized, singly-ionized Argon inductively-coupled gas discharge plasma that is weakly collisional. Wave excitation in the drift wave frequency range is accomplished by low-percentage amplitude modulation of the RF plasma source. Laser-induced fluorescence is adopted to study ion-density fluctuations in phase space. The laser is chopped to separate LIF from collisional fluorescence. A single negatively-biased Langmuir probe is used to detect ion-density fluctuations in the plasma. A ring array of Langmuir probes is also used to analyze the spatial and spectral structure of the excited waves. We apply coherent detection with respect to the wave frequency to obtain the ion distribution function associated with externally generated waves. Higher-order spectra are computed to evaluate the nonlinear coupling between fluctuations at various frequencies produced by the externally generated waves. Parametric decay of the waves is observed. This work is supported by U.S. DOE Grant No. DE-FG02-99ER54543.
Wave-kinetic description of nonlinear photons
Marklund, M; Brodin, G; Stenflo, L
2004-01-01
The nonlinear interaction, due to quantum electrodynamical (QED) effects, between photons is investigated using a wave-kinetic description. Starting from a coherent wave description, we use the Wigner transform technique to obtain a set of wave-kinetic equations, the so called Wigner-Moyal equations. These equations are coupled to a background radiation fluid, whose dynamics is determined by an acoustic wave equation. In the slowly varying acoustic limit, we analyse the resulting system of kinetic equations, and show that they describe instabilities, as well as Landau-like damping. The instabilities may lead to break-up and focusing of ultra-high intensity multi-beam systems, which in conjunction with the damping may result in stationary strong field structures. The results could be of relevance for the next generation of laser-plasma systems.
A nonlinear Schroedinger wave equation with linear quantum behavior
Energy Technology Data Exchange (ETDEWEB)
Richardson, Chris D.; Schlagheck, Peter; Martin, John; Vandewalle, Nicolas; Bastin, Thierry [Departement de Physique, University of Liege, 4000 Liege (Belgium)
2014-07-01
We show that a nonlinear Schroedinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum theory. The classical wave equation includes a nonlinear classicality enforcing potential which when eliminated transforms the wave equation into the linear Schroedinger equation. We show that it is not necessary to completely cancel this nonlinearity to recover the linear behavior of quantum mechanics. Scaling the classicality enforcing potential is sufficient to have quantum-like features appear and is equivalent to scaling Planck's constant.
Symmetry, phase modulation and nonlinear waves
Bridges, Thomas J
2017-01-01
Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.
Nonlinear waves in waveguides with stratification
Leble, Sergei B
1991-01-01
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Nonlinear Dispersion Effect on Wave Transformation
Institute of Scientific and Technical Information of China (English)
LI Ruijie; Dong-Young LEE
2000-01-01
A new nonlinear dispersion relation is given in this paper, which can overcome the limitation of the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple (1986), and which has a better approximation to Hedges＇ empirical relation than the modilied relations by Hedges (1987). Kirby and Dahymple (1987) for shallow waters. The new dispersion relation is simple in form. thus it can be used easily in practice. Meanwhile. a general explicil approximalion to the new dispersion rela tion and olher nonlinear dispersion relations is given. By use of the explicit approximation to the new dispersion relation along with the mild slope equation taking inlo account weakly nonlinear effect, a mathematical model is obtained, and it is applied to laboratory data. The results show that the model developed vith the new dispersion relation predicts wave translornation over complicated topography quite well.
Variational modelling of nonlinear water waves
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.
A method for generating highly nonlinear periodic waves in physical wave basins
DEFF Research Database (Denmark)
Zhang, Haiwen; Schäffer, Hemming A.; Bingham, Harry B.
2006-01-01
This abstract describes a new method for generating nonlinear waves of constant form in physical wave basins. The idea is to combine fully dispersive linear wavemaker theory with nonlinear shallow water wave generation theory; and use an exact nonlinear theory as the target. We refer to the metho...... as an ad-hoc unified wave generation theory, since there is no rigorous analysis behind the idea which is simply justified by the improved results obtained for the practical generation of steady nonlinear waves....
Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
NONLINEAR FLUID DAMPING IN STRUCTURE-WAKE OSCILLATORS IN MODELING VORTEX-INDUCED VIBRATIONS
Institute of Scientific and Technical Information of China (English)
LIN Li-ming; LING Guo-can; WU Ying-xiang; ZENG Xiao-hui
2009-01-01
A Nonlinear Fluid Damping(NFD)in the form of the square-velocity is applied in the response analysis of Vortex-Induced Vibrations(VIV).Its nonlinear hydrodynamic effects on the coupled wake and structure oscillators are investigated.A comparison between the coupled systems with the linear and nonlinear fluid dampings and experiments shows that the NFD model can well describe response characteristics,such as the amplification of body displacement at lock-in and frequency lock-in,both at high and low mass ratios.Particularly,the predicted peak amplitude of the body in the Griffin plot is in good agreement with experimental data and empirical equation,indicating the significant effect of the NFD on the structure motion.
Hall Effect in the Vortex Lattice of d-Wave Superconductors with Anisotropic Fermi Surfaces
Kohno, Wataru; Ueki, Hikaru; Kita, Takafumi
2017-02-01
On the basis of the augmented quasiclassical theory of superconductivity with the Lorentz force, we study the magnetic field dependence of the charge distribution due to the Lorentz force in a d-wave vortex lattice with anisotropic Fermi surfaces. Owing to the competition between the energy-gap and Fermi surface anisotropies, the charge profile in the vortex lattice changes dramatically with increasing magnetic field because of the overlaps of each nearest vortex-core charge. In addition, the accumulated charge in the core region may reverse its sign as a function of magnetic field. This strong field dependence of the vortex-core charge cannot be observed in the model with an isotropic Fermi surface.
Long wave-short wave resonance in nonlinear negative refractive index media.
Chowdhury, Aref; Tataronis, John A
2008-04-18
We show that long wave-short wave resonance can be achieved in a second-order nonlinear negative refractive index medium when the short wave lies on the negative index branch. With the medium exhibiting a second-order nonlinear susceptibility, a number of nonlinear phenomena such as solitary waves, paired solitons, and periodic wave trains are possible or enhanced through the cascaded second-order effect. Potential applications include the generation of terahertz waves from optical pulses.
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Non-planar and Non-linear Second Sound Waves in He Ⅱ
Institute of Scientific and Technical Information of China (English)
ZHANG Peng; KIMURA Seiji; MURAKAMI Masahide; WANG Ru-zhu
2000-01-01
Non-planar and non-linear second sound wave are experimentally investigated in an open He Ⅱ bath. It is found that second sound wave characterized by a negative tail part in an open He Ⅱ bath is different from that propagating through a channel, and the shape of the negative tail part of second sound wave varies at different location in an open He Ⅱ bath. Theoretical consideration is also carried out based on two-fluid model and vortex evolution equation. It is found that experimental and theoretical results agree rather well with each other. Second sound wave may develop into the thermal shock wave provided that the heat flux is large.
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium.
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-06-15
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.
NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD
Institute of Scientific and Technical Information of China (English)
Liu Zhifang; Zhang Shanyuan
2006-01-01
A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.
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
Characterizing Electron Trapping Nonlinearity in Langmuir Waves
Strozzi, D J; Rose, H A; Hinkel, D E; Langdon, A B; Banks, J W
2012-01-01
We assess when electron trapping nonlinearities are expected to be important in Langmuir waves. The basic criterion is that the effective lifetime, t_d, of resonant electrons in the trapping region of velocity space must exceed the period of trapped motion for deeply-trapped electrons, tau_B = (n_e/delta n)^{1/2} 2pi/omega_pe. A unitless figure of merit, the "bounce number" N_B = t_d/tau_B, encapsulates this condition and allows an effective threshold amplitude for which N_B=1 to be defined. The lifetime 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_B for side loss, and is significant for N_B ~ 1. The lifetime 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 way. A simple way to combine convec...
Nonlinear MHD waves in a Prominence Foot
Ofman, Leon; Kucera, Therese; Schmieder, Brigitte
2015-01-01
We study nonlinear waves in a prominence foot using 2.5D MHD model motivated by recent high-resolution observations with Hinode/SOT in Ca~II emission of a prominence on October 10, 2012 showing highly dynamic small-scale motions in the prominence material. Observations of H$\\alpha$ intensities and of Doppler shifts show similar propagating fluctuations. However the optically thick nature of the emission lines inhibits 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 ($\\delta I/I\\sim \\delta n/n$). 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 typical period in the range of 5-11 minutes, and wavelengths $\\sim <$2000 km. Recent Doppler shift observations show the transverse displacement of the propagating wav...
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.
Nonlinear Plasma Wave in Magnetized Plasmas
Bulanov, Sergei V; Kando, Masaki; Koga, James K; Hosokai, Tomonao; Zhidkov, Alexei G; Kodama, Ryosuke
2013-01-01
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 which has been observed in the image of the electron bunch in experiments [T. Hosokai, et al., Phys. Rev. Lett. 97, 075004 (2006)].
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
Institute of Scientific and Technical Information of China (English)
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
Saturation process of nonlinear standing waves
Institute of Scientific and Technical Information of China (English)
马大猷; 刘克
1996-01-01
The sound pressure of the nonlinear standing waves is distorted as expected, but also tends to saturate as being found in standing-wave tube experiments with increasing sinusoidal excitation. Saturation conditions were not actually reached, owing to limited excitation power, but the evidence of tendency to saturation is without question. It is the purpose of this investigation to find the law of saturation from the existing experimental data. The results of curve fitting indicate that negative feedback limits the growth of sound pressure with increasing excitation, the growth of the fundamental and the second harmonic by the negative feedback of their sound pressures, and the growth of the third and higher harmonics, however, by their energies (sound pressures squared). The growth functions of all the harmonics are derived, which are confirmed by the experiments. The saturation pressures and their properties are found.
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
Numerical simulation of terrain-induced vortex/wave shedding at the Hong Kong International Airport
Directory of Open Access Journals (Sweden)
Li Lei
2013-07-01
Full Text Available The present study aims at simulating the shedding of vortex/wave from a mountain nearby the Hong Kong International Airport using a computational fluid dynamics model by employing high resolution terrain data without smoothing. The successful simulation of this shedding would have an important application in the short-term forecasting of the chance of occurrence of terrain-induced windshear at an operating airport. Two typical cases of vortex/wave shedding are considered, namely, in neutral atmosphere associated with the passage of a typhoon, and in stably stratified atmosphere in spring-time easterly flow with continental origin. The model is found to successfully capture the salient features of the shedding. The simulated radial velocity fields of weather radar/LIDAR compare well with actual observations. In particular, the creation and the propagation of the vortex/wave through shedding from a mountain nearby the airport are captured well in the model simulation. The shedding periods are also reproduced. From the limited number of cases studied in this paper, it appears that the model has the capability of forecasting the occurrence of vortex/wave shedding by coupling with a mesoscale meteorological model.
Effect of air jet vortex generators on a shock wave boundary layer interaction
Souverein, L.J.; Debiève, J.-F.
2010-01-01
The effect of upstream injection by means of continuous air jet vortex generators (AJVGs) on a shock wave turbulent boundary layer interaction is experimentally investigated. The baseline interaction is of the impinging type, with a flow deflection angle of 9.5degrees and a Mach number Me = 2.3. Con
Effect on a shock wave boundary layer interaction of air jet vortex generators
Souverein, L.J.; Debieve, J.F.
2013-01-01
The effect of upstream injection by means of continuous Air Jet Vortex Generators (AJVGs) on a shock wave turbulent boundary layer interaction is experimentally investigated. The baseline interaction is of the impinging type, with a flow deflection angle of 9.5◦, a Mach number Me = 2.3, and a moment
Numerical simulation of terrain-induced vortex/wave shedding at the Hong Kong International Airport
Energy Technology Data Exchange (ETDEWEB)
Li, Lei; Zhang, Li-Jie; Mao, Hui [Shenzhen National Climate Observatory, Meteorological Bureau of Shenzhen Municipality (China); Chan, P.W. [Hong Kong Observatory (China)
2013-10-15
The present study aims at simulating the shedding of vortex/wave from a mountain nearby the Hong Kong International Airport using a computational fluid dynamics model by employing high resolution terrain data without smoothing. The successful simulation of this shedding would have an important application in the short-term forecasting of the chance of occurrence of terrain-induced windshear at an operating airport. Two typical cases of vortex/wave shedding are considered, namely, in neutral atmosphere associated with the passage of a typhoon, and in stably stratified atmosphere in spring-time easterly flow with continental origin. The model is found to successfully capture the salient features of the shedding. The simulated radial velocity fields of weather radar/LIDAR compare well with actual observations. In particular, the creation and the propagation of the vortex/wave through shedding from a mountain nearby the airport are captured well in the model simulation. The shedding periods are also reproduced. From the limited number of cases studied in this paper, it appears that the model has the capability of forecasting the occurrence of vortex/wave shedding by coupling with a mesoscale meteorological model. (orig.)
A new non-linear vortex lattice method:Applications to wing aerodynamic optimizations
Institute of Scientific and Technical Information of China (English)
Oliviu S? ugar Gabor; Andreea Koreanschi; Ruxandra Mihaela Botez
2016-01-01
This paper presents a new non-linear formulation of the classical Vortex Lattice Method (VLM) approach for calculating the aerodynamic properties of lifting surfaces. The method accounts for the effects of viscosity, and due to its low computational cost, it represents a very good tool to perform rapid and accurate wing design and optimization procedures. The mathematical model is constructed by using two-dimensional viscous analyses of the wing span-wise sections, according to strip theory, and then coupling the strip viscous forces with the forces generated by the vortex rings distributed on the wing camber surface, calculated with a fully three-dimensional vortex lifting law. The numerical results obtained with the proposed method are validated with experimental data and show good agreement in predicting both the lift and pitching moment, as well as in predicting the wing drag. The method is applied to modifying the wing of an Unmanned Aerial System to increase its aerodynamic efficiency and to calculate the drag reductions obtained by an upper surface morphing technique for an adaptable regional aircraft wing.
A new non-linear vortex lattice method: Applications to wing aerodynamic optimizations
Directory of Open Access Journals (Sweden)
Oliviu Şugar Gabor
2016-10-01
Full Text Available This paper presents a new non-linear formulation of the classical Vortex Lattice Method (VLM approach for calculating the aerodynamic properties of lifting surfaces. The method accounts for the effects of viscosity, and due to its low computational cost, it represents a very good tool to perform rapid and accurate wing design and optimization procedures. The mathematical model is constructed by using two-dimensional viscous analyses of the wing span-wise sections, according to strip theory, and then coupling the strip viscous forces with the forces generated by the vortex rings distributed on the wing camber surface, calculated with a fully three-dimensional vortex lifting law. The numerical results obtained with the proposed method are validated with experimental data and show good agreement in predicting both the lift and pitching moment, as well as in predicting the wing drag. The method is applied to modifying the wing of an Unmanned Aerial System to increase its aerodynamic efficiency and to calculate the drag reductions obtained by an upper surface morphing technique for an adaptable regional aircraft wing.
Nonlinear wave propagation in constrained solids subjected to thermal loads
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.
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
Extended models of nonlinear waves in liquid with gas bubbles
Kudryashov, Nikolay A
2016-01-01
In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for nonlinear waves. We also take into consideration high order terms with respect to the small parameter. Two new nonlinear differential equations are derived for long weakly nonlinear waves in a liquid with gas bubbles by the reductive perturbation method considering both high order terms with respect to the small parameter and the above mentioned physical properties. One of these equations is the perturbation of the Burgers equation and corresponds to main influence of dissipation on nonlinear waves propagation. The other equation is the perturbation of the Burgers--Korteweg--de Vries equation and corresponds to main influence of dispersion on nonlinear waves propagation.
Contribution of vortex Rossby wave to spiral rainband formation in tropical cyclones
Institute of Scientific and Technical Information of China (English)
阮鲲; 查勇; 黄泓; 胡友彬
2014-01-01
The contribution of the vortex Rossby wave (VRW) to the spiral rainband in the tropical cyclones (TCs) is studied in the framework of a barotropic non-divergent TC-like vortex model. The spectral function expanding method is used to analyze the disturbance evolution of a defined basic state vortex. The results show that the numerical solution of the model is a superposition of the continuous spectrum component (non-normal modes) and the discrete spectrum component (normal modes). Only the eyewall and the rainbands in the inner core-region in a TC are related to the VRW normal modes, whereas the continuous spectrum wave components play an important role in the formation of secondary-, principal-, and distant- rainbands, especially the outer rainband, through an indirect way. The continuous spectrum can promote the development of the TC circulation for the occurrence of a mesoscale instability. The convection under a favorable moisture condition will trigger the inertial-gravitational wave to cause the formation of unstable spiral bandliked-disturbances outside of the eyewall. The complicated interaction between the basic state-vortex and the VRW disturbances will cause a positive feedback between the TC circulation and the rainband.
The nonlinear standing wave inside the space of liquid
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Based on the basic equations of hydrodynamics, the nonlinear acoustic wave equation is obtained. By taking into account the boundary condition and properties of nonlinear standing wave, the equation is solved through perturbation method, and the stable expressions of fundamental wave and second harmonic are presented. The sound pressures in an ultrasonic cleaner are measured by hydrophones, and the relationship between the received voltages of hydrophones and the output voltages of the ultrasonic generator is researched. The study shows the existence of the nonlinear effect of liquid and analyzes the frequency spectrum of the received signals by hydrophones, by which the fundamental wave, second and high order harmonics are found coexisting in the bounded space filled with liquids. The theory and experimental results testify the existence of the nonlinear standing wave in liquid. Owing to the restricted applicability of perturbation method, the theoretical results of the fundamental wave and second harmonic are good only for the weak nonlinear phenomenon.
Exact periodic wave solutions for some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt); Elgarayhi, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: elgarayhi@yahoo.com; Elhanbaly, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)
2006-08-15
The periodic wave solutions for some nonlinear partial differential equations, including generalized Klein-Gordon equation, Kadomtsev-Petviashvili (KP) equation and Boussinesq equations, are obtained by using the solutions of Jacobi elliptic equation. Under limit conditions, exact solitary wave solutions, shock wave solutions and triangular periodic wave solutions have been recovered.
Energy Technology Data Exchange (ETDEWEB)
Roy Chowdhury, K. [Department of Physics, J.C.C. College, Kolkata 700 033 (India); Mishra, Amar P. [High Energy Physics Division, Department of Physics Jadavpur University, Kolkata 700 032 (India); Roy Chowdhury, A. [High Energy Physics Division, Department of Physics Jadavpur University, Kolkata 700 032 (India)
2006-07-15
A modified KdV equation is derived for the propagation of non-linear waves in a dusty plasma, containing N different dust grains with a size distribution and charge fluctuation with electrons in the background. The ions are assumed to obey a vortex like distribution due to their non-isothermal nature. The standard distribution for the dust size is a power law. The variation of the soliton width is studied with respect to normalized size of the dust grains. A numerical solution of the equation is done by considering the soliton solution of the modified KdV as the initial pulse. It shows considerable broadening of the pulse variation of width with {beta} {sub 1} is shown.
Tanuma, Yasunari; Hayashi, Nobuhiko; Tanaka, Yukio; Golubov, Alexandre Avraamovitch
2009-01-01
The local density of states is studied theoretically in terms of the odd-frequency (odd-ω) Cooper pairing induced around a vortex core. We find that a zero energy peak in the density of states at the vortex center is robust against nonmagnetic impurities in a chiral p-wave superconductor owing to an
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.
Travelling waves in nonlinear diffusion-convection-reaction
Gilding, B.H.; Kersner, R.
2001-01-01
The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the stu
Nonlinear propagation of short wavelength drift-Alfven waves
DEFF Research Database (Denmark)
Shukla, P. K.; Pecseli, H. L.; Juul Rasmussen, Jens
1986-01-01
Making use of a kinetic ion and a hydrodynamic electron description together with the Maxwell equation, the authors derive a set of nonlinear equations which governs the dynamics of short wavelength ion drift-Alfven waves. It is shown that the nonlinear drift-Alfven waves can propagate as two...
Weakly nonlinear electron plasma waves in collisional plasmas
DEFF Research Database (Denmark)
Pecseli, H. L.; Rasmussen, J. Juul; Tagare, S. G.
1986-01-01
The nonlinear evolution of a high frequency plasma wave in a weakly magnetized, collisional plasma is considered. In addition to the ponderomotive-force-nonlinearity the nonlinearity due to the heating of the electrons is taken into account. A set of nonlinear equations including the effect...... of a constantly maintained pump wave is derived and a general dispersion relation describing the modulation of the high frequency wave due to different low frequency responses is obtained. Particular attention is devoted to a purely growing modulation. The relative importance of the ponderomotive force...
Development of a Nonlinear Internal Wave Tactical Decision Aid
2016-06-07
of a Nonlinear Internal Wave Tactical Decision Aid 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER...Development of a Nonlinear Internal Wave Tactical Decision Aid Christopher R. Jackson Global Ocean Associates 6220 Jean Louise Way Alexandria...www.internalwaveatlas.com LONG-TERM GOALS The long term goal of the project is to develop a prediction methodology for the occurrence of nonlinear
Energy Technology Data Exchange (ETDEWEB)
Thomsen, J.R.; Pedersen, B. [LIC Engineering (Denmark); Nielsen, K.G.; Bryndum, M.B. [Dansk Hydraulisk Inst., (Denmark)
1999-07-01
Vortex induced vibrations of pipes generated by high and steep waves in the crest zone have been investigated by full-scale field testing, An instrumented cylinder has been suspended from a platform bridge in the North Sea. Adjacent to it a newly developed acoustic system capable of measuring the three dimensional wave kinematics was placed. The kinematics were measured all the way up to the instantaneous water surface elevation, i.e. it included the wave crest. The paper presents time series of measured water surface elevations and orbital velocities at the instantaneous water surface together with the response of the instrumented pipe in a storm. The sea state was measured to H{sub s} {approx_equal} 6.4 m and T{sub z} = 8.4 sec. It was clearly seen that vortex shedding locking-on takes place in some of the rather high modes at the passage of large waves. Intermittent cross flow vortex induced vibrations of between 0.3 diameters up to 0.8 diameters were found in the 8th and the 4th mode respectively. The Reynolds numbers and KC numbers were up to 5 . 10{sup 5} and KC {approx} 250 respectively. (au)
Distribution of the nonlinear random ocean wave period
Institute of Scientific and Technical Information of China (English)
HOU Yijun; LI Mingjie; SONG Guiting; SI Guangcheng; QI Peng; HU Po
2009-01-01
Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37°27.6′ N, 122°15.1′ E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (υ=0.3-0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional
Nonlinear Excitation of Inviscid Stationary Vortex in a Boundary-Layer Flow
Choudhari, Meelan; Duck, Peter W.
1996-01-01
We examine the excitation of inviscid stationary crossflow instabilities near an isolated surface hump (or indentation) underneath a three-dimensional boundary layer. As the hump height (or indentation depth) is increased from zero, the receptivity process becomes nonlinear even before the stability characteristics of the boundary layer are modified to a significant extent. This behavior contrasts sharply with earlier findings on the excitation of the lower branch Tollmien-Schlichting modes and is attributed to the inviscid nature of the crossflow modes, which leads to a decoupling between the regions of receptivity and stability. As a result of this decoupling, similarity transformations exist that allow the nonlinear receptivity of a general three-dimensional boundary layer to be studied with a set of canonical solutions to the viscous sublayer equations. The parametric study suggests that the receptivity is likely to become nonlinear even before the hump height becomes large enough for flow reversal to occur in the canonical solution. We also find that the receptivity to surface humps increases more rapidly as the hump height increases than is predicted by linear theory. On the other hand, receptivity near surface indentations is generally smaller in comparison with the linear approximation. Extension of the work to crossflow receptivity in compressible boundary layers and to Gortler vortex excitation is also discussed.
Nonlinear evolution of the modulational instability of whistler waves
DEFF Research Database (Denmark)
Karpman, V.I.; Hansen, F.R.; Huld, T.
1990-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves is investigated in two spatial dimensions by numerical simulations. The long time evolution of the modulational instability shows a quasirecurrent behavior with a slow spreading...... of the energy, originally confined to the lowest wave numbers, to larger and larger wave numbers resulting in an apparently chaotic or random wave field. © 1990 The American Physical Society...
Nonlinear physics of shear Alfvén waves
Energy Technology Data Exchange (ETDEWEB)
Zonca, Fulvio [Associazione EURATOM-ENEA sulla Fusione, C.P. 65-00044 Frascati, Italy and Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007 (China); Chen, Liu [Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007, P.R.C. and Department of Physics and Astronomy, University of California, Irvine, CA 92697 (United States)
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.
Complete mapping of the spin-wave spectrum in a vortex-state nanodisk
Taurel, B.; Valet, T.; Naletov, V. V.; Vukadinovic, N.; de Loubens, G.; Klein, O.
2016-05-01
We report a study on the complete spin-wave spectrum inside a vortex-state nanodisk. Transformation of this spectrum is continuously monitored as the nanodisk becomes gradually magnetized by a perpendicular magnetic field and encounters a second-order phase transition to the uniformly magnetized state. This reveals the bijective relationship that exists between the eigenmodes in the vortex state and the ones in the saturated state. It is found that the gyrotropic mode can be continuously viewed as a uniform phase precession, which uniquely softens (its frequency vanishes) at the saturation field to transform above into the Kittel mode. By contrast, the other spin-wave modes remain finite as a function of the applied field, while their character is altered by level anticrossing.
SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONS Ⅱ, NONLINEAR CAUSTIC
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operator is introduced to describe the caustic crossing. With the aid of the L∞ norms, it analyzes the relative errors in approximate solutions.
Nonlinear Whistler Wave Physics in the Radiation Belts
Crabtree, Chris
2016-10-01
Wave particle interactions between electrons and whistler waves are a dominant mechanism for controlling the dynamics of energetic electrons in the radiation belts. They are responsible for loss, via pitch-angle scattering of electrons into the loss cone, and energization to millions of electron volts. It has previously been theorized that large amplitude waves on the whistler branch may scatter their wave-vector nonlinearly via nonlinear Landau damping leading to important consequences for the global distribution of whistler wave energy density and hence the energetic electrons. It can dramatically reduce the lifetime of energetic electrons in the radiation belts by increasing the pitch angle scattering rate. The fundamental building block of this theory has now been confirmed through laboratory experiments. Here we report on in situ observations of wave electro-magnetic fields from the EMFISIS instrument on board NASA's Van Allen Probes that show the signatures of nonlinear scattering of whistler waves in the inner radiation belts. In the outer radiation belts, whistler mode chorus is believed to be responsible for the energization of electrons from 10s of Kev to MeV energies. Chorus is characterized by bursty large amplitude whistler mode waves with frequencies that change as a function of time on timescales corresponding to their growth. Theories explaining the chirping have been developed for decades based on electron trapping dynamics in a coherent wave. New high time resolution wave data from the Van Allen probes and advanced spectral techniques are revealing that the wave dynamics is highly structured, with sub-elements consisting of multiple chirping waves with discrete frequency hops between sub-elements. Laboratory experiments with energetic electron beams are currently reproducing the complex frequency vs time dynamics of whistler waves and in addition revealing signatures of wave-wave and beat-wave nonlinear wave-particle interactions. These new data
Nonlinear ultrasound wave propagation in thermoviscous fluids
DEFF Research Database (Denmark)
Sørensen, Mads Peter
coupled nonlinear partial differential equations, which resembles those of optical chi-2 materials. We think this result makes a remarkable link between nonlinear acoustics and nonlinear optics. Finally our analysis reveal an exact kink solution to the nonlinear acoustic problem. This kink solution...
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Nonlinear numerical simulation on extreme-wave kinematics
Institute of Scientific and Technical Information of China (English)
NING Dezhi; TENG Bin; LIU Shuxue
2009-01-01
A fully nonlinear numerical model based on a time-domain higher-order boundary element method (HOBEM) is founded to simulate the kinematics of extreme waves. In the model, the fully nonlinear free surface boundary conditions are satisfied and a semi-mixed Euler-Lagrange method is used to track free surface; a fourth-order Runga-Kutta technique is "adopted to refresh the wave elevation and velocity potential on the free surface at each time step; an image Green function is used in the numerical wave tank so that the integrations on the lateral surfaces and bottom are excluded. The extreme waves are generated by the method of wave focusing. The physical experiments are carried out in a wave flume. On the horizontal velocity of the measured point, numerical solutions agree well with experimental results. The characteristics of the nonlinear extreme-wave kinematics and the velocity distribution are studied here.
Transition waves and nonlinear interactions in the near wake of a circular cylinder
Institute of Scientific and Technical Information of China (English)
凌国灿; Allen T.Chwang; 牛家玉; 王冬(女菱)
1997-01-01
Transition waves and interactions between two kinds of instability-vortex shedding and transition wave in the near wake of a circular cylinder in the Reynolds number range 3 000-10 000 are studied by a domain decomposition hybrid numerical method.Based on high resolution power spectral analyses for velocity new results on the Reynolds-number dependence of the transition wave frequency,i.e.ft/fa~Re0.87 are obtained.The new predictions are in good agreement with the experimental results of Wei and Smith but different from Braza’s prediction and some early experimental results ft/fa-Re0.5 given by Bloor et al.The multi-interactions between two kinds of vortex are clearly visualized numerically.The strong nonlinear interactions between the two independent frequencies (ft,fa) leading to spectra broadening to form the coupling mfs±nft are predicted and analyzed numerically,and the characteristics of the transition are described.Longitudinal variations of the transition wave and its coupling are reported.Deta
Nonlinear Alfvén Waves in a Vlasov Plasma
DEFF Research Database (Denmark)
Bell, T.F.
1965-01-01
Stationary solutions to the nonlinear Vlasov—Boltzmann equations are considered which represent one-dimensional electromagnetic waves in a hot magnetoplasma. These solutions appear in arbitrary reference frames as circularly polarized, sinusoidal waves of unlimited amplitude, i.e., as nonlinear...... Alfvén waves. Solutions are found implicitly by deriving a set of integral dispersion relations which link the wave characteristics with the particle distribution functions. A physical discussion is given of the way in which the Alfvén waves can trap particles, and it is shown that the presence...
Nonlinear propagation and control of acoustic waves in phononic superlattices
Jiménez, Noé; Picó, Rubén; García-Raffi, Lluís M; Sánchez-Morcillo, Víctor J
2015-01-01
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 cancelled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime.
The Peridic Wave Solutions for Two Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-Liang; WANG Ming-Liang; CHENG Dong-Ming; FANG Zong-De
2003-01-01
By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobielliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions andthe other type of traveling wave solutions for the system are obtained.
Experimental characterization of nonlinear processes of whistler branch waves
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.
Nonlinear evolution of oblique waves on compressible shear layers
Goldstein, M. E.; Leib, S. J.
1989-01-01
The effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams are considered. The analysis shows that mean temperature nonuniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integrodifferential equation which bears some resemblance to the Landau equation, in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. Inviscid solutions always end in a singularity at a finite downstream distance, but viscosity can eliminate this singularity for certain parameter ranges.
Nonlinear acoustic waves in micro-inhomogeneous solids
Nazarov, Veniamin
2014-01-01
Nonlinear Acoustic Waves in Micro-inhomogeneous Solids covers the broad and dynamic branch of nonlinear acoustics, presenting a wide variety of different phenomena from both experimental and theoretical perspectives. The introductory chapters, written in the style of graduate-level textbook, present a review of the main achievements of classic nonlinear acoustics of homogeneous media. This enables readers to gain insight into nonlinear wave processes in homogeneous and micro-inhomogeneous solids and compare it within the framework of the book. The subsequent eight chapters covering: Physical m
Vortex Contribution to Specific Heat of Dirty $d$-Wave Superconductors: Breakdown of Scaling
Kuebert, C.; Hirschfeld, P. J.
1997-01-01
We consider the problem of the vortex contribution to thermal properties of dirty d-wave superconductors. In the clean limit, the main contribution to the density of states in a d-wave superconductor arises from extended quasiparticle states which may be treated semiclassically, giving rise to a specific heat contribution \\delta C(H)\\sim H^{1/2}. We show that the extended states continue to dominate the dirty limit, but lead to a H \\log H behavior at the lowest fields, H_{c1}\\ltsim H\\ll H_{c2...
Rapid energization of radiation belt electrons by nonlinear wave trapping
Directory of Open Access Journals (Sweden)
Y. Katoh
2008-11-01
Full Text Available We show that nonlinear wave trapping plays a significant role in both the generation of whistler-mode chorus emissions and the acceleration of radiation belt electrons to relativistic energies. We have performed particle simulations that successfully reproduce the generation of chorus emissions with rising tones. During this generation process we find that a fraction of resonant electrons are energized very efficiently by special forms of nonlinear wave trapping called relativistic turning acceleration (RTA and ultra-relativistic acceleration (URA. Particle energization by nonlinear wave trapping is a universal acceleration mechanism that can be effective in space and cosmic plasmas that contain a magnetic mirror geometry.
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.
Analysis of Wave Nonlinear Dispersion Relation
Institute of Scientific and Technical Information of China (English)
LI Rui-jie; TAO Jian-fu
2005-01-01
The nonlinear dispersion relations and modified relations proposed by Kirby and Hedges have the limitation of intermediate minimum value. To overcome the shortcoming, a new nonlinear dispersion relation is proposed. Based on the summarization and comparison of existing nonlinear dispersion relations, it can be found that the new nonlinear dispersion relation not only keeps the advantages of other nonlinear dispersion relations, but also significantly reduces the relative errors of the nonlinear dispersion relations for a range of the relative water depth of 1＜kh＜1.5 and has sufficient accuracy for practical purposes.
Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
Rogue and shock waves in nonlinear dispersive media
Resitori, Stefania; Baronio, Fabio
2016-01-01
This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists ...
A WEAKLY NONLINEAR WATER WAVE MODEL TAKING INTO ACCOUNT DISPERSION OF WAVE PHASE VELOCITY
Institute of Scientific and Technical Information of China (English)
李瑞杰; 李东永
2002-01-01
This paper presents a weakly nonlinear water wave model using a mild slope equation and a new explicit formulation which takes into account dispersion of wave phase velocity, approximates Hedges' (1987) nonlinear dispersion relationship, and accords well with the original empirical formula. Comparison of the calculating results with those obtained from the experimental data and those obtained from linear wave theory showed that the present water wave model considering the dispersion of phase velocity is rational and in good agreement with experiment data.
Controlling near shore nonlinear surging waves through bottom boundary conditions
Mukherjee, Abhik; Kundu, Anjan
2016-01-01
Instead of taking the usual passive view for warning of near shore surging waves including extreme waves like tsunamis, we aim to study the possibility of intervening and controlling nonlinear surface waves through the feedback boundary effect at the bottom. It has been shown through analytic result that the controlled leakage at the bottom may regulate the surface solitary wave amplitude opposing the hazardous variable depth effect. The theoretical results are applied to a real coastal bathymetry in India.
Nonlinear Waves in an Inhomogeneous Fluid Filled Elastic Tube
Institute of Scientific and Technical Information of China (English)
DUAN Wen-Shan
2004-01-01
In a thin-walled, homogeneous, straight, long, circular, and incompressible fluid filled elastic tube, small but finite long wavelength nonlinear waves can be describe by a KdV (Korteweg de Vries) equation, while the carrier wave modulations are described by a nonlinear Schrodinger equation (NLSE). However if the elastic tube is slowly inhomogeneous, then it is found, in this paper, that the carrier wave modulations are described by an NLSE-like equation. There are soliton-like solutions for them, but the stability and instability regions for this soliton-like waves will change,depending on what kind of inhomogeneity the tube has.
Nonlinear spin wave coupling in adjacent magnonic crystals
Energy Technology Data Exchange (ETDEWEB)
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)
2016-07-25
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
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.
Zhang, Xiaoqing; Feng, Heying; Qu, Chengwu
2016-10-01
Nonlinear standing waves and acoustic streaming in an axial-symmetrical resonator with exponentially varying cross-sectional area were studied. A two-dimensional gas-kinetic Bhatnagar-Gross-Krook scheme based on the non-structure triangular grid was established to simulate nonlinear acoustic oscillations in the resonator. Details of the transient and steady flow fields and streaming were developed. The effects of winding index of the exponential-shape resonator, the displacement amplitude of the acoustic piston on the streaming, and the vortex pattern were analyzed. The results demonstrate that the acoustic streaming pattern in such resonators is different from the typical Rayleigh flow in a constant cross-sectional area resonator. No obvious shock wave appeared inside the exponential-shape resonator. The comparison reveals that with increasing the displacement amplitude of the acoustic piston energy dissipation is accompanied by vortex break-up from a first-level to a second-level transition, and even into turbulent flow. This research demonstrates that the exponential-shape resonator, especially that with a winding index of 2.2 exhibits better acoustic features and suppression effects on shock-wave, acoustic streaming, and the vortex.
Vortex stabilization by means of spatial solitons in nonlocal media
Izdebskaya, Yana; Krolikowski, Wieslaw; Smyth, Noel F.; Assanto, Gaetano
2016-05-01
We investigate how optical vortices, which tend to be azimuthally unstable in local nonlinear materials, can be stabilized by a copropagating coaxial spatial solitary wave in nonlocal, nonlinear media. We focus on the formation of nonlinear vortex-soliton vector beams in reorientational soft matter, namely nematic liquid crystals, and report on experimental results, as well as numerical simulations.
Indian Academy of Sciences (India)
Aiyong Chen; Jibin Li; Chunhai Li; Yuanduo Zhang
2010-01-01
The bifurcation theory of dynamical systems is applied to an integrable non-linear wave equation. As a result, it is pointed out that the solitary waves of this equation evolve from bell-shaped solitary waves to W/M-shaped solitary waves when wave speed passes certain critical wave speed. Under different parameter conditions, all exact explicit parametric representations of solitary wave solutions are obtained.
GLOBAL ATTRACTOR FOR THE NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES
Institute of Scientific and Technical Information of China (English)
戴正德; 杜先云
2001-01-01
In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and thefiniteness of the Hausdorff and the fractal dimensions of the attractors.
Nonlinear waves in the terrestrial quasi-parallel foreshock
Hnat, B; O'Connell, D; Nakariakov, V M; Rowlands, G
2016-01-01
We study the applicability of the derivative nonlinear Schr\\"{o}dinger (DNLS) equation, for the evolution of high frequency nonlinear waves, observed at the foreshock region of the terrestrial quasi-parallel bow shock. The use of a pseudo-potential is elucidated and, in particular, the importance of canonical representation in the correct interpretation of solutions in this formulation is discussed. Numerical solutions of the DNLS equation are then compared directly with the wave forms observed by Cluster spacecraft. Non harmonic slow variations are filtered out by applying the empirical mode decomposition. We find large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency, followed in time by nearly harmonic low amplitude fluctuations. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfv\\'{e}n speed.
The periodic wave solutions for two systems of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
王明亮; 王跃明; 张金良
2003-01-01
The periodic wave solutions for the Zakharov system of nonlinear wave equations and a long-short-wave interaction system are obtained by using the F-expansion method, which can be regarded as an overall generalization of Jacobi elliptic function expansion proposed recently. In the limit cases, the solitary wave solutions for the systems are also obtained.
Numerical method of studying nonlinear interactions between long waves and multiple short waves
Institute of Scientific and Technical Information of China (English)
Xie Tao; Kuang Hai-Lan; William Perrie; Zou Guang-Hui; Nan Cheng-Feng; He Chao; Shen Tao; Chen Wei
2009-01-01
Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically,the solution is less tractable in more general cases involving multiple short waves.In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water.Specifically,this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves.Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train.From simulation results,we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train(expressed as wave train 2)leads to the energy focusing of the other short wave train(expressed as wave train 31.This mechanism Occurs on wave components with a narrow frequency bandwidth,whose frequencies are near that of wave train 3.
Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas
Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.
1997-01-01
We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.
Optical rogue waves and soliton turbulence in nonlinear fibre optics
DEFF Research Database (Denmark)
Genty, G.; Dudley, J. M.; de Sterke, C. M.
2009-01-01
We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required.......We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required....
TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.
NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE C OEFFICIENTS
Institute of Scientific and Technical Information of China (English)
冯绍继; 冯德兴
2003-01-01
The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
Defocusing regimes of nonlinear waves in media with negative dispersion
DEFF Research Database (Denmark)
Bergé, L.; Kuznetsov, E.A.; Juul Rasmussen, J.
1996-01-01
Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schrodinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called critical dimension cannot collapse in finite time...
New travelling wave solutions for nonlinear stochastic evolution equations
Indian Academy of Sciences (India)
Hyunsoo Kim; Rathinasamy Sakthivel
2013-06-01
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic Broer–Kaup equation and stochastic coupled Korteweg–de Vries (KdV) equation. The study highlights the significant features of the method employed and its capability of handling nonlinear stochastic problems.
Yang, Peng; Chen, Hui; Liu, Yingwen
2017-06-01
In this paper, a two-dimensional axisymmetric model of a thermoacoustic Stirling engine with a short tube where the cross section narrows has been developed. The transient streamlines and vortex formation through short tubes with different diameters in oscillatory flow have been investigated visually by computational fluid dynamics. Three dimensionless parameters, Reynolds number (Re), Keulegan-Carpenter number (KC), and Womersley number (Wo), are used to describe the flow regime and vortex characteristic throughout the short tube. High Re and Wo numbers indicate that the oscillatory flow develops into the turbulent flow through the short tube. The KC number has a direct effect on the transition of streamlines and the development of the vortex. For a small cross section where KC ≈ 1, streamlines rotate and the vortex forms at both sides of the short tube. The vortex stays in the main flow region, and intensity varies as streamlines are convected downstream. The velocity along the radius presents a Poiseuille profile within the influence of the vortex. For a large cross section where KC < 1, streamlines pass the short tube with little rotation and the vortex disappears in the main flow region and confines near the short tube. The velocity profile tends to be flat. The nonlinear effects including instantaneous pressure drop and power dissipation throughout the short tube are also discussed. It shows that the time averaged pressure drop is generated at the cost of power dissipation. Finally, the "effectiveness" is applied to evaluate the performance of the short tube. The results suggest that increasing the diameter of the short tube is in favor of reducing power dissipation, which is beneficial to improve "effectiveness."
Energy Technology Data Exchange (ETDEWEB)
Salhi, A. [Departement de Physique, Faculte des Sciences de Tunis, 1060 Tunis (Tunisia); Lehner, T. [LUTH, UMR 8102 CNRS, Observatoire de Paris-Meudon, 5 place de Janssen, F-92195 Meudon (France); Godeferd, F.; Cambon, C. [Laboratoire de Mecanique des Fluides et d' Acoustique, Ecole Centrale de Lyon, Universite de Lyon, UMR 5509, CNRS, INSA, UCB, F-69134 Ecully Cedex (France)
2013-07-10
We examine accretion disk flow under combined radial and vertical stratification utilizing a local Cartesian (or ''shearing box'') approximation. We investigate both axisymmetric and nonaxisymmetric disturbances with the Boussinesq approximation. Under axisymmetric disturbances, a new dispersion relation is derived. It reduces to the Solberg-Hoieland criterion in the case without vertical stratification. It shows that, asymptotically, stable radial and vertical stratification cannot induce any linear instability; Keplerian flow is accordingly stable. Previous investigations strongly suggest that the so-called bypass concept of turbulence (i.e., that fine-tuned disturbances of any inviscid smooth shear flow can reach arbitrarily large transient growth) can also be applied to Keplerian disks. We present an analysis of this process for three-dimensional plane-wave disturbances comoving with the shear flow of a general rotating shear flow under combined stable radial and vertical rotation. We demonstrate that large transient growth occurs for K{sub 2}/k{sub 1} >> 1 and k{sub 3} = 0 or k{sub 1} {approx} k{sub 3}, where k{sub 1}, K{sub 2}, and k{sub 3} are the azimuthal, radial, and vertical components of the initial wave vector, respectively. By using a generalized ''wave-vortex'' decomposition of the disturbance, we show that the large transient energy growth in a Keplerian disk is mainly generated by the transient dynamics of the vortex mode. The analysis of the power spectrum of total (kinetic+potential) energy in the azimuthal or vertical directions shows that the contribution coming from the vortex mode is dominant at large scales, while the contribution coming from the wave mode is important at small scales. These findings may be confirmed by appropriate numerical simulations in the high Reynolds number regime.
Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates
Energy Technology Data Exchange (ETDEWEB)
Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)
2010-10-15
Since the acoustic nonlinearity is sensitive to the minute variation of material properties, the nonlinear ultrasonic technique(NUT) has been considered as a promising method to evaluate the material degradation or fatigue. However, there are certain limitations to apply the conventional NUT using the bulk wave to thin plates. In case of plates, the use of Lamb wave can be considered, however, the propagation characteristics of Lamb wave are completely different with the bulk wave, and thus the separate study for the nonlinearity of Lamb wave is required. For this work, this paper analyzed first the conditions of mode pair suitable for the practical application as well as for the cumulative propagation of quadratic harmonic frequency and summarized the result in for conditions: phase matching, non-zero power flux, group velocity matching, and non-zero out-of-plane displacement. Experimental results in aluminum plates showed that the amplitude of the secondary Lamb wave and nonlinear parameter grew up with increasing propagation distance at the mode pair satisfying the above all conditions and that the ration of nonlinear parameters measured in Al6061-T6 and Al1100-H15 was closed to the ratio of the absolute nonlinear parameters
Nonlinear spin-wave excitations at low magnetic bias fields
Woltersdorf, Georg
We investigate experimentally and theoretically the nonlinear magnetization dynamics in magnetic films at low magnetic bias fields. Nonlinear magnetization dynamics is essential for the operation of numerous spintronic devices ranging from magnetic memory to spin torque microwave generators. Examples are microwave-assisted switching of magnetic structures and the generation of spin currents at low bias fields by high-amplitude ferromagnetic resonance. In the experiments we use X-ray magnetic circular dichroism to determine the number density of excited magnons in magnetically soft Ni80Fe20 thin films. Our data show that the common Suhl instability model of nonlinear ferromagnetic resonance is not adequate for the description of the nonlinear behavior in the low magnetic field limit. Here we derive a model of parametric spin-wave excitation, which correctly predicts nonlinear threshold amplitudes and decay rates at high and at low magnetic bias fields. In fact, a series of critical spin-wave modes with fast oscillations of the amplitude and phase is found, generalizing the theory of parametric spin-wave excitation to large modulation amplitudes. For these modes, we also find pronounced frequency locking effects that may be used for synchronization purposes in magnonic devices. By using this effect, effective spin-wave sources based on parametric spin-wave excitation may be realized. Our results also show that it is not required to invoke a wave vector-dependent damping parameter in the interpretation of nonlinear magnetic resonance experiments performed at low bias fields.
Nonlinear electron acoustic waves in presence of shear magnetic field
Energy Technology Data Exchange (ETDEWEB)
Dutta, Manjistha; Khan, Manoranjan [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India); Ghosh, Samiran [Department of Applied Mathematics, University of Calcutta 92, Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India)
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.
Parametric interaction and intensification of nonlinear Kelvin waves
Novotryasov, Vadim
2008-01-01
Observational evidence is presented for nonlinear interaction between mesoscale internal Kelvin waves at the tidal -- $\\omega_t$ or the inertial -- $\\omega_i$ frequency and oscillations of synoptic -- $\\Omega $ frequency of the background coastal current of Japan/East Sea. Enhanced coastal currents at the sum -- $\\omega_+ $ and dif -- $\\omega_-$ frequencies: $\\omega_\\pm =\\omega_{t,i}\\pm \\Omega$ have properties of propagating Kelvin waves suggesting permanent energy exchange from the synoptic band to the mesoscale $\\omega_\\pm $ band. The interaction may be responsible for the greater than predicted intensification, steepen and break of boundary trapped and equatorially trapped Kelvin waves, which can affect El Ni\\~{n}o. The problem on the parametric interaction of the nonlinear Kelvin wave at the frequency $\\omega $ and the low-frequency narrow-band nose with representative frequency $\\Omega\\ll\\omega $ is investigated with the theory of nonlinear week dispersion waves.
Statistical distribution of nonlinear random wave height in shallow water
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Here we present a statistical model of random wave,using Stokes wave theory of water wave dynamics,as well as a new nonlinear probability distribution function of wave height in shallow water.It is more physically logical to use the wave steepness of shallow water and the factor of shallow water as the parameters in the wave height distribution.The results indicate that the two parameters not only could be parameters of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution.The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated.The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution.The effect of wave steepness in shallow water is similar to that in deep water;but the factor of shallow water lowers the wave height distribution of the general wave with the reduced factor of wave steepness.It also makes the wave height distribution of shallow water more centralized.The results indicate that the new distribution fits the in situ measurements much better than other distributions.
Development of A Fully Nonlinear Numerical Wave Tank
Institute of Scientific and Technical Information of China (English)
陈永平; 李志伟; 张长宽
2004-01-01
A fully nonlinear numerical wave tank (NWT) based on the solution of the σ-transformed Navier-Stokes equation is developed in this study. The numerical wave is generated from the inflow boundary, where the surface elevation and/or velocity are specified by use of the analytical solution or the laboratory data. The Sommerfeld/Orlanski radiation condition in conjunction with an artificial damping zone is applied to reduce wave reflection from the outflow boundary. The whole numerical solution procedures are split into three steps, i.e., advection, diffusion and propagation, and a new method,the Lagrange-Euler Method, instead of the MAC or VOF method, is introduced to solve the free surface elevation at the new time step. Several typical wave cases, including solitary waves, regular waves and irregular waves, are simulated in the wave tank. The robustness and accuracy of the NWT are verified by the good agreement between the numerical results and the linear or nonlinear analytical solutions. This research will be further developed by study of wave-wave, wave-current, wave-structure or wave-jet interaction in the future.
Vivanco, F
2002-01-01
We present a simple experiment to study the interaction of surface waves with a vertical vortex in the deep water regime. Similarly to what occurs in the Quantum Mechanics Aharonov-Bohm problem for electron interacting with a magnetic potential, the effect of the vortex circulation is to introduce dislocations in the wavefront. These defects are explained taken into account the effects of advection on the propagating wavefront, due to the fluid motion. (Author)
A nonlinear RDF model for waves propagating in shallow water
Institute of Scientific and Technical Information of China (English)
王厚杰; 杨作升; 李瑞杰; 张军
2001-01-01
In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs’s relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refracti
Nonlinear evolution of parallel propagating Alfven waves: Vlasov - MHD simulation
Nariyuki, Y; Kumashiro, T; Hada, T
2009-01-01
Nonlinear evolution of circularly polarized Alfv\\'en waves are discussed by using the recently developed Vlasov-MHD code, which is a generalized Landau-fluid model. The numerical results indicate that as far as the nonlinearity in the system is not so large, the Vlasov-MHD model can validly solve time evolution of the Alfv\\'enic turbulence both in the linear and nonlinear stages. The present Vlasov-MHD model is proper to discuss the solar coronal heating and solar wind acceleration by Alfve\\'n waves propagating from the photosphere.
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.
Hamiltonian theory of nonlinear waves in planetary rings
Stewart, G. R.
1987-01-01
The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.
Exact travelling wave solutions for some important nonlinear physical models
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2013-05-01
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.
Energy Technology Data Exchange (ETDEWEB)
Horvath, J.E. (Sao Paulo Univ., SP (Brazil). Inst. Astronomico e Geofisico); Benvenuto, O.G. (La Plata Univ. Nacional (Argentina))
1991-08-15
We present structural constraints on the Crab and Vela pulsars imposed by the simultaneous assumptions of (a) surface temperatures close to those observed by the Einstein Observatory satellite, and (b) validity of the vortex creep theory in the non-linear regime for interpreting glitch observations and internal features predicted by it. The disagreement between both studies is quantified, thus pointing strongly to the need for linear regimes of creep, as recently suggested, or some alternative picture. (author).
Exact Nonlinear Internal Equatorial Waves in the f-plane
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.
Experimental observations of nonlinear effects of the Lamb waves
Institute of Scientific and Technical Information of China (English)
DENG Mingxi; D.C. Price; D.A.Scott
2004-01-01
The experimental observations of nonlinear effects of the primary Lamb waves have been reported. Firstly, the brief descriptions have been made for the nonlinear acoustic measurement system developed by Ritec. The detailed considerations for the acoustic experiment system established for observing of the nonlinear effects of the primary Lamb waves have been carried out. Especially, the analysis focuses on the time-domain responses of second harmonics of the primary Lame waves by employing a straightforward model. Based on the existence conditions of strong nonlinearity of the primary Lamb waves, the wedge transducers are designed to generate and detect the primary and secondary waves on the surface of an aluminum sheet. For the different distances between the transmitting and receiving wedge transducers,the amplitudes of the primary waves and the second harmonics on the sheet surface have been measured within a specified frequency range. In the immediate vicinity of the driving frequency,where the primary and the double frequency Lamb waves have the same phase velocities, the quantitative relations of second-harmonic amplitudes with the propagation distance have been analyzed. It is experimentally verified that the second harmonics of the primary Lamb waves do have a cumulative growth effect along with the propagation distance.
Elliptic Equation and New Solutions to Nonlinear Wave Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Kuo; LIU Shi-Da
2004-01-01
The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.
Quantification and prediction of rare events in nonlinear waves
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.
Linear and nonlinear propagation of water wave groups
Pierson, W. J., Jr.; Donelan, M. A.; Hui, W. H.
1992-01-01
Results are presented from a study of the evolution of waveforms with known analytical group shapes, in the form of both transient wave groups and the cloidal (cn) and dnoidal (dn) wave trains as derived from the nonlinear Schroedinger equation. The waveforms were generated in a long wind-wave tank of the Canada Centre for Inland Waters. It was found that the low-amplitude transients behaved as predicted by the linear theory and that the cn and dn wave trains of moderate steepness behaved almost as predicted by the nonlinear Schroedinger equation. Some of the results did not fit into any of the available theories for waves on water, but they provide important insight on how actual groups of waves propagate and on higher-order effects for a transient waveform.
GEOMETRICAL NONLINEAR WAVES IN FINITE DEFORMATION ELASTIC RODS
Institute of Scientific and Technical Information of China (English)
GUO Jian-gang; ZHOU Li-jun; ZHANG Shan-yuan
2005-01-01
By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave.If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.
Wave Propagation In Strongly Nonlinear Two-Mass Chains
Wang, Si Yin; Herbold, Eric B.; Nesterenko, Vitali F.
2010-05-01
We developed experimental set up that allowed the investigation of propagation of oscillating waves generated at the entrance of nonlinear and strongly nonlinear two-mass granular chains composed of steel cylinders and steel spheres. The paper represents the first experimental data related to the propagation of these waves in nonlinear and strongly nonlinear chains. The dynamic compressive forces were detected using gauges imbedded inside particles at depths equal to 4 cells and 8 cells from the entrance gauge detecting the input signal. At these relatively short distances we were able to detect practically perfect transparency at low frequencies and cut off effects at higher frequencies for nonlinear and strongly nonlinear signals. We also observed transformation of oscillatory shocks into monotonous shocks. Numerical calculations of signal transformation by non-dissipative granular chains demonstrated transparency of the system at low frequencies and cut off phenomenon at high frequencies in reasonable agreement with experiments. Systems which are able to transform nonlinear and strongly nonlinear waves at small sizes of the system are important for practical applications such as attenuation of high amplitude pulses.
Dynamics of optical rogue waves in inhomogeneous nonlinear waveguides
Institute of Scientific and Technical Information of China (English)
Zhang Jie-Fang; Jin Mei-Zhen; He Ji-Da; Lou Ji-Hui; Dai Chao-Qing
2013-01-01
We propose a unified theory to construct exact rogue wave solutions of the (2+1)-dimensional nonlinear Schr(o)dinger equation with varying coefficients.And then the dynamics of the first-and the second-order optical rogues are investigated.Finally,the controllability of the optical rogue propagating in inhomogeneous nonlinear waveguides is discussed.By properly choosing the distributed coefficients,we demonstrate analytically that rogue waves can be restrained or even be annihilated,or emerge periodically and sustain forever.We also figure out the center-of-mass motion of the rogue waves.
Thermal conductivity of nonlinear waves in disordered chains
Indian Academy of Sciences (India)
Sergej Flach; Mikhail Ivanchenko; Nianbei Li
2011-11-01
We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity (). We ﬁnd indications for an asymptotic low-temperature ∼ 4 and intermediate temperature ∼ 2 laws. These ﬁndings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (Laptyeva et al, Europhys. Lett. 91, 30001 (2010)).
Nonlinear mixing of laser generated narrowband Rayleigh surface waves
Bakre, Chaitanya; Rajagopal, Prabhu; Balasubramaniam, Krishnan
2017-02-01
This research presents the nonlinear mixing technique of two co-directionally travelling Rayleigh surface waves generated and detected using laser ultrasonics. The optical generation of Rayleigh waves on the specimen is obtained by shadow mask method. In conventional nonlinear measurements, the inherently small higher harmonics are greatly influenced by the nonlinearities caused by coupling variabilities and surface roughness between the transducer and specimen interface. The proposed technique is completely contactless and it should be possible to eliminate this problem. Moreover, the nonlinear mixing phenomenon yields not only the second harmonics, but also the sum and difference frequency components, which can be used to measure the acoustic nonlinearity of the specimen. In this paper, we will be addressing the experimental configurations for this technique. The proposed technique is validated experimentally on Aluminum 7075 alloy specimen.
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.
Dynamic scattering of electron vortex beams – A Bloch wave analysis
Energy Technology Data Exchange (ETDEWEB)
Mendis, B.G., E-mail: b.g.mendis@durham.ac.uk
2015-02-15
Two important applications of electron vortex beams are in electron magnetic chiral dichroism (EMCD) measurements and nanoparticle manipulation. In both cases orbital angular momentum (
Nonlinear wave propagation in a rapidly-spun fiber.
McKinstrie, C J; Kogelnik, H
2006-09-04
Multiple-scale analysis is used to study linear wave propagation in a rapidly-spun fiber and its predictions are shown to be consistent with results obtained by other methods. Subsequently, multiple-scale analysis is used to derive a generalized Schroedinger equation for nonlinear wave propagation in a rapidly-spun fiber. The consequences of this equation for pulse propagation and four-wave mixing are discussed briefly.
Nonlinear propagation of planet-generated tidal waves
Rafikov, Roman
2001-01-01
The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to the shock formation and wake dissipation, is followed in the weakly nonlinear regime. The local approach of Goodman & Rafikov (2001) is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process sp...
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS TO A COUPLED NONLINEAR WAVE SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Employ theory of bifurcations of dynamical systems to a system of coupled nonlin-ear equations, the existence of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions is obtained. Under different parametric conditions, various suffcient conditions to guarantee the existence of the above so-lutions are given. Some exact explicit parametric representations of travelling wave solutions are derived.
Twisted toroidal vortex-solitons in inhomogeneous media with repulsive nonlinearity
Kartashov, Y V; Shnir, Y; Torner, L
2014-01-01
Toroidal modes in the form of so-called Hopfions, with two independent winding numbers, a hidden one (twist, s), which characterizes a circular vortex thread embedded into a three-dimensional soliton, and the vorticity around the vertical axis m, appear in many fields, including the field theory, ferromagnetics, and semi- and superconductors. Such topological states are normally generated in multi-component systems, or as trapped quasi-linear modes in toroidal potentials. We uncover that stable solitons with this structure can be created, without any linear potential, in the single-component setting with the strength of repulsive nonlinearity growing fast enough from the center to the periphery, for both steep and smooth modulation profiles. Toroidal modes with s=1 and vorticity m=0,1,2 are produced. They are stable for m1. An approximate analytical solution is obtained for the twisted ring with s=1, m=0. Under the application of an external torque, it rotates like a solid ring. The setting can be implemented...
A Spectral Element Method for Nonlinear and Dispersive Water Waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bigoni, Daniele; Eskilsson, Claes
The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...... methods is of key interest. We present a high-order general-purpose three-dimensional numerical model solving fully nonlinear and dispersive potential flow equations with a free surface.......The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...
Nonlinear evolution of oblique whistler waves in radiation belts
Sharma, R. P.; Nandal, P.; Yadav, N.; Sharma, Swati
2017-02-01
Magnetic power spectrum and formation of coherent structures have been investigated in the present work applicable to Van Allen radiation belt. The nonlinear interaction of high frequency oblique whistler wave and low frequency magnetosonic wave has been investigated. Simulation was performed of the coupled equation of these two waves. The nonlinear interaction of these waves leads to the formation of the localized structures. These resulting localized structures are of complex nature. The associated magnetic power spectrum has also been studied. Dispersive nonlinear processes account for the high frequency part of the spectrum. The resulting magnetic power spectrum shows a scaling of k^{ - 4.5}. The energy transfer process from injection scales to smaller scales is explained by the results.
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...
Energy Technology Data Exchange (ETDEWEB)
Xie, Xi-Yang; Tian, Bo, E-mail: tian_bupt@163.com; Wang, Yu-Feng; Sun, Ya; Jiang, Yan
2015-11-15
In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.
Testik, Firat Yener
An experimental and theoretical study has been conducted to obtain a fundamental understanding of the dynamics of the sand, water and a solid object interaction as progressive gravity waves impinge on a sloping beach. Aside from obvious scientific interest, this exceedingly complex physical problem is important for naval applications, related to the behavior of disk/cylindrical shaped objects (mines) in the coastal waters. To address this problem, it was divided into a set of simpler basic problems. To begin, nonlinear progressive waves were investigated experimentally in a wave tank for the case of a rigid (impermeable) sloping bottom. Parameterizations for wave characteristics were proposed and compared with the experiments. In parallel, a numerical wave tank model (NWT) was calibrated using experimental data from a single run, and wave field in the wave tank was simulated numerically for the selected experiments. Subsequently, a layer of sand was placed on the slope and bottom topography evolution processes (ripple and sandbar dynamics, bottom topography relaxation under variable wave forcing, etc.) were investigated experimentally. Models for those processes were developed and verified by experimental measurements. Flow over a circular cylinder placed horizontally on a plane wall was also studied. The far-flow field of the cylinder placed in the wave tank was investigated experimentally and numerical results from the NWT simulations were compared with the experimental data. In the mean time, the near-flow velocity/vorticity field around a short cylinder under steady and oscillatory flow was studied in a towing tank. Horseshoe vortex formation and periodic shedding were documented and explained. With the understanding gained through the aforementioned studies, dynamics and burial/scour around the bottom objects in the wave tank were studied. Possible scenarios on the behavior of the disk-shaped objects were identified and explained. Scour around 3D cylindrical
Nonlinear Pressure Wave Analysis by Concentrated Mass Model
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.
Nonlinear internal wave penetration via parametric subharmonic instability
Ghaemsaidi, S J; Dauxois, T; Odier, P; Peacock, T
2016-01-01
We present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially-periodic boundary forcing from above of a density stratification comprising a strongly-stratified, thin upper layer sitting atop a weakly-stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability (PSI) in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly-stratified lower layer. We find that around $10\\%$ of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study.
Efficient computation method for two-dimensional nonlinear waves
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The theory and simulation of fully-nonlinear waves in a truncated two-dimensional wave tank in time domain are presented. A piston-type wave-maker is used to generate gravity waves into the tank field in finite water depth. A damping zone is added in front of the wave-maker which makes it become one kind of absorbing wave-maker and ensures the prescribed Neumann condition. The efficiency of nmerical tank is further enhanced by installation of a sponge layer beach (SLB) in front of downtank to absorb longer weak waves that leak through the entire wave train front. Assume potential flow, the space- periodic irrotational surface waves can be represented by mixed Euler- Lagrange particles. Solving the integral equation at each time step for new normal velocities, the instantaneous free surface is integrated following time history by use of fourth-order Runge- Kutta method. The double node technique is used to deal with geometric discontinuity at the wave- body intersections. Several precise smoothing methods have been introduced to treat surface point with high curvature. No saw-tooth like instability is observed during the total simulation.The advantage of proposed wave tank has been verified by comparing with linear theoretical solution and other nonlinear results, excellent agreement in the whole range of frequencies of interest has been obtained.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
Energy Technology Data Exchange (ETDEWEB)
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.
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.
Simulation of Fully Nonlinear 3-D Numerical Wave Tank
Institute of Scientific and Technical Information of China (English)
张晓兔; 滕斌; 宁德志
2004-01-01
A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.
Time-Reversal of Nonlinear Waves - Applicability and Limitations
Ducrozet, G; Chabchoub, A
2016-01-01
Time-reversal (TR) refocusing of waves is one of 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 backwards. Lately, laboratory experiments 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 TR using a uni-directional 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' configu...
Nonlinear diffraction of water waves by offshore stuctures
Directory of Open Access Journals (Sweden)
Matiur Rahman
1986-01-01
Full Text Available This paper is concerned with a variational formulation of a nonaxisymmetric water wave problem. The full set of equations of motion for the problem in cylindrical polar coordinates is derived. This is followed by a review of the current knowledge on analytical theories and numerical treatments of nonlinear diffraction of water waves by offshore cylindrical structures. A brief discussion is made on water waves incident on a circular harbor with a narrow gap. Special emphasis is given to the resonance phenomenon associated with this problem. A new theoretical analysis is also presented to estimate the wave forces on large conical structures. Second-order (nonlinear effects are included in the calculation of the wave forces on the conical structures. A list of important references is also given.
Institute of Scientific and Technical Information of China (English)
ZHENG Feng
2009-01-01
Using the NCEP reanalysis at 1° ×1° resolution in conjunction with satellite imagery, a study is undertaken of easterly wave related rainstorm events on August 3～4, 2001 in seaboards between northern Fujian and southern Zhejiang, expounding the scheme for computing helicity, and exploring the rainstorm evolution and the genesis of the Yandang mountains-triggered a meso-vortex (Duan and Chen, 2005) by means of helicity and Q vector divergence. Besides, MM5V2 is employed to simulate the easterly wave caused meso-vortex. Results show that the development of the central intensity and location of the high-valued helicity is well indicative of the fallout area and the genesis of the meso-vortex, discovering that the space/time evolutions of helicity serve as indicators of some utility for the rainfall occurrence; it is revealed that the calculated helicity is of higher precision than MM5V2 simulations in predicting the initial position and the track of the meso-vortex, with their combination contributing to the improvement of predicting the meso-vortex, also, the space/time evolutions in the superimposition of the zone of large-value helicity gradients upon that of high-value Q vector divergence gradients can be used to accurately forecast the rainstorm happening and initial position of the meso-vortex, thereby illustrating the higher ability of diagnosing the precipitation and its system in the superimposed region.
Energy Technology Data Exchange (ETDEWEB)
Romeo, Francesco [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: francesco.romeo@uniromal.it; Rega, Giuseppe [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: giuseppe.rega@uniromal.it
2006-02-01
Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration.
Nonlinear Alfvén wave dynamics in plasmas
Energy Technology Data Exchange (ETDEWEB)
Sarkar, Anwesa; Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India); Schamel, Hans [Theoretical Physics, University of Bayreuth, D-95440 Bayreuth (Germany)
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 Alfvén wave dynamics in plasmas
Sarkar, Anwesa; Chakrabarti, Nikhil; Schamel, Hans
2015-07-01
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
Directory of Open Access Journals (Sweden)
Shi Jing
2014-01-01
Full Text Available The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method can be used to solve other similar nonlinear wave equations.
Diffractive optics based four-wave, six-wave, ..., nu-wave nonlinear spectroscopy.
Miller, R J Dwayne; Paarmann, Alexander; Prokhorenko, Valentyn I
2009-09-15
A detailed understanding of chemical processes requires information about both structure and dynamics. By definition, a reaction involves nonstationary states and is a dynamic process. Structure describes the atomic positions at global minima in the nuclear potential energy surface. Dynamics are related to the anharmonicities in this potential that couple different minima and lead to changes in atomic positions (reactions) and correlations. Studies of molecular dynamics can be configured to directly access information on the anharmonic interactions that lead to chemical reactions and are as central to chemistry as structural information. In this regard, nonlinear spectroscopies have distinct advantages over more conventional linear spectroscopies. Because of this potential, nonlinear spectroscopies could eventually attain a comparable level of importance for studying dynamics on the relevant time scales to barrier crossings and reactive processes as NMR has for determining structure. Despite this potential, nonlinear spectroscopy has not attained the same degree of utility as linear spectroscopy largely because nonlinear studies are more technically challenging. For example, unlike the linear spectrometers that exist in almost all chemistry departments, there are no "black box" four-wave mixing spectrometers. This Account describes recent advances in the application of diffractive optics (DOs) to nonlinear spectroscopy, which reduces the complexity level of this technology to be closer to that of linear spectroscopy. The combination of recent advances in femtosecond laser technology and this single optic approach could bring this form of spectroscopy out of the exclusive realm of specialists and into the general user community. However, the real driving force for this research is the pursuit of higher sensitivity limits, which would enable new forms of nonlinear spectroscopy. This Account chronicles the research that has now extended nonlinear spectroscopy to six-wave
Energy Technology Data Exchange (ETDEWEB)
Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)
2015-03-31
This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.
Cutoff parameter and vortex core size in d-wave superconductors
Directory of Open Access Journals (Sweden)
Belova P.
2014-07-01
Full Text Available There is some evidence that the electron-phonon mechanism is not strong enough to produce observed high critical temperatures in unconventional superconductors; this is the case in both the cuprates and Fe-based superconductors. The d-wave pairing in strongly correlated systems is consistent with the observation of nodal quasiparticles in the heavily hole doped superconductor KFe2As2 with Tc = 3 K and high-Tc cuprates. In this work the Eilenberger equations are solved for anisotropic dx2−y2-wave superconductors. The cutoﬀ parameter ξh and vortex core size ξ2 (the distance from the vortex center to the radius where the current density reaches its maximum value in the mixed state are investigated numerically. The cutoﬀ parameter determines the ﬁeld distribution in the generalized London equation obtained as a projection of the quasiclassical theory. It can be used for the fitting of the µSR and small-angle neutron scattering (SANS experimental data. Field and temperature dependences of ξh/ξc2 in dx2−y2-wave superconductors are similar to those in s-wave superconductors: ξh/ξc2(B/Bc2dependence has minimum at high temperatures and shows monotonously increasing behavior at low temperatures. Here, ξc2 is determined by the relation Bc2 =Φ0/2πξc22. The ξ2/ξc2(B/Bc2 dependence is monotonously decreasing function at intermediate and high temperatures.
Analytical and numerical investigation of nonlinear internal gravity waves
Directory of Open Access Journals (Sweden)
S. P. Kshevetskii
2001-01-01
Full Text Available The propagation of long, weakly nonlinear internal waves in a stratified gas is studied. Hydrodynamic equations for an ideal fluid with the perfect gas law describe the atmospheric gas behaviour. If we neglect the term Ͽ dw/dt (product of the density and vertical acceleration, we come to a so-called quasistatic model, while we name the full hydro-dynamic model as a nonquasistatic one. Both quasistatic and nonquasistatic models are used for wave simulation and the models are compared among themselves. It is shown that a smooth classical solution of a nonlinear quasistatic problem does not exist for all t because a gradient catastrophe of non-linear internal waves occurs. To overcome this difficulty, we search for the solution of the quasistatic problem in terms of a generalised function theory as a limit of special regularised equations containing some additional dissipation term when the dissipation factor vanishes. It is shown that such solutions of the quasistatic problem qualitatively differ from solutions of a nonquasistatic nature. It is explained by the fact that in a nonquasistatic model the vertical acceleration term plays the role of a regularizator with respect to a quasistatic model, while the solution qualitatively depends on the regularizator used. The numerical models are compared with some analytical results. Within the framework of the analytical model, any internal wave is described as a system of wave modes; each wave mode interacts with others due to equation non-linearity. In the principal order of a perturbation theory, each wave mode is described by some equation of a KdV type. The analytical model reveals that, in a nonquasistatic model, an internal wave should disintegrate into solitons. The time of wave disintegration into solitons, the scales and amount of solitons generated are important characteristics of the non-linear process; they are found with the help of analytical and numerical investigations. Satisfactory
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces
Jin, Boyuan
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...
Numerical modelling of nonlinear full-wave acoustic propagation
Energy Technology Data Exchange (ETDEWEB)
Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx [Grupo de Acústica y Vibraciones, Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Ciudad Universitaria, Apartado Postal 70-186, C.P. 04510, México D.F., México (Mexico)
2015-10-28
The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on a GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.
Nonlinear scattering of radio waves by metal objects
Shteynshleyger, V. B.
1984-07-01
Nonlinear scattering of radio waves by metal structures with resulting harmonic and intermodulation interference is analyzed from both theoretical and empirical standpoints, disregarding nonlinear effects associated with the nonlinear dependence of the electric or magnetic polarization vector on respectively the electric or magnetic field intensity in the wave propagating medium. Nonlinear characteristics of metal-oxide-metal contacts where the thin oxide film separation two metal surfaces has properties approximately those of a dielectric or a high-resistivity semiconductor are discussed. Tunneling was found to be the principal mechanism of charge carrier transfer through such a contact with a sufficiently thin film, the contact having usually a cubic or sometimes an integral sign current-voltage characteristic at 300 K and usually S-form or sometimes a cubic current-voltage characteristic at 77 K.
Nonlinear surface waves in soft, weakly compressible elastic media.
Zabolotskaya, Evgenia A; Ilinskii, Yurii A; Hamilton, Mark F
2007-04-01
Nonlinear surface waves in soft, weakly compressible elastic media are investigated theoretically, with a focus on propagation in tissue-like media. The model is obtained as a limiting case of the theory developed by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569-2575 (1992)] for nonlinear surface waves in arbitrary isotropic elastic media, and it is consistent with the results obtained by Fu and Devenish [Q. J. Mech. Appl. Math. 49, 65-80 (1996)] for incompressible isotropic elastic media. In particular, the quadratic nonlinearity is found to be independent of the third-order elastic constants of the medium, and it is inversely proportional to the shear modulus. The Gol'dberg number characterizing the degree of waveform distortion due to quadratic nonlinearity is proportional to the square root of the shear modulus and inversely proportional to the shear viscosity. Simulations are presented for propagation in tissue-like media.
Kinetic equation for nonlinear resonant wave-particle interaction
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.
The Gouy phase shift in nonlinear interactions of waves
Lastzka, Nico; Schnabel, Roman
2007-06-01
We theoretically analyze the influence of the Gouy phase shift on the nonlinear interaction between waves of different frequencies. We focus on χ(2)interaction of optical fields, e.g. through birefringent crystals, and show that focussing, stronger than suggested by the Boyd-Kleinman factor, can further improve nonlinear processes. An increased value of 3.32 for the optimal focussing parameter for a single pass process is found. The new value builds on the compensation of the Gouy phase shift by a spatially varying, instead constant, wave vector phase mismatch. We analyze the single-ended, singly resonant standing wave nonlinear cavity and show that in this case the Gouy phase shift leads to an additional phase during backreflection. Our numerical simulations may explain ill-understood experimental observations in such devices.
Stress wave propagation analysis on vortex-induced vibration of marine risers
Li, Hua-jun; Wang, Chao; Liu, Fu-shun; Hu, Sau-Lon James
2017-03-01
To analyze the stress wave propagation associated with the vortex-induced vibration (VIV) of a marine riser, this paper employed a multi-signal complex exponential method. This method is an extension of the classical Prony's method which decomposes a complicated signal into a number of complex exponential components. Because the proposed method processes multiple signals simultaneously, it can estimate the "global" dominating frequencies (poles) shared by those signals. The complex amplitude (residues) corresponding to the estimated frequencies for those signals is also obtained in the process. As the signals were collected at different locations along the axial direction of a marine riser, the phenomena of the stress wave propagation could be analyzed through the obtained residues of those signals. The Norwegian Deepwater Program (NDP) high mode test data were utilized in the numerical studies, including data sets in both the in-line (IL) and cross-flow (CF) directions. It was found that the most dominant component in the IL direction has its stress wave propagation along the riser being dominated by a standing wave, while that in the CF direction dominated by a traveling wave.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Energy Technology Data Exchange (ETDEWEB)
Alka, W.; Goyal, Amit [Department of Physics, Panjab University, Chandigarh-160014 (India); Nagaraja Kumar, C., E-mail: cnkumar@pu.ac.i [Department of Physics, Panjab University, Chandigarh-160014 (India)
2011-01-17
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.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
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.
Nonlinear Alfv\\'en waves in extended magnetohydrodynamics
Abdelhamid, Hamdi M
2015-01-01
Large-amplitude Alfv\\'en waves are observed in various systems in space and laboratories, demonstrating an interesting property that the wave shapes are stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model predicts that an Alfv\\'en wave keeps an arbitrary shape constant when it propagates on a homogeneous ambient magnetic field. However, such arbitrariness is an artifact of the idealized model that omits the dispersive effects. Only special wave forms, consisting of two component sinusoidal functions, can maintain the shape; we derive fully nonlinear Alfv\\'en waves by an extended MHD model that includes both the Hall and electron inertia effects. Interestingly, these \\small-scale effects" change the picture completely; the large-scale component of the wave cannot be independent of the small scale component, and the coexistence of them forbids the large scale component to have a free wave form. This is a manifestation of the nonlinearity-dispersion interplay, which is somewhat differ...
NONLINEAR APPROXIMATION WITH GENERAL WAVE PACKETS
Institute of Scientific and Technical Information of China (English)
L. Borup; M. Nielsen
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...... characterization of the approximation spaces is derived....
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces.
Jin, Boyuan; Argyropoulos, Christos
2016-06-27
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.
New traveling wave solutions for nonlinear evolution equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Madkour, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-06-11
The generalized Jacobi elliptic function expansion method is used with a computerized symbolic computation for constructing the new exact traveling wave solutions. The validity and reliability of the method is tested by its applications on a class of nonlinear evolution equations of special interest in mathematical physics. As a result, many exact traveling wave solutions are obtained which include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
Propagation of Quasi-plane Nonlinear Waves in Tubes
Directory of Open Access Journals (Sweden)
P. Koníček
2002-01-01
Full Text Available This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicability of the KZK equation and the GBE equation for describing nonlinear waves in tubes are discussed.
Nonlinear fast sausage waves in homogeneous magnetic flux tubes
Mikhalyaev, Badma B.; Ruderman, Michael S.
2015-12-01
> We consider fast sausage waves in straight homogeneous magnetic tubes. The plasma motion is described by the ideal magnetohydrodynamic equations in the cold plasma approximation. We derive the nonlinear Schrödinger equation describing the nonlinear evolution of an envelope of a carrier wave. The coefficients of this equation are expressed in terms Bessel and modified Bessel functions. They are calculated numerically for various values of parameters. In particular, we show that the criterion for the onset of the modulational or Benjamin-Fair instability is satisfied. The implication of the obtained results for solar physics is discussed.
A general theory of two-wave mixing in nonlinear media
DEFF Research Database (Denmark)
Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael
2009-01-01
A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...
Nonlinear waves in a fluid-filled thin viscoelastic tube
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
Ducrozet, G.; Fink, M.; Chabchoub, A.
2016-09-01
Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.
Nonlinear waves in a fluid-filled thin viscoelastic tube
Institute of Scientific and Technical Information of China (English)
Zhang Shan-Yuan; Zhang Tao
2010-01-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incom-pressible 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 prop-agation 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 expo-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.
Properties of GH4169 Superalloy Characterized by Nonlinear Ultrasonic Waves
Directory of Open Access Journals (Sweden)
Hongjuan Yan
2015-01-01
Full Text Available The nonlinear wave motion equation is solved by the perturbation method. The nonlinear ultrasonic coefficients β and δ are related to the fundamental and harmonic amplitudes. The nonlinear ultrasonic testing system is used to detect received signals during tensile testing and bending fatigue testing of GH4169 superalloy. The results show that the curves of nonlinear ultrasonic parameters as a function of tensile stress or fatigue life are approximately saddle. There are two stages in relationship curves of relative nonlinear coefficients β′ and δ′ versus stress and fatigue life. The relative nonlinear coefficients β′ and δ′ increase with tensile stress when tensile stress is lower than 65.8% of the yield strength, and they decrease with tensile stress when tensile stress is higher than 65.8% of the yield strength. The nonlinear coefficients have the extreme values at 53.3% of fatigue life. For the second order relative nonlinear coefficient β′, there is good agreement between the experimental data and the comprehensive model. For the third order relative nonlinear coefficient δ′, however, the experiment data does not accord with the theoretical model.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Shallow water modal evolution due to nonlinear internal waves
Badiey, Mohsen; Wan, Lin; Luo, Jing
2017-09-01
Acoustic modal behavior is reported for an L-shape hydrophone array during the passage of a strong nonlinear internal wave packet. Acoustic track is nearly parallel to the front of nonlinear internal waves. Through modal decomposition at the vertical array, acoustic modes are identified. Modal evolution along the horizontal array then is examined during a passing internal wave. Strong intensity fluctuations of individual modes are observed before and during the internal waves packet passes the fixed acoustic track showing a detailed evolution of the waveguide modal behavior. Acoustic refraction created either uneven distribution of modal energy over the horizontal array or additional returns observable at the entire L-shape array. Acoustic ray-mode simulations are used to phenomenologically explain the observed modal behavior.
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.
Nonlinear reflection of internal gravity wave onto a slope
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
Sampath, Vimal; D'Souza, Noel; Bhattacharya, Dhritiman; Atkinson, Gary M.; Bandyopadhyay, Supriyo; Atulasimha, Jayasimha
2016-09-01
We report manipulation of the magnetic states of elliptical cobalt magnetostrictive nanomagnets (of nominal dimensions ~ 340 nm x 270 nm x 12 nm) delineated on bulk 128{\\deg} Y-cut lithium niobate with Surface Acoustic Waves (SAWs) launched from interdigitated electrodes. Isolated nanomagnets that are initially magnetized to a single domain state with magnetization pointing along the major axis of the ellipse are driven into a vortex state by surface acoustic waves that modulate the stress anisotropy of these nanomagnets. The nanomagnets remain in the vortex state until they are reset by a strong magnetic field to the initial single domain state, making the vortex state non-volatile. This phenomenon is modeled and explained using a micromagnetic framework and could lead to the development of extremely energy efficient magnetization switching methodologies.
Integral and integrable algorithms for a nonlinear shallow-water wave equation
Camassa, Roberto; Huang, Jingfang; Lee, Long
2006-08-01
An asymptotic higher-order model of wave dynamics in shallow water is examined in a combined analytical and numerical study, with the aim of establishing robust and efficient numerical solution methods. Based on the Hamiltonian structure of the nonlinear equation, an algorithm corresponding to a completely integrable particle lattice is implemented first. Each "particle" in the particle method travels along a characteristic curve. The resulting system of nonlinear ordinary differential equations can have solutions that blow-up in finite time. We isolate the conditions for global existence and prove l1-norm convergence of the method in the limit of zero spatial step size and infinite particles. The numerical results show that this method captures the essence of the solution without using an overly large number of particles. A fast summation algorithm is introduced to evaluate the integrals of the particle method so that the computational cost is reduced from O( N2) to O( N), where N is the number of particles. The method possesses some analogies with point vortex methods for 2D Euler equations. In particular, near singular solutions exist and singularities are prevented from occurring in finite time by mechanisms akin to those in the evolution of vortex patches. The second method is based on integro-differential formulations of the equation. Two different algorithms are proposed, based on different ways of extracting the time derivative of the dependent variable by an appropriately defined inverse operator. The integro-differential formulations reduce the order of spatial derivatives, thereby relaxing the stability constraint and allowing large time steps in an explicit numerical scheme. In addition to the Cauchy problem on the infinite line, we include results on the study of the nonlinear equation posed in the quarter (space-time) plane. We discuss the minimum number of boundary conditions required for solution uniqueness and illustrate this with numerical
2011-01-01
International audience; 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...
Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential
Institute of Scientific and Technical Information of China (English)
化存才; 刘延柱
2002-01-01
For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation.
Non-linear high-frequency waves in the magnetosphere
Indian Academy of Sciences (India)
S Moolla; R Bharuthram; S V Singh; G S Lakhina
2003-12-01
Using ﬂuid theory, a set of equations is derived for non-linear high-frequency waves propagating oblique to an external magnetic ﬁeld in a three-component plasma consisting of hot electrons, cold electrons and cold ions. For parameters typical of the Earth’s magnetosphere, numerical solutions of the governing equations yield sinusoidal, sawtooth or bipolar wave-forms for the electric ﬁeld.
Nonlinear Dynamic Characteristics of Combustion Wave in SHS Process
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The characteristic of combustion wave and its change were analyzed by numerical value calculation and computer simulation,based on the combustion dynamical model of SHS process. It is shown that with the change of condition parameters in SHS process various time-space order combustion waves appear.It is concluded from non-liner dynamical mechanism analysis that the strong coupling of two non-linear dynamical processes is the dynamical mechanism causing the time-space order dissipation structures.
Travelling wave solutions for ( + 1)-dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2010-10-01
In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of ( + 1)-dimensional nonlinear evolution equations. Four models, the ( + 1)-dimensional generalized Boussinesq equation, ( + 1)-dimensional sine-cosine-Gordon equation, ( + 1)-double sinh-Gordon equation and ( + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.
On the so called rogue waves in nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Y. Charles Li
2016-04-01
Full Text Available The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schrodinger equation (NLS provides a mechanism. A Peregrine wave solution can be obtained by taking the infinite spatial period limit to the homoclinic solutions. In this article, from the perspective of the phase space structure of these homoclinic orbits in the infinite dimensional phase space where the NLS defines a dynamical system, we examine the observability of these homoclinic orbits (and their approximations. Our conclusion is that these approximate homoclinic orbits are the most observable solutions, and they should correspond to the most common deep ocean waves rather than the rare rogue waves. We also discuss other possibilities for the mechanism of a rogue wave: rough dependence on initial data or finite time blow up.
Analysis of nonlinear internal waves in the New York Bight
Liu, Antony K.
1988-01-01
An analysis of the nonlinear-internal-wave evolution in the New York Bight was performed on the basis of current meter mooring data obtained in the New York Bight during the SAR Internal Wave Signature Experiment (SARSEX). The solitary wave theory was extended to include dissipation and shoaling effects, and a series of numerical experiments were performed by solving the wave evolution equation, with waveforms observed in the SARSEX area as initial conditions. The results of calculations demonstrate that the relative balance of dissipation and shoaling effects is crucial to the detailed evolution of internal wave packets. From an observed initial wave packet at the upstream mooring, the numerical evolution simulation agreed reasonably well with the measurements at the distant mooring for the leading two large solitons.
Blanchard, Antoine; Bergman, Lawrence A.; Vakakis, Alexander F.
2017-07-01
We computationally investigate the dynamics of a linearly-sprung circular cylinder immersed in an incompressible flow and undergoing transverse vortex-induced vibration (VIV), to which is attached a rotational nonlinear energy sink (NES) consisting of a mass that freely rotates at constant radius about the cylinder axis, and whose motion is restrained by a rotational linear viscous damper. The inertial coupling between the rotational motion of the attached mass and the rectilinear motion of the cylinder is ;essentially nonlinear;, which, in conjunction with dissipation, allows for one-way, nearly irreversible targeted energy transfer (TET) from the oscillating cylinder to the nonlinear dissipative attachment. At the intermediate Reynolds number Re = 100, the NES-equipped sprung cylinder undergoes repetitive cycles of slowly decaying oscillations punctuated by intervals of chaotic instabilities. During the slowly decaying portion of each cycle, the dynamics of the cylinder is regular and, for large enough values of the ratio ε of the NES mass to the total mass (i.e., NES mass plus cylinder mass), can lead to significant vortex street elongation with partial stabilization of the wake. As ε approaches zero, no such vortex elongation is observed and the wake patterns appear similar to that for a sprung cylinder with no NES. We apply proper orthogonal decomposition (POD) to the velocity flow field during a slowly decaying portion of the solution and show that, in situations where vortex elongation occurs, the NES, though not in direct contact with the surrounding fluid, has a drastic effect on the underlying flow structures, imparting significant and continuous passive redistribution of energy among POD modes. We construct a POD-based reduced-order model for the lift coefficient to characterize energy transactions between the fluid and the cylinder throughout the slowly decaying cycle. We introduce a quantitative signed measure of the work done by the fluid on the
Linear and Nonlinear Surface Waves in Electrohydrodynamics
Hunt, Matthew; Vanden-broeck, Jean-Marc; Papageorgiou, Demetrios
2015-01-01
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical scalings and to derive a Kadomtsev-Petviashvili equation withan additional non-local term arising in interfacial electrohydrodynamics.When the Bond number is equal to 1/3, dispersion disappears and shock waves could potentially form. In the additional limit of vanishing electric fields, a new evolution equation is obtained which contains third and fifth-order dispersion as well as a non-local electric field term.
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Ba Phi [Central University of Construction, Tuy Hoa (Viet Nam); Kim, Ki Hong [Ajou University, Suwon (Korea, Republic of)
2014-02-15
We study numerically the dynamics of an initially localized wave packet in one-dimensional nonlinear Schroedinger lattices with both local and nonlocal nonlinearities. Using the discrete nonlinear Schroedinger equation generalized by including a nonlocal nonlinear term, we calculate four different physical quantities as a function of time, which are the return probability to the initial excitation site, the participation number, the root-mean-square displacement from the excitation site and the spatial probability distribution. We investigate the influence of the nonlocal nonlinearity on the delocalization to self-trapping transition induced by the local nonlinearity. In the non-self-trapping region, we find that the nonlocal nonlinearity compresses the soliton width and slows down the spreading of the wave packet. In the vicinity of the delocalization to self-trapping transition point and inside the self-trapping region, we find that a new kind of self-trapping phenomenon, which we call partial self-trapping, takes place when the nonlocal nonlinearity is sufficiently strong.
A Numerical Wave Tank for Nonlinear Waves with Passive Absorption
Institute of Scientific and Technical Information of China (English)
周宗仁; 尹彰; 石瑞祥
2001-01-01
A numerical wave tank with passive absorption for irregular waves is considered in this paper. Waves with spectralshapes corresponding to that of the Mitsuyasu-Bretschneider type are used as the initial condition at one end of theflume. An absorbing boundary is imposed at the other end of the wave flume to minimize reflection. By use of aLagrangian description for the surface elevation, and finite difference for approximation of the time derivative, the problem is then solved by the boundary element method. The effects of the absorbing boundary are investigated by varyingthe values of the absorption coefficient μ, and studying the time histories of the surface elevations "recorded" on pre-se-lected locations.
Nakamura, K.
Bose-Einstein condensate(BEC) provides a nice stage when the nonlinearSchrödinger equation plays a vital role. We study the dynamics of multi-component repulsive BEC in 2 dimensions with harmonic traps by using the nonlinear Schrödinger (or Gross-Pitaevskii) equation. Firstly we consider a driven two-component BEC with each component trapped in different vertical positions. The appropriate tuning of the oscillation frequency of the magnetic field leads to a striking anti-gravity transport of BEC. This phenomenon is a manifestation of macroscopic non-adiabatic tunneling in a system with two internal(electronic) degrees of freedom. The dynamics splits into a fast complex spatio-temporal oscillation of each condensate wavefunctions together with a slow levitation of the total center of mass. Secondly, we examine the three-component repulsive BEC in 2 dimensions in a harmonic trap in the absence of magnetic field, and construct a model of conservative chaos based on a picture of vortex molecules. We obtain an effective nonlinear dynamics for three vortex cores, which represents three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance r_{ij} on short scale and logarithmic in r_{ij} on large scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager. We then explore ``the chaos in the three-body problem" in the context of vortices with inertia.
Kurosaka, M.; Goodman, J. R.; Chu, J. Q.
1982-06-01
An acoustic streaming model of the total temperature separation mechanism present in the air flow in a Ranque-Hilsch tube is detailed. Previous explanations of the phenomenon of cold air encountered in the core flow and elevated temperatures of the radial wall flow in a tube where the inlet stream enters tangentially are reviewed. The emergence of a vortex whistle is shown to be a selective amplification of background noise, present in the swirling flow, and drawing energy from the flow itself. Taking the base flow to be a helix with a constant axial velocity and a swirl which is a Rankine vortex, the imposition of unsteady disturbances is demonstrated to result in the establishment of an unsteady boundary forming an annular viscous region around an inviscid core. A feedback occurs between the acoustic streaming in the outer layer and the inviscid core. Results are given for calculations of the frequency, the form of the second-order waves, and the tangential acoustic streaming at the outer edge of the unsteady viscous layer.
Simulations of nonlinear continuous wave pressure fields in FOCUS
Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.
2017-03-01
The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.
NEW EXACT TRAVELLING WAVE SOLUTIONS TO THREE NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
Sirendaoreji
2004-01-01
Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation.
EXACT SOLITARY WAVE SOLUTIONS OF THETWO NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
ZhuYanjuan; ZhangChunhua
2005-01-01
The solitary wave solutions of the combined KdV-mKdV-Burgers equation and the Kolmogorov-Petrovskii-Piskunov equation are obtained by means of the direct algebra method, which can be generalized to deal with high dimensional nonlinear evolution equations.
Nonlinear wave mechanics from classical dynamics and scale covariance
Energy Technology Data Exchange (ETDEWEB)
Hammad, F. [Departement TC-SETI, Universite A.Mira de Bejaia, Route Targa Ouzemmour, 06000 Bejaia (Algeria)], E-mail: fayhammad@yahoo.fr
2007-10-29
Nonlinear Schroedinger equations proposed by Kostin and by Doebner and Goldin are rederived from Nottale's prescription for obtaining quantum mechanics from classical mechanics in nondifferentiable spaces; i.e., from hydrodynamical concepts and scale covariance. Some soliton and plane wave solutions are discussed.
Non-Linear Langmuir Wave Modulation in Collisionless Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans
1977-01-01
A non-linear Schrodinger equation for Langmuir waves is presented. The equation is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics. The two formulations lead to significant differences in the final results, especially...
Nonlinear wave propagation studies, dispersion modeling, and signal parameters correction
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk
..: ..., 2004, 00. [European Workshop on FP6-AERONEWS /1./. Naples (IT), 13.09.2004-16.09.2004] EU Projects: European Commission(XE) 502927 - AERO-NEWS Institutional research plan: CEZ:AV0Z2076919 Keywords : nodestructive testing * nonlinear elastic wave spectroscopy Subject RIV: BI - Acoustics
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.
Exact controllability for a nonlinear stochastic wave equation
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available The exact controllability for a semilinear stochastic wave equation with a boundary control is established. The target and initial spaces are L 2 ( G × H −1 ( G with G being a bounded open subset of R 3 and the nonlinear terms having at most a linear growth.
Stability of planar diffusion wave for nonlinear evolution equation
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
It is known that the one-dimensional nonlinear heat equation ut = f(u)x1x1,f'(u) 0,u(±∞,t) = u±,u+ = u_ has a unique self-similar solution u(x1/1+t).In multi-dimensional space,u(x1/1+t) is called a planar diffusion wave.In the first part of the present paper,it is shown that under some smallness conditions,such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation:ut-△f(u) = 0,x ∈ Rn.The optimal time decay rate is obtained.In the second part of this paper,it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping:utt + utt+ △f(u) = 0,x ∈ Rn.The time decay rate is also obtained.The proofs are given by an elementary energy method.
An inhomogeneous wave equation and non-linear Diophantine approximation
DEFF Research Database (Denmark)
Beresnevich, V.; Dodson, M. M.; Kristensen, S.;
2008-01-01
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...... is studied. Both the Lebesgue and Hausdorff measures of this set are obtained....
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
). In the present paper we use a single layer of quadratic (in 2D) and prismatic (in 3D) elements. The model has been stabilized through a combination of over-integration of the Galerkin projections and a mild modal filter. We present numerical tests of nonlinear waves serving as a proof-of-concept validation...
NUMERICAL SIMULATIONS OF NONLINEAR WAVE TRANSFORMATION AROUND WAVE-PERMEABLE STRUCTURE
Institute of Scientific and Technical Information of China (English)
Li Xi; YAN Yi-xin
2005-01-01
The problem of wave partial/full reflection and transmission by wave-permeable structure is approached by solving the shape-related function with focus on the understanding of wave attenuation.2D depth-averaged Boussinesq type wave equations are given with new damping item in simulating the nonlinear wave transmission through wave-permeable structure.1D wave equation is examined to give the analytical expression of the absorbing coefficient, and is compared with laboratory data in flume to calibrate the coefficients, and the expression is applied directly in modified Boussinesq type equations.Compared with wave basin data for various incident wave conditions,the accurate predictions of combined diffraction-refraction effects in simulating nonlinear wave going through wave-permeable breakwater in the engineering application can be obtained.It shows that wave-permeable breakwaters with proper absorbing effects can be used as an effective alternative to massive gravity breakwaters in reduction of wave transmission in shallow water.
Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types
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.
Nonlinear single Compton scattering of an electron wave-packet
Angioi, A; Di Piazza, A
2016-01-01
In the presence of a sufficiently intense electromagnetic laser field, an electron can absorb on average a large number of photons from the laser and emit a high-energy one (nonlinear single Compton scattering). The case of nonlinear single Compton scattering by an electron with definite initial momentum has been thoroughly investigated in the literature. Here, we consider a more general initial state of the electron and use a wave-packet obtained as a superposition of Volkov wave functions. In particular, we investigate the energy spectrum of the emitted radiation at fixed observation direction and show that in typical experimental situations the sharply peaked structure of nonlinear single Compton scattering spectra of an electron with definite initial energy is almost completely washed out. Moreover, we show that at comparable 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, relate...
Nonlinear Acoustic Wave Interactions in Layered Media.
1980-03-06
Generated Components in Dispersive Media. . . . . . . . . . . . . 62 4.4 Dispersion in Medium II . . . . . . . . .. 68 V. CONCLUSIONS...give rise to leaky wave modes which are more thoroughly discussed 17 18 by Kapany and Burke, and by Marcuse . Leaky modes are C.C. Ghizoni, J.M...1977), 843-848. 1 7N.S. Kapany and J.J. Burke, Optical Waveeeuides, (New York: Academic Press, 1972), pp. 24-34. D. Marcuse , Theory of Dielectric Optical
Nearly linear dynamics of nonlinear dispersive waves
Erdogan, M B; Zharnitsky, V
2010-01-01
Dispersive averaging e?ffects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.
Controlling nonlinear waves in excitable media
Energy Technology Data Exchange (ETDEWEB)
Puebla, Hector [Departamento de Energia, Universidad Autonoma Metropolitana, Av. San Pablo No. 180, Reynosa-Tamaulipas, Azcapotzalco 02200, DF, Mexico (Mexico)], E-mail: hpuebla@correo.azc.uam.mx; Martin, Roland [Laboratoire de Modelisation et d' Imagerie en Geosciences, CNRS UMR and INRIA Futurs Magique-3D, Universite de Pau (France); Alvarez-Ramirez, Jose [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa (Mexico); Aguilar-Lopez, Ricardo [Departamento de Biotecnologia y Bioingenieria, CINVESTAV-IPN (Mexico)
2009-01-30
A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system's slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.
The nonlinear evolution of rogue waves generated by means of wave focusing technique
Hu, HanHong; Ma, Ning
2011-01-01
Generating the rogue waves in offshore engineering is investigated, first of all, to forecast its occurrence to protect the offshore structure from being attacked, to study the mechanism and hydrodynamic properties of rouge wave experimentally as well as the rouge/structure interaction for the structure design. To achieve these purposes demands an accurate wave generation and calculation. In this paper, we establish a spatial domain model of fourth order nonlinear Schrödinger (NLS) equation for describing deep-water wave trains in the moving coordinate system. In order to generate rogue waves in the experimental tank efficiently, we take care that the transient water wave (TWW) determines precisely the concentration of time/place. First we simulate the three-dimensional wave using TWW in the numerical tank and modeling the deepwater basin with a double-side multi-segmented wave-maker in Shanghai Jiao Tong University (SJTU) under the linear superposing theory. To discuss its nonlinearity for guiding the experiment, we set the TWW as the initial condition of the NLS equation. The differences between the linear and nonlinear simulations are presented. Meanwhile, the characteristics of the transient water wave, including water particle velocity and wave slope, are investigated, which are important factors in safeguarding the offshore structures.
Energy Technology Data Exchange (ETDEWEB)
Zhou Yubin; Wang Mingliang; Miao Tiande
2004-03-15
The periodic wave solutions for a class of nonlinear partial differential equations, including the Davey-Stewartson equations and the generalized Zakharov equations, are obtained by using the F-expansion method, which can be regarded as an overall generalization of the Jacobi elliptic function expansion method recently proposed. In the limit cases the solitary wave solutions of the equations are also obtained.
Evolution of Nonlinear Internal Waves in China Seas
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.
Weak bond detection in composites using highly nonlinear solitary waves
Singhal, Taru; Kim, Eunho; Kim, Tae-Yeon; Yang, Jinkyu
2017-05-01
We experimentally investigate a diagnostic technique for identifying a weak bond in composites using highly nonlinear solitary waves (HNSWs). We set up a one-dimensional chain of granular crystals, consisting of spherical particles with nonlinear interactions, to generate HNSWs. These solitary wave packets are transmitted into an inspection area of composites by making a direct contact with the chain. We demonstrate that a strong type of solitary waves injected to the weak bond area can break the weak bond of laminates, thereby causing delamination. Then, to identify the creation of the delamination, we transmit a weak type of solitary waves by employing the same apparatus, and measure the solitary waves reflected from the specimens. By analyzing these reflected solitary waves, we differentiate the weak bond samples with the pristine bond ones in an efficient and fast manner. The diagnostic results based on the proposed method are compared with the strength and energy release rate at bond interfaces, which are measured via standard testing methods such as three point bending and end notched flexure tests. This study shows the potential of solitary wave-based detection of weak bonds for hot spot monitoring of composite-based structures.
Indian Academy of Sciences (India)
O Rahman; A A Mamun
2013-06-01
A theoretical investigation of dust-acoustic solitary waves in three-component unmagnetized dusty plasma consisting of trapped electrons, Maxwellian ions, and arbitrarily charged cold mobile dust was done. It has been found that, owing to the departure from the Maxwellian electron distribution to a vortex-like one, the dynamics of small but finite amplitude dust-acoustic (DA) waves is governed by a nonlinear equation of modified Korteweg–de Vries (mKdV) type (instead of KdV). The reductive perturbation method was employed to study the basic features (amplitude, width, speed, etc.) of DA solitary waves which are significantly modified by the presence of trapped electrons. The implications of our results in space and laboratory plasmas are briefly discussed.
Nonlinear interaction of waves in boundary-layer flows
Nayfeh, A. H.; Bozatli, A. N.
1979-01-01
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed by using the method of multiple scales. For the case of two waves, a strong nonlinear interaction exists if one of the frequencies w2 is twice the other frequency w1. Numerical results for flow past a flat plate show that this interaction mechanism is strongly destabilizing even in regions where either the fundamental or its harmonic is damped in the absence of the interaction. For the case of three waves, a strong nonlinear interaction exists when w3 = w2- w1. This combination resonance causes the amplitude of the wave with the difference frequency w3 to multiply many times in magnitude in a short distance even if it is damped in the absence of the interaction. The initial amplitudes play a dominant role in determining the changes in the amplitudes of the waves in both of these mechanisms.
Nonlinear dynamic behaviors of a floating structure in focused waves
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.
Alfven waves in the solar atmosphere. III - Nonlinear waves on open flux tubes
Hollweg, J. V.; Jackson, S.; Galloway, D.
1982-01-01
Consideration is given the nonlinear propagation of Alfven waves on solar magnetic flux tubes, where the tubes are taken to be vertical, axisymmetric and initially untwisted and the Alfven waves are time-dependent axisymmetric twists. The propagation of the waves into the chromosphere and corona is investigated through the numerical solution of a set of nonlinear, time-dependent equations coupling the Alfven waves into motions that are parallel to the initial magnetic field. It is concluded that Alfven waves can steepen into fast shocks in the chromosphere, pass through the transition region to produce high-velocity pulses, and then enter the corona, which they heat. The transition region pulses have amplitudes of about 60 km/sec, and durations of a few tens of seconds. In addition, the Alfven waves exhibit a tendency to drive upward flows, with many of the properties of spicules.
2015-09-30
Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves Lian Shen St. Anthony Falls Laboratory and Department of Mechanical...on studying surface gravity wave evolution and spectrum in the presence of surface currents caused by strongly nonlinear internal solitary waves...interaction of surface and internal gravity waves in the South China Sea. We will seek answers to the following questions: 1) How does the wind-wave
Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua
2015-08-01
Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping. Copyright © 2015 Elsevier B.V. All rights reserved.
Nonlinear interaction of two waves in boundary-layer flows
Nayfeh, A. H.; Bozatli, A. N.
1980-01-01
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed using the method of multiple scales. Numerical results for flow past a flat plate show that the spatial detuning wipes out resonant interactions unless the initial amplitudes are very large. Thus, a wave having a moderate amplitude has little influence on its subharmonic although it has a strong influence on its second harmonic. Moreover, two waves having moderate amplitudes have a strong influence on their difference frequency. The results show that the difference frequency can be very unstable when generated by the nonlinear interaction, even though it may be stable when introduced by itself in the boundary layer.
A Stochastic Nonlinear Water Wave Model for Efficient Uncertainty Quantification
Bigoni, Daniele; Eskilsson, Claes
2014-01-01
A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a stochastic formulation of a fully nonlinear and dispersive potential flow water wave model for the probabilistic description of the evolution waves. This model is discretized using the Stochastic Collocation Method (SCM), which provides an approximate surrogate of the model. This can be used to accurately and efficiently estimate the probability distribution of the unknown time dependent stochastic solution after the forward propagation of uncertainties. We revisit experimental benchmarks often used for validation of deterministic water wave models. We do this using a fully nonlinear and dispersive model and show how uncertainty in the model input can influence the model output. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in compa...
Weak Nonlinear Matter Waves in a Trapped Spin-1 Condensates
Institute of Scientific and Technical Information of China (English)
CAI Hong-Qiang; YANG Shu-Rong; XUE Ju-Kui
2011-01-01
The dynamics of the weak nonlinear matter solitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coefficient Korteweg-de Vries (KdV) equation. The reduction to the (KdV) equation may be useful to understand the dynamics of nonlinear matter waves in spinor BEGs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation freauencv are also obtained.
Viscous Fluid Conduits as a Prototypical Nonlinear Dispersive Wave Platform
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 in electromigration dispersion in a capillary
Christov, Ivan C
2016-01-01
We construct exact solutions to an unusual nonlinear advection--diffusion equation arising in the study of Taylor--Aris (also known as shear) dispersion due to electroosmotic flow during electromigration in a capillary. An exact reduction to a Darboux equation is found under a traveling-wave anzats. The equilibria of this ordinary differential equation are analyzed, showing that their stability is determined solely by the (dimensionless) wave speed without regard to any (dimensionless) physical parameters. Integral curves, connecting the appropriate equilibria of the Darboux equation that governs traveling waves, are constructed, which in turn are shown to be asymmetric kink solutions ({\\it i.e.}, non-Taylor shocks). Furthermore, it is shown that the governing Darboux equation exhibits bistability, which leads to two coexisting non-negative kink solutions for (dimensionless) wave speeds greater than unity. Finally, we give some remarks on other types of traveling-wave solutions and a discussion of some approx...
Liu, Chang
2015-01-01
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.
On a nonlinear gravitational wave. Geodesics
Culetu, Hristu
2016-01-01
An exact, plane wave solution of the gravitational field equations is investigated. The source stress tensor is represented by an anisotropic null fluid with energy flux to which the energy density $\\rho$ and the pressure $p_{z}$ are negative but finite throughout the spacetime. They depend on a constant length (taken of the order of the Planck length) and acquire Planck values close to the null surface $t - z = 0$, $Oz$ axis being the direction of propagation. The timelike geodesics of a test particle are contained in a plane whose normal has constant direction and the null trajectories are comoving with a plane of fixed direction.
Exact Solitary Wave and Periodic Wave Solutions of a Class of Higher-Order Nonlinear Wave Equations
Directory of Open Access Journals (Sweden)
Lijun Zhang
2015-01-01
Full Text Available We study the exact traveling wave solutions of a general fifth-order nonlinear wave equation and a generalized sixth-order KdV equation. We find the solvable lower-order subequations of a general related fourth-order ordinary differential equation involving only even order derivatives and polynomial functions of the dependent variable. It is shown that the exact solitary wave and periodic wave solutions of some high-order nonlinear wave equations can be obtained easily by using this algorithm. As examples, we derive some solitary wave and periodic wave solutions of the Lax equation, the Ito equation, and a general sixth-order KdV equation.
Caplan, Ronald Meyer
We numerically study the dynamics and interactions of vortex rings in the nonlinear Schrodinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex rings are investigated, including scattering and merging of two colliding rings, leapfrogging interactions of co-traveling rings, as well as co-moving steady-state multi-ring ensembles. Simulations of choreographed multi-ring setups are also performed, leading to intriguing interaction dynamics. Due to the inherent lack of a close form solution for vortex rings and the dimensionality where they live, efficient numerical methods to integrate the NLSE have to be developed in order to perform the extensive number of required simulations. To facilitate this, compact high-order numerical schemes for the spatial derivatives are developed which include a new semi-compact modulus-squared Dirichlet boundary condition. The schemes are combined with a fourth-order Runge-Kutta time-stepping scheme in order to keep the overall method fully explicit. To ensure efficient use of the schemes, a stability analysis is performed to find bounds on the largest usable time step-size as a function of the spatial step-size. The numerical methods are implemented into codes which are run on NVIDIA graphic processing unit (GPU) parallel architectures. The codes running on the GPU are shown to be many times faster than their serial counterparts. The codes are developed with future usability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with a MEX-compiler interface. Reproducibility of results is achieved by combining the codes into a code package called NLSEmagic which is freely distributed on a dedicated website.
Xiao, Jianyuan; Qin, Hong; Yu, Zhi; Xiang, Nong
2015-01-01
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 cur...
Energy Technology Data Exchange (ETDEWEB)
Huang Dingjiang [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)]. E-mail: hdj8116@163.com; Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)
2006-08-15
Many travelling wave solutions of nonlinear evolution equations can be written as a polynomial in several elementary or special functions which satisfy a first order nonlinear ordinary differential equation with a sixth-degree nonlinear term. From that property, we deduce an algebraic method for constructing those solutions by determining only a finite number of coefficients. Being concise and straightforward, the method is applied to three nonlinear evolution equations. As a result, many exact travelling wave solutions are obtained which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions.
Generation and propagation of nonlinear internal waves in Massachusetts Bay
Scotti, A.; Beardsley, R.C.; Butman, B.
2007-01-01
During the summer, nonlinear internal waves (NLIWs) are commonly observed propagating in Massachusetts Bay. The topography of the area is unique in the sense that the generation area (over Stellwagen Bank) is only 25 km away from the shoaling area, and thus it represents an excellent natural laboratory to study the life cycle of NLIWs. To assist in the interpretation of the data collected during the 1998 Massachusetts Bay Internal Wave Experiment (MBIWE98), a fully nonlinear and nonhydrostatic model covering the generation/shoaling region was developed, to investigate the response of the system to the range of background and driving conditions observed. Simplified models were also used to elucidate the role of nonlinearity and dispersion in shaping the NLIW field. This paper concentrates on the generation process and the subsequent evolution in the basin. The model was found to reproduce well the range of propagation characteristics observed (arrival time, propagation speed, amplitude), and provided a coherent framework to interpret the observations. Comparison with a fully nonlinear hydrostatic model shows that during the generation and initial evolution of the waves as they move away from Stellwagen Bank, dispersive effects play a negligible role. Thus the problem can be well understood considering the geometry of the characteristics along which the Riemann invariants of the hydrostatic problem propagate. Dispersion plays a role only during the evolution of the undular bore in the middle of Stellwagen Basin. The consequences for modeling NLIWs within hydrostatic models are briefly discussed at the end.
Amplitude-dependent contraction/elongation of nonlinear Lamb waves
Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2016-04-01
Nonlinear elastic guided waves find application in various disciplines of science and engineering, such as non- destructive testing and structural health monitoring. Recent recognition and quantification of their amplitude- dependent changes in spectral properties has contributed to the development of new monitoring concepts for mechanical structures. The focus of this work is to investigate and predict amplitude-dependent shifts in Lamb wave dispersion curves. The theory for frequency/wavenumber shifts for plate waves, based on a Lindstedt-Poincaré perturbation approach, was presented by the authors in previous years. Equivalently, spectral properties changes can be seen as wavelength contraction/elongation. Within the proposed framework, the wavelength of a Lamb wave depends on several factors; e.g., wave amplitude and second-, third- and fourth-order elastic constants, and others. Various types of nonlinear effects are considered in presented studies. Sensitivity studies for model parameters, i.e. higher-order elastic constants, are performed to quantify their influence on Lamb wave frequency/wavenumber shifting, and to identify the key parameters governing wavelength tuning.
Energy Technology Data Exchange (ETDEWEB)
Mamun, A.A. [Institut fuer Theoretische Physik IV, Fakultaet fuer Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany); Eliasson, B. [Institut fuer Theoretische Physik IV, Fakultaet fuer Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)]. E-mail: bengt@tp4.rub.de; Shukla, P.K. [Institut fuer Theoretische Physik IV, Fakultaet fuer Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)
2004-11-22
It is shown that the nonlinear propagation of dust-acoustic waves in a strongly coupled dusty plasma is governed by a modified Korteweg-de-Vries-Burgers (KdV-Burgers) equation. The latter is derived from a set of generalized hydrodynamic equations for strongly correlated dust grains in a liquid-like state, a Boltzmann electron distribution, and a non-isothermal vortex-like ion distribution. The numerical solutions of the modified KdV-Burgers equation are presented in order to provide some salient features of dust-acoustic solitary and shock structures that may exist in laboratory dusty plasmas where the dust grains are in a strongly coupled liquid phase.
Garfinkel, Chaim I.; Oman, Luke David; Barnes, Elizabeth A.; Waugh, Darryn W.; Hurwitz, Margaret H.; Molod, Andrea M.
2013-01-01
A robust connection between the drag on surface-layer winds and the stratospheric circulation is demonstrated in NASA's Goddard Earth Observing System Chemistry-Climate Model (GEOSCCM). Specifically, an updated parameterization of roughness at the air-sea interface, in which surface roughness is increased for moderate wind speeds (4ms to 20ms), leads to a decrease in model biases in Southern Hemispheric ozone, polar cap temperature, stationary wave heat flux, and springtime vortex breakup. A dynamical mechanism is proposed whereby increased surface roughness leads to improved stationary waves. Increased surface roughness leads to anomalous eddy momentum flux convergence primarily in the Indian Ocean sector (where eddies are strongest climatologically) in September and October. The localization of the eddy momentum flux convergence anomaly in the Indian Ocean sector leads to a zonally asymmetric reduction in zonal wind and, by geostrophy, to a wavenumber-1 stationary wave pattern. This tropospheric stationary wave pattern leads to enhanced upwards wave activity entering the stratosphere. The net effect is an improved Southern Hemisphere vortex: the vortex breaks up earlier in spring (i.e., the spring late-breakup bias is partially ameliorated) yet is no weaker in mid-winter. More than half of the stratospheric biases appear to be related to the surface wind speed biases. As many other chemistry climate models use a similar scheme for their surface layer momentum exchange and have similar biases in the stratosphere, we expect that results from GEOSCCM may be relevant for other climate models.
Moulin, F.; Flor, J.
We present the results of an experimental investigation on the material transport across the shear zone of a cyclonic vortex induced by the breaking of inertia-gravity waves. As has been suggested by McIntyre (1995) this could be a possible mechamism of ozone transport across the dynamical barrier of the polar vortex. The experiments were conducted in a 1 meter size tank containing a rotating stratified fluid. Barotropic vortices were generated by siphoning off fluid with a long perforated tube and per- turbed by planar internal waves generated by the vertical oscillation of a horizontal circular cylinder. As predicted by theorical results based on the WKB approximation, the waves opposing the vortex velocity field were trapped in the outer edge of the vor- tex. In some cases, the increase of wave energy in this region was strong enough to lead to 3-dimensional breaking of the wave pattern. Experimental visualization tech- niques were used to determine the class of instability responsible for this breaking and to measure the induced mixing. A simple model to predict the efficiency of the mixing process will be presented.
Focusing of Spherical Nonlinear Pulses for Nonlinear Wave Equations Ⅲ. Subcritical Case
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
This paper studied spherical pulses of solutions of the system of semilinear wave equations with the pulses focusing at a point in three space variables. It is shown that there is no nonlinear effect at leading terms of pulses, when the initial data is subcritical.
2010-09-30
Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING
Geodesic deviation in a nonlinear gravitational wave spacetime
Culetu, Hristu
2016-01-01
The tidal effects generated by a nonlinear gravitational wave are investigated in double-null v - u coordinates, as an exact solution of Einstein's field equations. The components $\\xi^{v}$ and $\\xi^{u}$ of the separation vector behave as in flat space but the transversal components $\\xi^{x}$ and $\\xi^{y}$ depend nonlinearly on $v$ through the Bessel and Neumann functions, far from the null surface $v = 0$. We show that the same results are obtained by means of the tetrad formalism.
Traveling wave solutions for some factorized nonlinear PDEs
Cornejo-Pérez, Octavio
2009-01-01
In this work, some new special traveling wave solutions of the convective Fisher equation, the time-delayed Burgers-Fisher equation, the Burgers-Fisher equation and a nonlinear dispersive-dissipative equation (Kakutani and Kawahara 1970 J. Phys. Soc. Japan 29 1068) are obtained through the factorization technique. All of them share the same type of factorization scheme, which reduces the original equation to a Riccati equation of the same kind, whose general solution is given in terms of Bessel and Neumann functions. In addition, some novel particular solutions of the nonlinear dispersive-dissipative equation are provided.
Detecting nonlinear acoustic waves in liquids with nonlinear dipole optical antennae
Maksymov, Ivan S
2015-01-01
Ultrasound is an important imaging modality for biological systems. High-frequency ultrasound can also (e.g., via acoustical nonlinearities) be used to provide deeply penetrating and high-resolution imaging of vascular structure via catheterisation. The latter is an important diagnostic in vascular health. Typically, ultrasound requires sources and transducers that are greater than, or of order the same size as the wavelength of the acoustic wave. Here we design and theoretically demonstrate that single silver nanorods, acting as optical nonlinear dipole antennae, can be used to detect ultrasound via Brillouin light scattering from linear and nonlinear acoustic waves propagating in bulk water. The nanorods are tuned to operate on high-order plasmon modes in contrast to the usual approach of using fundamental plasmon resonances. The high-order operation also gives rise to enhanced optical third-harmonic generation, which provides an important method for exciting the higher-order Fabry-Perot modes of the dipole...
NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER
Institute of Scientific and Technical Information of China (English)
菅永军; 鄂学全; 柏威
2003-01-01
In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode bysolving potential equations of water waves in a rigid circular cylinder, which is subject to avertical oscillation. It is assumed that the fluid in the circular cylindrical vessel is inviscid ,incompressible and the motion is irrotational, a nonlinear amplitude equation with cubicand vertically excited terms of the vessel was derived by expansion of two-time scales withoutconsidering the effect of surface tension. It is shown by numerical computation that differentfree surface standing wave patterns will be formed in different excited frequencies andamplitudes. The contours of free surface waves are agreed well with the experimental resultswhich were carried out several years ago.
Collapse of Nonlinear Gravitational Waves in Moving-Puncture Coordinates
Hilditch, David; Weyhausen, Andreas; Dietrich, Tim; Bruegmann, Bernd; Montero, Pedro J; Mueller, Ewald
2013-01-01
We study numerical evolutions of nonlinear gravitational waves in moving-puncture coordinates. We adopt two different types of initial data -- Brill and Teukolsky waves -- and evolve them with two independent codes producing consistent results. We find that Brill data fail to produce long-term evolutions for common choices of coordinates and parameters, unless the initial amplitude is small, while Teukolsky wave initial data lead to stable evolutions, at least for amplitudes sufficiently far from criticality. The critical amplitude separates initial data whose evolutions leave behind flat space from those that lead to a black hole. For the latter we follow the interaction of the wave, the formation of a horizon, and the settling down into a time-independent trumpet geometry. We explore the differences between Brill and Teukolsky data and show that for less common choices of the parameters -- in particular negative amplitudes -- Brill data can be evolved with moving-puncture coordinates, and behave similarly t...
Energy Technology Data Exchange (ETDEWEB)
Van Gorder, Robert A., E-mail: Robert.VanGorder@maths.ox.ac.uk [Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG (United Kingdom)
2015-09-15
In a recent paper, we give a study of the purely rotational motion of general stationary states in the two-dimensional local induction approximation (2D-LIA) governing superfluid turbulence in the low-temperature limit [B. Svistunov, “Superfluid turbulence in the low-temperature limit,” Phys. Rev. B 52, 3647 (1995)]. Such results demonstrated that variety of stationary configurations are possible from vortex filaments exhibiting purely rotational motion in addition to commonly discussed configurations such as helical or planar states. However, the filaments (or, more properly, waves along these filaments) can also exhibit translational motion along the axis of orientation. In contrast to the study on vortex configurations for purely rotational stationary states, the present paper considers non-stationary states which exhibit a combination of rotation and translational motions. These solutions can essentially be described as waves or disturbances which ride along straight vortex filament lines. As expected from our previous work, there are a number of types of structures that can be obtained under the 2D-LIA. We focus on non-stationary states, as stationary states exhibiting translation will essentially take the form of solutions studied in [R. A. Van Gorder, “General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation,” Phys. Fluids 26, 065105 (2014)], with the difference being translation along the reference axis, so that qualitative appearance of the solution geometry will be the same (even if there are quantitative differences). We discuss a wide variety of general properties of these non-stationary solutions and derive cases in which they reduce to known stationary states. We obtain various routes to Kelvin waves along vortex filaments and demonstrate that if the phase and amplitude of a disturbance both propagate with the same wave speed, then Kelvin waves will result. We also consider the self
2-D Composite Model for Numerical Simulations of Nonlinear Waves
Institute of Scientific and Technical Information of China (English)
2000-01-01
－ A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational region Ω is divided into two subregions. In the near-field around a structure, Ω2, the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulence closure model of k-ε equations and numerically solved by the improved VOF method; whereas in the subregion Ω1 (Ω1 = Ω - Ω2) the flow is governed by one-D Boussinesq equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundary of the two subregions. Numerical tests have been conducted for the case of wave propagation and interaction with a wave barrier. It is shown that the composite model can help perform efficient computation of nonlinear waves in a large region with the complicated flow fields near structures taken into account.
The Nonlinear Landau Damping Rate of a Driven Plasma Wave
Energy Technology Data Exchange (ETDEWEB)
Benisti, D; Strozzi, D J; Gremillet, L; Morice, O
2009-08-04
In this Letter, we discuss the concept of the nonlinear Landau damping rate, {nu}, of a driven electron plasma wave, and provide a very simple, practical, analytic formula for {nu} which agrees very well with results inferred from Vlasov simulations of stimulated Raman scattering. {nu} actually is more complicated an operator than a plain damping rate, and it may only be seen as such because it assumes almost constant values before abruptly dropping to 0. The decrease of {nu} to 0 is moreover shown to occur later when the wave amplitude varies in the direction transverse to its propagation.
Optimal Control Of Nonlinear Wave Energy Point Converters
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Zhou, Qiang; Kramer, Morten
2013-01-01
In this paper the optimal control law for a single nonlinear point absorber in irregular sea-states is derived, and proven to be a closed-loop controller with feedback from measured displacement, velocity and acceleration of the floater. However, a non-causal integral control component dependent...... idea behind the control strategy is to enforce the stationary velocity response of the absorber into phase with the wave excitation force at any time. The controller is optimal under monochromatic wave excitation. It is demonstrated that the devised causal controller, in plane irregular sea states......, absorbs almost the same power as the optimal controller....
Nonlinear electrostatic wave equations for magnetized plasmas - II
DEFF Research Database (Denmark)
Dysthe, K. B.; Mjølhus, E.; Pécseli, H. L.
1985-01-01
For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent (electrosta......For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent...... (electrostatic) cut-off implies that various cases must be considered separately, leading to equations with rather different properties. Various equations encountered previously in the literature are recovered as limiting cases....
Multisymplectic five-point scheme for the nonlinear wave equation
Institute of Scientific and Technical Information of China (English)
WANG Yushun; WANG Bin; YANG Hongwei; WANG Yunfeng
2003-01-01
In this paper, we introduce the multisymplectic structure of the nonlinear wave equation, and prove that the classical five-point scheme for the equation is multisymplectic. Numerical simulations of this multisymplectic scheme on highly oscillatory waves of the nonlinear Klein-Gordon equation and the collisions between kink and anti-kink solitons of the sine-Gordon equation are also provided. The multisymplectic schemes do not need to discrete PDEs in the space first as the symplectic schemes do and preserve not only the geometric structure of the PDEs accurately, but also their first integrals approximately such as the energy, the momentum and so on. Thus the multisymplectic schemes have better numerical stability and long-time numerical behavior than the energy-conserving scheme and the symplectic scheme.
Collapse of nonlinear electron plasma waves in a plasma layer
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.
Modulational development of nonlinear gravity-wave groups
Chereskin, T. K.; Mollo-Christensen, E.
1985-01-01
Observations of the development of nonlinear surface gravity-wave groups are presented, and the amplitude and phase modulations are calculated using Hilbert-transform techniques. With increasing propagation distance and wave steepness, the phase modulation develops local phase reversals whose locations correspond to amplitude minima or nodes. The concomitant frequency modulation develops jumps or discontinuities. The observations are compared with recent similar results for wavetrains. The observations are modelled numerically using the cubic nonlinear Schroedinger equation. The motivation is twofold: to examine quantitatively the evolution of phase as well as amplitude modulation, and to test the inviscid predictions for the asymptotic behavior of groups versus long-time observations. Although dissipation rules out the recurrence, there is a long-time coherence of the groups. The phase modulation is found to distinguish between dispersive and soliton behavior.
Application of the nonlinear vortex-lattice concept to aircraft-interference problems
Kandil, O. A.; Mook, D. T.; Nayfeh, A. H.
1976-01-01
A discrete-vortex model was developed to account for the hazardous effects of the vortex trail issued from the edges of separation of a large leading wing on a small trailing wing. The model is divided into three main parts: the leading wing and its near wake, the near and far wakes of the leading wing, and the trailing wing and the portion of the far wake in its vicinity. The normal force, pitching moment, and rolling moment coefficients for the trailing wing are calculated. The circulation distribution in the vortex trail is calculated in the first part of the model where the leading wing is far upstream and hence is considered isolated. A numerical example is solved to demonstrate the feasibility of using this method to study interference between aircraft. The numerical results show the correct trends: The following wing experiences a loss in lift between the wing-tip vortex systems of the leading wing, a gain outside this region, and strong rolling moments which can change sign as the lateral relative position changes. All the results are strongly dependent on the vertical relative position.
Current-vortex filament model of nonlinear Alfven perturbations in a finite-pressure plasma
Lakhin, V. P.; Schep, T. J.; Westerhof, E.
1998-01-01
A low-beta, two-fluid model is shown to possess solutions in the form of current-vortex filaments. The model can be viewed as that of reduced magnetohydrodynamics, extended with electron inertia, the Hall term and parallel electron pressure. These drift-Alfven filaments are the plasma analogs of poi
Adaptive modeling of shallow fully nonlinear gravity waves
Dutykh, Denys; Mitsotakis, Dimitrios
2014-01-01
This paper presents an extended version of the celebrated Serre-Green-Naghdi (SGN) system. This extension is based on the well-known Bona-Smith-Nwogu trick which aims to improve the linear dispersion properties. We show that in the fully nonlinear setting it results in modifying the vertical acceleration. Even if this technique is well-known, the effect of this modification on the nonlinear properties of the model is not clear. The first goal of this study is to shed some light on the properties of solitary waves, as the most important class of nonlinear permanent solutions. Then, we propose a simple adaptive strategy to choose the optimal value of the free parameter at every instance of time. This strategy is validated by comparing the model prediction with the reference solutions of the full Euler equations and its classical counterpart. Numerical simulations show that the new adaptive model provides a much better accuracy for the same computational complexity.
Numerical Simulation of Seabed Response and Liquefaction due to Non-linear Waves
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-feng; ZHANG Qing-he; HAN Tao; QIN Chong-ren
2005-01-01
Based on Biot's consolidation theory, a two-dimensional model for computation of the seabed response to waves is presented with the finite element method. Numerical results for different wave conditions are obtained, and the effects of wave non-linearity on the wave-induced seabed response are examined. Moreover, the wave-induced momentary liquefaction in uniform and inhomogeneous seabeds is investigated. It is shown that the wave non-linearity affects the distribution of the wave-induced pore pressure and effective stresses, while the influence of wave non-linearity on the seabed liquefaction potential is not so significant.
Institute of Scientific and Technical Information of China (English)
周涛; 朱乐东; 郭震山
2011-01-01
利用涡激共振竖向位移响应,基于广义谐波函数KBM法并引入缓变参数的概念,对Scanlan经验非线性模型进行处理,识别其中的气动参数,并得到Seanlan非线性涡激力.对识别得到的Scanlan非线性涡激力,分别通过:用Newmarkβ反求响应与实测响应进行比较;与从大平同步测得的合力中提取出实测的涡激力进行比较,对识别精度做出评价.试验是在同济大学TJ-1号风洞均匀流场中进行的,以象山港大桥初始设计阶段节段模型为例,用激光位移计采集模型的位移响应,并用一维梁式应变测力天平同步采集模型所受的力.%Aerodynamic parameters of Scanlan' s nonlinear empirical model were identified by using the data of vertical vortex response. Based on the generalized harmonic wave functionH KBM method and under the presupposition of slowly varying parameters, the function of Scanlan' s nonlinear empirical model was solved. And then the aerodynamic parameters of the model and the Scanlan' s nonlinear vortex-induced force were identified. The identification precision was evaluated via the following two methods: the response calculated according to the Newmark β method was compared with the field measured response; and the self-excited VIV force extracted from the total force collected by the one-dimensional balances was compared with the field measured exciting force. The experiment was carried out in TJ-1 wind tunnel of Tongji University using the preliminarily designed section model of Xiangshangang bridge. The vertical response of the section model was collected by the laser displacement sensor, and meanwhile the total force was collected by beam-type strain force balances of one-dimension.
Solitary wave solutions to nonlinear evolution equations in mathematical physics
Indian Academy of Sciences (India)
Anwar Ja’afar Mohamad Jawad; M Mirzazadeh; Anjan Biswas
2014-10-01
This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.
SINGULAR AND RAREFACTIVE SOLUTIONS TO A NONLINEAR VARIATIONAL WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Following a recent paper of the authors in Communications in Partial Differential Equations, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed conditions on the initial data so that the solutions can contain singularities (blow-up). Propagation of local oscillations along one family of characteristics remains under control despite singularity formation in the other family of characteristics.
Energy Technology Data Exchange (ETDEWEB)
Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg [School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Zhou, Yu [Advanced Remanufacturing and Technology Center (ARTC), 3 Clean Tech Loop, CleanTech Two, Singapore 637143 (Singapore)
2016-07-15
Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonant frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.
Quantum corrections to nonlinear ion acoustic wave with Landau damping
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, Abhik; Janaki, M. S. [Saha Institute of Nuclear Physics, Calcutta (India); Bose, Anirban [Serampore College, West Bengal (India)
2014-07-15
Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.
Fried, Jasper P.; Fangohr, Hans; Kostylev, Mikhail; Metaxas, Peter J.
2016-12-01
We have performed micromagnetic simulations of low-amplitude gyrotropic dynamics of magnetic vortices in the presence of spatially uniform out-of-plane magnetic fields. For disks having small lateral dimensions, we observe a frequency drop-off when approaching the disk's out-of-plane saturation field. This nonlinear frequency response is shown to be associated with a vortex core deformation driven by nonuniform demagnetizing fields that act on the shifted core. The deformation results in an increase in the average out-of-plane magnetization of the displaced vortex state (contrasting the effect of gyrofield-driven deformation at low field), which causes the exchange contribution to the vortex stiffness to switch from positive to negative. This generates an enhanced reduction of the core stiffness at high field, leading to a nonlinear field dependence of the gyrotropic mode frequency.
Energy Technology Data Exchange (ETDEWEB)
Hayashi, Nobuhiko, E-mail: n-hayashi@21c.osakafu-u.ac.jp [NanoSquare Research Center (N2RC), Osaka Prefecture University, 1-2 Gakuen-cho, Naka-ku, Sakai 599-8570 (Japan); CREST(JST), 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan); Higashi, Yoichi [NanoSquare Research Center (N2RC), Osaka Prefecture University, 1-2 Gakuen-cho, Naka-ku, Sakai 599-8570 (Japan); Department of Mathematical Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531 (Japan); CREST(JST), 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan); Nakai, Noriyuki; Suematsu, Hisataka [NanoSquare Research Center (N2RC), Osaka Prefecture University, 1-2 Gakuen-cho, Naka-ku, Sakai 599-8570 (Japan); CREST(JST), 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan)
2013-01-15
Highlights: ► We study non-magnetic impurity effect on a vortex in moderately clean regime. ► Impurity effect on s-wave vortex core in unitary limit is weaker than in Born one. ► Kramer–Pesch vortex core shrinkage is stronger in unitary limit than in Born one. -- Abstract: We theoretically investigate a non-magnetic impurity effect on the temperature dependence of the vortex core shrinkage (Kramer–Pesch effect) in a single-band s-wave superconductor. The Born limit and the unitary limit scattering are compared within the framework of the quasiclassical theory of superconductivity. We find that the impurity effect inside a vortex core in the unitary limit is weaker than in the Born one when a system is in the moderately clean regime, which results in a stronger core shrinkage in the unitary limit than in the Born one.
Nonlinear dynamic analysis of traveling wave-type ultrasonic motors.
Nakagawa, Yosuke; Saito, Akira; Maeno, Takashi
2008-03-01
In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.
Identification and determination of solitary wave structures in nonlinear wave propagation
Energy Technology Data Exchange (ETDEWEB)
Newman, W.I.; Campbell, D.K.; Hyman, J.M.
1991-01-01
Nonlinear wave phenomena are characterized by the appearance of solitary wave coherent structures'' traveling at speeds determined by their amplitudes and morphologies. Assuming that these structures are briefly noninteracting, we propose a method for the identification of the number of independent features and their respective speeds. Using data generated from an exact two-soliton solution to the Korteweg-de-Vries equation, we test the method and discuss its strengths and limitations. 41 refs., 2 figs.
Spectrograms of ship wakes: identifying linear and nonlinear wave signals
Pethiyagoda, Ravindra; Moroney, Timothy J
2016-01-01
A spectrogram is a useful way of using short-time discrete Fourier transforms to visualise surface height measurements taken of ship wakes in real world conditions. For a steadily moving ship that leaves behind small-amplitude waves, the spectrogram is known to have two clear linear components, a sliding-frequency mode caused by the divergent waves and a constant-frequency mode for the transverse waves. However, recent observations of high speed ferry data have identified three additional components of the spectrograms that are not yet explained. We use computer simulations of linear and nonlinear ship wave patterns and apply time-frequency analysis to generate spectrograms for an idealised ship. We clarify the role of the linear dispersion relation and ship speed on the two linear components. Further, we show that additional features in the experimental data are caused by nonlinearity. Finally, we explain a discrepancy between the high speed ferry spectrograms and linear theory by accounting for ship acceler...
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Energy Technology Data Exchange (ETDEWEB)
Lepri, Stefano, E-mail: stefano.lepri@isc.cnr.it [Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Pikovsky, Arkady [Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str 24/25, Potsdam (Germany); Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
Nonlinear Propagation of Planet-Generated Tidal Waves
Rafikov, R. R.
2002-01-01
The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to shock formation and wake dissipation, is followed in the weakly nonlinear regime. The 2001 local approach of Goodman and Rafikov is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process spanning a significant fraction of the disk. Torques induced by the planet could be significant drivers of disk evolution on timescales of approx. 10(exp 6)-10(exp 7) yr, even in the absence of strong background viscosity. A global prescription for angular momentum deposition is developed that could be incorporated into the study of gap formation in a gaseous disk around the planet.
Nonlinear propagation of planet-generated tidal waves
Rafikov, R R
2002-01-01
The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to the shock formation and wake dissipation, is followed in the weakly nonlinear regime. The local approach of Goodman & Rafikov (2001) is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process spanning a significant fraction of the disk. Torques induced by the planet could be significant drivers of disk evolution on timescales of the order 1-10 Myr even in the absence of strong background viscosity. A global prescription for angular momentum deposition is developed which could be incorporated into the study of gap formation in a gaseous disk around the planet.
New Relativistic Effects in the Dynamics of Nonlinear Hydrodynamical Waves
Rezzolla, L
2002-01-01
In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity. When the fluid is allowed to relax, one of three possible wave-patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a special relativistic Riemann problem when velocities tangential to the initial discontinuity surface are present. We show that a smooth transition from one wave-pattern to another can be produced by varying the initial tangential velocities while otherwise maintaining the initial states unmodified. These special relativistic effects are produced by the coupling through the relativistic Lorentz factors and do not have a Newtonian counterpart.
Nonlinear electromagnetic waves in a degenerate electron-positron plasma
Energy Technology Data Exchange (ETDEWEB)
El-Labany, S.K., E-mail: skellabany@hotmail.com [Department of Physics, Faculty of Science, Damietta University, New Damietta (Egypt); El-Taibany, W.F., E-mail: eltaibany@hotmail.com [Department of Physics, College of Science for Girls in Abha, King Khalid University, Abha (Saudi Arabia); El-Samahy, A.E.; Hafez, A.M.; Atteya, A., E-mail: ahmedsamahy@yahoo.com, E-mail: am.hafez@sci.alex.edu.eg, E-mail: ahmed_ateya2002@yahoo.com [Department of Physics, Faculty of Science, Alexandria University, Alexandria (Egypt)
2015-08-15
Using the reductive perturbation technique (RPT), the nonlinear propagation of magnetosonic solitary waves in an ultracold, degenerate (extremely dense) electron-positron (EP) plasma (containing ultracold, degenerate electron, and positron fluids) is investigated. The set of basic equations is reduced to a Korteweg-de Vries (KdV) equation for the lowest-order perturbed magnetic field and to a KdV type equation for the higher-order perturbed magnetic field. The solutions of these evolution equations are obtained. For better accuracy and searching on new features, the new solutions are analyzed numerically based on compact objects (white dwarf) parameters. It is found that including the higher-order corrections results as a reduction (increment) of the fast (slow) electromagnetic wave amplitude but the wave width is increased in both cases. The ranges where the RPT can describe adequately the total magnetic field including different conditions are discussed. (author)
Probabilistic approach to nonlinear wave-particle resonant interaction
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2017-02-01
In this paper we provide a theoretical model describing the evolution of the charged-particle distribution function in a system with nonlinear wave-particle interactions. Considering a system with strong electrostatic waves propagating in an inhomogeneous magnetic field, we demonstrate that individual particle motion can be characterized by the probability of trapping into the resonance with the wave and by the efficiency of scattering at resonance. These characteristics, being derived for a particular plasma system, can be used to construct a kinetic equation (or generalized Fokker-Planck equation) modeling the long-term evolution of the particle distribution. In this equation, effects of charged-particle trapping and transport in phase space are simulated with a nonlocal operator. We demonstrate that solutions of the derived kinetic equations agree with results of test-particle tracing. The applicability of the proposed approach for the description of space and laboratory plasma systems is also discussed.
Analytical description of nonlinear acoustic waves in the solar chromosphere
Litvinenko, Yuri E.; Chae, Jongchul
2017-02-01
Aims: Vertical propagation of acoustic waves of finite amplitude in an isothermal, gravitationally stratified atmosphere is considered. Methods: Methods of nonlinear acoustics are used to derive a dispersive solution, which is valid in a long-wavelength limit, and a non-dispersive solution, which is valid in a short-wavelength limit. The influence of the gravitational field on wave-front breaking and shock formation is described. The generation of a second harmonic at twice the driving wave frequency, previously detected in numerical simulations, is demonstrated analytically. Results: Application of the results to three-minute chromospheric oscillations, driven by velocity perturbations at the base of the solar atmosphere, is discussed. Numerical estimates suggest that the second harmonic signal should be detectable in an upper chromosphere by an instrument such as the Fast Imaging Solar Spectrograph installed at the 1.6-m New Solar Telescope of the Big Bear Observatory.
Nonlinear Electromagnetic Waves in a Degenerate Electron-Positron Plasma
El-Labany, S. K.; El-Taibany, W. F.; El-Samahy, A. E.; Hafez, A. M.; Atteya, A.
2015-08-01
Using the reductive perturbation technique (RPT), the nonlinear propagation of magnetosonic solitary waves in an ultracold, degenerate (extremely dense) electron-positron (EP) plasma (containing ultracold, degenerate electron, and positron fluids) is investigated. The set of basic equations is reduced to a Korteweg-de Vries (KdV) equation for the lowest-order perturbed magnetic field and to a KdV type equation for the higher-order perturbed magnetic field. The solutions of these evolution equations are obtained. For better accuracy and searching on new features, the new solutions are analyzed numerically based on compact objects (white dwarf) parameters. It is found that including the higher-order corrections results as a reduction (increment) of the fast (slow) electromagnetic wave amplitude but the wave width is increased in both cases. The ranges where the RPT can describe adequately the total magnetic field including different conditions are discussed.
Institute of Scientific and Technical Information of China (English)
WEI Ke; CHEN Wen
2012-01-01
Using ECWMF ERA-40 and Interim reanalysis data, the planetary wave fluxes associated with the February extreme stratospheric polar vortex were studied. Using the three-dimensional Eliassen-Palm （EP） flux as a measure of the wave activity propagation, the authors show that the unusual warm years in the Arctic feature an anomalous weak stratosphere-troposphere coupling and weak downward wave flux at the lower stratosphere, especially over the North America and North Atlantic （NANA） region. The extremely cold years are characterized by strong stratosphere-troposphere coupling and strong downward wave flux in this region. The refractive index is used to examine the conception of planetary wave reflection, which shows a large refractive index （low reflection） for the extremely warm years and a small refractive index （high reflection） for the extremely cold years. This study reveals the importance of the downward planetary wave propagation from the stratosphere to the troposphere for explaining the unusual state of the stratospheric polar vortex in February.
Irregular Wave Forces on Monopile Foundations. Effect af Full Nonlinearity and Bed Slope
DEFF Research Database (Denmark)
Schløer, Signe; Bredmose, Henrik; Bingham, Harry B.
2011-01-01
Forces on a monopile from a nonlinear irregular unidirectional wave model are investigated. Two seabed profiles of different slopes are considered. Morison’s equation is used to investigate the forcing from fully nonlinear irregular waves and to compare the results with those obtained from linear...... wave theory and with stream function wave theory. The latter of these theories is only valid on a flat bed. The three predictions of wave forces are compared and the influence of the bed slope is investigated. Force-profiles of two selected waves from the irregular wave train are further compared...... with the corresponding forceprofiles from stream function theory. The results suggest that the nonlinear irregular waves give rise to larger extreme wave forces than those predicted by linear theory and that a steeper bed slope increases the wave forces both for linear and nonlinear waves. It is further found...
Feng, Q S; Wang, Q; Zheng, C Y; Liu, Z J; Cao, L H; He, X T
2016-01-01
The properties of the nonlinear frequency shift (NFS) especially the fluid NFS from the harmonic generation of the ion-acoustic wave (IAW) in multi-ion species plasmas have been researched by Vlasov simulation. The pictures of the nonlinear frequency shift from harmonic generation and particles trapping are shown to explain the mechanism of NFS qualitatively. The theoretical model of the fluid NFS from harmonic generation in multi-ion species plasmas is given and the results of Vlasov simulation are consistent to the theoretical result of multi-ion species plasmas. When the wave number $k\\lambda_{De}$ is small, such as $k\\lambda_{De}=0.1$, the fluid NFS dominates in the total NFS and will reach as large as nearly $15\\%$ when the wave amplitude $|e\\phi/T_e|\\sim0.1$, which indicates that in the condition of small $k\\lambda_{De}$, the fluid NFS dominates in the saturation of stimulated Brillouin scattering especially when the nonlinear IAW amplitude is large.
Nonlinear Wave-Currents interactions in shallow water
Lannes, David
2015-01-01
We study here the propagation of long waves in the presence of vorticity. In the irrotational framework, the Green-Naghdi equations (also called Serre or fully nonlinear Boussinesq equations) are the standard model for the propagation of such waves. These equations couple the surface elevation to the vertically averaged horizontal velocity and are therefore independent of the vertical variable. In the presence of vorticity, the dependence on the vertical variable cannot be removed from the vorticity equation but it was however shown in [?] that the motion of the waves could be described using an extended Green-Naghdi system. In this paper we propose an analysis of these equations, and show that they can be used to get some new insight into wave-current interactions. We show in particular that solitary waves may have a drastically different behavior in the presence of vorticity and show the existence of solitary waves of maximal amplitude with a peak at their crest, whose angle depends on the vorticity. We als...
LES of shock wave/turbulent boundary layer interaction affected by microramp vortex generators
Joly, Laurent; Grebert, Arnaud; Jamme, Stéphane; Bodart, Julien; Aerodynamics, Energetics; Propulsion Dep. Team
2016-11-01
At large Mach numbers, the interaction of an oblique shock wave with a turbulent boundary layer (SWTBLI) developing over a flat plate gives rise to a separation bubble known to exhibit low-frequency streamwise oscillations around StL = 0 . 03 (a Strouhal number based on the separated region length). Because these oscillations yield wall pressure or load fluctuations, efforts are made to reduce their amplitude. We perform large eddy simulations to reproduce the experiments by Wang etal (2012) where a rake of microramp vortex generators (MVGs) were inserted upstream the SWTBLI with consequences yet to be fully understood. There is no consensus on the flow structure downstream MVGs and this is first clarified in the case of MVGs protruding by 0 . 47 δ in a TBL at Mach number M = 2 . 7 and Reynolds number Reθ = 3600 . Large-scale vortices intermittently shed downstream the MVGs are characterized by a streamwise period close to twice the TBL thickness and a frequency f 0 . 5Ue / δ , two orders of magnitude higher than the one of the uncontrolled SWTBLI. We then characterize the interaction between the unsteady wake of the MVGs with the SWTBLI resulting in the reduction of the interaction length and the high-frequency modulation of the shock feet motions.
Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media
Luna, Manuel
2011-05-01
Solitary wave formation is a well studied nonlinear phenomenon arising in propagation of dispersive nonlinear waves under suitable conditions. In non-homogeneous materials, dispersion may happen due to effective reflections between the material interfaces. This dispersion has been used along with nonlinearities to find solitary wave formation using the one-dimensional p-system. These solitary waves are called stegotons. The main goal in this work is to find two-dimensional stegoton formation. To do so we consider the nonlinear two-dimensional p-system with variable coefficients and solve it using finite volume methods. The second goal is to obtain effective equations that describe the macroscopic behavior of the variable coefficient system by a constant coefficient one. This is done through a homogenization process based on multiple-scale asymptotic expansions. We compare the solution of the effective equations with the finite volume results and find a good agreement. Finally, we study some stability properties of the homogenized equations and find they and one-dimensional versions of them are unstable in general.
New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schr(o)dinger Equation
Institute of Scientific and Technical Information of China (English)
YANG Qin; DAI Chao-Qing; ZHANG Jie-Fang
2005-01-01
Some new exact travelling wave and period solutions of discrete nonlinear Schrodinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differentialdifferent models.
Excitation of nonlinear ion acoustic waves in CH plasmas
Feng, Q S; Liu, Z J; Xiao, C Z; Wang, Q; He, X T
2016-01-01
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\\lambda_{De} $ 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 $k\\lambda_{De}$ increasing. When $k\\lambda_{De}$ is not large, such as $k\\lambda_{De}=0.1, 0.3, 0.5$, the nonlinear IAW can be excited by the driver with the linear frequency of the modes. However, when $k\\lambda_{De}$ is large, such as $k\\lambda_{De}=0.7$, the linear ...
Nonlinear electrostatic waves in inhomogeneous dense dusty magnetoplasmas
Energy Technology Data Exchange (ETDEWEB)
Mahmood, S., E-mail: shahzad_mahmoodpk@yahoo.co [Theoretical Plasma Physics Division, PINSTECH, P.O. Nilore, Islamabad (Pakistan); Haque, Q. [Theoretical Plasma Physics Division, PINSTECH, P.O. Nilore, Islamabad (Pakistan)
2010-01-25
The nonlinear electrostatic drift waves are studied using quantum hydrodynamic model in dusty quantum magnetoplasmas. The dissipative effects due to collisions between ions and dust particles have also been taken into account. The Korteweg-de Vries Burgers (KdVB) like equation is derived and analytical solution is obtained using tanh method. The limiting cases of KdV type solitary waves, Burger type monotonic shock waves and oscillatory shock solutions are also presented. It is found that both hump and dip type solitary structures are possible in quantum dusty plasmas. However, amplitude and width of the nonlinear structure depend on the dust charge polarity and its concentration in electron-ion quantum plasmas. The monotonic shock like structure is independent of the quantum parameter. It is found that shock strength is increased in the presence of positively charged particles in comparison with negatively charged dust particles. The oscillatory shock structures are also obtained and it is found that change in dust charge polarity only shifts the phase of the oscillatory shock in plasmas. The numerical results are also presented for illustration.
Rotation-induced nonlinear wavepackets in internal waves
Energy Technology Data Exchange (ETDEWEB)
Whitfield, A. J., E-mail: ashley.whitfield.12@ucl.ac.uk; Johnson, E. R., E-mail: e.johnson@ucl.ac.uk [Department of Mathematics, University College London, London WC1E 6BT (United Kingdom)
2014-05-15
The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets. It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.
Rotation-induced nonlinear wavepackets in internal waves
Whitfield, A. J.; Johnson, E. R.
2014-05-01
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.
Enhanced continuous-wave four-wave mixing efficiency in nonlinear AlGaAs waveguides.
Apiratikul, Paveen; Wathen, Jeremiah J; Porkolab, Gyorgy A; Wang, Bohan; He, Lei; Murphy, Thomas E; Richardson, Christopher J K
2014-11-03
Enhancements of the continuous-wave four-wave mixing conversion efficiency and bandwidth are accomplished through the application of plasma-assisted photoresist reflow to reduce the sidewall roughness of sub-square-micron-modal area waveguides. Nonlinear AlGaAs optical waveguides with a propagation loss of 0.56 dB/cm demonstrate continuous-wave four-wave mixing conversion efficiency of -7.8 dB. Narrow waveguides that are fabricated with engineered processing produce waveguides with uncoated sidewalls and anti-reflection coatings that show group velocity dispersion of +0.22 ps²/m. Waveguides that are 5-mm long demonstrate broadband four-wave mixing conversion efficiencies with a half-width 3-dB bandwidth of 63.8-nm.
Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media
Directory of Open Access Journals (Sweden)
Maxim A. Molchan
2007-08-01
Full Text Available On the basis of the competing cubic-quintic nonlinearity model, stability (instability of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the Gaussian white noise. It is shown that for different response functions of a medium nonlocality suppresses, as a rule, both the growth rate peak and bandwidth of instability caused by random parameters. At the same time, for a special form of the response functions there can be an ''anomalous'' subjection of nonlocality to the instability development which leads to further increase of the growth rate. Along with the second-order moments of the modulational amplitude, higher-order moments are taken into account.
Beach steepness effects on nonlinear infragravity-wave interactions : A numerical study
de Bakker, A. T M; Tissier, M. F S; Ruessink, B. G.
2016-01-01
The numerical model SWASH is used to investigate nonlinear energy transfers between waves for a diverse set of beach profiles and wave conditions, with a specific focus on infragravity waves. We use bispectral analysis to study the nonlinear triad interactions, and estimate energy transfers to deter
Nonlinear acoustic waves in a collisional self-gravitating dusty plasma
Institute of Scientific and Technical Information of China (English)
Guo Zhi-Rong; Yang Zeng-Qiang; Yin Bao-Xiang; Sun Mao-Zhu
2010-01-01
Using the reductive perturbation method,we investigate the small amplitude nonlinear acoustic wave in a collisional self-gravitating dusty plasma.The result shows that the small amplitude dust acoustic wave can be expressed by a modified Korteweg-de Vries equation,and the nonlinear wave is instable because of the collisions between the neutral gas molecules and the charged particles.
Effect of scalar nonlinearity on zonal flow generation by Rossby waves
Mikhailovskii, A. B.; Lominadze, J. G.; Erokhin, N. N.; Erokhin, N. S.; Smolyakov, A. I.; Tsypin, V. S.
2007-01-01
Effects of scalar nonlinearity on the generation of zonal flow by Rossby waves in shallow rotating fluid are considered. Zonal flows are generated via the action of Reynolds stress due to vector nonlinearity together with the effects of scalar nonlinearity. It is shown that the scalar nonlinearity r
Optical Multi-hysteresises and "Rogue Waves" in Nonlinear Plasma
Kaplan, A E
2010-01-01
An overdense plasma layer irradiated by an intense light can exhibit dramatic nonlinear-optical effects due to a relativistic mass-effect of free electrons: highly-multiple hysteresises of reflection and transition, and emergence of gigantic "rogue waves". Those are trapped quasi-soliton field spikes inside the layer, sustained by an incident radiation with a tiny fraction of their peak intensity once they have been excited by orders of magnitude larger pumping. The phenomenon persists even in the layers with "soft" boundaries, as well as in a semi-infinite plasma with low absorption.
Exact travelling wave solutions of nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish) Suez Canal University, AL-Arish 45111 (Egypt)]. E-mail: asoliman_99@yahoo.com; Abdou, M.A. [Theoretical Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-04-15
An extended Fan-sub equation method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. The key idea of this method is to take full advantage of the general elliptic equation, involving five parameters, which has more new solutions and whose degeneracies can lead to special sub equation involving three parameters. As an illustration of the extended Fan method, more new solutions are obtained for three models namely, generalized KdV, Drinfeld-Sokolov system and RLW equation.
Fourth order wave equations with nonlinear strain and source terms
Liu, Yacheng; Xu, Runzhang
2007-07-01
In this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms. First we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions. Then we obtain a threshold result of global existence and nonexistence. Finally we discuss the global existence of solutions for the problem with critical initial condition I(u0)[greater-or-equal, slanted]0, E(0)=d. So the Esquivel-Avila's results are generalized and improved.
Critical exponent for damped wave equations with nonlinear memory
Fino, Ahmad
2010-01-01
We consider the Cauchy problem in $\\mathbb{R}^n,$ $n\\geq 1,$ for a semilinear damped wave equation with nonlinear memory. Global existence and asymptotic behavior as $t\\to\\infty$ of small data solutions have been established in the case when $1\\leq n\\leq3.$ Moreover, we derive a blow-up result under some positive data for in any dimensional space. It turns out that the critical exponent indeed coincides with the one to the corresponding semilinear heat equation.
Azimuthal and radial shaping of vortex beams generated in twisted nonlinear photonic crystals.
Shemer, Keren; Voloch-Bloch, Noa; Shapira, Asia; Libster, Ana; Juwiler, Irit; Arie, Ady
2013-12-15
We experimentally demonstrate that the orbital angular momentum (OAM) of a second harmonic (SH) beam, generated within twisted nonlinear photonic crystals, depends both on the OAM of the input pump beam and on the quasi-angular momentum of the crystal. In addition, when the pump's radial index is zero, the radial index of the SH beam is equal to that of the nonlinear crystal. Furthermore, by mixing two noncollinear pump beams in this crystal, we generate, in addition to the SH beams, a new "virtual beam" having multiple values of OAM that are determined by the nonlinear process.
High-order finite difference solution for 3D nonlinear wave-structure interaction
DEFF Research Database (Denmark)
Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter;
2010-01-01
This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme...... OceanWave3D presented in [1, 2]. A nonlinear decomposition of the solution into incident and scattered fields is used to increase the efficiency of the wave-structure interaction problem resolution. Application of the method to the diffraction of nonlinear waves around a fixed, bottom mounted circular...
Theoretical Study of Wave Breaking for Nonlinear Water Waves Propagating on a Sloping Bottom
Chen, Y. Y.; Hsu, H. C.; Li, M. S.
2012-04-01
In this paper, a third-order asymptotic solution in a Lagrangian framework describing nonlinear water wave propagation on the surface of a uniform sloping bottom is presented. A two-parameter perturbation method is used to develop a new mathematical derivation. The particle trajectories, wave pressure and Lagrangian velocity potential are obtained as a function of the nonlinear wave steepness and the bottom slope perturbed to third order. This theoretical solution in Lagrangian form satisfies state of the normal pressure at the free surface. The condition of the conservation of mass flux is examined in detail for the first time. The two important properties in Lagrangian coordinates, Lagrangian wave frequency and Lagrangian mean level, are included in the third-order solution. The solution can also be used to estimate the mean return current for waves progressing over the sloping bottom. The Lagrangian solution untangle the description of the features of wave shoaling in the direction of wave propagation from deep to shallow water, as well as the process of successive deformation of a wave profile and water particle trajectories leading to wave breaking. A series of experiment was conducted to validate the obtained theoretical solution. The proposed solution will be used to determine the wave shoaling and breaking process and the comparisons between the experimental and theoretical results are excellent. For example, the variations of phase velocity on sloping bottom are obtained by 7 set of two close wave gauges and the theoretical result could accurately predict the measured phase velocity. The theoretical wave breaking index can be derived by use of the kinematic stability parameter (K.P.S). The comparisons between the theory, experiment (present study, Iwagali et al.(1974), Deo et al.(2003) and Tsai et al.(2005)) and empirical formula of Goda (2004) for the breaking index(u/C) versus the relative water depth(d/L) under two different bottom slopes shows that the
Periodic Wave Solutions of Generalized Derivative Nonlinear Schr(o)dinger Equation
Institute of Scientific and Technical Information of China (English)
ZHA Qi-Lao; LI Zhi-Bin
2008-01-01
A Darboux transformation of the generalized derivative nonlinear Schr(o)dinger equation is derived. As an application, some new periodic wave solutions of the generalized derivative nonlinear Schr(o)dinger equation are explicitly given.
On global attraction to stationary states for wave equations with concentrated nonlinearities
Kopylova, E.
2016-01-01
The global attraction to stationary states is established for solutions to 3D wave equations with concentrated nonlinearities: each finite energy solution converges as $t\\to\\pm\\infty$ to stationary states. The attraction is caused by nonlinear energy radiation.
Nonlinear dynamics of soliton gas with application to "freak waves"
Shurgalina, Ekaterina
2017-04-01
So-called "integrable soliton turbulence" attracts much attention of scientific community nowadays. We study features of soliton interactions in the following integrable systems: Korteweg - de Vries equation (KdV), modified Korteweg - de Vries equation (mKdV) and Gardner equations. The polarity of interacted solitons dramatically influences on the process of soliton interaction. Thus if solitons have the same polarity the maximum of the wave field decreases during the process of nonlinear interactions as well statistical moments (skewness and kurtosis). In this case there is no abnormally large wave formation and this scenario is possible for all considered equation. Completely different results can be obtained for a soliton gas consisted of solitons with different polarities: such interactions lead to an increase of resulting impulse and kurtosis. Tails of distribution functions can grow significantly. Abnormally large waves (freak waves) appear in such solitonic fields. Such situations are possible just in case of mKdV and Gardner equations which admit the existence of bipolar solitons. New effect of changing a defect's moving direction in soliton lattices and soliton gas is found in the present study. Manifestation of this effect is possible as the result of negative phase shift of small soliton in the moment of nonlinear interaction with large solitons. It is shown that the effect of negative velocity is the same for KdV and mKdV equations and it can be found from the kinematic assumption without applying the kinetic theory. Averaged dynamics of the "smallest" soliton (defect) in a soliton gas, consisting of solitons with random amplitudes is investigated. The averaged criterion of velocity sign change confirmed by numerical simulation is obtained.
Nonlinear interactions of electromagnetic waves with the auroral ionosphere
Wong, Alfred Y.
1999-09-01
The ionosphere provides us with an opportunity to perform plasma experiments in an environment with long confinement times, very large-scale lengths, and no confining walls. The auroral ionosphere with its nearly vertical magnetic field geometry is uniquely endowed with large amount of free energy from electron and ion precipitation along the magnetic field and mega-ampere current across the magnetic field. To take advantage of this giant outdoor laboratory, two facilities HAARP and HIPAS, with frequencies ranging from the radio to optical bands, are now available for active probing of and interaction with this interesting region. The ponderomotive pressures from the self-consistent wave fields have produced significant local perturbations of density and particle distributions at heights where the incident EM frequency matches a plasma resonance. This paper will review theory and experiments covering the nonlinear phenomena of parametric decay instability to wave collapse processes. At HF frequencies plasma lenses can be created by preconditioning pulses to focus what is a normally divergent beam into a high-intensity spot to further enhance nonlinear phenomena. At optical wavelengths a large rotating liquid metal mirror is used to focus laser pulses up to a given height. Such laser pulses are tuned to the same wavelengths of selected atomic and molecular resonances, with resulting large scattering cross sections. Ongoing experiments on dual-site experiments and excitation of ELF waves will be presented. The connection of such basic studies to environmental applications will be discussed. Such applications include the global communication using ELF waves, the ozone depletion and remediation and the control of atmospheric CO2 through the use of ion cyclotron resonant heating.
Mitri, F G
2016-09-01
Energy and angular momentum flux density characteristics of an optical nondiffracting nonparaxial vector Bessel vortex beam of fractional order are examined based on the dual-field method for the generation of symmetric electric and magnetic fields. Should some conditions determined by the polarization state, the half-cone angle as well as the beam-order (or topological charge) be met, the axial energy and angular momentum flux densities vanish (representing Poynting singularities), before they become negative. These negative counterintuitive properties suggest retrograde (negative) propagation as well as a rotation reversal of the angular momentum with respect to the beam handedness. These characteristics of nondiffracting nonparaxial Bessel fractional vortex beams of progressive waves open new capabilities in optical tractor beam tweezers, optical spanners, invisibility cloaks, optically engineered metamaterials, and other applications.
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich
2011-01-01
A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves...
Energy Technology Data Exchange (ETDEWEB)
Tsuchiya, T. [Dia Consultants Company, Tokyo (Japan)
1996-10-01
Nonlinear full-wave tomography (FWT) is under investigation to improve the estimation accuracy of Vp/Vs distributions. Full-wave tomography is one of the underground structure exploration methods mainly using Tarantola`s nonlinear local optimization method (LOM). Numerical experiment for FWT was carried out assuming relatively weak nonlinear underground structure. In the case of inversion by local optimization method, adequate preconditioning is important. Utilization of geological information is also effective in estimating low-frequency components of a model. As far as data are obtained under proper observation arrangement, even in actual field, precise estimation of Vp/Vs distributions is possible by FWT using explosion in a hole as wave source. In full-wave tomography, selection of observation arrangement is essential for both Vp and Vs. However, the proper arrangement is different between Vp and Vs. Approach to different analyses for Vp and Vs is also necessary by using only proper data for Vp and Vs among obtained data sets. 4 figs.
2D wave-front shaping in optical superlattices using nonlinear volume holography.
Yang, Bo; Hong, Xu-Hao; Lu, Rong-Er; Yue, Yang-Yang; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan
2016-07-01
Nonlinear volume holography is employed to realize arbitrary wave-front shaping during nonlinear processes with properly designed 2D optical superlattices. The concept of a nonlinear polarization wave in nonlinear volume holography is investigated. The holographic imaging of irregular patterns was performed using 2D LiTaO3 crystals with fundamental wave propagating along the spontaneous polarization direction, and the results agree well with the theoretical predictions. This Letter not only extends the application area of optical superlattices, but also offers an efficient method for wave-front shaping technology.
On the Amplitude Equations for Weakly Nonlinear Surface Waves
Benzoni-Gavage, Sylvie; Coulombel, Jean-François
2012-09-01
Nonlocal generalizations of Burgers' equation were derived in earlier work by Hunter (Contemp Math, vol 100, pp 185-202. AMS, 1989), and more recently by Benzoni-Gavage and Rosini (Comput Math Appl 57(3-4):1463-1484, 2009), as weakly nonlinear amplitude equations for hyperbolic boundary value problems admitting linear surface waves. The local-in-time well-posedness of such equations in Sobolev spaces was proved by Benzoni-Gavage (Differ Integr Equ 22(3-4):303-320, 2009) under an appropriate stability condition originally pointed out by Hunter. The same stability condition has also been shown to be necessary for well-posedness in Sobolev spaces in a previous work of the authors in collaboration with Tzvetkov (Benzoni-Gavage et al. in Adv Math 227(6):2220-2240, 2011). In this article, we show how the verification of Hunter's stability condition follows from natural stability assumptions on the original hyperbolic boundary value problem, thus avoiding lengthy computations in each particular situation. We also show that the resulting amplitude equation has a Hamiltonian structure when the original boundary value problem has a variational origin. Our analysis encompasses previous equations derived for nonlinear Rayleigh waves in elasticity.
Recent progress in nonlinear kinetic Alfvén waves
Directory of Open Access Journals (Sweden)
D. J. Wu
2004-01-01
Full Text Available This paper presents a review of recent progress in nonlinear kinetic Alfvén wave (KAW hereafter. We start with the two-fluid theory of KAWs and show how the difference between the motions of electrons and ions in small-scale fields of KAWs modifies the Alfvén wave properties. Then, we focus on nonlinear solitary structures of KAWs. A general criterion of the existence for solitary KAW (SKAW hereafter and its exact analytical solution in a low-β plasma (βe/mi are presented, where the electron drift velocity along the background magnetic field is larger than the thermal speed within a SKAW, and hence can excite, for instance, ion acoustic turbulence as showed by in situ observations of satellites in space plasmas. In consequence, the turbulence results in kinetic dissipation of the SKAW and dynamical evolution in its structure. We further discuss the structure of the dissipated SKAW (DSKAW hereafter that evolves from the SKAW due to the dissipation. The result shows that the DSKAW has a local shock-like structure in its density profile and a net electric potential drop over the shock-like structure. In particular, the electric potential drop of the DSKAW can be expected to accelerate electrons efficiently to the order of the local Alfvén speed. The application of the DSKAW acceleration mechanism to the auroral electron acceleration is also discussed. Finally, a few perspectives of KAW studies in future are presented.
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.
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.
Acoustic-gravity nonlinear structures
Directory of Open Access Journals (Sweden)
D. Jovanović
2002-01-01
Full Text Available A catalogue of nonlinear vortex structures associated with acoustic-gravity perturbations in the Earth's atmosphere is presented. Besides the previously known Kelvin-Stewart cat's eyes, dipolar and tripolar structures, new solutions having the form of a row of counter-rotating vortices, and several weakly two-dimensional vortex chains are given. The existence conditions for these nonlinear structures are discussed with respect to the presence of inhomogeneities of the shear flows. The mode-coupling mechanism for the nonlinear generation of shear flows in the presence of linearly unstable acoustic-gravity waves, possibly also leading to intermittency and chaos, is presented.
Lp-decay rates to nonlinear diffusion waves for p-system with nonlinear damping
Institute of Scientific and Technical Information of China (English)
ZHU Changjiang; JIANG Mina
2006-01-01
In this paper, we study the Lp (2 ≤ p ≤ +∞) convergence rates of the solutions to the Cauchy problem of the so-called p-system with nonlinear damping. Precisely, we show that the corresponding Cauchy problem admits a unique global solution (v(x,t),u(x,t)) and such a solution tends time-asymptotically to the corresponding nonlinear diffusion wave (-v(x, t), -u(x, t)) governed by the classical Darcy's law provided that the corresponding prescribed initial error function (w0(x), z0(x))lies in (H3 × H2) (R) and |v+ - v-| + ‖w0‖3 + ‖z0‖2 is sufficiently small.Furthermore, the Lp (2 ≤ p ≤ +∞) convergence rates of the solutions are also obtained.
A nonlinear wave equation with a nonlinear integral equation involving the boundary value
Directory of Open Access Journals (Sweden)
Thanh Long Nguyen
2004-09-01
Full Text Available We consider the initial-boundary value problem for the nonlinear wave equation $$displaylines{ u_{tt}-u_{xx}+f(u,u_{t}=0,quad xin Omega =(0,1,; 0
Weak Turbulence in the Magnetosphere: Formation of Whistler Wave Cavity by Nonlinear Scattering
Crabtree, C; Ganguli, G; Mithaiwala, M; Galinsky, V; Shevchenko, V
2011-01-01
We consider the weak turbulence of whistler waves in the in low-\\beta\\ inner magnetosphere of the Earth. Whistler waves with frequencies, originating in the ionosphere, propagate radially outward and can trigger nonlinear induced scattering by thermal electrons provided the wave energy density is large enough. Nonlinear scattering can substantially change the direction of the wave vector of whistler waves and hence the direction of energy flux with only a small change in the frequency. A portion of whistler waves return to the ionosphere with a smaller perpendicular wave vector resulting in diminished linear damping and enhanced ability to pitch-angle scatter trapped electrons. In addition, a portion of the scattered wave packets can be reflected near the ionosphere back into the magnetosphere. Through multiple nonlinear scatterings and ionospheric reflections a long-lived wave cavity containing turbulent whistler waves can be formed with the appropriate properties to efficiently pitch-angle scatter trapped e...
Abbasnia,Arash; Ghiasi,Mahmoud
2014-01-01
Fully nonlinear wave interaction with a fixed breakwater is investigated in a numerical wave tank (NWT). The potential theory and high-order boundary element method are used to solve the boundary value problem. Time domain simulation by a mixed Eulerian-Lagrangian (MEL) formulation and high-order boundary integral method based on non uniform rational B-spline (NURBS) formulation is employed to solve the equations. At each time step, Laplace equation is solved in Eulerian frame and fully non-l...
Yeganeh, Mohammad; Dashti, Mohsen; Slussarenko, Sergei; Santamato, Enrico; Karimi, Ebrahim
2013-01-01
A novel approach based on the two-channel moir\\'e deflectometry has been used to measure both wave-front and transverse component of the Poynting vector of an optical vortex beam. Generated vortex beam by the q-plate, an inhomogeneous liquid crystal cell, has been analyzed with such technique. The measured topological charge of generated beams are in an excellent agreement with theoretical prediction.
Rayleigh scattering and nonlinear inversion of elastic waves
Energy Technology Data Exchange (ETDEWEB)
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.
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.
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase transition point
Nixon, Sean; Yang, Jianke
2012-01-01
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase-transition point are analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of novel phenomena known to exist in this envelope equation are shown to also exist in the full equation including wave blowup, periodic bound states and solitary wave solutions.
Management of the orbital angular momentum of vortex beams in a quadratic nonlinear interaction
Bovino, Fabio A; Bertolotti, Mario; Sibilia, Concita
2011-01-01
Light intensity control of the orbital angular momentum of the fundamental beam in a quadratic nonlinear process is theoretically and numerically presented. In particular we analyzed a seeded second harmonic generation process in presence of orbital angular momentum of the interacting beams due both to on axis and off axis optical vortices. Examples are proposed and discussed.
Institute of Scientific and Technical Information of China (English)
WU; Shaoping(吴少平); YI; Fan(易帆)
2002-01-01
By using FICE scheme, a numerical simulation of nonlinear propagation of gravity wave packet in three-dimension compressible atmosphere is presented. The whole nonlinear propagation process of the gravity wave packet is shown; the basic characteristics of nonlinear propagation and the influence of the ambient winds on the propagation are analyzed. The results show that FICE scheme can be extended in three-dimension by which the calculation is steady and kept for a long time; the increase of wave amplitude is faster than the exponential increase according to the linear gravity theory; nonlinear propagation makes the horizontal perturbation velocity increase greatly which can lead to enhancement of the local ambient winds; the propagation path and the propagation velocity of energy are different from the results expected by the linear gravity waves theory, the nonlinearity causes the change in propagation characteristics of gravity wave; the ambient winds alter the propagation path and group velocity of gravity wave.
Study of nonlinear waves in astrophysical quantum plasmas
Energy Technology Data Exchange (ETDEWEB)
Hossen, M.R.; Mamun, A.A., E-mail: rasel.plasma@gmail.com [Department of Physics, Jahangirnagar University, Savar, Dhaka (Bangladesh)
2015-10-01
The nonlinear propagation of the electron acoustic solitary waves (EASWs) in an unmagnetized, collisionless degenerate quantum plasma system has been investigated theoretically. Our considered model consisting of two distinct groups of electrons (one of inertial non-relativistic cold electrons and other of inertialess ultrarelativistic hot electrons) and positively charged static ions. The Korteweg-de Vries (K-dV) equation has been derived by employing the reductive perturbation method and numerically examined to identify the basic features (speed, amplitude, width, etc.) of EASWs. It is shown that only rarefactive solitary waves can propagate in such a quantum plasma system. It is found that the effect of degenerate pressure and number density of hot and cold electron fluids, and positively charged static ions, significantly modify the basic features of EASWs. It is also noted that the inertial cold electron fluid is the source of dispersion for EA waves and is responsible for the formation of solitary structures. The applications of this investigation in astrophysical compact objects (viz. non-rotating white dwarfs, neutron stars, etc.) are briefly discussed. (author)
Misra, A P
2015-01-01
The nonlinear propagation of dust-acoustic (DA) waves in a magnetized dusty plasma with a pair of trapped ions is investigated. Starting from a set of hydrodynamic equations for massive dust fluids as well as kinetic Vlasov equations for ions, and applying the reductive perturbation technique, a Korteweg-de Vries (KdV)-like equation with a complex coefficient of nonlinearity is derived, which governs the evolution of small-amplitude DA waves in plasmas. The complex coefficient arises due to vortex-like distributions of both positive and negative ions. An analytical as well as numerical solution of the KdV equation are obtained and analyzed with the effects of external magnetic field, the dust pressure as well as different mass and temperatures of positive and negative ions.
A flexible genuinely nonlinear approach for nonlinear wave propagation, breaking and run-up
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.
Computation of nonlinear water waves with a high-order Boussinesq model
DEFF Research Database (Denmark)
Fuhrman, David R.; Madsen, Per A.; Bingham, Harry
2005-01-01
-crested waves in shallow/deep water, resulting in hexagonal/rectangular surface patterns; crescent waves, resulting from unstable perturbations of plane progressive waves; and highly-nonlinear wave-structure interactions. The emphasis is on physically demanding problems, and in eachcase qualitative and (when...
Kink wave determined by parabola solution of a nonlinear ordinary differential equation
Institute of Scientific and Technical Information of China (English)
LI Ji-bin; LI Ming; NA Jing
2007-01-01
By finding a parabola solution connecting two equilibrium points of a planar dynamical system, the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown. Some exact explicit parametric representations of kink wave solutions are given. Explicit parameter conditions to guarantee the existence of kink wave solutions are determined.
Variational space–time (dis)continuous Galerkin method for nonlinear free surface water waves
Gagarina, E.; Ambati, V.R.; Vegt, van der J.J.W.; Bokhove, O.
2014-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles’ variational principle for water waves together with a finite element
Variational space-time (dis)continuous Galerkin method for nonlinear free surface waves
Gagarina, E.; Vegt, van der J.J.W.; Ambati, V.R.; Bokhove, O.
2013-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a space-time finite element discretization that is cont
The Nonlinear Interaction Process in the Wave Assimilation Model and Its Experiments
Institute of Scientific and Technical Information of China (English)
杨永增; 纪永刚; 袁业立
2003-01-01
This paper presents a composite interaction formula based on the discrete-interactionoperator of wave-wave nonlinear interaction for deriving its adjoint source function in the wave assimilation model. Assimilation experiments were performed using the significant wave heights observed by the TOPES/POSEIDON satellite, and the gradient distribution in the physical space wasalso analyzed preliminarily.
Reduced order prediction of rare events in unidirectional nonlinear water waves
Cousins, Will
2015-01-01
We consider the problem of short-term prediction of rare, extreme water waves in unidirectional fields, a critical topic for ocean structures and naval operations. One possible mechanism for the occurrence of such rare, unusually-intense waves is nonlinear wave focusing. Recent results have demonstrated that random localizations of energy, induced by the dispersive mixing of different harmonics, can grow significantly due to localized nonlinear focusing. Here we show how the interplay between i) statistical properties captured through linear information such as the waves power spectrum and ii) nonlinear dynamical properties of focusing localized wave groups defines a critical length scale associated with the formation of extreme events. The energy that is locally concentrated over this length scale acts as the "trigger" of nonlinear focusing for wave groups and the formation of subsequent rare events. We use this property to develop inexpensive, short-term predictors of large water waves. Specifically, we sho...
An improved wave-vector frequency-domain method for nonlinear wave modeling.
Jing, Yun; Tao, Molei; Cannata, Jonathan
2014-03-01
In this paper, a recently developed wave-vector frequency-domain method for nonlinear wave modeling is improved and verified by numerical simulations and underwater experiments. Higher order numeric schemes are proposed that significantly increase the modeling accuracy, thereby allowing for a larger step size and shorter computation time. The improved algorithms replace the left-point Riemann sum in the original algorithm by the trapezoidal or Simpson's integration. Plane waves and a phased array were first studied to numerically validate the model. It is shown that the left-point Riemann sum, trapezoidal, and Simpson's integration have first-, second-, and third-order global accuracy, respectively. A highly focused therapeutic transducer was then used for experimental verifications. Short high-intensity pulses were generated. 2-D scans were conducted at a prefocal plane, which were later used as the input to the numerical model to predict the acoustic field at other planes. Good agreement is observed between simulations and experiments.
Modeling of Propagation and Transformation of Transient Nonlinear Waves on A Current
Institute of Scientific and Technical Information of China (English)
Wojciech Sulisz; Maciej Paprota
2013-01-01
A novel theoretical approach is applied to predict the propagation and transformation of transient nonlinear waves on a current. The problem was solved by applying an eigenfunction expansion method and the derived semi-analytical solution was employed to study the transformation of wave profile and the evolution of wave spectrum arising from the nonlinear interactions of wave components in a wave train which may lead to the formation of very large waves. The results show that the propagation of wave trains is significantly affected by a current. A relatively small current may substantially affect wave train components and the wave train shape. This is observed for both opposing and following current. The results demonstrate that the application of the nonlinear model has a substantial effect on the shape of a wave spectrum. A train of originally linear and very narrow-banded waves changes its one-peak spectrum to a multi-peak one in a fairly short distance from an initial position. The discrepancies between the wave trains predicted by applying the linear and nonlinear models increase with the increasing wavelength and become significant in shallow water even for waves with low steepness. Laboratory experiments were conducted in a wave flume to verify theoretical results. The free-surface elevations recorded by a system of wave gauges are compared with the results provided by the nonlinear model. Additional verification was achieved by applying a Fourier analysis and comparing wave amplitude spectra obtained from theoretical results with experimental data. A reasonable agreement between theoretical results and experimental data is observed for both amplitudes and phases. The model predicts fairly well multi-peak spectra, including wave spectra with significant nonlinear wave components.
Hitting probabilities for non-linear systems of stochastic waves
Dalang, Robert C
2012-01-01
We consider a $d$-dimensional random field $u = \\{u(t,x)\\}$ that solves a non-linear system of stochastic wave equations in spatial dimensions $k \\in \\{1,2,3\\}$, driven by a spatially homogeneous Gaussian noise that is white in time. We mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent $\\beta$. Using Malliavin calculus, we establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of $\\IR^d$, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that appears in the Hausdorff measure is close to optimal, and shows that when $d(2-\\beta) > 2(k+1)$, points are polar for $u$. Conversely, in low dimensions $d$, points are not polar. There is however an interval in which the question of polarity of points remains open.
Non-linear Oscillations of Compact Stars and Gravitational Waves
Passamonti, A
2006-01-01
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem has been treated by developing a gauge invariant formalism based on the 2-parameter perturbation theory (Sopuerta, Bruni and Gualtieri, 2004) where the radial and non-radial perturbations have been separately parameterized. The non-linear perturbations obey inhomogeneous partial differential equations, where the structure of the differential operator is given by the previous perturbative orders and the source terms are quadratic in the first order perturbations. In the exterior spacetime the sources vanish, thus the gravitational wave properties are completely described by the second order Zerilli and Regge-Wheeler functions. As main initial configuration we have considered a first order differentially rotating and radially pulsating star. Although at first perturbative or...
Nonlinear Evolution of a Baroclinic Wave and Imbalanced Dissipation
Nadiga, Balasubramanya T
2015-01-01
We consider the nonlinear evolution of an unstable baroclinic wave in a regime of rotating stratified flow that is of relevance to interior circulation in the oceans and in the atmosphere---a regime characterized by small large-scale Rossby and Froude numbers, a small vertical to horizontal aspect ratio, and no bounding horizontal surfaces. Using high-resolution simulations of the non-hydrostatic Boussinesq equations and companion integrations of the balanced quasi-geostrophic equations, we present evidence for a local route to dissipation of balanced energy directly through interior turbulent cascades. Analysis of simulations presented in this study suggest that a developing baroclinic instability can lead to secondary instabilities that can cascade a small fraction of the energy forward to unbalanced scales. Mesoscale shear and strain resulting from the hydrostatic geostrophic baroclinic instability drive frontogenesis. The fronts in turn support ageostrophic secondary circulation and instabilities. These t...
Inverse problem for multi-body interaction of nonlinear waves
Marruzzo, Alessia; Antenucci, Fabrizio; Pagnani, Andrea; Leuzzi, Luca
2016-01-01
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable {\\em temperature}-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems.
Mitri, F
2014-12-01
Stemming from the Rayleigh-Sommerfeld surface integral, the addition theorems for the spherical wave and Legendre functions, and a weighting function describing the behavior of the radial component vp1 of the normal velocity at the surface of a finite circular radiating source, partial-wave series expansions are derived for the incident field of acoustic spiraling (vortex) beams in a spherical coordinate system centered on the axis of wave propagation. Examples for vortex beams, comprising ρ-vortex, zeroth-order and higher order Bessel-Gauss and Bessel, truncated Neumann-Gauss and Hankel- Gauss, Laguerre-Gauss, and other Gaussian-type vortex beams are considered. The mathematical expressions are exact solutions of the Helmholtz equation. The results presented here are particularly useful to accurately evaluate analytically and compute numerically the acoustic scattering and other mechanical effects of finite vortex beams, such as the axial and 3-D acoustic radiation force and torque components on a sphere of any (isotropic, anisotropic, etc.) material (fluid, elastic, viscoelastic, etc.), either centered on the beam's axis of wave propagation, or placed off-axially. Numerical predictions allow optimal design of parameters in applications including but not limited to acoustical tweezers, acousto-fluidics, beamforming design, and imaging, to name a few.
Nonlinearity Role in Long-Term Interaction of the Ocean Gravity Waves
2012-09-30
the Nonlinear Schrodinger equation and its exact solutions. Numerical simulations of the fully nonlinear Euler equation have also been performed in... Schrodinger breathers, Proceedings of ECMWF Workshop on "Ocean Waves" - 25 to 27 June 2012 [published] • Onorato, M. and Proment, D.; Approximate rogue wave
The influence of storms on finite amplitude sand wave dynamics: an idealized nonlinear model
Campmans, G.H.P.; Roos, P.C.; de Vriend, H.J.; Hulscher, S.J.M.H.
2017-01-01
We investigate the effects of storms on finite amplitude sand wave growth using a new idealized nonlinear morphodynamic model. We find that the growth speed initially linearly increases with sand wave amplitude, after which nonlinear effects cause the growth to decrease. This finally leads to an
Similarity Reduction and Integrability for the Nonlinear Wave Equations from EPM Model
Institute of Scientific and Technical Information of China (English)
YAN ZhenYa
2001-01-01
Four types of similarity reductions are obtained for the nonlinear wave equation arising in the elasto-plasticmicrostructure model by using both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou. As a result, the nonlinear wave equation is not integrable.``
Kazantseva, E. V.; Maimistov, A. I.
2016-08-01
In a model which describes asymmetric oppositely directed nonlinear waveguide coupler it was observed in the numerical simulation a phenomenon of solitary wave formation from the input constant continuous wave set at the entrance of a waveguide with negative index of refraction. Threshold value of the amplitude of the constant continuous wave, which defines the condition of appearance of the first solitary wave, decreases with increasing of the parameter of nonlinearity. The period of solitary wave formation decreases with increasing of the continuum wave amplitude.
Dynamical understanding of loop soliton solution for several nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
Ji-bin LI
2007-01-01
It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution.
Nonlinear Shock and Kink Waves with Complete Coriolis Force in Earth's Atmosphere
Institute of Scientific and Technical Information of China (English)
YU Xin; ZHAO Qiang
2009-01-01
Nonlinear waves in a Boussinesq fluid model which includes both the vertical and horizontal components of Coriolis force are studied by using the semi-geostrophic approximation and the method of travelling-wave solution.Taylor series expansion has been employed to isolate the characteristics of the linear Rossby waves and to identify the nonlinear shock and kink waves.The KdV-Burgers and the compound KdV-Burgers equations are derived,their shock wave and kink wave solution are also obtained.
Institute of Scientific and Technical Information of China (English)
GU Ji-jun; AN Chen; LEVI Carlos; SU Jian
2012-01-01
The Generalized Integral Transform Technique (GITT) was applied to predict dynamic response of Vortex-Induced Vibration (VIV) of a long flexible cylinder.A nonlinear wake oscillator model was used to represent the cross-flow force acting on the cylinder,leading to a coupled system of second-order Partial Differential Equations (PDEs) in temporal variable.The GITT approach was used to transform the system of PDEs to a system of Ordinary Differential Equations (ODEs),which was numerically solved by using the Adams-Moulton and Gear method (DIVPAG) developed by the International Mathematics and Statistics Library (IMSL).Numerical results were presented for comparison to those given by the finite difference method and experimental results,allowing a critical evaluation of the technique performance.The influence of variation of mean axial tension induced by elongation of flexible cylinder was evaluated,which was shown to be not negligible in numerical simulation of VIV of a long flexible cylinder.
Nonlinear mechanisms for drift wave saturation and induced particle transport
Energy Technology Data Exchange (ETDEWEB)
Dimits, A.M. (Maryland Univ., College Park, MD (USA). Lab. for Plasma Research); Lee, W.W. (Princeton Univ., NJ (USA). 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.
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.
Numerical and experimental investigation of nonlinear ultrasonic Lamb waves at low frequency
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.
Institute of Scientific and Technical Information of China (English)
LI Qian; Hans-F. GRAF; CUI Xuefeng
2011-01-01
Using 1958-2002 NCEP/NCAR reanalysis data, we investigate stationary and transient planetary wave propagation and its role in wave-mean flow interaction which influences the state of the polar vortex (PV)in the stratosphere in Northern Hemisphere (NH) winter. This is done by analyzing the Eliassen-Palm (E-P) flux and its divergence. We find that the stationary and transient waves propagate upward and equatorward in NH winter, with stronger upward propagation of stationary waves from the troposphere to the stratosphere, and stronger equatorward propagation of transient waves from mid-latitudes to the subtropics in the troposphere. Stationary waves exhibit more upward propagation in the polar stratosphere during the weak polar vortex regime (WVR) than during the strong polar vortex regime (SVR). On the other hand, transient waves have more upward propagation during SVR than during WVR in the subpolar stratosphere, with a domain of low frequency waves. With different paths of upward propagation, both stationary and transient waves contribute to the maintenance of the observed stratospheric PV regimes in NH winter.
Institute of Scientific and Technical Information of China (English)
Chang Jing; Gao Yi-xian; Cai Hua
2014-01-01
In this paper, the generalized extended tanh-function method is used for constructing the traveling wave solutions of nonlinear evolution equations. We choose Fisher’s equation, the nonlinear schr¨odinger equation to illustrate the validity and ad-vantages of the method. Many new and more general traveling wave solutions are obtained. Furthermore, this method can also be applied to other nonlinear equations in physics.
Auroral vortex street formed by the magnetosphere-ionosphere coupling instability
Hiraki, Yasutaka
2014-01-01
By performing three-dimensional nonlinear MHD simulations including Alfven eigenmode perturbations most unstable to the ionospheric feedback effects, we reproduced the auroral vortex street that often appears just before substorm onset. We found that an initially placed arc splits, intensifies, and rapidly deforms into a vortex street. We also found that there is a critical convection electric field for growth of the Alfven eigenmodes. The vortex street is shown to be a consequence of coupling between the magnetospheric Alfven waves carrying field-aligned currents and the ionospheric density waves driven by Pedersen/Hall currents.
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.
A NUMERICAL CALCULATION METHOD FOR EIGENVALUE PROBLEMS OF NONLINEAR INTERNAL WAVES
Institute of Scientific and Technical Information of China (English)
SHI Xin-gang; FAN Zhi-song; LIU Hai-long
2009-01-01
Generally speaking, the background shear current U(z)must be taken into account in eigenvalue problems of nonlinear internal waves in ocean, as is different from those of linear internal waves. A numerical calculation method for eigenvalue problems of nonlinear internal waves is presented in this paper on the basis of the Thompson-Haskell's calculation method. As an application of this method, at a station (21°N, 117°15′E) in the South China Sea, a modal structure and parameters of nonlinear internal waves are calculated, and the results closely agree with the calculated results based on observation by Yang et al..
Rogue Waves of Nonlinear Schrödinger Equation with Time-Dependent Linear Potential Function
Directory of Open Access Journals (Sweden)
Ni Song
2016-01-01
Full Text Available The rogue waves of the nonlinear Schrödinger equation with time-dependent linear potential function are investigated by using the similarity transformation in this paper. The first-order and second-order rogue waves solutions are obtained and the nonlinear dynamic behaviors of these solutions are discussed in detail. In addition, the amplitudes of the rogue waves under the effect of the gravity field and external magnetic field changing with the time are analyzed by using numerical simulation. The results can be used to study the matter rogue waves in the Bose-Einstein condensates and other fields of nonlinear science.
Observations of Shoaling Nonlinear Internal Waves: Formation of Trapped Cores
Lien, R.; D'Asaro, E. A.; Chang, M.; Tang, T.; Yang, Y.
2006-12-01
Large-amplitude nonlinear internal waves (NLIWs) shoaling on the continental slope in the northern South China Sea are observed. Observed NLIWs often reach the breaking limit, the maximum horizontal current velocity exceeding the wave speed, and trapped cores are formed with recirculating fluid. The conjugate flow does not form. The vertical position of the maximum horizontal velocity is displaced from surface to subsurface, via the formation of the trapped core. Trapped-core NLIWs are strongly dissipative and evolve rapidly into trains of NLIWs. The vertical overturning is as large as 75 m, and the turbulence kinetic energy dissipation rate is estimated as O(10^{-5}) W kg-1. We propose that the formation and the evolution of trapped cores catalyze the generation of the trains of NLIWs on the Dongsha plateau often captured by satellite images and by recent field observations. The generation, evolution, fission, dissipation, and energetics of observed trapped-core NLIWs will be discussed and compared with results of numerical models and laboratory experiments.
Landau damping and steepening of interplanetary nonlinear hydromagnetic waves
Barnes, A.; Chao, J. K.
1977-01-01
According to collisionless shock theories, the thickness of a shock front should be of the order of the characteristic lengths of the plasmas (the Debye length, the proton and Larmor radii, etc.). Chao and Lepping (1974), found, however, that 30% of the observed interplanetary shocks at 1 AU have thicknesses much larger than these characteristic lengths. It is the objective of the present paper to investigate whether the competition between nonlinear steepening and Landau damping can result in a wave of finite width that does not steepen into a shock. A heuristic model of such a wave is developed and tested by the examples of two structures that are qualitatively shocklike, but thicker than expected from theory. It is found that both events are in the process of steepening and their limiting thicknesses due to Landau damping are greater than the corresponding proton Larmor radius for both structures as observed at Mariner 5 (nearer the sun than 1 AU) but are comparable to the proton Larmor radius for Explorer (near 1 AU) observations.
Nonlinear vibration behaviors of casing pipe in the deep water
Tang, You-Gang; Zhang, Su-Xia; Yi, Cong
2006-10-01
The vortex-induced nonlinear vibration of casing pipes in the deep water was investigated considering the loads of current and combined wave-current. The vortex-induced vibration equation of a casing pipe was set up with considering the beam mode and Morison's nonlinear fluid loads as well as the vortex-excited loads. The approach of calculating vortex-excited nonlinear vibration by Galerkin's method was proposed. The natural vibration frequencies and modes were obtained, and the response including primary resonance induced by current and the composite resonance under combined wave-current for the 170 m long casing pipe in the 160 m depth of water were investigated. The results show that the dynamics response of casing pipe obviously increases, and the complicated response behaviors of casing pipe are described under combined wave-current.
On the nonlinear shaping mechanism for gravity wave spectrum in the atmosphere
Directory of Open Access Journals (Sweden)
I. P. Chunchuzov
2009-11-01
Full Text Available The nonlinear mechanism of shaping of a high vertical wave number spectral tail in the field of a few discrete internal gravity waves in the atmosphere is studied in this paper. The effects of advection of fluid parcels by interacting gravity waves are taken strictly into account by calculating wave field in Lagrangian variables, and performing a variable transformation from Lagrangian to Eulerian frame. The vertical profiles and vertical wave number spectra of the Eulerian displacement field are obtained for both the case of resonant and non-resonant wave-wave interactions. The evolution of these spectra with growing parameter of nonlinearity of the internal wave field is studied and compared to that of a broad band spectrum of gravity waves with randomly independent amplitudes and phases. The calculated vertical wave number spectra of the vertical displacements or relative temperature fluctuations are found to be consistent with the observed spectra in the middle atmosphere.
Generation of polarization vortex beams by segmented quarter-wave plates
Institute of Scientific and Technical Information of China (English)
Jingtao Xin; Xiaoping Lou; Zhehai Zhou; Mingli Dong; Lianqing Zhu
2016-01-01
A spatially variable retardation device,an SQWP,is designed to generate polarization vortex beams.The transformation of Laguerre-Gaussian beams by the SQWP is further studied,and it is found that the SQWPs can also be used to generate helical beams and measure the topological charges of helical beams.
Nonlinear Alfvén wave dynamics at a 2D magnetic null point: ponderomotive force
Thurgood, J. O.; McLaughlin, J. A.
2013-07-01
Context. In the linear, β = 0 MHD regime, the transient properties of magnetohydrodynamic (MHD) waves in the vicinity of 2D null points are well known. The waves are decoupled and accumulate at predictable parts of the magnetic topology: fast waves accumulate at the null point; whereas Alfvén waves cannot cross the separatricies. However, in nonlinear MHD mode conversion can occur at regions of inhomogeneous Alfvén speed, suggesting that the decoupled nature of waves may not extend to the nonlinear regime. Aims: We investigate the behaviour of low-amplitude Alfvén waves about a 2D magnetic null point in nonlinear, β = 0 MHD. Methods: We numerically simulate the introduction of low-amplitude Alfvén waves into the vicinity of a magnetic null point using the nonlinear LARE2D code. Results: Unlike in the linear regime, we find that the Alfvén wave sustains cospatial daughter disturbances, manifest in the transverse and longitudinal fluid velocity, owing to the action of nonlinear magnetic pressure gradients (viz. the ponderomotive force). These disturbances are dependent on the Alfvén wave and do not interact with the medium to excite magnetoacoustic waves, although the transverse daughter becomes focused at the null point. Additionally, an independently propagating fast magnetoacoustic wave is generated during the early stages, which transports some of the initial Alfvén wave energy towards the null point. Subsequently, despite undergoing dispersion and phase-mixing due to gradients in the Alfvén-speed profile (∇cA ≠ 0) there is no further nonlinear generation of fast waves. Conclusions: We find that Alfvén waves at 2D cold null points behave largely as in the linear regime, however they sustain transverse and longitudinal disturbances - effects absent in the linear regime - due to nonlinear magnetic pressure gradients.
An Approximate Method for Analysis of Solitary Waves in Nonlinear Elastic Materials
Rushchitsky, J. J.; Yurchuk, V. N.
2016-05-01
Two types of solitary elastic waves are considered: a longitudinal plane displacement wave (longitudinal displacements along the abscissa axis of a Cartesian coordinate system) and a radial cylindrical displacement wave (displacements in the radial direction of a cylindrical coordinate system). The basic innovation is the use of nonlinear wave equations similar in form to describe these waves and the use of the same approximate method to analyze these equations. The distortion of the wave profile described by Whittaker (plane wave) or Macdonald (cylindrical wave) functions is described theoretically
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.
2016-06-01
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.
Institute of Scientific and Technical Information of China (English)
Jeong Ja Bae
2012-01-01
In this article,we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials,one component is a Kirchhoff type wave equation with nonlinear time dependent localized dissipation which is effective only on a neighborhood of certain part of the boundary,while the other is a Kirchhoff type wave equation with nonlinear memory.
New Exact Explicit Nonlinear Wave Solutions for the Broer-Kaup Equation
Directory of Open Access Journals (Sweden)
Zhenshu Wen
2014-01-01
Full Text Available We study the nonlinear wave solutions for the Broer-Kaup equation. Many exact explicit expressions of the nonlinear wave solutions for the equation are obtained by exploiting the bifurcation method and qualitative theory of dynamical systems. These solutions contain solitary wave solutions, singular solutions, periodic singular solutions, and kink-shaped solutions, most of which are new. Some previous results are extended.
Existence and breaking property of real loop-solutions of two nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
Ji-bin LI
2009-01-01
Dynamical analysis has revealed that,for some nonlinear wave equations,loop- and inverted loop-soliton solutions are actually visual artifacts. The so-called loop-soliton solution consists of three solutions,and is not a real solution. This paper answers the question as to whether or not nonlinear wave equations exist for which a "real" loop-solution exists,and if so,what are the precise parametric representations of these loop traveling wave solutions.
Nonlinear unified equations for water waves propagating over uneven bottoms in the nearshore region
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Considering the continuous characteristics for water waves propagating over complex topography in the nearshore region, the unified nonlinear equations, based on the hypothesis for a typical uneven bottom, are presented by employing the Hamiltonian variational principle for water waves. It is verified that the equations include the following special cases: the extension of Airy's nonlinear shallow-water equations, the generalized mild-slope equation, the dispersion relation for the second-order Stokes waves and the higher order Boussinesq-type equations.
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.
Long-term evolution of strongly nonlinear internal solitary waves in a rotating channel
Directory of Open Access Journals (Sweden)
J. C. Sánchez-Garrido
2009-09-01
Full Text Available The evolution of internal solitary waves (ISWs propagating in a rotating channel is studied numerically in the framework of a fully-nonlinear, nonhydrostatic numerical model. The aim of modelling efforts was the investigation of strongly-nonlinear effects, which are beyond the applicability of weakly nonlinear theories. Results reveal that small-amplitude waves and sufficiently strong ISWs evolve differently under the action of rotation. At the first stage of evolution an initially two-dimensional ISW transforms according to the scenario described by the rotation modified Kadomtsev-Petviashvili equation, namely, it starts to evolve into a Kelvin wave (with exponential decay of the wave amplitude across the channel with front curved backwards. This transition is accompanied by a permanent radiation of secondary Poincaré waves attached to the leading wave. However, in a strongly-nonlinear limit not all the energy is transmitted to secondary radiated waves. Part of it returns to the leading wave as a result of nonlinear interactions with secondary Kelvin waves generated in the course of time. This leads to the formation of a slowly attenuating quasi-stationary system of leading Kelvin waves, capable of propagating for several hundreds hours as a localized wave packet.
Energy Technology Data Exchange (ETDEWEB)
King, G P [Instituto de Oceanografia, Faculdade de Ciencias, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa (Portugal); Rudman, Murray [CSIRO Manufacturing and Infrastructure Technology, P.O. Box 56, Highett, Vic. 3190 (Australia); Rowlands, G [Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)], E-mail: gkinglisboa@gmail.com, E-mail: Murray.Rudman@csiro.au, E-mail: G.Rowlands@warwick.ac.uk
2008-01-31
The dimensionless effective axial diffusion coefficient, D{sub z}, calculated from particle trajectories in steady wavy vortex flow in a narrow gap Taylor-Couette system, has been determined as a function of Reynolds number (R = Re/Re{sub c}), axial wavelength ({lambda}{sub z}), and the number of azimuthal waves (m). Two regimes of Reynolds number were found: (i) when R < 3.5, D{sub z} has a complex and sometimes multi-modal dependence on Reynolds number; (ii) when R > 3.5, D{sub z} decreases monotonically. Eulerian quantities measuring the departure from rotational symmetry, {psi}{sub {theta}}, and flexion-free flow, {psi}{sub {nu}}, were calculated. The space-averaged quantities {phi}-bar{sub {theta}} and {phi}-bar{sub {nu}} were found to have, unlike D{sub z}, a simple unimodal dependence on R. In the low R regime the correlation between D{sub z} and {psi}{sub {theta}}{psi}{sub {nu}} was complicated and was attributed to variations in the spatial distribution of the wavy disturbance occurring in this range of R. In the large R regime, however, the correlation simplified to D{sub z}{approx}{phi}-bar{sub {theta}}{phi}-bar{sub {nu}} for all wave states, and this was attributed to the growth of an integrable vortex core and the concentration of the wavy disturbance into narrow regions near the outflow and inflow jets. A reservoir model of a wavy vortex was used to determine the rate of escape across the outflow and inflow boundaries, the size of the 'escape basins' (associated with escape across the outflow and inflow boundaries), and the size of the trapping region in the vortex core. In the low R regime after the breakup of all KAM tori, the outflow basin ({gamma}{sub O}) is larger than the inflow basin ({gamma}{sub I}), and both {gamma}{sub O} and {gamma}{sub I} are (approximately) independent of R. In the large R regime, with increasing Reynolds number the trapping region grows, the outflow basin decreases, and the inflow basin shows a slight increase
Institute of Scientific and Technical Information of China (English)
WANG Zhong; LU Xiao-ping
2011-01-01
Up to now, there are no satisfactory numerical methods for simulating wave resistance of trimarans, mainly due to the difficulty related with the strong nonlinear features of the piece hull wave making and their interference. This article proposes a numerical method for quick and effective calculation of wave resistance of trimarans to be used in engineering applications. Based on Wyatt's work、 the nonlinear free surface boundary condition, the time domain concept, and the full nonlinear wave making theory,using the Rankine source Green function, the 3-D surface panel method is expanded to solve the trimaran wave making problems,with high order nonlinear factors being taken into account, such as the influence of the sinking and trim, transom, and ship wave immersed hull surface. And the software is successfully developed to implement the method, which is validated. Several trimaran models, including a practical trimaran with a sonar dome and the transom, are used as numerical calculation samples, their wave making resistance is calculated both by the present method and some other methods such as linear (Dawson) methods. Moreover,sample model resistance tests were carried out to provide data for comparison, validation and analysis. Through the validation by model experiments, it is concluded that present method can well predict the wave making resistance, sinking and trim, and the accuracy of wave making resistance calculation is significantly improved by taking the trim and sinking into account, especially at high speeds.
Pulse wave attenuation measurement by linear and nonlinear methods in nonlinearly elastic tubes.
Bertram, C D; Pythoud, F; Stergiopulos, N; Meister, J J
1999-04-01
Reasons for the continuing difficulty in making definitive measurements of pulse wave attenuation in elastic tubes and arteries in the presence of reflections are sought. The measurement techniques available were re-examined in elastic tubes mimicking the arterial compliance nonlinearity, under conditions of strong reflection. The pulse was of physiological shape, and two different pulse amplitudes in the physiological range were used. Measurements of pressure, flow-rate and diameter pulsation allowed the deployment of four of the classical linear methods of analysis. In addition, a method of separating the forward- and backward-travelling waves that does not require linearising assumptions was used, and the attenuation in the forward and reverse directions was calculated from the resulting waveforms. Overall, the results obtained here suggest that a fully satisfactory way of measuring arterial attenuation has yet to be devised. The classical linear methods all provided comparable attenuation estimates in terms of average value and degree of scatter across frequency. Increased scatter was generally found at the higher pulse amplitude. When the forward waveforms from the separation were similarly compared in terms of frequency components, the average value at energetic harmonics was similar to both the value indicated by the linear methods and the values predicted from linear theory on the basis of estimated viscous and viscoelastic parameter data. The backward waveforms indicated a physically unreasonable result, attributed as the expression for this technique of the same difficulties that normally manifest in scatter. Data in the literature suggesting that one of the classical methods, the three-point, systematically over-estimates attenuation were not supported, but it was confirmed that this method becomes prone to negative attenuation estimates at low harmonics as pulse amplitude increases. Although the goal of definitive attenuation measurement remains elusive
Three kinds of nonlinear dispersive waves in elastic rods with finite deformation
Institute of Scientific and Technical Information of China (English)
ZHANG Shan-yuan; LIU Zhi-fang
2008-01-01
On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.
Travelling Wave Solutions to a Special Type of Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
XU Gui-Qiong; LI Zhi-Bin
2003-01-01
A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of "rank". The key idea of this method is to make use of the arbitrariness of the manifold in Painleve analysis. We selected a new expansion variable and thus obtained a rich variety of travelling wave solutions to nonlinear evolution equation, which covered solitary wave solutions, periodic wave solutions, Weierstrass elliptic function solutions, and rational solutions. Three illustrative equations are investigated by this means, and abundant travelling wave solutions are obtained in a systematic way. In addition, some new solutions are firstly reported here.
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.
Theory of director precession and nonlinear waves in nematic liquid crystals under elliptical shear.
Krekhov, A P; Kramer, L
2005-09-01
We study theoretically the slow director precession and nonlinear waves observed in homeotropically oriented nematic liquid crystals subjected to circular or elliptical Couette and Poiseuille flow and an electric field. From a linear analysis of the nematodynamic equations it is found that in the presence of the flow the electric bend Fréedericksz transition is transformed into a Hopf-type bifurcation. In the framework of an approximate weakly nonlinear analysis we have calculated the coefficients of the modified complex Ginzburg-Landau equation, which slightly above onset describes nonlinear waves with strong nonlinear dispersion. We also derive the equation describing the precession and waves well above the Fréedericksz transition and for small flow amplitudes. Then the nonlinear waves are of diffusive nature. The results are compared with full numerical simulations and with experimental data.
Energy Technology Data Exchange (ETDEWEB)
Hayashi, Nobuhiko, E-mail: n-hayashi@21c.osakafu-u.ac.jp [NanoSquare Research Center (N2RC), Osaka Prefecture University, 1-2 Gakuen-cho, Naka-ku, Sakai 599-8570 (Japan); Kurosawa, Noriyuki [Department of Basic Science, University of Tokyo, Komaba, Meguro, Tokyo 153-8902 (Japan); Arahata, Emiko [Institute of Industrial Science, University of Tokyo, Komaba, Meguro, Tokyo 153-8505 (Japan); Kato, Yusuke [Department of Basic Science, University of Tokyo, Komaba, Meguro, Tokyo 153-8902 (Japan); Tanuma, Yasunari [Faculty of Engineering and Resource Science, Akita University, Akita 010-8502 (Japan); Tanaka, Yukio [Department of Applied Physics, Nagoya University, Nagoya 464-8603 (Japan); Golubov, Alexander A. [Faculty of Science and Technology and MESA Institute for Nanotechnology, University of Twente, 7500 AE Enshede (Netherlands)
2013-11-15
Highlights: •We theoretically study an impurity scattering effect on the vortex core structure in a chiral p-wave superconductor. •A low-temperature vortex core shrinkage (or Kramer–Pesch effect) is investigated. •The robustness of the Kramer–Pesch effect against an impurity scattering in the Born limit is lost in the unitary limit. -- Abstract: We theoretically investigate a non-magnetic impurity effect on the temperature dependence of the vortex core shrinkage (Kramer–Pesch effect) in a chiral p-wave superconductor. The Born limit and the unitary limit scattering are compared within the framework of the quasiclassical theory of superconductivity. We find that the robustness of the Kramer–Pesch effect against the impurity scattering in the Born limit is lost in the unitary limit.
Mitri, F G
2017-02-01
The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and prolate spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure standing waves cases, the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle and order of the Bessel vortex beam, as well as the dimensionless size parameter. A generalized expression for the radiation force function is derived for cases encompassing the progressive, standing and quasi-standing waves of Bessel vortex beams. This expression can be reduced to other types of beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite plane wave case by appropriate selection of the beam parameters. The results for progressive waves reveal a tractor beam behavior, characterized by the emergence of an attractive pulling force acting in opposite direction of wave propagation. Moreover, the transition to the quasi-standing and pure standing wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex beams. Applications in acoustic levitation, particle manipulation and acousto
A double optical solitary wave in a nonlinear Schr(o)dinger-type equation
Institute of Scientific and Technical Information of China (English)
Yin Jiu-Li; Ding Shan-Yu
2013-01-01
A qualitative analysis method to efficiently solve the shallow wave equations is improved,so that a more complicated nonlinear Schr(o)dinger equation can be considered.By using the detailed study,some quite strange optical solitary waves are obtained in which the bright and dark optical solitary waves are allowed to coexist.
Compound waves in a higher order nonlinear model of thermoviscous fluids
DEFF Research Database (Denmark)
Rønne Rasmussen, Anders; Sørensen, Mads Peter; Gaididei, Yuri B.
2016-01-01
A generalized traveling wave ansatz is used to investigate compound shock waves in a higher order nonlinear model of a thermoviscous fluid. The fluid velocity potential is written as a traveling wave plus a linear function of space and time. The latter offers the possibility of predicting...
Cross-polarized wave generation by effective cubic nonlinear optical interaction.
Petrov, G I; Albert, O; Etchepare, J; Saltiel, S M
2001-03-15
A new cubic nonlinear optical effect in which a linearly polarized wave propagating in a single quadratic medium is converted into a wave that is cross polarized to the input wave is observed in BBO crystal. The effect is explained by cascading of two different second-order processes: second-harmonic generation and difference frequency mixing.
Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma
El-Shamy, E. F.
2015-03-01
The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.
Nonlinear instability and chaos in plasma wave-wave interactions. II. Numerical methods and results
Energy Technology Data Exchange (ETDEWEB)
Kueny, C.S.; Morrison, P.J.
1995-05-01
In Part I of this work and Physics of Plasmas, June 1995, the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. It was shown that explosive instability arises from nonlinear coupling between modes of positive and negative energy, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. Several sets of waves are considered, comprising systems of two and three degrees of freedom. The time evolution is modelled with an explicit symplectic integration algorithm derived using Lie algebraic methods. When initial wave amplitudes are large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region for explosive triplets. Phase space orbits then experience diffusive growth to amplitudes that are sufficient for explosive instability, thus effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, small perturbations might still grow to arbitrary size via Arnold diffusion. Numerical experiments do not show diffusion in this case, although the actual diffusion rate is probably underestimated due to the simplicity of the model.
Extreme physical information and the nonlinear wave equation
Frieden, B. R.
1995-09-01
The nonlinear wave equation an be derived from a principle of extreme physical information (EPI) K. This is for a scenario where a probe electron moves through a medium in a weak magnetic field. The field is caused by a probabilistic line current source. Assume that the probability current density S of the electron is approximately constant, and directed parallel to the current source. Both the source probability amplitudes (rho) and the electron probability amplitudes (phi) are unknowns (called 'modes') of the problem. The net physical information K here consists of two components: functional K1[(phi) ] due to modes (phi) and K2[(rho) ] due to modes (rho) , respectively. To form K1[(phi) ], the Fisher information functional I1[(phi) ] for the electron modes is first constructed. This is of a fixed mathematical form. Then, a unitary transformation on (phi) to a physical space is sought that leaves I1 invariant, as form J1. This is, of course, the Fourier transformation, where the transform coordinates are momenta and I1 is essentially the mean-square electron momentum. Information K1[(phi) ] is then defined as (I1 - J1). Information K2 is formed similarly. The total information K is formed as the sum of the two components K1[(phi) ] and K2[(rho) ], by the additivity of Fisher information, and is then extremized in both (phi) and (rho) . Extremizing first in (rho) gives a Taylor series in powers of (phi) n*(phi) n, which is cut off at the quadratic term. Back-substituting this into the total Lagrangian gives one that is quadratic in (phi) n*(phi) n. Now varying (phi) * gives the required cubic wave equation in (phi) .
Nonlinear wave structures as exact solutions of Vlasov-Maxwell equations.
Dasgupta, B.; Tsurutani, B. T.; Janaki, M. S.; Sharma, A. S.
2001-12-01
Many recent observations by POLAR and Geotail spacecraft of the low-latitudes magnetopause boundary layer (LLBL) and the polar cap boundary layer (PCBL) have detected nonlinear wave structures [Tsurutani et al, Geophys. Res. Lett., 25, 4117, 1998]. These nonlinear waves have electromagnetic signatures that are identified with Alfven and Whistler modes. Also solitary waves with mono- and bi-polar features were observed. In general such electromagnetic structures are described by the full Vlasov-Maxwell equations for waves propagating at an angle to the ambient magnetic field, but it has been a diffficult task obtaining the solutions because of the inherent nonlinearity. We have obtained an exact nonlinear solution of the full Vlasov-Maxwell equations in the presence of an electromagnetic wave propagating at an arbitrary direction with an ambient magnetic field. This is accomplished by finding the constants of motion of the charged particles in the electromagnetic field of the wave and then constructing a realistic distribution function as a function of these constants of motion. The corresponding trapping conditions for such waves are obtained, yielding the self-consistent description for the particles in the presence of the nonlinear waves. The interpretation of the observed nonlinear structures in terms of these general solutions will be presented.
Detailed Characterization of Continuous-Wave and Pulsed-Pump Four-Wave Mixing in Nonlinear Fibers
DEFF Research Database (Denmark)
Lillieholm, Mads; Galili, Michael; Grüner-Nielsen, Lars;
2016-01-01
We explore the parametric gain differences for continuous-wave and pulse-pumped four-wave mixing, using various highly nonlinear fibers. Detailed simulations support our findings that the dispersion slope determines the experimentally observed differences, limiting the pulsed-pump performance....
Institute of Scientific and Technical Information of China (English)
张卫国
2003-01-01
In this paper, we have obtained the bell-type and kink-type solitary wave solutions of the generalized symmetric regularized long-wave equations with high-order nonlinear terms by means of proper transformation and undetermined assumption method.