NASA Astrophysics Data System (ADS)
Yan, Zhen-Ya
2010-11-01
We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black—Scholes model. These rogue wave solutions may he used to describe the possible physical mechanisms for rogue wave phenomenon in financial markets and related fields.
NASA Astrophysics Data System (ADS)
Yan, Zhenya
2011-11-01
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black-Scholes option pricing model. In this Letter, we analytically propose vector financial rogue waves of the coupled nonlinear volatility and option pricing model without an embedded w-learning. Moreover, we exhibit their dynamical behaviors for chosen different parameters. The vector financial rogue wave (rogon) solutions may be used to describe the possible physical mechanisms for the rogue wave phenomena and to further excite the possibility of relative researches and potential applications of vector rogue waves in the financial markets and other related fields.
Solli, D R; Ropers, C; Koonath, P; Jalali, B
2007-12-13
Recent observations show that the probability of encountering an extremely large rogue wave in the open ocean is much larger than expected from ordinary wave-amplitude statistics. Although considerable effort has been directed towards understanding the physics behind these mysterious and potentially destructive events, the complete picture remains uncertain. Furthermore, rogue waves have not yet been observed in other physical systems. Here, we introduce the concept of optical rogue waves, a counterpart of the infamous rare water waves. Using a new real-time detection technique, we study a system that exposes extremely steep, large waves as rare outcomes from an almost identically prepared initial population of waves. Specifically, we report the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation--a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input. We model the generation of these rogue waves using the generalized nonlinear Schrödinger equation and demonstrate that they arise infrequently from initially smooth pulses owing to power transfer seeded by a small noise perturbation. PMID:18075587
NASA Astrophysics Data System (ADS)
Frisquet, Benoit; Kibler, Bertrand; Morin, Philippe; Baronio, Fabio; Conforti, Matteo; Millot, Guy; Wabnitz, Stefan
2016-02-01
Photonics enables to develop simple lab experiments that mimic water rogue wave generation phenomena, as well as relativistic gravitational effects such as event horizons, gravitational lensing and Hawking radiation. The basis for analog gravity experiments is light propagation through an effective moving medium obtained via the nonlinear response of the material. So far, analogue gravity kinematics was reproduced in scalar optical wave propagation test models. Multimode and spatiotemporal nonlinear interactions exhibit a rich spectrum of excitations, which may substantially expand the range of rogue wave phenomena, and lead to novel space-time analogies, for example with multi-particle interactions. By injecting two colliding and modulated pumps with orthogonal states of polarization in a randomly birefringent telecommunication optical fiber, we provide the first experimental demonstration of an optical dark rogue wave. We also introduce the concept of multi-component analog gravity, whereby localized spatiotemporal horizons are associated with the dark rogue wave solution of the two-component nonlinear Schrödinger system.
Frisquet, Benoit; Kibler, Bertrand; Morin, Philippe; Baronio, Fabio; Conforti, Matteo; Millot, Guy; Wabnitz, Stefan
2016-01-01
Photonics enables to develop simple lab experiments that mimic water rogue wave generation phenomena, as well as relativistic gravitational effects such as event horizons, gravitational lensing and Hawking radiation. The basis for analog gravity experiments is light propagation through an effective moving medium obtained via the nonlinear response of the material. So far, analogue gravity kinematics was reproduced in scalar optical wave propagation test models. Multimode and spatiotemporal nonlinear interactions exhibit a rich spectrum of excitations, which may substantially expand the range of rogue wave phenomena, and lead to novel space-time analogies, for example with multi-particle interactions. By injecting two colliding and modulated pumps with orthogonal states of polarization in a randomly birefringent telecommunication optical fiber, we provide the first experimental demonstration of an optical dark rogue wave. We also introduce the concept of multi-component analog gravity, whereby localized spatiotemporal horizons are associated with the dark rogue wave solution of the two-component nonlinear Schrödinger system. PMID:26864099
Frisquet, Benoit; Kibler, Bertrand; Morin, Philippe; Baronio, Fabio; Conforti, Matteo; Millot, Guy; Wabnitz, Stefan
2016-01-01
Photonics enables to develop simple lab experiments that mimic water rogue wave generation phenomena, as well as relativistic gravitational effects such as event horizons, gravitational lensing and Hawking radiation. The basis for analog gravity experiments is light propagation through an effective moving medium obtained via the nonlinear response of the material. So far, analogue gravity kinematics was reproduced in scalar optical wave propagation test models. Multimode and spatiotemporal nonlinear interactions exhibit a rich spectrum of excitations, which may substantially expand the range of rogue wave phenomena, and lead to novel space-time analogies, for example with multi-particle interactions. By injecting two colliding and modulated pumps with orthogonal states of polarization in a randomly birefringent telecommunication optical fiber, we provide the first experimental demonstration of an optical dark rogue wave. We also introduce the concept of multi-component analog gravity, whereby localized spatiotemporal horizons are associated with the dark rogue wave solution of the two-component nonlinear Schrödinger system. PMID:26864099
Controllable parabolic-cylinder optical rogue wave
NASA Astrophysics Data System (ADS)
Zhong, Wei-Ping; Chen, Lang; Belić, Milivoj; Petrović, Nikola
2014-10-01
We demonstrate controllable parabolic-cylinder optical rogue waves in certain inhomogeneous media. An analytical rogue wave solution of the generalized nonlinear Schrödinger equation with spatially modulated coefficients and an external potential in the form of modulated quadratic potential is obtained by the similarity transformation. Numerical simulations are performed for comparison with the analytical solutions and to confirm the stability of the rogue wave solution obtained. These optical rogue waves are built by the products of parabolic-cylinder functions and the basic rogue wave solution of the standard nonlinear Schrödinger equation. Such rogue waves may appear in different forms, as the hump and paw profiles.
Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.
Chen, Shihua; Grelu, Philippe; Soto-Crespo, J M
2014-01-01
Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves. PMID:24580164
Akhmediev, N.; Ankiewicz, A.; Soto-Crespo, J. M.
2009-10-15
We propose initial conditions that could facilitate the excitation of rogue waves. Understanding the initial conditions that foster rogue waves could be useful both in attempts to avoid them by seafarers and in generating highly energetic pulses in optical fibers.
Are Rogue Waves Really Unexpected?
NASA Astrophysics Data System (ADS)
Fedele, Francesco
2016-05-01
An unexpected wave is defined by Gemmrich & Garrett (2008) as a wave that is much taller than a set of neighboring waves. Their definition of "unexpected" refers to a wave that is not anticipated by a casual observer. Clearly, unexpected waves defined in this way are predictable in a statistical sense. They can occur relatively often with a small or moderate crest height, but large unexpected waves that are rogue are rare. Here, this concept is elaborated and statistically described based on a third-order nonlinear model. In particular, the conditional return period of an unexpected wave whose crest exceeds a given threshold is developed. This definition leads to greater return periods or on average less frequent occurrences of unexpected waves than those implied by the conventional return periods not conditioned on a reference threshold. Ultimately, it appears that a rogue wave that is also unexpected would have a lower occurrence frequency than that of a usual rogue wave. As specific applications, the Andrea and WACSIS rogue wave events are examined in detail. Both waves appeared without warning and their crests were nearly $2$-times larger than the surrounding $O(10)$ wave crests, and thus unexpected. The two crest heights are nearly the same as the threshold~$h_{0.3\\cdot10^{6}}\\sim1.6H_{s}$ exceeded on average once every~$0.3\\cdot 10^{6}$ waves, where $H_s$ is the significant wave height. In contrast, the Andrea and WACSIS events, as both rogue and unexpected, would occur slightly less often and on average once every~$3\\cdot10^{6}$ and~$0.6\\cdot10^6$ waves respectively.
Rogue Waves and Modulational Instability
NASA Astrophysics Data System (ADS)
Zakharov, V. E.; Dyachenko, A.
2015-12-01
The most plausible cause of rogue wave formation in a deep ocean is development of modulational instability of quasimonochromatic wave trains. An adequate model for study of this phenomenon is the Euler equation for potential flow of incompressible fluid with free surface in 2-D geometry. Numerical integration of these equations confirms completely the conjecture of rogue wave formation from modulational instability but the procedure is time consuming for determination of rogue wave appearance probability for a given shape of wave energy spectrum. This program can be realized in framework of simpler model using replacement of the exact interaction Hamiltonian by more compact Hamiltonian. There is a family of such models. The popular one is the Nonlinear Schrodinger equation (NLSE). This model is completely integrable and suitable for numerical simulation but we consider that it is oversimplified. It misses such important phenomenon as wave breaking. Recently, we elaborated much more reliable model that describes wave breaking but is as suitable as NLSE from the point of numerical modeling. This model allows to perform massive numerical experiments and study statistics of rogue wave formation in details.
Evolution of rogue waves in dusty plasmas
Tolba, R. E. El-Bedwehy, N. A.; Moslem, W. M.; El-Labany, S. K.
2015-04-15
The evolution of rogue waves associated with the dynamics of positively charged dust grains that interact with streaming electrons and ions is investigated. Using a perturbation method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE). The rational solution of the NLSE is presented, which proposed as an effective tool for studying the rogue waves in Jupiter. It is found that the existence region of rogue waves depends on the dust-acoustic speed and the streaming densities of the ions and electrons. Furthermore, the supersonic rogue waves are much taller than the subsonic rogue waves by ∼25 times.
Acoustic Remote Sensing of Rogue Waves
NASA Astrophysics Data System (ADS)
Parsons, Wade; Kadri, Usama
2016-04-01
We propose an early warning system for approaching rogue waves using the remote sensing of acoustic-gravity waves (AGWs) - progressive sound waves that propagate at the speed of sound in the ocean. It is believed that AGWs are generated during the formation of rogue waves, carrying information on the rogue waves at near the speed of sound, i.e. much faster than the rogue wave. The capability of identifying those special sound waves would enable detecting rogue waves most efficiently. A lot of promising work has been reported on AGWs in the last few years, part of which in the context of remote sensing as an early detection of tsunami. However, to our knowledge none of the work addresses the problem of rogue waves directly. Although there remains some uncertainty as to the proper definition of a rogue wave, there is little doubt that they exist and no one can dispute the potential destructive power of rogue waves. An early warning system for such extreme waves would become a demanding safety technology. A closed form expression was developed for the pressure induced by an impulsive source at the free surface (the Green's function) from which the solution for more general sources can be developed. In particular, we used the model of the Draupner Wave of January 1st, 1995 as a source and calculated the induced AGW signature. In particular we studied the AGW signature associated with a special feature of this wave, and characteristic of rogue waves, of the absence of any local set-down beneath the main crest and the presence of a large local set-up.
The destructive impact of the rogue waves
NASA Astrophysics Data System (ADS)
Shamin, Roman
2013-04-01
In our talk rogue waves at the ocean will be considered. By means of numerical modeling dangerous impact of rogue waves on the ships and oil rigs is calculated. Cases when these waves can bring in accident are considered. Using statistics of emergence of waves (see [1]-[2]), it is possible to estimate risks in each case. These results can be used for safety of the ships and oil rigs from rogue waves. References [1] V.E. Zakharov, A.I. Dyachenko, R.V. Shamin. How probability for freak wave formation can be found // THE EUROPEAN PHYSICAL JOURNAL - SPECIAL TOPICS Volume 185, Number 1, 113-124, DOI: 10.1140/epjst/e2010-01242-y [2] V.E. Zakharov, R.V. Shamin. Statistics of rogue waves in computer experiments // JETP Letters, 2012, V. 96, Issue 1, pp 66-69.
NASA Astrophysics Data System (ADS)
Nikolkina, I.; Didenkulova, I.
2012-04-01
Nowadays rogue waves are frequently registered all over the world by various instrumental measurements (range finders installed on offshore platforms or deployed buoys, SAR image processing, etc.). They are confirmed to exist in both deep and shallow areas of the World Ocean and even at the coast. Usually coastal rogue events result in a short-time sudden flooding of the coast, or strong impact upon the steep bank or coastal structures. The relevant descriptions, although at times suffering from too emotional character, are still very important as they considerably broaden the understanding of possible rogue wave occurrence. Although there exist hundreds of instrumental freak wave records, the pool of existing data is still insufficient to build reliable statistics and to give a definite answer concerning the nature of rogue waves. Therefore, it is important further to collect and to analyse all existing data of rogue wave events. It can bring us to new ideas of its nature and mechanisms of formation. In this study the evidence of rogue wave existence all over the world during last years has been collected based mainly on mass media sources. The waves occurred not only in deep and shallow zones of the World Ocean, but also at the coast. From the total number of 131 events reported in 2006-2010, 78 were identified as evidence of rogue waves (which are expected to be at least twice larger than the significant wave height). The background significant wave height was estimated from the satellite wave data. The rogue waves at the coast, where the significant wave height is unknown or meaningless, were selected based on their unexpectedness and hazardous character. In addition, the information on wind speed has been provided when available. The annual and seasonal statistics of rogue waves in each group and overall statistics of rogue wave occurrence has been discussed. The geography of freak wave events has been analyzed. The occurrence of multiple extreme waves (two
Nonlinear Talbot effect of rogue waves
NASA Astrophysics Data System (ADS)
Zhang, Yiqi; Belić, Milivoj R.; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Song, Jianping; Zhang, Yanpeng
2014-03-01
Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.
Book review: Rogue waves in the ocean
Geist, Eric L.
2011-01-01
Review info: Rogue Waves in the Ocean. Advances in Geophysical and Environmental Mechanics and Mathematics. By Christian Kharif, Efim Pelinovsky and Alexey Slunyaev, 2009. ISBN: 978-3540884187, xiii, 216 pp.
Rogue waves and NLSE Lie point symmetries
NASA Astrophysics Data System (ADS)
Lechuga, Antonio
2015-04-01
In past decades rogues waves have been reported to be the main cause of shipping incidents. The unexpectedness and sudden appearance can be seen as their trait more characteristic. Rogue wave damages are linked with this unexpectedness. Therefore many studies have been carried out to ascertain the possible mechanisms of generation of rogue waves. Since the pioneering work of Zakharov researchers have found the so called Nonlinear Schrödinger Equation as the source of solutions to different kinds of rogue waves, Akhmediev, Peregrine , Matveev and many others. Following the well-known Lie group theory many researchers found the Lie point symmetries of the NLSE. Invariants of this equation are the scaling transformations, Galilean transformations and phase transformations. There are different approaches, which mathematical treatment is outside the scope of this work, but at the end, in a travelling frame ,after preserving the Hamiltonian structure we get an ordinary differential equation that is the Duffing equation(well-known as a model of nonlinear oscillations). The next step is the qualitative analysis of this equation. Solutions of the Duffing equation for different coefficients can be put as Jacobi elliptic functions. In particular, in the case of the focusing NLSE, we are concerned with the instabilities, in the sense of Lyapunov, of the transition between some of the solutions. We thought that these instabilities could be the origin of some kind of rogue waves.
Nonparaxial rogue waves in optical Kerr media.
Temgoua, D D Estelle; Kofane, T C
2015-06-01
We consider the inhomogeneous nonparaxial nonlinear Schrödinger (NLS) equation with varying dispersion, nonlinearity, and nonparaxiality coefficients, which governs the nonlinear wave propagation in an inhomogeneous optical fiber system. We present the similarity and Darboux transformations and for the chosen specific set of parameters and free functions, the first- and second-order rational solutions of the nonparaxial NLS equation are generated. In particular, the features of rogue waves throughout polynomial and Jacobian elliptic functions are analyzed, showing the nonparaxial effects. It is shown that the nonparaxiality increases the intensity of rogue waves by increasing the length and reducing the width simultaneously, by the way it increases their speed and penalizes interactions between them. These properties and the characteristic controllability of the nonparaxial rogue waves may give another opportunity to perform experimental realizations and potential applications in optical fibers. PMID:26172812
Nonparaxial rogue waves in optical Kerr media
NASA Astrophysics Data System (ADS)
Temgoua, D. D. Estelle; Kofane, T. C.
2015-06-01
We consider the inhomogeneous nonparaxial nonlinear Schrödinger (NLS) equation with varying dispersion, nonlinearity, and nonparaxiality coefficients, which governs the nonlinear wave propagation in an inhomogeneous optical fiber system. We present the similarity and Darboux transformations and for the chosen specific set of parameters and free functions, the first- and second-order rational solutions of the nonparaxial NLS equation are generated. In particular, the features of rogue waves throughout polynomial and Jacobian elliptic functions are analyzed, showing the nonparaxial effects. It is shown that the nonparaxiality increases the intensity of rogue waves by increasing the length and reducing the width simultaneously, by the way it increases their speed and penalizes interactions between them. These properties and the characteristic controllability of the nonparaxial rogue waves may give another opportunity to perform experimental realizations and potential applications in optical fibers.
Optical Rogue Waves in Vortex Turbulence
NASA Astrophysics Data System (ADS)
Gibson, Christopher J.; Yao, Alison M.; Oppo, Gian-Luca
2016-01-01
We present a spatiotemporal 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 spatiotemporal vortex-mediated 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 density functions (PDFs) with long tails typical of extreme optical events.
Dynamics of nonautonomous rogue waves in Bose-Einstein condensate
Zhao, Li-Chen
2013-02-15
We study rogue waves of Bose-Einstein condensate (BEC) analytically in a time-dependent harmonic trap with a complex potential. Properties of the nonautonomous rogue waves are investigated analytically. It is reported that there are possibilities to 'catch' rogue waves through manipulating nonlinear interaction properly. The results provide many possibilities to manipulate rogue waves experimentally in a BEC system. - Highlights: Black-Right-Pointing-Pointer One more generalized rogue wave solutions are presented. Black-Right-Pointing-Pointer Present one possible way to catch a rouge wave. Black-Right-Pointing-Pointer Properties of rogue waves are investigated analytically for the first time. Black-Right-Pointing-Pointer Provide many possibilities to manipulate rogue waves in BEC.
Optical rogue waves associated with the negative coherent coupling in an isotropic medium.
Sun, Wen-Rong; Tian, Bo; Jiang, Yan; Zhen, Hui-Ling
2015-02-01
Optical rogue waves of the coupled nonlinear Schrödinger equations with negative coherent coupling, which describe the propagation of orthogonally polarized optical waves in an isotropic medium, are reported. We construct and discuss a family of the vector rogue-wave solutions, including the bright rogue waves, four-petaled rogue waves, and dark rogue waves. A bright rogue wave without a valley can split up, giving birth to two bright rogue waves, and an eye-shaped rogue wave can split up, giving birth to two dark rogue waves. PMID:25768624
Early detection of rogue waves by the wavelet transforms
NASA Astrophysics Data System (ADS)
Bayındır, Cihan
2016-01-01
We discuss the possible advantages of using the wavelet transform over the Fourier transform for the early detection of rogue waves. We show that the triangular wavelet spectra of the rogue waves can be detected at early stages of the development of rogue waves in a chaotic wave field. Compared to the Fourier spectra, the wavelet spectra are capable of detecting not only the emergence of a rogue wave but also its possible spatial (or temporal) location. Due to this fact, wavelet transform is also capable of predicting the characteristic distances between successive rogue waves. Therefore multiple simultaneous breaking of the successive rogue waves on ships or on the offshore structures can be predicted and avoided by smart designs and operations.
Spatial Rogue Waves in Photorefractive Ferroelectrics
NASA Astrophysics Data System (ADS)
Pierangeli, D.; Di Mei, F.; Conti, C.; Agranat, A. J.; DelRe, E.
2015-08-01
Rogue waves are observed as light propagates in the extreme nonlinear regime that occurs when a photorefractive ferroelectric crystal is undergoing a structural phase transition. The transmitted spatial light distribution contains bright localized spots of anomalously large intensity that follow a signature long-tail statistics that disappears as the nonlinearity is weakened. The isolated wave events form as out-of-equilibrium response and disorder enhance the Kerr-saturated nonlinearity at the critical point. Self-similarity associable to the individual observed filaments and numerical simulations of the generalized nonlinear Schrödinger equation suggests that dynamics of soliton fusions and scale invariance can microscopically play an important role in the observed rogue intensities and statistics.
A coupled "AB" system: Rogue waves and modulation instabilities
NASA Astrophysics Data System (ADS)
Wu, C. F.; Grimshaw, R. H. J.; Chow, K. W.; Chan, H. N.
2015-10-01
Rogue waves are unexpectedly large and localized displacements from an equilibrium position or an otherwise calm background. For the nonlinear Schrödinger (NLS) model widely used in fluid mechanics and optics, these waves can occur only when dispersion and nonlinearity are of the same sign, a regime of modulation instability. For coupled NLS equations, rogue waves will arise even if dispersion and nonlinearity are of opposite signs in each component as new regimes of modulation instability will appear in the coupled system. The same phenomenon will be demonstrated here for a coupled "AB" system, a wave-current interaction model describing baroclinic instability processes in geophysical flows. Indeed, the onset of modulation instability correlates precisely with the existence criterion for rogue waves for this system. Transitions from "elevation" rogue waves to "depression" rogue waves are elucidated analytically. The dispersion relation as a polynomial of the fourth order may possess double pairs of complex roots, leading to multiple configurations of rogue waves for a given set of input parameters. For special parameter regimes, the dispersion relation reduces to a cubic polynomial, allowing the existence criterion for rogue waves to be computed explicitly. Numerical tests correlating modulation instability and evolution of rogue waves were conducted.
Generation of rogue waves in a wave tank
NASA Astrophysics Data System (ADS)
Lechuga, A.
2012-04-01
Rogue waves have been reported as causing damages and ship accidents all over the oceans of the world. For this reason in the past decades theoretical studies have been carried out with the double aim of improving the knowledge of their main characteristics and of attempting to predict its sudden appearance. As an effort on this line we are trying to generate them in a water tank. The description of the procedure to do that is the objective of this presentation. After Akhmediev et al. (2011) we use a symmetric spectrum as input on the wave maker to produce waves with a rate(Maximun wave height/ significant wave height) of 2.33 and a kurtosis of 4.77, clearly between the limits of rogue waves. As it was pointed out by Janssen (2003), Onorato et al. (2006) and Kharif, Pelinovsky and Slunyaev (2009) modulation instability is enhanced when waves depart from Gaussian statistics (i.e. big kurtosis) and therefore both numbers enforce the criterion that we are generating genuine rogue waves. The same is confirmed by Shemer (2010) and Dudley et al.(2009) from a different perspective. If besides being symmetrical the spectrum is triangular, following Akhmediev(2011),the generated waves are even more conspicuously rogue waves.
Rogue wave spectra of the Kundu-Eckhaus equation
NASA Astrophysics Data System (ADS)
Bayındır, Cihan
2016-06-01
In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrödinger equation (NLSE) analogs and show that the spectra of the individual rogue waves significantly differ from their NLSE analogs. A remarkable difference is the one-sided development of the triangular spectrum before the rogue wave becomes evident in time. Also we show that increasing the skewness of the rogue wave results in increased asymmetry in the triangular Fourier spectra. Additionally, the triangular spectra of the rogue waves of the KEE begin to develop at earlier stages of their development compared to their NLSE analogs, especially for larger skew angles. This feature may be used to enhance the early warning times of the rogue waves. However, we show that in a chaotic wave field with many spectral components the triangular spectra remain as the main attribute as a universal feature of the typical wave fields produced through modulation instability and characteristic features of the KEE's analytical rogue wave spectra may be suppressed in a realistic chaotic wave field.
Rogue wave spectra of the Kundu-Eckhaus equation.
Bayındır, Cihan
2016-06-01
In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrödinger equation (NLSE) analogs and show that the spectra of the individual rogue waves significantly differ from their NLSE analogs. A remarkable difference is the one-sided development of the triangular spectrum before the rogue wave becomes evident in time. Also we show that increasing the skewness of the rogue wave results in increased asymmetry in the triangular Fourier spectra. Additionally, the triangular spectra of the rogue waves of the KEE begin to develop at earlier stages of their development compared to their NLSE analogs, especially for larger skew angles. This feature may be used to enhance the early warning times of the rogue waves. However, we show that in a chaotic wave field with many spectral components the triangular spectra remain as the main attribute as a universal feature of the typical wave fields produced through modulation instability and characteristic features of the KEE's analytical rogue wave spectra may be suppressed in a realistic chaotic wave field. PMID:27415263
Time-reversal generation of rogue waves.
Chabchoub, Amin; Fink, Mathias
2014-03-28
The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS. PMID:24724652
Time-Reversal Generation of Rogue Waves
NASA Astrophysics Data System (ADS)
Chabchoub, Amin; Fink, Mathias
2014-03-01
The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.
Optical rogue waves in integrable turbulence.
Walczak, Pierre; Randoux, Stéphane; Suret, Pierre
2015-04-10
We report optical experiments allowing us to investigate integrable turbulence in the focusing regime of the one-dimensional nonlinear Schrödinger equation (1D NLSE). In analogy with broad spectrum excitation of a one-dimensional water tank, we launch random initial waves in a single mode optical fiber. Using an original optical sampling setup, we measure precisely the probability density function of optical power of the partially coherent waves rapidly fluctuating with time. The probability density function is found to evolve from the normal law to a strong heavy-tailed distribution, thus revealing the formation of rogue waves in integrable turbulence. Numerical simulations of 1D NLSE with stochastic initial conditions quantitatively reproduce the experiments. Our numerical investigations suggest that the statistical features experimentally observed rely on the stochastic generation of coherent analytic solutions of 1D NLSE. PMID:25910126
Integrable turbulence and formation of rogue waves
NASA Astrophysics Data System (ADS)
Agafontsev, D. S.; Zakharov, V. E.
2015-08-01
In the framework of the focusing nonlinear Schrödinger equation we study numerically the nonlinear stage of the modulation instability (MI) of the condensate. The development of the MI leads to the formation of ‘integrable turbulence’ (Zakharov 2009 Stud. Appl. Math. 122 219-34). We study the time evolution of its major characteristics averaged across realizations of initial data—the condensate solution seeded by small random noise with fixed statistical properties. We observe that the system asymptotically approaches to the stationary integrable turbulence, however this is a long process. During this process momenta, as well as kinetic and potential energies, oscillate around their asymptotic values. The amplitudes of these oscillations decay with time t as t-3/2, the phases contain the nonlinear phase shift that decays as t-1/2, and the frequency of the oscillations is equal to the double maximum growth rate of the MI. The evolution of wave-action spectrum is also oscillatory, and characterized by formation of the power-law region ˜|k|-α in the small vicinity of the zeroth harmonic k = 0 with exponent α close to 2/3. The corresponding modes form ‘quasi-condensate’, that acquires very significant wave action and macroscopic potential energy. The probability density function of wave amplitudes asymptotically approaches the Rayleigh distribution in an oscillatory way. Nevertheless, in the beginning of the nonlinear stage the MI slightly increases the occurrence of rogue waves. This takes place at the moments of potential energy modulus minima, where the PDF acquires ‘fat tales’ and the probability of rogue waves occurrence is by about two times larger than in the asymptotic stationary state. Presented facts need a theoretical explanation.
Rogue waves in the ocean - review and progress
NASA Astrophysics Data System (ADS)
Pelinovsky, Efim; Kharif, Christian; Slunyaev, Alexey
2010-05-01
Rogue waves in the ocean and physical mechanisms of their appearance are discussed. Theyse waves are among waves naturally observed by people on the sea surface that represent inseparable feature of the Ocean. Rogue waves appear from nowhere, cause danger and disappear at once. They may occur at the surface of a relatively calm sea, reach not very high amplitudes, but be fatal for ships and crew due to their unexpectedness and abnormal features. The billows appear suddenly exceeding the surrounding waves twice and more, and obtained many names: abnormal, exceptional, extreme, giant, huge, sudden, episodic, freak, monster, rogue, vicious, killer, mad- or rabid-dog waves; cape rollers, holes in the sea, walls of water, three sisters… Freak monsters, though living for seconds, were able to arouse superstitious fear of the crew, cause damage, death of heedless sailors or the whole ship. All these epithets are full of human fear and feebleness. The serious studies of the phenomenon started about 20-30 years ago and have been intensified during the recent decade. The research is being conducted in different fields: in physics (search of physical mechanisms and adequate models of wave enhancement and statistics), in geoscience (determining the regions and weather conditions when rogue waves are most probable), and in ocean and coastal engineering (estimations of the wave loads on fixed and drifting floating structures). Thus, scientists and engineers specializing in different subject areas are involved in the solution of the problem. The state-of-art of the rogue wave study is summarized in our book [Kharif, Ch., Pelinovsky, E., and Slunyaev, A. Rogue Waves in the Ocean. Springer, 2009] and presented in given review. Firstly, we start with a brief introduction to the problem of freak waves aiming at formulating what is understood as rogue or freak waves, what consequences their existence imply in our life, why people are so worried about them. Then we discuss existing
Caustics and Rogue Waves in an Optical Sea
NASA Astrophysics Data System (ADS)
Mathis, Amaury; Froehly, Luc; Toenger, Shanti; Dias, Frédéric; Genty, Goëry; Dudley, John M.
2015-08-01
There are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with particular recent interest in optics. Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes. In this paper, we report a detailed experimental study of linear rogue waves in an optical system, using a spatial light modulator to impose random phase structure on a coherent optical field. After free space propagation, different random intensity patterns are generated, including partially-developed speckle, a broadband caustic network, and an intermediate pattern with characteristics of both speckle and caustic structures. Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra. In addition, the electric field statistics of the intermediate pattern shows properties of an “optical sea” with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed.
Potential changes of wave steepness and occurrence of rogue waves
NASA Astrophysics Data System (ADS)
Bitner-Gregersen, Elzbieta M.; Toffoli, Alessandro
2015-04-01
Wave steepness is an important characteristic of a sea state. It is also well established that wave steepness is one of the parameter responsible for generation of abnormal waves called also freak or rogue waves. The study investigates changes of wave steepness in the past and future wave climate in the North Atlantic. The fifth assessment report IPCC (2013) uses four scenarios for future greenhouse gas concentrations in the atmosphere called Representative Concentration Pathways (RCP). Two of these scenarios RCP 4.5 and RCP 8.5 have been selected to project future wave conditions in the North Atlantic. RCP 4.5 is believed to achieve the political target of a maximum global mean temperature increase of 2° C while RPC 8.5 is close to 'business as usual' and expected to give a temperature increase of 4° C or more. The analysis includes total sea, wind sea and swell. Potential changes of wave steepness for these wave systems are shown and compared with wave steepness derived from historical data. Three historical data sets with different wave model resolutions are used. The investigations show also changes in the mean wind direction as well as in the relative direction between wind sea and swell. Consequences of wave steepness changes for statistics of surface elevation and generation of rogue waves are demonstrated. Uncertainties associated with wave steepness projections are discussed.
NASA Astrophysics Data System (ADS)
Yu, Fajun
2016-05-01
We study multi-rogue wave solutions of a Schro¨dinger equation with higher-order terms employing the generalized Darboux transformation. Some properties of the nonautonomous rogue waves are investigated analytically for the combined Hirota-Lakshmanan-Porsezian-Daniel (LPD) equation. We consider the controllable behaviors of this nonautonomous rogue wave solution with the nonlinearity management function and gain/loss coefficient. It is reported that there are possibilities to 'catch' rogue waves through manipulating nonlinear function and gain/loss coefficient. Our approach can provide many possibilities to manipulate rogue waves and present the potential applications for the rogue wave phenomena.
Rogue Waves in Near Gaussian Sea States
NASA Astrophysics Data System (ADS)
Osborne, Alfred R.
2015-04-01
The field of nonlinear waves often emphasizes the importance of small amplitude modulations in the nonlinear Schroedinger equation (NLS). The Akhmediev and Peregrine breather trains are examples which manifest themselves from the usual linear instability analyses of NLS. In reality, however, oceanic sea states generated by wind waves are very nearly Gaussian processes and so the modulus of the Hilbert transform envelope is approximately Rayleigh distributed (with of course the possibility of a large amplitude tail) and is therefore never a small amplitude modulation. How can we then reconcile our usual perceptions with this fact? What are indeed the solutions of the nonlinear Schroedinger equation non Gaussianity have on the actual types of solutions that are likely to occur in the real ocean? I discuss how finite gap theory for NLS allows us to answer these and many more questions about rogue sea states. I analyze data from various laboratory and oceanic experiments to illustrate the method. Finally, I discuss whether breather trains such as Akhmediev, Peregrine and Ma-Kuznetsov can actually occur in ocean wave data.
Modulational Instability and Rogue Waves in Shallow Water Models
NASA Astrophysics Data System (ADS)
Grimshaw, R.; Chow, K. W.; Chan, H. N.
It is now well known that the focussing nonlinear Schrödinger equation allows plane waves to be modulationally unstable, and at the same time supports breather solutions which are often invoked as models for rogue waves. This suggests a direct connection between modulation instability and the existence of rogue waves. In this chapter we review this connection for a suite of long wave models, such as the Korteweg-de Vries equation, the extended Korteweg-de Vries (Gardner) equation, often used to describe surface and internal waves in shallow water, a Boussinesq equation and, also a coupled set of Korteweg-de Vries equations.
Electrostatic rogue-waves in relativistically degenerate plasmas
Akbari-Moghanjoughi, M.
2014-10-15
In this paper, we investigate the modulational instability and the possibility of electrostatic rogue-wave propagations in a completely degenerate plasma with arbitrary degree of degeneracy, i.e., relativistically degenerate plasma, ranging from solid density to the astrophysical compact stars. The hydrodynamic approach along with the perturbation method is used to reduce the governing equations to the nonlinear Schrödinger equation from which the modulational instability, the growth rate of envelope excitations and the occurrence of rogue as well as super-rogue waves in the plasma, is evaluated. It is observed that the modulational instability in a fully degenerate plasma can be quite sensitive to the plasma number-density and the wavenumber of envelop excitations. It is further revealed that the relativistically degeneracy plasmas (R{sub 0} > 1) are almost always modulationally unstable. It is found, however, that the highly energetic sharply localized electrostatic rogue as well as super-rogue waves can exist in the astrophysical compact objects like white dwarfs and neutron star crusts. The later may provide a link to understand many physical processes in such stars and it may lead us to the origin of the random-localized intense short gamma-ray bursts, which “appear from nowhere and disappear without a trace” quite similar to oceanic rogue structures.
Real world ocean rogue waves explained without the modulational instability.
Fedele, Francesco; Brennan, Joseph; Ponce de León, Sonia; Dudley, John; Dias, Frédéric
2016-01-01
Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually takes place in the ocean. In this work, we question the oceanic relevance of this paradigm. In particular, we analyze several sets of field data in various European locations with various tools, and find that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability. This implies that rogue waves are likely to be rare occurrences of weakly nonlinear random seas. PMID:27323897
Real world ocean rogue waves explained without the modulational instability
Fedele, Francesco; Brennan, Joseph; Ponce de León, Sonia; Dudley, John; Dias, Frédéric
2016-01-01
Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually takes place in the ocean. In this work, we question the oceanic relevance of this paradigm. In particular, we analyze several sets of field data in various European locations with various tools, and find that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability. This implies that rogue waves are likely to be rare occurrences of weakly nonlinear random seas. PMID:27323897
Rogue waves and their generating mechanisms in different physical contexts
NASA Astrophysics Data System (ADS)
Onorato, M.; Residori, S.; Bortolozzo, U.; Montina, A.; Arecchi, F. T.
2013-07-01
Rogue waves is the name given by oceanographers to isolated large amplitude waves, that occur more frequently than expected for normal, Gaussian distributed, statistical events. Rogue waves are ubiquitous in nature and appear in a variety of different contexts. Besides water waves, they have been recently reported in liquid Helium, in nonlinear optics, microwave cavities, etc. The first part of the review is dedicated to rogue waves in the oceans and to their laboratory counterpart with experiments performed in water basins. Most of the work and interpretation of the experimental results will be based on the nonlinear Schrödinger equation, an universal model, that rules the dynamics of weakly nonlinear, narrow band surface gravity waves. Then, we present examples of rogue waves occurring in different physical contexts and we discuss the related anomalous statistics of the wave amplitude, which deviates from the Gaussian behavior that were expected for random waves. The third part of the review is dedicated to optical rogue waves, with examples taken from the supercontinuum generation in photonic crystal fibers, laser fiber systems and two-dimensional spatiotemporal systems. In particular, the extreme waves observed in a two-dimensional spatially extended optical cavity allow us to introduce a description based on two essential conditions for the generation of rogue waves: nonlinear coupling and nonlocal coupling. The first requirement is needed in order to introduce an elementary size, such as that of the solitons or breathers, whereas the second requirement implies inhomogeneity, a mechanism needed to produce the events of mutual collisions and mutual amplification between the elementary solitons or wavepackets. The concepts of “granularity” and “inhomogeneity” as joint generators of optical rogue waves are introduced on the basis of a linear experiment. By extending these concepts to other systems, rogue waves can be classified as phenomena occurring in
High-order rogue waves for the Hirota equation
Li, Linjing; Wu, Zhiwei; Wang, Lihong; He, Jingsong
2013-07-15
The Hirota equation is better than the nonlinear Schrödinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux transformation. Several types of this kind of solutions are classified by their structures. -- Highlights: •The determinant representation of the N-fold Darboux transformation of the Hirota equation. •Properties of the fundamental pattern of the higher order rogue wave. •Ring structure and triangular structure of the higher order rogue waves.
Vector rogue waves and baseband modulation instability in the defocusing regime.
Baronio, Fabio; Conforti, Matteo; Degasperis, Antonio; Lombardo, Sara; Onorato, Miguel; Wabnitz, Stefan
2014-07-18
We report and discuss analytical solutions of the vector nonlinear Schrödinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between modulational instability (MI) and rogue waves is displayed by showing that only a peculiar kind of MI, namely baseband MI, can sustain rogue-wave formation. The existence of vector rogue waves in the defocusing regime is expected to be a crucial progress in explaining extreme waves in a variety of physical scenarios described by multicomponent systems, from oceanography to optics and plasma physics. PMID:25083646
On shallow water rogue wave formation in strongly inhomogeneous channels
NASA Astrophysics Data System (ADS)
Didenkulova, Ira; Pelinovsky, Efim
2016-05-01
Rogue wave formation in shallow water is often governed by dispersive focusing and wave-bottom interaction. In this study we try to combine these mechanisms by considering dispersive nonreflecting wave propagation in shallow strongly inhomogeneous channels. Nonreflecting wave propagation provides extreme wave amplification and the transfer of wave energy over large distances, while dispersive effects allow formation of a short-lived wave of extreme height (rogue wave). We found several types of water channels, where this mechanism can be realized, including (i) channels with a monotonically decreasing cross-section (normal dispersion), (ii) an inland basin described by a half of elliptic paraboloid (abnormal dispersion) and (iii) an underwater hill described by a half of hyperbolic paraboloid (normal dispersion). Conditions for variations of local frequency in the wave train providing optimal focusing of the wave train are also found.
Observation of three dimensional optical rogue waves through obstacles
Leonetti, Marco; Conti, Claudio
2015-06-22
We observe three-dimensional rogue waves in the speckle distribution of a spatially modulated optical beam. Light is transmitted beyond a partially reflecting obstacle generating optical rogue waves at a controlled position in the shadow of the barrier. When the barrier transmits only 0.07% of the input laser power, we observe the mostly localized event. These results demonstrate that an optimum amount of spatial non-homogeneity maximizes the probability of a gigantic event while the technique we exploit enables to control light behind a fully reflective wall.
Rogue Waves and New Multi-wave Solutions of the (2+1)-Dimensional Ito Equation
NASA Astrophysics Data System (ADS)
Tian, Ying-hui; Dai, Zheng-de
2015-06-01
A three-soliton limit method (TSLM) for seeking rogue wave solutions to nonlinear evolution equation (NEE) is proposed. The (2+1)-dimensional Ito equation is used as an example to illustrate the effectiveness of the method. As a result, two rogue waves and a family of new multi-wave solutions are obtained. The result shows that rogue wave can be obtained not only from extreme form of breather solitary wave but also from extreme form of double-breather solitary wave. This is a new and interesting discovery.
Solar wind implication on dust ion acoustic rogue waves
NASA Astrophysics Data System (ADS)
Abdelghany, A. M.; Abd El-Razek, H. N.; Moslem, W. M.; El-Labany, S. K.
2016-06-01
The relevance of the solar wind with the magnetosphere of Jupiter that contains positively charged dust grains is investigated. The perturbation/excitation caused by streaming ions and electron beams from the solar wind could form different nonlinear structures such as rogue waves, depending on the dominant role of the plasma parameters. Using the reductive perturbation method, the basic set of fluid equations is reduced to modified Korteweg-de Vries (KdV) and further modified (KdV) equation. Assuming that the frequency of the carrier wave is much smaller than the ion plasma frequency, these equations are transformed into nonlinear Schrödinger equations with appropriate coefficients. Rational solution of the nonlinear Schrödinger equation shows that rogue wave envelopes are supported by the present plasma model. It is found that the existence region of rogue waves depends on the dust-acoustic speed and the streaming temperatures for both the ions and electrons. The dependence of the maximum rogue wave envelope amplitude on the system parameters has been investigated.
Solitary waves and rogue waves in a plasma with nonthermal electrons featuring Tsallis distribution
NASA Astrophysics Data System (ADS)
Wang, Yue-Yue; Li, Ji-Tao; Dai, Chao-Qing; Chen, Xin-Fen; Zhang, Jie-Fang
2013-11-01
In this Letter, we discuss the electron acoustic (EA) waves in plasmas, which consist of nonthermal hot electrons featuring the Tsallis distribution, and obtain the corresponding governing equation, that is, a nonlinear Schrödinger (NLS) equation. By means of Modulation Instability (MI) analysis of the EA waves, it is found that both electron acoustic solitary wave and rogue wave can exist in such plasmas. Basing on the Darboux transformation method, we derive the analytical expressions of nonlinear solutions of NLS equations, such as single/double solitary wave solutions and single/double rogue wave solutions. The existential regions and amplitude of solitary wave solutions and the rogue wave solutions are influenced by the nonextensive parameter q and nonthermal parameter α. Moreover, the interaction of solitary wave and how to postpone the excitation of rogue wave are also studied.
Coexisting rogue waves within the (2+1)-component long-wave-short-wave resonance.
Chen, Shihua; Soto-Crespo, Jose M; Grelu, Philippe
2014-09-01
The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics. PMID:25314555
Spatial rogue waves in a photorefractive pattern-forming system.
Marsal, N; Caullet, V; Wolfersberger, D; Sciamanna, M
2014-06-15
We have experimentally analyzed pattern formation in an optical system composed of a bulk photorefractive crystal subjected to a single optical feedback. In a highly nonlinear regime far above the modulational instability threshold, we are reporting on turbulent spatiotemporal dynamics that leads to rare, intense localized optical peaks. We have proven that the statistics and features of those peaks correspond to the signatures of two-dimensional spatial rogue events. These optical rogue waves occur erratically in space and time and live typically the same amount of time as the response time of the photorefractive material. PMID:24978569
Integrable Turbulence and Rogue Waves: Breathers or Solitons?
Soto-Crespo, J M; Devine, N; Akhmediev, N
2016-03-11
Turbulence in dynamical systems is one of the most intriguing phenomena of modern science. Integrable systems offer the possibility to understand, to some extent, turbulence. Recent numerical and experimental data suggest that the probability of the appearance of rogue waves in a chaotic wave state in such systems increases when the initial state is a random function of sufficiently high amplitude. We provide explanations for this effect. PMID:27015481
Dust-acoustic rogue waves in a nonextensive plasma
Moslem, W. M.; Shukla, P. K.; Sabry, R.; El-Labany, S. K.
2011-12-15
We present an investigation for the generation of a dust-acoustic rogue wave in a dusty plasma composed of negatively charged dust grains, as well as nonextensive electrons and ions. For this purpose, the reductive perturbation technique is used to obtain a nonlinear Schroedinger equation. The critical wave-number threshold k{sub c}, which indicates where the modulational instability sets in, has been determined precisely for various regimes. Two different behaviors of k{sub c} against the nonextensive parameter q are found. For small k{sub c}, it is found that increasing q would lead to an increase of k{sub c} until q approaches a certain value q{sub c}, then further increase of q beyond q{sub c} decreases the value of k{sub c}. For large k{sub c}, the critical wave-number threshold k{sub c} is always increasing with q. Within the modulational instability region, a random perturbation of the amplitude grows and thus creates dust-acoustic rogue waves. In order to show that the characteristics of the rogue waves are influenced by the plasma parameters, the relevant numerical analysis of the appropriate nonlinear solution is presented. The nonlinear structure, as reported here, could be useful for controlling and maximizing highly energetic pulses in dusty plasmas.
Dust-acoustic rogue waves in a nonextensive plasma.
Moslem, W M; Sabry, R; El-Labany, S K; Shukla, P K
2011-12-01
We present an investigation for the generation of a dust-acoustic rogue wave in a dusty plasma composed of negatively charged dust grains, as well as nonextensive electrons and ions. For this purpose, the reductive perturbation technique is used to obtain a nonlinear Schrödinger equation. The critical wave-number threshold k(c), which indicates where the modulational instability sets in, has been determined precisely for various regimes. Two different behaviors of k(c) against the nonextensive parameter q are found. For small k(c), it is found that increasing q would lead to an increase of k(c) until q approaches a certain value q(c), then further increase of q beyond q(c) decreases the value of k(c). For large k(c), the critical wave-number threshold k(c) is always increasing with q. Within the modulational instability region, a random perturbation of the amplitude grows and thus creates dust-acoustic rogue waves. In order to show that the characteristics of the rogue waves are influenced by the plasma parameters, the relevant numerical analysis of the appropriate nonlinear solution is presented. The nonlinear structure, as reported here, could be useful for controlling and maximizing highly energetic pulses in dusty plasmas. PMID:22304203
Nonlinear time series analysis: towards an effective forecast of rogue waves
NASA Astrophysics Data System (ADS)
Steinmeyer, Günter; Birkholz, Simon; Brée, Carsten; Demircan, Ayhan
2016-03-01
Rogue waves are extremely large waves that exceed any expectation based on long-term observation and Gaussian statistics. Ocean rogue waves exceed the significant wave height in the ocean by a factor 2. Similar phenomena have been observed in a multiplicity of optical systems. While the optical systems show a much higher frequency of rogue events than the ocean, it appears nevertheless questionable what conclusions can be drawn for the prediction of ocean rogue waves. Here we tackle the problem from a different perspective and analyze the predictability of rogue events in two optical systems as well as in the ocean using nonlinear time-series analysis. Our analysis is exclusively based on experimental data. The results appear rather surprising as the optical rogue wave scenario of fiber-based supercontinuum generation does not allow any prediction whereas real ocean rogue waves and a multifilament scenario do bear a considerable amount of determinism, which allows, at least in principle, the prediction of extreme events. It becomes further clear that there exist two fundamentally different types of rogue-wave supporting systems. One class of rogue waves is obviously seeded by quantum fluctuations whereas in the other class, linear random interference of waves seems to prevail.
Emergent rogue wave structures and statistics in spontaneous modulation instability
Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M.
2015-01-01
The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude “rogue waves” emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised “breather” or “soliton on finite background (SFB)” structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions. PMID:25993126
High-order rogue waves in vector nonlinear Schrödinger equations.
Ling, Liming; Guo, Boling; Zhao, Li-Chen
2014-04-01
We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber. PMID:24827185
Optical rogue waves in whispering-gallery-mode resonators
NASA Astrophysics Data System (ADS)
Coillet, Aurélien; Dudley, John; Genty, Goëry; Larger, Laurent; Chembo, Yanne K.
2014-01-01
We report a theoretical study showing that rogue waves can emerge in whispering-gallery-mode resonators as the result of the chaotic interplay between Kerr nonlinearity and anomalous group-velocity dispersion. The nonlinear dynamics of the propagation of light in a whispering-gallery-mode resonator is investigated using the Lugiato-Lefever equation, and we give evidence of a range of parameters where rare and extreme events associated with non-Gaussian statistics of the field maxima are observed.
Roadmap on optical rogue waves and extreme events
NASA Astrophysics Data System (ADS)
Akhmediev, Nail; Kibler, Bertrand; Baronio, Fabio; Belić, Milivoj; Zhong, Wei-Ping; Zhang, Yiqi; Chang, Wonkeun; Soto-Crespo, Jose M.; Vouzas, Peter; Grelu, Philippe; Lecaplain, Caroline; Hammani, K.; Rica, S.; Picozzi, A.; Tlidi, Mustapha; Panajotov, Krassimir; Mussot, Arnaud; Bendahmane, Abdelkrim; Szriftgiser, Pascal; Genty, Goery; Dudley, John; Kudlinski, Alexandre; Demircan, Ayhan; Morgner, Uwe; Amiraranashvili, Shalva; Bree, Carsten; Steinmeyer, Günter; Masoller, C.; Broderick, Neil G. R.; Runge, Antoine F. J.; Erkintalo, Miro; Residori, S.; Bortolozzo, U.; Arecchi, F. T.; Wabnitz, Stefan; Tiofack, C. G.; Coulibaly, S.; Taki, M.
2016-06-01
The pioneering paper ‘Optical rogue waves’ by Solli et al (2007 Nature 450 1054) started the new subfield in optics. This work launched a great deal of activity on this novel subject. As a result, the initial concept has expanded and has been enriched by new ideas. Various approaches have been suggested since then. A fresh look at the older results and new discoveries has been undertaken, stimulated by the concept of ‘optical rogue waves’. Presently, there may not by a unique view on how this new scientific term should be used and developed. There is nothing surprising when the opinion of the experts diverge in any new field of research. After all, rogue waves may appear for a multiplicity of reasons and not necessarily only in optical fibers and not only in the process of supercontinuum generation. We know by now that rogue waves may be generated by lasers, appear in wide aperture cavities, in plasmas and in a variety of other optical systems. Theorists, in turn, have suggested many other situations when rogue waves may be observed. The strict definition of a rogue wave is still an open question. For example, it has been suggested that it is defined as ‘an optical pulse whose amplitude or intensity is much higher than that of the surrounding pulses’. This definition (as suggested by a peer reviewer) is clear at the intuitive level and can be easily extended to the case of spatial beams although additional clarifications are still needed. An extended definition has been presented earlier by N Akhmediev and E Pelinovsky (2010 Eur. Phys. J. Spec. Top. 185 1–4). Discussions along these lines are always useful and all new approaches stimulate research and encourage discoveries of new phenomena. Despite the potentially existing disagreements, the scientific terms ‘optical rogue waves’ and ‘extreme events’ do exist. Therefore coordination of our efforts in either unifying the concept or in introducing alternative definitions must be continued. From
Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field
NASA Astrophysics Data System (ADS)
Bayindir, Cihan
2016-03-01
In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, k . The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plane-wave solution; however, direction of propagation is controlled by the β parameter, the constant in front of the Raman-effect term. We have also calculated the probabilities of the rogue wave occurrence for various values of propagation constant k and showed that the probability of rogue wave occurrence depends on k . Additionally, we have showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE. Statistical comparisons between the KEE and the cubic nonlinear Schrödinger equation have also been presented.
Dust-acoustic waves modulational instability and rogue waves in a polarized dusty plasma
Bouzit, Omar; Tribeche, Mouloud
2015-10-15
The polarization force-induced changes in the dust-acoustic waves (DAWs) modulational instability (MI) are examined. Using the reductive perturbation method, the nonlinear Schrödinger equation that governs the MI of the DAWs is obtained. It is found that the effect of the polarization term R is to narrow the wave number domain for the onset of instability. The amplitude of the wave envelope decreases as R increases, meaning that the polarization force effects render weaker the associated DA rogue waves. The latter may therefore completely damp in the vicinity of R ∼ 1, i.e., as the polarization force becomes close to the electrostatic one (the net force acting on the dust particles becomes vanishingly small). The DA rogue wave profile is very sensitive to any change in the restoring force acting on the dust particles. It turns out that the polarization effects may completely smear out the DA rogue waves.
Controlling formation and suppression of fiber-optical rogue waves.
Brée, Carsten; Steinmeyer, Günter; Babushkin, Ihar; Morgner, Uwe; Demircan, Ayhan
2016-08-01
Fiber-optical rogue waves appear as rare but extreme events during optical supercontinuum generation in photonic crystal fibers. This process is typically initiated by the decay of a high-order fundamental soliton into fundamental solitons. Collisions between these solitons as well as with dispersive radiation affect the soliton trajectory in frequency and time upon further propagation. Launching an additional dispersive wave at carefully chosen delay and wavelength enables statistical manipulation of the soliton trajectory in such a way that the probability of rogue wave formation is either enhanced or reduced. To enable efficient control, parameters of the dispersive wave have to be chosen to allow trapping of dispersive radiation in the nonlinear index depression created by the soliton. Under certain conditions, direct manipulation of soliton properties is possible by the dispersive wave. In other more complex scenarios, control is possible via increasing or decreasing the number of intersoliton collisions. The control mechanism reaches a remarkable efficiency, enabling control of relatively large soliton energies. This scenario appears promising for highly dynamic all-optical control of supercontinua. PMID:27472607
NASA Astrophysics Data System (ADS)
Wang, Chuanjian; Dai, Zhengde; Liu, Changfu
2014-07-01
In this paper, two types of multi-parameter breather homoclinic wave solutions—including breather homoclinic wave and rational homoclinic wave solutions—are obtained by using the Hirota technique and ansätz with complexity of parameter for the coupled Schrödinger-Boussinesq equation. Rogue waves in the form of the rational homoclinic solution are derived when the periods of breather homoclinic wave go to infinite. Some novel features of homoclinic wave solutions are discussed and presented. In contrast to the normal bright rogue wave structure, a structure like a four-petaled flower in temporal-spatial distribution is exhibited. Further with the change of the wave number of the plane wave, the bright and dark rogue wave structures may change into each other. The bright rogue wave structure results from the full merger of two nearby peaks, and the dark rogue wave structure results from the full merger of two nearby holes. The dark rogue wave for the uncoupled Boussinesq equation is finally obtained. Its structural properties show that it never takes on bright rogue wave features with the change of parameter. It is hoped that these results might provide us with useful information on the dynamics of the relevant fields in physics.
Rational solitary wave and rogue wave solutions in coupled defocusing Hirota equation
NASA Astrophysics Data System (ADS)
Huang, Xin
2016-06-01
We derive and study a general rational solution of a coupled defocusing Hirota equation which can be used to describe evolution of light in a two-mode fiber with defocusing Kerr effect and some certain high-order effects. We find some new excitation patterns in the model, such as M-shaped soliton, W-shaped soliton, anti-eye-shaped rogue wave and four-petaled flower rogue wave. The results are compared with the solutions obtained in other coupled systems like vector nonlinear Schrödinger equation, coupled focusing Hirota and Sasa-Satsuma equations. We explain the new characters by modulational instability properties. This further indicates that rational solution does not necessarily correspond to rogue wave excitation dynamics and the quantitative relation between nonlinear excitations and modulational instability should exist.
Yomba, Emmanuel; Zakeri, Gholam-Ali
2016-08-01
The coupled inhomogeneous Schrödinger equations with a wide range of applications describing a field of pluses with the right and the left polarizations that take into account cross-phase modulations, stimulated Ramani scattering, and absorption effects are investigated. A combination of several different approaches is used in a novel way to obtain the explicit expressions for the rogue-pair and dark-bright-rogue waves. We study the dynamics of these structurally stable rogues and analyze the effects of a parameter that controls the region of stability that intrinsically connects the cross-phase modulation and other Kerr nonlinearity factors. The effects of the right and left polarizations on the shape of the rogue-pair and other solitary rogue waves are graphically analyzed. These rogue-pair waves are studied on periodic and non-periodic settings. We observe that rogue-pair wave from the right and left polarizations has a similar structure while the dark-bright-rogue waves have quite different intensity profiles. PMID:27586611
Construction of rogue wave and lump solutions for nonlinear evolution equations
NASA Astrophysics Data System (ADS)
Lü, Zhuosheng; Chen, Yinnan
2015-07-01
Based on symbolic computation and an ansatz, we present a constructive algorithm to seek rogue wave and lump solutions for nonlinear evolution equations. As illustrative examples, we consider the potential-YTSF equation and a variable coefficient KP equation, and obtain nonsingular rational solutions of the two equations. The solutions can be rogue wave or lump solutions under different parameter conditions. We also present graphic illustration of some special solutions which would help better understand the evolution of solution waves.
NASA Astrophysics Data System (ADS)
Xie, Xi-Yang; Tian, Bo; Wang, Yu-Feng; Sun, Ya; Jiang, Yan
2015-11-01
In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable-coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.
Nonlinear dynamics of trapped waves on jet currents and rogue waves.
Shrira, V I; Slunyaev, A V
2014-04-01
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrow band in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonlinear theory based on the modal approach of Shrira and Slunyaev [J. Fluid. Mech. 738, 65 (2014)] leads to the one-dimensional modified nonlinear Schrödinger equation of self-focusing type for a single mode. Its solutions such as envelope solitons and breathers are considered to be prototypes of rogue waves; these solutions, in contrast to waves in the absence of currents, are robust with respect to transverse perturbations, which suggests a potentially higher probability of rogue waves. Robustness of the long-lived analytical solutions describing modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations. PMID:24827178
Nonlinear dynamics of trapped waves on jet currents and rogue waves
NASA Astrophysics Data System (ADS)
Shrira, V. I.; Slunyaev, A. V.
2014-04-01
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrow band in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonlinear theory based on the modal approach of Shrira and Slunyaev [J. Fluid. Mech. 738, 65 (2014), 10.1017/jfm.2013.584] leads to the one-dimensional modified nonlinear Schrödinger equation of self-focusing type for a single mode. Its solutions such as envelope solitons and breathers are considered to be prototypes of rogue waves; these solutions, in contrast to waves in the absence of currents, are robust with respect to transverse perturbations, which suggests a potentially higher probability of rogue waves. Robustness of the long-lived analytical solutions describing modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations.
Manipulating matter rogue waves and breathers in Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Manikandan, K.; Muruganandam, P.; Senthilvelan, M.; Lakshmanan, M.
2014-12-01
We construct higher-order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps: (i) the time-independent expulsive trap, (ii) time-dependent monotonous trap, and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second- and third-order rogue waves transform into the first-order-like rogue waves. We also analyze the density profiles of breather solutions. Here we also show that the shapes of the breathers change when we tune the strength of the trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.
NASA Astrophysics Data System (ADS)
Tchinang Tchameu, J. D.; Togueu Motcheyo, A. B.; Tchawoua, C.
2016-09-01
The discrete multi-rogue waves (DMRW) as solution of the discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearities is studied numerically. These biological rogue waves represent the complex probability amplitude of finding an amide-I vibrational quantum at a site. We observe that the growth in the higher order saturable nonlinearity implies the formation of DMRW including an increase in the short-living DMRW and a decrease in amplitude of the long-living DMRW.
NASA Astrophysics Data System (ADS)
Zhang, Hai-Qiang; Yuan, Sha-Sha; Wang, Yue
2016-05-01
In this paper, the generalized Darboux transformation for the coherently-coupled nonlinear Schrödinger (CCNLS) system is constructed in terms of determinant representations. Based on the Nth-iterated formula, the vector bright soliton solution and vector rogue wave solution are systematically derived under the nonvanishing background. The general first-order vector rogue wave solution can admit many different fundamental patterns including eye-shaped and four-petaled rogue waves. It is believed that there are many more abundant patterns for high order vector rogue waves in CCNLS system.
Wave Turbulence in Superfluid {sup 4}He: Energy Cascades and Rogue Waves in the Laboratory
Efimov, V. B.; Ganshin, A. N.; McClintock, P. V. E.; Kolmakov, G. V.; Mezhov-Deglin, L. P.
2008-11-13
Recent work on second sound acoustic turbulence in superfluid {sup 4}He is reviewed. Observations of forward and inverse energy cascades are described. The onset of the inverse cascade occurs above a critical driving energy and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomenon is outlined and shown to be in good agreement with the experiments.
Ion-acoustic super rogue waves in ultracold neutral plasmas with nonthermal electrons
El-Tantawy, S. A.; El-Bedwehy, N. A.; El-Labany, S. K.
2013-07-15
The ion-acoustic rogue waves in ultracold neutral plasmas consisting of ion fluid and nonthermal electrons are reported. A reductive perturbation method is used to obtain a nonlinear Schrödinger equation for describing the system and the modulation instability of the ion-acoustic wave is analyzed. The critical wave number k{sub c}, which indicates where the modulational instability sets in, has been determined. Moreover, the possible region for the ion-acoustic rogue waves to exist is defined precisely. The effects of the nonthermal parameter β and the ions effective temperature ratio σ{sub *} on the critical wave number k{sub c} are studied. It is found that there are two critical wave numbers in our plasma system. For low wave number, increasing β would lead to cringe k{sub c} until β approaches to its critical value β{sub c}, then further increase of β beyond β{sub c} would enhance the values of k{sub c}. For large wave numbers, the increase of β would lead to a decrease of k{sub c}. However, increasing σ{sub *} would lead to the reduction of k{sub c} for all values of the wave number. The dependence of the rogue waves profile on the plasma parameters is numerically examined. It is found that the rogue wave amplitudes have complex behavior with increasing β. Furthermore, the enhancement of σ{sub *} and the carrier wave number k reduces the rogue wave amplitude. It is noticed that near to the critical wave number, the rogue wave amplitude becomes high, but it shrinks whenever we stepped away from k{sub c}. The implications of our results in laboratory ultracold neutral plasma experiments are briefly discussed.
Dust ion-acoustic rogue waves in a three-species ultracold quantum dusty plasmas
Sun, Wen-Rong; Tian, Bo Liu, Rong-Xiang; Liu, De-Yin
2014-10-15
Dust ion-acoustic (DIA) rogue waves are reported for a three-component ultracold quantum dusty plasma comprised of inertialess electrons, inertial ions, and negatively charged immobile dust particles. The nonlinear Schrödinger (NLS) equation appears for the low frequency limit. Modulation instability (MI) of the DIA waves is analyzed. Influence of the modulation wave number, ion-to-electron Fermi temperature ratio ρ and dust-to-ion background density ratio N{sub d} on the MI growth rate is discussed. The first- and second-order DIA rogue-wave solutions of the NLS equation are examined numerically. It is found that the enhancement of N{sub d} and carrier wave number can increase the envelope rogue-wave amplitudes. However, the increase of ρ reduces the envelope rogue-wave amplitudes. - Highlights: • The nonlinear Schrödinger equation is derived for the low frequency limit. • Modulational instability growth rate is discussed. • The first- and second-order dust ion-acoustic rogue waves are examined numerically.
Rogue wave variational modelling through the interaction of two solitary waves
NASA Astrophysics Data System (ADS)
Gidel, Floriane; Bokhove, Onno
2016-04-01
The extreme and unexpected characteristics of Rogue waves have made them legendary for centuries. It is only on the 1st of January 1995 that these mariners' tales started to raise scientist's curiosity, when such a wave was recorded in the North Sea; a sudden wall of water hit the Draupner offshore platform, more than twice higher than the other waves, providing evidence of the existence of rogue or freak waves. Since then, studies have shown that these surface gravity waves of high amplitude (at least twice the height of the other sea waves [Dyste et al., 2008]) appear in non-linear dispersive water motion [Drazin and Johnson, 1989], at any depth, and have caused a lot of damage in recent years [Nikolkina and Didenkulova, 2011 ]. So far, most of the studies have tried to determine their probability of occurrence, but no conclusion has been achieved yet, which means that we are currently unenable to predict or avoid these monster waves. An accurate mathematical and numerical water-wave model would enable simulation and observation of this external forcing on boats and offshore structures and hence reduce their threat. In this work, we aim to model rogue waves through a soliton splash generated by the interaction of two solitons coming from different channels at a specific angle. Kodama indeed showed that one way to produce extreme waves is through the intersection of two solitary waves, or one solitary wave and its oblique reflection on a vertical wall [Yeh, Li and Kodama, 2010 ]. While he modelled Mach reflection from Kadomtsev-Petviashvili (KP) theory, we aim to model rogue waves from the three-dimensional potential flow equations and/or their asymptotic equivalent described by Benney and Luke [Benney and Luke, 1964]. These theories have the advantage to allow wave propagation in several directions, which is not the case with KP equations. The initial solitary waves are generated by removing a sluice gate in each channel. The equations are derived through a
Dudley, J. M.; Sarano, V.; Dias, F.
2013-01-01
The Hokusai woodcut entitled The great wave off Kanagawa has been interpreted as an unusually large storm wave, likely to be classed as a rogue wave, and possibly generated from nonlinear wave dynamics (J. H. E. Cartwright and H. Nakamura, Notes Rec. R. Soc. 63, 119–135 (2009)). In this paper, we present a complementary discussion of this hypothesis, discussing in particular how linear and nonlinear mechanisms can both contribute to the emergence of rogue wave events. By making reference to the Great wave's simultaneous transverse and longitudinal localization, we show that the purely linear mechanism of directional focusing also predicts characteristics consistent with those of the Great wave. In addition, we discuss the properties of a particular rogue wave photographed on the open ocean in sub-Antarctic waters, which shows two-dimensional localization and breaking dynamics remarkably similar to Hokusai's depiction in the woodcut. PMID:24687148
Akhmediev breathers, Kuznetsov-Ma solitons and rogue waves in a dispersion varying optical fiber
NASA Astrophysics Data System (ADS)
Sun, Wen-Rong; Tian, Bo; Sun, Ya; Chai, Jun; Jiang, Yan
2016-03-01
Dispersion varying fibres have applications in optical pulse compression techniques. We investigate Akhmediev breathers, Kuznetsov-Ma (KM) solitons and optical rogue waves in a dispersion varying optical fibre based on a variable-coefficient nonlinear Schrödinger equation. Analytical solutions in the forms of Akhmediev breathers, KM solitons and rogue waves up to the second order of that equation are obtained via the generalised Darboux transformation and integrable constraint. The properties of Akhmediev breathers, KM solitons and rogue waves in a dispersion varying optical fibre, e.g. dispersion decreasing fibre (DDF) or a periodically distributed system (PDS), are discussed: in a DDF we observe the compression behaviours of KM solitons and rogue waves on a monotonically increasing background. The amplitude of each peak of the KM soliton increases, while the width of each peak of the KM soliton gradually decreases along the propagation distance; in a PDS, the amplitude of each peak of the KM soliton varies periodically along the propagation distance on a periodic background. Different from the KM soliton, the Akhmediev breather and rogue waves repeat their behaviours along the propagation distance without the compression.
The nonlinear evolution of rogue waves generated by means of wave focusing technique
NASA Astrophysics Data System (ADS)
Hu, HanHong; Ma, Ning
2011-01-01
Generating the rogue waves in offshore engineering is investigated, first of all, to forecast its occurrence to protect the offshore structure from being attacked, to study the mechanism and hydrodynamic properties of rouge wave experimentally as well as the rouge/structure interaction for the structure design. To achieve these purposes demands an accurate wave generation and calculation. In this paper, we establish a spatial domain model of fourth order nonlinear Schrödinger (NLS) equation for describing deep-water wave trains in the moving coordinate system. In order to generate rogue waves in the experimental tank efficiently, we take care that the transient water wave (TWW) determines precisely the concentration of time/place. First we simulate the three-dimensional wave using TWW in the numerical tank and modeling the deepwater basin with a double-side multi-segmented wave-maker in Shanghai Jiao Tong University (SJTU) under the linear superposing theory. To discuss its nonlinearity for guiding the experiment, we set the TWW as the initial condition of the NLS equation. The differences between the linear and nonlinear simulations are presented. Meanwhile, the characteristics of the transient water wave, including water particle velocity and wave slope, are investigated, which are important factors in safeguarding the offshore structures.
NASA Astrophysics Data System (ADS)
Li, Long-Xing; Liu, Jun; Dai, Zheng-De; Liu, Ren-Lang
2014-09-01
In this work, the rational homoclinic solution (rogue wave solution) can be obtained via the classical homoclinic solution for the nonlinear Schrödinger (NLS) equation and the coupled nonlinear Schrödinger (CNLS) equation, respectively. This is a new way for generating rogue wave comparing with direct constructing method and Darboux dressing technique
NASA Astrophysics Data System (ADS)
Tsai, Ya-Yi; Tsai, Jun-Yi; I, Lin
2016-06-01
Rogue waves--rare uncertainly emerging localized events with large amplitudes--have been experimentally observed in many nonlinear wave phenomena, such as water waves, optical waves, second sound in superfluid He II (ref. ) and ion acoustic waves in plasmas. Past studies have mainly focused on one-dimensional (1D) wave behaviour through modulation instabilities, and to a lesser extent on higher-dimensional behaviour. The question whether rogue waves also exist in nonlinear 3D acoustic-type plasma waves, the kinetic origin of their formation and their correlation with surrounding 3D waveforms are unexplored fundamental issues. Here we report the direct experimental observation of dust acoustic rogue waves in dusty plasmas and construct a picture of 3D particle focusing by the surrounding tilted and ruptured wave crests, associated with the higher probability of low-amplitude holes for rogue-wave generation.
On the rogue waves propagation in non-Maxwellian complex space plasmas
NASA Astrophysics Data System (ADS)
El-Tantawy, S. A.; El-Awady, E. I.; Tribeche, M.
2015-11-01
The implications of the non-Maxwellian electron distributions (nonthermal/or suprathermal/or nonextensive distributions) are examined on the dust-ion acoustic (DIA) rogue/freak waves in a dusty warm plasma. Using a reductive perturbation technique, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation. The latter is used to study the nonlinear evolution of modulationally unstable DIA wavepackets and to describe the rogue waves (RWs) propagation. Rogue waves are large-amplitude short-lived wave groups, routinely observed in space plasmas. The possible region for the rogue waves to exist is defined precisely for typical parameters of space plasmas. It is shown that the RWs strengthen for decreasing plasma nonthermality and increasing superthermality. For nonextensive electrons, the RWs amplitude exhibits a bit more complex behavior, depending on the entropic index q. Moreover, our numerical results reveal that the RWs exist with all values of the ion-to-electron temperature ratio σ for nonthermal and superthermal distributions and there is no limitation for the freak waves to propagate in both two distributions in the present plasma system. But, for nonextensive electron distribution, the bright- and dark-type waves can propagate in this case, which means that there is a limitation for the existence of freak waves. Our systematic investigation should be useful in understanding the properties of DIA solitary waves that may occur in non-Maxwellian space plasmas.
On the rogue waves propagation in non-Maxwellian complex space plasmas
El-Tantawy, S. A. El-Awady, E. I.; Tribeche, M. E-mail: mtribeche@usthb.dz
2015-11-15
The implications of the non-Maxwellian electron distributions (nonthermal/or suprathermal/or nonextensive distributions) are examined on the dust-ion acoustic (DIA) rogue/freak waves in a dusty warm plasma. Using a reductive perturbation technique, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation. The latter is used to study the nonlinear evolution of modulationally unstable DIA wavepackets and to describe the rogue waves (RWs) propagation. Rogue waves are large-amplitude short-lived wave groups, routinely observed in space plasmas. The possible region for the rogue waves to exist is defined precisely for typical parameters of space plasmas. It is shown that the RWs strengthen for decreasing plasma nonthermality and increasing superthermality. For nonextensive electrons, the RWs amplitude exhibits a bit more complex behavior, depending on the entropic index q. Moreover, our numerical results reveal that the RWs exist with all values of the ion-to-electron temperature ratio σ for nonthermal and superthermal distributions and there is no limitation for the freak waves to propagate in both two distributions in the present plasma system. But, for nonextensive electron distribution, the bright- and dark-type waves can propagate in this case, which means that there is a limitation for the existence of freak waves. Our systematic investigation should be useful in understanding the properties of DIA solitary waves that may occur in non-Maxwellian space plasmas.
NASA Astrophysics Data System (ADS)
Ling, Liming; Feng, Bao-Feng; Zhu, Zuonong
2016-07-01
In the present paper, we are concerned with the general analytic solutions to the complex short pulse (CSP) equation including soliton, breather and rogue wave solutions. With the aid of a generalized Darboux transformation, we construct the N-bright soliton solution in a compact determinant form, the N-breather solution including the Akhmediev breather and a general higher order rogue wave solution. The first and second order rogue wave solutions are given explicitly and analyzed. The asymptotic analysis is performed rigorously for both the N-soliton and the N-breather solutions. All three forms of the analytical solutions admit either smoothed-, cusped- or looped-type ones for the CSP equation depending on the parameters. It is noted that, due to the reciprocal (hodograph) transformation, the rogue wave solution to the CSP equation can be a smoothed, cusponed or a looped one, which is different from the rogue wave solution found so far.
Amplification of matter rogue waves and breathers in quasi-two-dimensional Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Manikandan, K.; Senthilvelan, M.; Kraenkel, R. A.
2016-02-01
We construct rogue wave and breather solutions of a quasi-two-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap. We show that the trapping potential and an arbitrary functional parameter that present in the similarity transformation should satisfy a constraint for the considered equation to be integrable and yield the desired solutions. We consider two different forms of functional parameters and investigate how the density of the rogue wave and breather profiles vary with respect to these functional parameters. We also construct vector localized solutions of a two coupled quasi-two-dimensional Bose-Einstein condensate system. We then investigate how the vector localized density profiles modify in the constant density background with respect to the functional parameters. Our results may help to manipulate matter rogue waves experimentally in the two-dimensional Bose-Einstein condensate systems.
Rogue waves for a system of coupled derivative nonlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Chan, Hiu Ning; Malomed, Boris; Chow, Kwok Wing
2015-11-01
Previous works in the literature on water waves have demonstrated that the fourth-order evolution of gravity waves in deep water will be governed by a higher order nonlinear Schrödinger equation. In the presence of two wave trains, the system is described by a higher order coupled nonlinear Schrödinger system. Through a gauge transformation, these evolution equations are reduced to a coupled derivative nonlinear Schrödinger system. The goal here is to study rogue waves, unexpectedly large displacements from an equilibrium position, through the Hirota bilinear transformation theoretically. The connections between the onset of rogue waves and modulation instability are investigated. The range of cubic nonlinearity allowing rogue wave formation is elucidated. Under a finite group velocity mismatch between the two components, the existence regime for rogue waves is extended as compared to the case with a single wave train. The amplification ratio of the amplitude can be higher than that of the single component nonlinear Schrödinger equation. Partial financial support has been provided by the Research Grants Council through contracts HKU711713E and HKU17200815.
Rogue wave modes for a derivative nonlinear Schrödinger model.
Chan, Hiu Ning; Chow, Kwok Wing; Kedziora, David Jacob; Grimshaw, Roger Hamilton James; Ding, Edwin
2014-03-01
Rogue waves in fluid dynamics and optical waveguides are unexpectedly large displacements from a background state, and occur in the nonlinear Schrödinger equation with positive linear dispersion in the regime of positive cubic nonlinearity. Rogue waves of a derivative nonlinear Schrödinger equation are calculated in this work as a long-wave limit of a breather (a pulsating mode), and can occur in the regime of negative cubic nonlinearity if a sufficiently strong self-steepening nonlinearity is also present. This critical magnitude is shown to be precisely the threshold for the onset of modulation instabilities of the background plane wave, providing a strong piece of evidence regarding the connection between a rogue wave and modulation instability. The maximum amplitude of the rogue wave is three times that of the background plane wave, a result identical to that of the Peregrine breather in the classical nonlinear Schrödinger equation model. This amplification ratio and the resulting spectral broadening arising from modulation instability correlate with recent experimental results of water waves. Numerical simulations in the regime of marginal stability are described. PMID:24730920
Amplitude modulation of hydromagnetic waves and associated rogue waves in magnetoplasmas.
Sabry, R; Moslem, W M; Shukla, P K
2012-09-01
It is shown that the dynamics of amplitude-modulated compressional dispersive Alfvénic (CDA) waves in a collisional megnetoplasma is governed by a complex Ginzburg-Landau (CGL) equation. The nonlinear dispersion relation for the modulational instability of the CDA waves is derived and investigated numerically. It is found that the growth rate of the modulational instability decreases (increases) with the increase of the normalized electron-ion collision frequency α (the plasma β). The modulational instability criterion for the CGL equation is defined precisely and investigated numerically. The region of the modulational instability becomes narrower with the increase of α and β, indicating that the system dissipates the wave energy by collisions, and a stable CDA wave envelope packet in the form of a hole will be a dominant localized pulse. For a collisionless plasma, i.e., α=0, the CGL equation reduces to the standard nonlinear Schrödinger (NLS) equation. The latter is used to investigate the modulational (in)stability region for the CDA waves in a collisionless magnetoplasma. It is shown that, within unstable regions, a random set of nonlinearly interacting CDA perturbations leads to the formation of CDA rogue waves. In order to demonstrate that the characteristics of the CDA rogue waves are influenced by the plasma β, the relevant numerical analysis of the appropriate nonlinear solution of the NLS equation is presented. The application of our investigation to space and laboratory magnetoplasmas is discussed. PMID:23031035
Raman rogue waves in a partially mode-locked fiber laser.
Runge, Antoine F J; Aguergaray, Claude; Broderick, Neil G R; Erkintalo, Miro
2014-01-15
We report on an experimental study of spectral fluctuations induced by intracavity Raman conversion in a passively partially mode-locked, all-normal dispersion fiber laser. Specifically, we use dispersive Fourier transformation to measure single-shot spectra of Raman-induced noise-like pulses, demonstrating that for low cavity gain values Raman emission is sporadic and follows rogue-wave-like probability distributions, while a saturated regime with Gaussian statistics is obtained for high pump powers. Our experiments further reveal intracavity rogue waves originating from cascaded Raman dynamics. PMID:24562136
Rogue wave triggered at a critical frequency of a nonlinear resonant medium
NASA Astrophysics Data System (ADS)
He, Jingsong; Xu, Shuwei; Porsezian, K.; Cheng, Yi; Dinda, P. Tchofo
2016-06-01
We consider a two-level atomic system interacting with an electromagnetic field controlled in amplitude and frequency by a high intensity laser. We show that the amplitude of the induced electric field admits an envelope profile corresponding to a breather soliton. We demonstrate that this soliton can propagate with any frequency shift with respect to that of the control laser, except a critical frequency, at which the system undergoes a structural discontinuity that transforms the breather in a rogue wave. A mechanism of generation of rogue waves by means of an intense laser field is thus revealed.
Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence.
Chen, Shihua; Soto-Crespo, Jose M; Grelu, Philippe
2014-11-01
We investigate dark rogue wave dynamics in normally dispersive birefringent optical fibers, based on the exact rational solutions of the coupled nonlinear Schrödinger equations. Analytical solutions are derived up to the second order via a nonrecursive Darboux transformation method. Vector dark "three-sister" rogue waves as well as their existence conditions are demonstrated. The robustness against small perturbations is numerically confirmed in spite of the onset of modulational instability, offering the possibility to observe such extreme events in normal optical fibers with random birefringence, or in other Manakov-type vector nonlinear media. PMID:25401907
Rogue wave triggered at a critical frequency of a nonlinear resonant medium.
He, Jingsong; Xu, Shuwei; Porsezian, K; Cheng, Yi; Dinda, P Tchofo
2016-06-01
We consider a two-level atomic system interacting with an electromagnetic field controlled in amplitude and frequency by a high intensity laser. We show that the amplitude of the induced electric field admits an envelope profile corresponding to a breather soliton. We demonstrate that this soliton can propagate with any frequency shift with respect to that of the control laser, except a critical frequency, at which the system undergoes a structural discontinuity that transforms the breather in a rogue wave. A mechanism of generation of rogue waves by means of an intense laser field is thus revealed. PMID:27415249
Effect of a weak CW trigger on optical rogue waves in the femtosecond supercontinuum generation.
Li, Qian; Duan, Xiaoqi
2015-06-15
We numerically study the characteristics of optical rogue waves in the femtosecond supercontinuum (SC) generation and use the CW triggering mechanism to control the SC generation. Detailed simulation results show for the first time that a weak CW trigger can manipulate the behaviors of optical rogue waves in the femtosecond SC regime. For the proposed CW triggering technique which requires only wavelength tuning and is a handy approach for the active control of SC, the resultant spectrum can be greatly broadened, and the noise properties of the SC can be significantly improved in terms of both of the coherence and intensity stability. PMID:26193609
Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents
Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan
2014-01-01
Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves. PMID:24711719
Vector rogue waves and dark-bright boomeronic solitons in autonomous and nonautonomous settings.
Mareeswaran, R Babu; Charalampidis, E G; Kanna, T; Kevrekidis, P G; Frantzeskakis, D J
2014-10-01
In this work we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schrödinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as spatiotemporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark-bright boomeronlike soliton solutions of the latter are converted back into ones of the original nonautonomous model. Using direct numerical simulations we find that, in most cases, the rogue wave formation is rapidly followed by a modulational instability that leads to the emergence of an expanding soliton train. Scenarios different than this generic phenomenology are also reported. PMID:25375572
NASA Astrophysics Data System (ADS)
Su, Chuan-Qi; Gao, Yi-Tian; Xue, Long; Yu, Xin
2015-10-01
Under investigation in this article is a higher-order nonlinear Schrödinger-Maxwell-Bloch (HNLS-MB) system for the optical pulse propagation in an erbium-doped fiber. Lax pair, Darboux transformation (DT), and generalised DT for the HNLS-MB system are constructed. Soliton solutions and rogue wave solutions are derived based on the DT and generalised DT, respectively. Properties of the solitons and rogue waves are graphically presented. The third-order dispersion parameter, fourth-order dispersion parameter, and frequency detuning all influence the characteristic lines and velocities of the solitons. The frequency detuning also affects the amplitudes of solitons. The separating function has no effect on the properties of the first-order rogue waves, except for the locations where the first-order rogue waves appear. The third-order dispersion parameter affects the propagation directions and shapes of the rogue waves. The frequency detuning influences the rogue-wave types of the module for the measure of polarization of resonant medium and the extant population inversion. The fourth-order dispersion parameter impacts the rogue-wave interaction range and also has an effect on the rogue-wave type of the extant population inversion. The value of separating function affects the spatial-temporal separation of constituting elementary rogue waves for the second-order and third-order rogue waves. The second-order and third-order rogue waves can exhibit the triangular and pentagon patterns under different choices of separating functions.
Observation of a hierarchy of up to fifth-order rogue waves in a water tank.
Chabchoub, A; Hoffmann, N; Onorato, M; Slunyaev, A; Sergeeva, A; Pelinovsky, E; Akhmediev, N
2012-11-01
We present experimental observations of the hierarchy of rational breather solutions of the nonlinear Schrödinger equation (NLS) generated in a water wave tank. First, five breathers of the infinite hierarchy have been successfully generated, thus confirming the theoretical predictions of their existence. Breathers of orders higher than five appeared to be unstable relative to the wave-breaking effect of water waves. Due to the strong influence of the wave breaking and relatively small carrier steepness values of the experiment these results for the higher-order solutions do not directly explain the formation of giant oceanic rogue waves. However, our results are important in understanding the dynamics of rogue water waves and may initiate similar experiments in other nonlinear dispersive media such as fiber optics and plasma physics, where the wave propagation is governed by the NLS. PMID:23214897
Influence of optical activity on rogue waves propagating in chiral optical fibers
NASA Astrophysics Data System (ADS)
Temgoua, D. D. Estelle; Kofane, T. C.
2016-06-01
We derive the nonlinear Schrödinger (NLS) equation in chiral optical fiber with right- and left-hand nonlinear polarization. We use the similarity transformation to reduce the generalized chiral NLS equation to the higher-order integrable Hirota equation. We present the first- and second-order rational solutions of the chiral NLS equation with variable and constant coefficients, based on the modified Darboux transformation method. For some specific set of parameters, the features of chiral optical rogue waves are analyzed from analytical results, showing the influence of optical activity on waves. We also generate the exact solutions of the two-component coupled nonlinear Schrödinger equations, which describe optical activity effects on the propagation of rogue waves, and their properties in linear and nonlinear coupling cases are investigated. The condition of modulation instability of the background reveals the existence of vector rogue waves and the number of stable and unstable branches. Controllability of chiral optical rogue waves is examined by numerical simulations and may bring potential applications in optical fibers and in many other physical systems.
Rogue wave formation under the action of quasi-stationary pressure
NASA Astrophysics Data System (ADS)
Abrashkin, A. A.; Oshmarina, O. E.
2016-05-01
The process of rogue wave formation on deep water is considered. A wave of extreme amplitude is born against the background of uniform waves (Gerstner waves) under the action of external pressure on free surface. The pressure distribution has a form of a quasi-stationary "pit". The fluid motion is supposed to be a vortex one and is described by an exact solution of equations of 2D hydrodynamics for an ideal fluid in Lagrangian coordinates. Liquid particles are moving around circumferences of different radii in the absence of drift flow. Values of amplitude and wave steepness optimal for rogue wave formation are found numerically. The influence of vorticity distribution and pressure drop on parameters of the fluid is investigated.
Two-dimensional linear and nonlinear Talbot effect from rogue waves
NASA Astrophysics Data System (ADS)
Zhang, Yiqi; Belić, Milivoj R.; Petrović, Milan S.; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Lu, Keqing; Zhang, Yanpeng
2015-03-01
We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a π phase shift; no other recurrences are observed. Differing from the nonlinear Talbot effect, the linear effect displays the usual fractional Talbot images as well. We also find that the smaller the period of incident rogue waves, the shorter the Talbot length. Increasing the beam intensity increases the Talbot length, but above a threshold this leads to a catastrophic self-focusing phenomenon which destroys the effect. We also find that the Talbot recurrence can be viewed as a self-Fourier transform of the initial periodic beam that is automatically performed during propagation. In particular, linear Talbot effect can be viewed as a fractional self-Fourier transform, whereas the nonlinear Talbot effect can be viewed as the regular self-Fourier transform. Numerical simulations demonstrate that the rogue-wave initial condition is sufficient but not necessary for the observation of the effect. It may also be observed from other periodic inputs, provided they are set on a finite background. The 2D effect may find utility in the production of 3D photonic crystals.
Kinetic Alfvén solitary and rogue waves in superthermal plasmas
Bains, A. S.; Li, Bo Xia, Li-Dong
2014-03-15
We investigate the small but finite amplitude solitary Kinetic Alfvén waves (KAWs) in low β plasmas with superthermal electrons modeled by a kappa-type distribution. A nonlinear Korteweg-de Vries (KdV) equation describing the evolution of KAWs is derived by using the standard reductive perturbation method. Examining the dependence of the nonlinear and dispersion coefficients of the KdV equation on the superthermal parameter κ, plasma β, and obliqueness of propagation, we show that these parameters may change substantially the shape and size of solitary KAW pulses. Only sub-Alfvénic, compressive solitons are supported. We then extend the study to examine kinetic Alfvén rogue waves by deriving a nonlinear Schrödinger equation from the KdV equation. Rational solutions that form rogue wave envelopes are obtained. We examine how the behavior of rogue waves depends on the plasma parameters in question, finding that the rogue envelopes are lowered with increasing electron superthermality whereas the opposite is true when the plasma β increases. The findings of this study may find applications to low β plasmas in astrophysical environments where particles are superthermally distributed.
Mechanical energy fluctuations in granular chains: the possibility of rogue fluctuations or waves.
Han, Ding; Westley, Matthew; Sen, Surajit
2014-09-01
The existence of rogue or freak waves in the ocean has been known for some time. They have been reported in the context of optical lattices and the financial market. We ask whether such waves are generic to late time behavior in nonlinear systems. In that vein, we examine the dynamics of an alignment of spherical elastic beads held within fixed, rigid walls at zero precompression when they are subjected to sufficiently rich initial conditions. Here we define such waves generically as unusually large energy fluctuations that sustain for short periods of time. Our simulations suggest that such unusually large fluctuations ("hot spots") and occasional series of such fluctuations through space and time ("rogue fluctuations") are likely to exist in the late time dynamics of the granular chain system at zero dissipation. We show that while hot spots are common in late time evolution, rogue fluctuations are seen in purely nonlinear systems (i.e., no precompression) at late enough times. We next show that the number of such fluctuations grows exponentially with increasing nonlinearity whereas rogue fluctuations decrease superexponentially with increasing precompression. Dissipation-free granular alignment systems may be possible to realize as integrated circuits and hence our observations may potentially be testable in the laboratory. PMID:25314501
Semirational and symbiotic self-similar rogue waves in a (2+1)-dimensional graded-index waveguide
NASA Astrophysics Data System (ADS)
De, Kanchan Kumar; Soloman Raju, Thokala; Kumar, C. N.; Panigrahi, Prasanta K.
2016-07-01
We have investigated the (?)-dimensional variable coefficient-coupled nonlinear Schrödinger equation (vc-CNLSE) in a graded-index waveguide. Similarity transformations are used to convert the vc-CNLSE into constant coefficient CNLSE. Under certain functional constraints we could extract semirational, multi-parametric solution of the associated Manakov system. This family of solutions include known Peregrine soliton, mixture of either bright soliton and rogue wave or dark soliton and rogue wave or breather and rogue wave. Under a distinct set of self-phase modulation and cross-phase modulation coefficients we could establish symbiotic existence of different soliton pairs as solutions. These soliton pairs may constitute of one bright and a dark soliton, two bright solitons or two dark solitons. Finally, when two wave components are directly proportional, we find bright and dark similaritons, self-similar breathers, and rogue waves as different solutions.
Two-dimensional cylindrical ion-acoustic solitary and rogue waves in ultrarelativistic plasmas
Ata-ur-Rahman; Ali, S.; Moslem, W. M.; Mushtaq, A.
2013-07-15
The propagation of ion-acoustic (IA) solitary and rogue waves is investigated in a two-dimensional ultrarelativistic degenerate warm dense plasma. By using the reductive perturbation technique, the cylindrical Kadomtsev–Petviashvili (KP) equation is derived, which can be further transformed into a Korteweg–de Vries (KdV) equation. The latter admits a solitary wave solution. However, when the frequency of the carrier wave is much smaller than the ion plasma frequency, the KdV equation can be transferred to a nonlinear Schrödinger equation to study the nonlinear evolution of modulationally unstable modified IA wavepackets. The propagation characteristics of the IA solitary and rogue waves are strongly influenced by the variation of different plasma parameters in an ultrarelativistic degenerate dense plasma. The present results might be helpful to understand the nonlinear electrostatic excitations in astrophysical degenerate dense plasmas.
NASA Astrophysics Data System (ADS)
Gupta, Samit Kumar; Sarma, Amarendra K.
2016-07-01
In this work, we have studied the peregrine rogue wave dynamics, with a solitons on finite background (SFB) ansatz, in the recently proposed (Ablowitz and Musslimani, (2013) [31]) continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity. We have found that the continuous nonlinear Schrödinger system with PT-symmetric nonlinearity also admits Peregrine soliton solution. Motivated by the fact that Peregrine solitons are regarded as prototypical solutions of rogue waves, we have studied Peregrine rogue wave dynamics in the c-PTNLSE model. Upon numerical computation, we observe the appearance of low-intense Kuznetsov-Ma (KM) soliton trains in the absence of transverse shift (unbroken PT-symmetry) and well-localized high-intense Peregrine rogue waves in the presence of transverse shift (broken PT-symmetry) in a definite parametric regime.
Analytical solutions and rogue waves in (3+1)-dimensional nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Ma, Zheng-Yi; Ma, Song-Hua
2012-03-01
Analytical solutions in terms of rational-like functions are presented for a (3+1)-dimensional nonlinear Schrödinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.
Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test
Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco
2013-01-01
Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship. PMID:23405086
Dissipative rogue waves induced by soliton explosions in an ultrafast fiber laser.
Liu, Meng; Luo, Ai-Ping; Xu, Wen-Cheng; Luo, Zhi-Chao
2016-09-01
We reported on the observation of dissipative rogue waves (DRWs) induced by soliton explosions in an ultrafast fiber laser. It was found that the soliton explosions could be obtained in the fiber laser at a critical pump power level. During the process of the soliton explosion, the high-amplitude waves that fulfill the rogue wave criteria could be detected. The appearance of the DRWs was identified by characterizing the intensity statistics of the time-stretched soliton profile based on the dispersive Fourier-transform method. Our findings provide the first experimental demonstration that the DRWs could be observed in the soliton explosion regime and further enhance the understanding of the physical mechanism of optical RW generation. PMID:27607935
Classification of homoclinic rogue wave solutions of the nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Osborne, A. R.
2014-01-01
Certain homoclinic solutions of the nonlinear Schrödinger (NLS) equation, with spatially periodic boundary conditions, are the most common unstable wave packets associated with the phenomenon of oceanic rogue waves. Indeed the homoclinic solutions due to Akhmediev, Peregrine and Kuznetsov-Ma are almost exclusively used in scientific and engineering applications. Herein I investigate an infinite number of other homoclinic solutions of NLS and show that they reduce to the above three classical homoclinic solutions for particular spectral values in the periodic inverse scattering transform. Furthermore, I discuss another infinity of solutions to the NLS equation that are not classifiable as homoclinic solutions. These latter are the genus-2N theta function solutions of the NLS equation: they are the most general unstable spectral solutions for periodic boundary conditions. I further describe how the homoclinic solutions of the NLS equation, for N = 1, can be derived directly from the theta functions in a particular limit. The solutions I address herein are actual spectral components in the nonlinear Fourier transform theory for the NLS equation: The periodic inverse scattering transform. The main purpose of this paper is to discuss a broader class of rogue wave packets1 for ship design, as defined in the Extreme Seas program. The spirit of this research came from D. Faulkner (2000) who many years ago suggested that ship design procedures, in order to take rogue waves into account, should progress beyond the use of simple sine waves. 1An overview of other work in the field of rogue waves is given elsewhere: Osborne 2010, 2012 and 2013. See the books by Olagnon and colleagues 2000, 2004 and 2008 for the Brest meetings. The books by Kharif et al. (2008) and Pelinovsky et al. (2010) are excellent references.
NASA Astrophysics Data System (ADS)
Rodin, Artem; Rodina, Natalia
2016-04-01
Every year marine natural disasters claim thousands of lives. Only rogue waves during the last 10 years caused the death of 125 and injury of 169 people. In addition to studying the physical mechanisms of generation of rogue waves is important to study the mechanisms of human behavior in such extreme situations. The impact as large-scale natural disasters, as well as less severe (in its consequences) disaster strikes must be assessed on the basis of the entire set of conditions, in whose framework the community of people appears to be, taking into account both the power of the elements, and the available resources at their disposal to restore an acceptable level of life, including social and psychological context. Here particular relevance acquire interdisciplinary researches. This interaction is extremely important not only for sociologists and psychologists, but also for the representatives of the natural sciences (physics, chemistry, mathematics) since the ultimate goal of all efforts is to minimize the harm produced by any element or negative influence of technological progress.This also work contains statistical analysis of the appearance of rogue waves on the wind wave background in the shallow bay, obtained during the experiment in the Baltic Sea.
Rogue waves of the Hirota and the Maxwell-Bloch equations
NASA Astrophysics Data System (ADS)
Li, Chuanzhong; He, Jingsong; Porseizan, K.
2013-01-01
In this paper, we derive a Darboux transformation of the Hirota and the Maxwell-Bloch (H-MB) system which is governed by femtosecond pulse propagation through an erbium doped fiber and further generalize it to the matrix form of the n-fold Darboux transformation of this system. This n-fold Darboux transformation implies the determinant representation of nth solutions of (E[n],p[n],η[n]) generated from the known solution of (E,p,η). The determinant representation of (E[n],p[n],η[n]) provides soliton solutions, positon solutions, and breather solutions (both bright and dark breathers) of the H-MB system. From the breather solutions, we also construct a bright and dark rogue wave solution for the H-MB system, which is currently one of the hottest topics in mathematics and physics. Surprisingly, the rogue wave solution for p and η has two peaks because of the order of the numerator and denominator of them. Meanwhile, after fixing the time and spatial parameters and changing two other unknown parameters α and β, we generate a rogue wave shape.
Families of quasi-rational solutions of the NLS equation and multi-rogue waves
NASA Astrophysics Data System (ADS)
Gaillard, Pierre
2011-10-01
We construct a multi-parametric family of the solutions of the focusing nonlinear Schrödinger equation (NLS) from the known results describing the multi-phase almost-periodic elementary solutions given in terms of Riemann theta functions. We give a new representation of their solutions in terms of Wronskians determinants of order 2N composed of elementary trigonometric functions. When we perform a special passage to the limit when all the periods tend to infinity, we obtain a family of quasi-rational solutions. This leads to efficient representations for the Peregrine breathers of orders N = 1, 2, 3 first constructed by Akhmediev and his co-workers and also allows us to obtain a simpler derivation of the generic formulas corresponding the three or six rogue-wave formation in the frame of the NLS model first explained by V B Matveev in 2010. Our formulation allows us to isolate easily the second- or third-order Peregrine breathers from ‘generic’ solutions and also to compute the Peregrine breathers of orders 2 and 3 easily with respect to other approaches. In the cases N = 2, 3, we obtain the comfortable formulas to study the deformation of a higher Peregrine breather of order 2 to the three rogue-wave or order 3 to the six rogue-wave solutions via the variation of the free parameters of our construction.
NASA Astrophysics Data System (ADS)
Guo, Shimin; Mei, Liquan; He, Yaling; Li, Ying
2016-02-01
The nonlinear propagation of ion-acoustic waves is theoretically reported in a collisional plasma containing strongly coupled ions and nonthermal electrons featuring Tsallis distribution. For this purpose, the nonlinear integro-differential form of the generalized hydrodynamic model is used to investigate the strong-coupling effect. The modified complex Ginzburg-Landau equation with a linear dissipative term is derived for the potential wave amplitude in the hydrodynamic regime, and the modulation instability of ion-acoustic waves is examined. When the dissipative effect is neglected, the modified complex Ginzburg-Landau equation reduces to the nonlinear Schrödinger equation. Within the unstable region, two different types of second-order ion-acoustic rogue waves including single peak type and rogue wave triplets are discussed. The effect of the plasma parameters on the rogue waves is also presented.
A comparison of the measured North Sea Andrea rogue wave with numerical simulations
NASA Astrophysics Data System (ADS)
Bitner-Gregersen, E. M.; Fernandez, L.; Lefèvre, J. M.; Monbaliu, J.; Toffoli, A.
2013-09-01
A coupling of a spectral wave model with a nonlinear phase resolving model is used to reconstruct the evolution of wave statistics during a storm crossing the North Sea on 8-9 November 2007. During this storm a rogue wave (named the Andrea wave) was recorded at the Ekofisk field. The wave has characteristics comparable to the well-known New Year wave measured by Statoil at the Draupner platform the 1 January 1995. Hindcast data of the storm are here applied as input to calculate random realizations of sea surface and evolution of its statistical properties associated with this specific wave event by solving the Euler equations with a Higher Order Spectral Method (HOSM). The numerical results are compared with the Andrea wave profile as well as characteristics of the Andrea wave record measured by the down-looking lasers at the Ekofisk field.
Akhmediev, N; Soto-Crespo, J M; Devine, N
2016-08-01
Turbulence in integrable systems exhibits a noticeable scientific advantage: it can be expressed in terms of the nonlinear modes of these systems. Whether the majority of the excitations in the system are breathers or solitons defines the properties of the turbulent state. In the two extreme cases we can call such states "breather turbulence" or "soliton turbulence." The number of rogue waves, the probability density functions of the chaotic wave fields, and their physical spectra are all specific for each of these two situations. Understanding these extreme cases also helps in studies of mixed turbulent states when the wave field contains both solitons and breathers, thus revealing intermediate characteristics. PMID:27627303
NASA Astrophysics Data System (ADS)
Su, Chuan-Qi; Gao, Yi-Tian; Xue, Long; Wang, Qi-Min
2016-07-01
Under investigation in this paper is the Gross-Pitaevskii equation which describes the dynamics of the Bose-Einstein condensate. Lax pair, conservation laws and Darboux transformation (DT) are constructed. Nonautonomous solitons and breathers are derived based on the DT obtained. A kind of modulation instability process is generated. Nonautonomous rogue waves are obtained via the generalized DT. Influence of the nonlinearity, linear external potential, harmonic external potential, and spectral parameter on the propagation and interaction of the nonautonomous solitons, breathers and rogue waves is also discussed. Amplitude of the first-order nonautonomous soliton is proportional to the imaginary part of the spectral parameter and inversely proportional to the nonlinearity parameter. Linear external potential parameter affects the location of the first-order nonautonomous soliton. Head-on interaction, overtaking interaction and bound-state-like nonautonomous solitons can be formed based on the signs of the real parts of the spectral parameters. Quasi-periodic behaviors are exhibited for the nonautonomous breathers. If the harmonic external potential parameter is negative, quasi-period decreases along the positive time axis, with an increase in the amplitude and a compression in the width. Quasi-period decreases with the increase of the nonlinearity parameter. The second-order nonautonomous rogue wave can split into three first-order ones. Nonlinearity parameter has an effect on the amplitude of the rogue wave. Linear external potential parameter influences the location of the rogue wave, while harmonic external potential parameter affects the curved direction of the background.
Capillary wave measurements on helically-supported capillary channels
NASA Astrophysics Data System (ADS)
Chandurwala, Fahim; Thiessen, David
2010-10-01
NASA is considering power generation by the Rankine cycle to save weight on long-duration manned missions to the moon or Mars. Phase separation technology is critical to this process in microgravity. Arrays of capillary channels might be useful for filtering liquid drops from a flowing vapor. The efficiency of droplet capture by a helically-supported capillary channel is being studied. A droplet impinging on the channel launches capillary waves that propagate down the channel helping to dissipate some of the drop's kinetic energy. High-speed video of the channel combined with image processing allows for measurement of the amplitude and speed of the wave packets. Increasing the pitch of the support structure decreases the wave speed. An understanding of the dynamic response of the channel to drop impact is a first step in predicting drop-capture efficiency.
Ion-acoustic solitons, double layers and rogue waves in plasma having superthermal electrons
NASA Astrophysics Data System (ADS)
Singh Saini, Nareshpal
2016-07-01
Most of the space and astrophysical plasmas contain different type of charged particles with non-Maxwellian velocity distributions (e.g., nonthermal, superthermal, Tsallis ). These distributions are commonly found in the auroral region of the Earth's magnetosphere, planetary magnetosphere, solar and stellar coronas, solar wind, etc. The observations from various satellite missions have confirmed the presence of superthermal particles in space and astrophysical environments. Over the last many years, there have been a much interest in studying the different kind of properties of the electrostatic nonlinear excitations (solitons, double layers, rogue waves etc.) in a multi-component plasmas in the presence of superthermal particles. It has been analyzed that superthermal distributions are more appropriate than Maxwellian distribution for the modeling of space data. It is interesting to study the dynamics of various kinds of solitary waves, Double layers, Shocks etc. in varieties of plasma systems containing different kind of species obeying Lorentzian (kappa-type)/Tsallis distribution. In this talk, I have focused on the study of large amplitude IA solitary structures (bipolar solitary structures, double layers etc.), modulational instability and rogue waves in multicomponent plasmas. The Sagdeev potential method has been employed to setup an energy balance equation, from which we have studied the characteristics of large amplitude solitary waves under the influence of superthermality of charged particles and other plasma parameters. The critical Mach number has been determined, above which solitary structures are observed and its variation with superthermality of electrons and other parameters has also been discussed. Double layers have also been discussed. Multiple scale reductive perturbation method has been employed to derive NLS equation. From the different kind of solutions of this equation, amplitude modulation of envelope solitons and rogue waves have been
NASA Astrophysics Data System (ADS)
Abdel-Gawad, H. I.; Tantawy, M.; Abo Elkhair, R. E.
2016-07-01
Rogue waves are more precisely defined as waves whose height is more than twice the significant wave height. This remarkable height was measured (by Draupner in 1995). Thus, the need for constructing a mechanism for the rogue waves is of great utility. This motivated us to suggest a mechanism, in this work, that rogue waves may be constructed via nonlinear interactions of solitons and periodic waves. This suggestion is consolidated here, in an example, by studying the behavior of solutions of the complex (KdV). This is done here by the extending the solutions of its real version.
NASA Astrophysics Data System (ADS)
Goyal, Amit; Raju, Thokala Soloman; Kumar, C. N.; Panigrahi, Prasanta K.
2016-04-01
We analytically explore optical rogue waves in a nonlinear graded-index waveguide, with spatially modulated dispersion, nonlinearity, and linear refractive-index. We study the evolution of first-order rogue wave and rogue wave triplet on Airy-Bessel, sech2, and tanh background beams, and reveal that the characteristics of RWs are well maintained while the amplitude of the first-order RW gets enhanced three times the maximum value of the Airy-Bessel and sech2 background beams and five times in the case of RW triplet. These results could be of great interest in realizing the RWs in experimentally realizable situations on small-amplitude background beams in nonlinear optics.
Soliton, Breather, and Rogue Wave for a (2+1)-Dimensional Nonlinear Schrödinger Equation
NASA Astrophysics Data System (ADS)
Zhang, Hai-Qiang; Liu, Xiao-Li; Wen, Li-Li
2016-02-01
In this paper, a (2+1)-dimensional nonlinear Schrödinger (NLS) equation, which is a generalisation of the NLS equation, is under investigation. The classical and generalised N-fold Darboux transformations are constructed in terms of determinant representations. With the non-vanishing background and iterated formula, a family of the analytical solutions of the (2+1)-dimensional NLS equation are systematically generated, including the bright-line solitons, breathers, and rogue waves. The interaction mechanisms between two bright-line solitons and among three bright-line solitons are both elastic. Several patterns for first-, second, and higher-order rogue wave solutions fixed at space are displayed, namely, the fundamental pattern, triangular pattern, and circular pattern. The two-dimensional space structures of first-, second-, and third-order rogue waves fixed at time are also demonstrated.
Nonlinear waves in capillary electrophoresis
Ghosal, Sandip; Chen, Zhen
2011-01-01
Electrophoretic separation of a mixture of chemical species is a fundamental technique of great usefulness in biology, health care and forensics. In capillary electrophoresis the sample migrates in a microcapillary in the presence of a background electrolyte. When the ionic concentration of the sample is sufficiently high, the signal is known to exhibit features reminiscent of nonlinear waves including sharp concentration ‘shocks’. In this paper we consider a simplified model consisting of a single sample ion and a background electrolyte consisting of a single co-ion and a counterion in the absence of any processes that might change the ionization states of the constituents. If the ionic diffusivities are assumed to be the same for all constituents the concentration of sample ion is shown to obey a one dimensional advection diffusion equation with a concentration dependent advection velocity. If the analyte concentration is sufficiently low in a suitable non-dimensional sense, Burgers’ equation is recovered, and thus, the time dependent problem is exactly solvable with arbitrary initial conditions. In the case of small diffusivity either a leading edge or trailing edge shock is formed depending on the electrophoretic mobility of the sample ion relative to the background ions. Analytical formulas are presented for the shape, width and migration velocity of the sample peak and it is shown that axial dispersion at long times may be characterized by an effective diffusivity that is exactly calculated. These results are consistent with known observations from physical and numerical simulation experiments. PMID:20238181
NASA Astrophysics Data System (ADS)
Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan
2016-02-01
We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.
Compressional Alfvénic rogue and solitary waves in magnetohydrodynamic plasmas
Panwar, Anuraj; Rizvi, H.; Ryu, C. M.
2013-08-15
Generation of compressional Alfvénic rogue and solitary waves in magnetohydrodynamic plasmas is investigated. Dispersive effect caused by non-ideal electron inertia currents perpendicular to the ambient magnetic field can balance the nonlinear steepening of waves leading to the formation of a soliton. The reductive perturbation method is used to obtain a Korteweg–de Vries (KdV) equation describing the evolution of the solitary wave. The height of a soliton is proportional to the soliton speed “U” and inversely proportional to plasma “β” (ratio of plasma thermal pressure to pressure of the confining magnetic field) and the width of soliton is proportional to the electron inertial length. KdV equation is used to study the nonlinear evolution of modulationally unstable compressional Alfvénic wavepackets via the nonlinear Schrödinger equation. The characteristics of rogue wave influenced by plasma “β” and the electron inertial length are described.
Dissipative rogue wave generation in multiple-pulsing mode-locked fiber laser
NASA Astrophysics Data System (ADS)
Lecaplain, C.; Grelu, Ph; Soto-Crespo, J. M.; Akhmediev, N.
2013-06-01
Following the first experimental observation of a new mechanism leading to optical rogue wave (RW) formation briefly reported in Lecaplain et al (2012 Phys. Rev. Lett. 108 233901), we provide an extensive study of the experimental conditions under which these RWs can be detected. RWs originate from the nonlinear interactions of bunched chaotic pulses that propagate in a fiber laser cavity, and manifest as rare events of high optical intensity. The crucial influence of the electrical detection bandwidth is illustrated. We also clarify the observation of RWs with respect to other pulsating regimes, such as Q-switching instability, that also lead to L-shaped probability distribution functions.
Rogue waves lead to the instability in GaN semiconductors
Yahia, M. E.; Tolba, R. E.; El-Bedwehy, N. A.; El-Labany, S. K.; Moslem, W. M.
2015-01-01
A new approach to understand the electron/hole interfaced plasma in GaN high electron mobility transistors (HEMTs). A quantum hydrodynamic model is constructed to include electrons/holes degenerate pressure, Bohm potential, and the exchange/correlation effect and then reduced to the nonlinear Schrödinger equation (NLSE). Numerical analysis of the latter predicts the rough (in)stability domains, which allow for the rogue waves to occur. Our results might give physical solution rather than the engineering one to the intrinsic problems in these high frequency/power transistors. PMID:26206731
Controllable Discrete Rogue Wave Solutions of the Ablowitz—Ladik Equation in Optics
NASA Astrophysics Data System (ADS)
Wen, Xiao-Yong
2016-07-01
With the aid of symbolic computation Maple, the discrete Ablowitz—Ladik equation is studied via an algebra method, some new rational solutions with four arbitrary parameters are constructed. By analyzing related parameters, the discrete rogue wave solutions with alterable positions and amplitude for the focusing Ablowitz—Ladik equations are derived. Some properties are discussed by graphical analysis, which might be helpful for understanding physical phenomena in optics. Supported by the Beijing Natural Science Foundation under Grant No. 1153004, and China Postdoctoral Science Foundation under Grant No. 2015M570161 and the Natural Science Foundation of China under Grant No. 61471406
Phase randomization of three-wave interactions in capillary waves.
Punzmann, H; Shats, M G; Xia, H
2009-08-01
We present new experimental results on the transition from coherent-phase to random-phase three-wave interactions in capillary waves under parametric excitation. Above the excitation threshold, coherent wave harmonics spectrally broaden. An increase in the pumping amplitude increases spectral widths of wave harmonics and eventually causes a strong decrease in the degree of the three-wave phase coupling. The results point to the modulation instability of capillary waves, which leads to breaking of continuous waves into ensembles of short-lived wavelets or envelope solitons, as the reason for the phase randomization of three-wave interactions. PMID:19792572
Transversally periodic solitary gravity-capillary waves.
Milewski, Paul A; Wang, Zhan
2014-01-01
When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity-capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity-capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles. PMID:24399922
Dust kinetic Alfvén solitary and rogue waves in a superthermal dusty plasma
NASA Astrophysics Data System (ADS)
Saini, N. S.; Singh, Manpreet; Bains, A. S.
2015-11-01
Dust kinetic Alfvén solitary waves (DKASWs) have been examined in a low-β dusty plasma comprising of negatively charged dust grains, superthermal electrons, and ions. A nonlinear Korteweg-de Vries (KdV) equation has been derived using the reductive perturbation method. The combined effects of superthermality of charged particles (via κ), plasma β, obliqueness of propagation (θ), and dust concentration (via f) on the shape and size of the DKASWs have been examined. Only negative potential (rarefactive) structures are observed. Further, characteristics of dust kinetic Alfvén rogue waves (DKARWs), by deriving the non-linear Schrödinger equation (NLSE) from the KdV equation, are studied. Rational solutions of NLSE show that rogue wave envelopes are supported by this plasma model. It is observed that the influence of various plasma parameters (superthermality, plasma β, obliqueness, and dust concentration) on the characteristics of the DKARWs is very significant. This fundamental study may be helpful in understanding the formation of coherent nonlinear structures in space and astrophysical plasma environments where superthermal particles are present.
Dust kinetic Alfvén solitary and rogue waves in a superthermal dusty plasma
Saini, N. S. Singh, Manpreet; Bains, A. S.
2015-11-15
Dust kinetic Alfvén solitary waves (DKASWs) have been examined in a low-β dusty plasma comprising of negatively charged dust grains, superthermal electrons, and ions. A nonlinear Korteweg-de Vries (KdV) equation has been derived using the reductive perturbation method. The combined effects of superthermality of charged particles (via κ), plasma β, obliqueness of propagation (θ), and dust concentration (via f) on the shape and size of the DKASWs have been examined. Only negative potential (rarefactive) structures are observed. Further, characteristics of dust kinetic Alfvén rogue waves (DKARWs), by deriving the non-linear Schrödinger equation (NLSE) from the KdV equation, are studied. Rational solutions of NLSE show that rogue wave envelopes are supported by this plasma model. It is observed that the influence of various plasma parameters (superthermality, plasma β, obliqueness, and dust concentration) on the characteristics of the DKARWs is very significant. This fundamental study may be helpful in understanding the formation of coherent nonlinear structures in space and astrophysical plasma environments where superthermal particles are present.
Wang, Lei Li, Min; Qi, Feng-Hua; Xu, Tao
2015-03-15
Under investigation in this paper is a variable-coefficient derivative nonlinear Schrödinger (vc-DNLS) equation modeling the nonlinear Alfvén waves in the inhomogeneous plasmas. The modulation instability is examined for this inhomogeneous nonlinear model. The nonautonomous breather and rogue wave solutions of the vc-DNLS equation are obtained via the modified Darboux transformation. It is found that the velocity and amplitude of the breather can be controlled by the inhomogeneous magnetic field and nonuniform density. Such novel phenomena as breather amplification and nonlinear Talbot effect-like property are demonstrated with the proper choices of the inhomogeneous parameters. Furthermore, dynamics of the fundamental rogue wave, periodical rogue wave, and composite rogue wave are graphically discussed. The trajectories and amplitudes of the rogue waves can be manipulated by the inhomogeneous magnetic field and nonuniform density. In addition, the nonlinear tunneling of the rogue waves and breathers is studied. As an application, a sample model is treated with our results, and the graphical illustrations exhibit the compressing, expanding, and fluctuating phenomena of the Alfvén rogue waves.
Sun, Wen-Rong; Tian, Bo Jiang, Yan; Zhen, Hui-Ling
2014-04-15
Plasmas are the main constituent of the Universe and the cause of a vast variety of astrophysical, space and terrestrial phenomena. The inhomogeneous nonlinear Schrödinger equation is hereby investigated, which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping. By virtue of the double Wronskian identities, the equation is proved to possess the double-Wronskian soliton solutions. Analytic one- and two-soliton solutions are discussed. Amplitude and velocity of the soliton are related to the damping coefficient. Asymptotic analysis is applied for us to investigate the interaction between the two solitons. Overtaking interaction, head-on interaction and bound state of the two solitons are given. From the non-zero potential Lax pair, the first- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation, and influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed. -- Highlights: •Double-Wronskian soliton solutions are obtained and proof is finished by virtue of some double Wronskian identities. •Asymptotic analysis is applied for us to investigate the interaction between the two solitons. •First- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation. •Influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed.
Theoretical and experimental evidence of non-symmetric doubly localized rogue waves
He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin
2014-01-01
We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water. PMID:25383023
NASA Astrophysics Data System (ADS)
Lu, Luyao; Xia, Ling; Ye, Xuesong; Cheng, Heping
2010-06-01
Calcium homeostasis is considered to be one of the most important factors for the contraction and relaxation of the heart muscle. However, under some pathological conditions, such as heart failure (HF), calcium homeostasis is disordered, and spontaneous waves may occur. In this study, we developed a mathematical model of formation and propagation of a calcium wave based upon a governing system of diffusion-reaction equations presented by Izu et al (2001 Biophys. J. 80 103-20) and integrated non-clustered or 'rogue' ryanodine receptors (rogue RyRs) into a two-dimensional (2D) model of ventricular myocytes isolated from failing hearts in which sarcoplasmic reticulum (SR) Ca2+ pools are partially unloaded. The model was then used to simulate the effect of rogue RyRs on initiation and propagation of the calcium wave in ventricular myocytes with HF. Our simulation results show that rogue RyRs can amplify the diastolic SR Ca2+ leak in the form of Ca2+ quarks, increase the probability of occurrence of spontaneous Ca2+ waves even with smaller SR Ca2+ stores, accelerate Ca2+ wave propagation, and hence lead to delayed afterdepolarizations (DADs) and cardiac arrhythmia in the diseased heart. This investigation suggests that incorporating rogue RyRs in the Ca2+ wave model under HF conditions provides a new view of Ca2+ dynamics that could not be mimicked by adjusting traditional parameters involved in Ca2+ release units and other ion channels, and contributes to understanding the underlying mechanism of HF.
Two different kinds of rogue waves in weakly crossing sea states.
Ruban, V P
2009-06-01
Formation of giant waves in sea states with two spectral maxima centered at close wave vectors k_{0}+/-Deltak/2 in the Fourier plane is numerically simulated using the fully nonlinear model for long-crested water waves [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Depending on an angle theta between the vectors k_{0} and Deltak , which determines a typical orientation of interference stripes in the physical plane, rogue waves arise having different spatial structure. If theta less, < or = arctan(1/sqrt[2]) , then typical giant waves are relatively long fragments of essentially two-dimensional (2D) ridges, separated by wide valleys and consisting of alternating oblique crests and troughs. At nearly perpendicular k_{0} and Deltak , the interference minima develop to coherent structures similar to the dark solitons of the nonlinear Schrodinger equation, and a 2D freak wave looks much as a piece of a one-dimensional freak wave bounded in the transversal direction by two such dark solitons. PMID:19658553
Guo, Shimin Mei, Liquan
2014-11-15
The amplitude modulation of ion-acoustic waves is investigated in an unmagnetized plasma containing positive ions, negative ions, and electrons obeying a kappa-type distribution that is penetrated by a positive ion beam. By considering dissipative mechanisms, including ionization, negative-positive ion recombination, and electron attachment, we introduce a comprehensive model for the plasma with the effects of sources and sinks. Via reductive perturbation theory, the modified nonlinear Schrödinger equation with a dissipative term is derived to govern the dynamics of the modulated waves. The effect of the plasma parameters on the modulation instability criterion for the modified nonlinear Schrödinger equation is numerically investigated in detail. Within the unstable region, first- and second-order dissipative ion-acoustic rogue waves are present. The effect of the plasma parameters on the characteristics of the dissipative rogue waves is also discussed.
NASA Astrophysics Data System (ADS)
Xie, Xi-Yang; Tian, Bo; Jiang, Yan; Sun, Wen-Rong; Sun, Ya; Gao, Yi-Tian
2016-07-01
Under investigation in this paper is an inhomogeneous nonlinear system, which describes the marginally-unstable baroclinic wave packets in a geophysical fluid or ultra-short pulses in nonlinear optics with certain inhomogeneous medium existing. By virtue of a kind of the Darboux transformation, under the Painlevé integrable condition, the first- and second-order bright and dark rogue-wave solutions are derived. Properties of the first- and second-order bright and dark rogue waves with α(t), which measures the state of the basic flow, and β(t), representing the interaction of the wave packet and mean flow, are graphically presented and analyzed: α(t) and β(t) have no influence on the wave packet, but affect the correction of the basic flow. When we choose α(t) as a constant and linear function, respectively, the shapes of the first- and second-order dark rogue waves change, and the peak heights and widths of them alter with the value of β(t) changing.
The role of PR in the formation of psychological readiness for a rogue wave events.
NASA Astrophysics Data System (ADS)
Chaykovskaya, N.; Rodin, A.
2012-04-01
In recent years the study of psychological foundations of human behavior when dealing with rogue waves has received increasing attention. However, this problem is only in the interest of a narrow circle of specialists, while the task is to explain the rules of behavior when dealing with the phenomenon to anyone who can get into this situation. This problem can only be solved by media and PR-specialists working in this field. PR- specialists are required to convey to people the need of correct action stereotype for assault element, because, as it is known, a fact only becomes a fact when it is written about in a newspaper or is made a story about in a summary of radio or TV news. This publication is devoted to the developing of forms and methods of PR-specialists activity in this area.
Rogue waves for a system of coupled derivative nonlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Chan, H. N.; Malomed, B. A.; Chow, K. W.; Ding, E.
2016-01-01
Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schrödinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics, plasmas, etc., exhibits RWs only in the regime of modulation instability (MI) of the background. For a system of multiple waveguides, the governing coupled NLSEs can produce regimes of MI and RWs, even if each component has dispersion and cubic nonlinearity of opposite signs. A similar effect is demonstrated here for a system of coupled derivative NLSEs (DNLSEs) where the special feature is the nonlinear self-steepening of narrow pulses. More precisely, these additional regimes of MI and RWs for coupled DNLSEs depend on the mismatch in group velocities between the components, and the parameters for cubic nonlinearity and self-steepening. RWs considered in this paper differ from those of the NLSEs in terms of the amplification ratio and criteria of existence. Applications to optics and plasma physics are discussed.
A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale
NASA Astrophysics Data System (ADS)
Wang, Jinghua; Ma, Q. W.; Yan, S.
2016-05-01
A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale is proposed in this paper. It is formed by combining the derived fifth order Enhanced Nonlinear Schrödinger Equation based on Fourier transform, the Enhanced Spectral Boundary Integral (ESBI) method and its simplified version. The numerical techniques and algorithm for coupling three models on time scale are suggested. Using the algorithm, the switch between the three models during the computation is triggered automatically according to wave nonlinearities. Numerical tests are carried out and the results indicate that this hybrid model could simulate rogue waves both accurately and efficiently. In some cases discussed, the hybrid model is more than 10 times faster than just using the ESBI method, and it is also much faster than other methods reported in the literature.
Laser absorption waves in metallic capillaries
NASA Astrophysics Data System (ADS)
Anisimov, V. N.; Arutiunian, R. V.; Bol'Shov, L. A.; Kanevskii, M. F.; Kondrashov, V. V.
1987-07-01
The propagation of laser absorption waves in metallic capillaries was studied experimentally and numerically during pulsed exposure to CO2 laser radiation. The dependence of the plasma front propagation rate on the initial air pressure in the capillary is determined. In a broad range of parameters, the formation time of the optically opaque plasma layer is governed by the total laser pulse energy from the beginning of the exposure to the instant screening appears, and is weakly dependent on the pulse shape and gas pressure.
Inverse scattering transform analysis of rogue waves using local periodization procedure
NASA Astrophysics Data System (ADS)
Randoux, Stéphane; Suret, Pierre; El, Gennady
2016-07-01
The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra.
Inverse scattering transform analysis of rogue waves using local periodization procedure
Randoux, Stéphane; Suret, Pierre; El, Gennady
2016-01-01
The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra. PMID:27385164
Inverse scattering transform analysis of rogue waves using local periodization procedure.
Randoux, Stéphane; Suret, Pierre; El, Gennady
2016-01-01
The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra. PMID:27385164
NASA Astrophysics Data System (ADS)
Liu, Junyang; Hang, Chao; Huang, Guoxiang
2016-06-01
We propose a scheme to demonstrate the existence of optical Peregrine rogue waves and Akhmediev and Kuznetsov-Ma breathers and realize their active control via electromagnetically induced transparency (EIT). The system we suggest is a cold, Λ -type three-level atomic gas interacting with a probe and a control laser fields and working under EIT condition. We show that, based on EIT with an incoherent optical pumping, which can be used to cancel optical absorption, (1+1)-dimensional optical Peregrine rogue waves, Akhmediev breathers, and Kuznetsov-Ma breathers can be generated with very low light power. In addition, we demonstrate that the Akhmediev and Kuznetsov-Ma breathers in (2+1)-dimensions obtained can be actively manipulated by using an external magnetic field. As a result, these breathers can display trajectory deflections and bypass obstacles during propagation.
NASA Astrophysics Data System (ADS)
El-Tantawy, S. A.
2016-05-01
We examine the likelihood of the ion-acoustic rogue waves propagation in a non-Maxwellian electronegative plasma in the framework of the family of the Korteweg-de Vries (KdV) equations (KdV/modified KdV/Extended KdV equation). For this purpose, we use the reductive perturbation technique to carry out this study. It is known that the family of the KdV equations have solutions of distinct structures such as solitons, shocks, kinks, cnoidal waves, etc. However, the dynamics of the nonlinear rogue waves is governed by the nonlinear Schrödinger equation (NLSE). Thus, the family of the KdV equations is transformed to their corresponding NLSE developing a weakly nonlinear wave packets. We show the possible region for the existence of the rogue waves and define it precisely for typical parameters of space plasmas. We investigate numerically the effects of relevant physical parameters, namely, the negative ion relative concentration, the nonthermal parameter, and the mass ratio on the propagation of the rogue waves profile. The present study should be helpful in understanding the salient features of the nonlinear structures such as, ion-acoustic solitary waves, shock waves, and rogue waves in space and in laboratory plasma where two distinct groups of ions, i.e. positive and negative ions, and non-Maxwellian (nonthermal) electrons are present.
Wen, Xiao-Yong; Yang, Yunqing; Yan, Zhenya
2015-07-01
In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc., and may be useful to study the physical mechanism of multirogue waves in optics. The dynamical behaviors of these multi-rogue-wave solutions are illustrated using numerical simulations. The same Darboux matrix can also be used to investigate the Gerjikov-Ivanov equation such that its multi-rogue-wave solutions and their wave structures are also found. The method can also be extended to find multi-rogue-wave solutions of other nonlinear integrable equations. PMID:26274257
NASA Astrophysics Data System (ADS)
Wen, Xiao-Yong; Yan, Zhenya
2015-12-01
We study higher-order rogue wave (RW) solutions of the coupled integrable dispersive AB system (also called Pedlosky system), which describes the evolution of wave-packets in a marginally stable or unstable baroclinic shear flow in geophysical fluids. We propose its continuous-wave (CW) solutions and existent conditions for their modulation instability to form the rogue waves. A new generalized N-fold Darboux transformation (DT) is proposed in terms of the Taylor series expansion for the spectral parameter in the Darboux matrix and its limit procedure and applied to the CW solutions to generate multi-rogue wave solutions of the coupled AB system, which satisfy the general compatibility condition. The dynamical behaviors of these higher-order rogue wave solutions demonstrate both strong and weak interactions by modulating parameters, in which some weak interactions can generate the abundant triangle, pentagon structures, etc. Particularly, the trajectories of motion of peaks and depressions of profiles of the first-order RWs are explicitly analyzed. The generalized DT method used in this paper can be extended to other nonlinear integrable systems. These results may be useful for understanding the corresponding rogue-wave phenomena in fluid mechanics and related fields.
Wen, Xiao-Yong; Yan, Zhenya
2015-12-01
We study higher-order rogue wave (RW) solutions of the coupled integrable dispersive AB system (also called Pedlosky system), which describes the evolution of wave-packets in a marginally stable or unstable baroclinic shear flow in geophysical fluids. We propose its continuous-wave (CW) solutions and existent conditions for their modulation instability to form the rogue waves. A new generalized N-fold Darboux transformation (DT) is proposed in terms of the Taylor series expansion for the spectral parameter in the Darboux matrix and its limit procedure and applied to the CW solutions to generate multi-rogue wave solutions of the coupled AB system, which satisfy the general compatibility condition. The dynamical behaviors of these higher-order rogue wave solutions demonstrate both strong and weak interactions by modulating parameters, in which some weak interactions can generate the abundant triangle, pentagon structures, etc. Particularly, the trajectories of motion of peaks and depressions of profiles of the first-order RWs are explicitly analyzed. The generalized DT method used in this paper can be extended to other nonlinear integrable systems. These results may be useful for understanding the corresponding rogue-wave phenomena in fluid mechanics and related fields. PMID:26723154
Predictability of Rogue Events
NASA Astrophysics Data System (ADS)
Birkholz, Simon; Brée, Carsten; Demircan, Ayhan; Steinmeyer, Günter
2015-05-01
Using experimental data from three different rogue wave supporting systems, determinism, and predictability of the underlying dynamics are evaluated with methods of nonlinear time series analysis. We included original records from the Draupner platform in the North Sea as well as time series from two optical systems in our analysis. One of the latter was measured in the infrared tail of optical fiber supercontinua, the other in the fluence profiles of multifilaments. All three data sets exhibit extreme-value statistics and exceed the significant wave height in the respective system by a factor larger than 2. Nonlinear time series analysis indicates a different degree of determinism in the systems. The optical fiber scenario is found to be driven by quantum noise whereas rogue waves emerge as a consequence of turbulence in the others. With the large number of rogue events observed in the multifilament system, we can systematically explore the predictability of such events in a turbulent system. We observe that rogue events do not necessarily appear without a warning, but are often preceded by a short phase of relative order. This surprising finding sheds some new light on the fascinating phenomenon of rogue waves.
Guo, Shimin; Research Group MAC, Centrum Wiskunde and Informatica, Amsterdam, 1098XG ; Mei, Liquan; Center for Computational Geosciences, Xi’an Jiaotong University, Xi’an, 710049 ; Sun, Anbang
2013-05-15
The nonlinear propagation of planar and nonplanar (cylindrical and spherical) ion-acoustic waves in an unmagnetized electron–positron–ion–dust plasma with two-electron temperature distributions is investigated in the context of the nonextensive statistics. Using the reductive perturbation method, a modified nonlinear Schrödinger equation is derived for the potential wave amplitude. The effects of plasma parameters on the modulational instability of ion-acoustic waves are discussed in detail for planar as well as for cylindrical and spherical geometries. In addition, for the planar case, we analyze how the plasma parameters influence the nonlinear structures of the first- and second-order ion-acoustic rogue waves within the modulational instability region. The present results may be helpful in providing a good fit between the theoretical analysis and real applications in future spatial observations and laboratory plasma experiments. -- Highlights: ► Modulational instability of ion-acoustic waves in a new plasma model is discussed. ► Tsallis’s statistics is considered in the model. ► The second-order ion-acoustic rogue wave is studied for the first time.
Investigation of resonances in gravity-capillary wave turbulence
NASA Astrophysics Data System (ADS)
Aubourg, Quentin; Mordant, Nicolas
2016-06-01
We report experimental results on nonlinear wave coupling in surface wave turbulence on water at scales close to the crossover between surface gravity waves and capillary waves. We study three-wave correlations either in the frequency domain or in the wave-vector domain. We observe that in a weakly nonlinear regime, the dominant nonlinear interactions correspond to waves that are collinear or close to collinear. Although the resonant coupling of pure gravity waves is supposed to involve four waves, at the capillary crossover we observe a nonlocal coupling between a gravity wave and two capillary waves. Furthermore, nonlinear spectral spreading permits three-gravity wave coupling. These observations raise the question of the relevance of these processes in the oceanographic context and in particular the range of frequencies of gravity waves that may be impacted.
Kedziora, David J; Ankiewicz, Adrian; Akhmediev, Nail
2012-06-01
We present an explicit analytic form for the two-breather solution of the nonlinear Schrödinger equation with imaginary eigenvalues. It describes various nonlinear combinations of Akhmediev breathers and Kuznetsov-Ma solitons. The degenerate case, when the two eigenvalues coincide, is quite involved. The standard inverse scattering technique does not generally provide an answer to this scenario. We show here that the solution can still be found as a special limit of the general second-order expression and appears as a mixture of polynomials with trigonometric and hyperbolic functions. A further restriction of this particular case, where the two eigenvalues are equal to i, produces the second-order rogue wave with two free parameters considered as differential shifts. The illustrations reveal a precarious dependence of wave profile on the degenerate eigenvalues and differential shifts. Thus we establish a hierarchy of second-order solutions, revealing the interrelated nature of the general case, the rogue wave, and the degenerate breathers. PMID:23005231
Guo, Shimin Mei, Liquan
2014-08-15
Dust-ion-acoustic (DIA) rogue waves are investigated in a three-dimensional magnetized plasma containing nonthermal electrons featuring Tsallis distribution, both positive and negative ions, and immobile dust grains having both positive and negative charges. Via the reductive perturbation method, a (3 + 1)-dimensional nonlinear Schrödinger (NLS) equation is derived to govern the dynamics of the DIA wave packets. The modulation instability of DIA waves described by the (3 + 1)-dimensional NLS equation is investigated. By means of the similarity transformation and symbolic computation, both the first- and second-order rogue wave solutions of the (3 + 1)-dimensional NLS equation are constructed in terms of rational functions. Moreover, the dynamics properties and the effects of plasma parameters on the nonlinear structures of rogue waves are discussed in detail. The results could be useful for understanding the physical mechanism of rogue waves in laboratory experiments where pair-ion plasmas with electrons and dust grains can be found.
NASA Astrophysics Data System (ADS)
Wang, Qi-Min; Gao, Yi-Tian; Su, Chuan-Qi; Zuo, Da-Wei
2015-10-01
In this paper, a higher-order nonlinear Schrödinger-Maxwell-Bloch system with quintic terms is investigated, which describes the propagation of ultrashort optical pulses, up to the attosecond duration, in an erbium-doped fiber. Multi-soliton, breather and rogue-wave solutions are derived by virtue of the Darboux transformation and the limiting procedure. Features and interaction patterns of the solitons, breathers and rogue waves are discussed. (i) The solitonic amplitudes, widths and velocities are exhibited, and solitonic amplitudes and widths are proved to have nothing to do with the higher-order terms. (ii) The higher-order terms and frequency detuning affect the growth rate of periodic modulation and skewing angle for the breathers, except for the range of the frequency of modulation. (iii) The quintic terms and frequency detuning have the effects on the temporal duration for the rogue waves. (iv) Breathers are classified into two types, according to the range of the modulation instability. (v) Interaction between the two solitons is elastic. When the two solitons interact with each other, the periodic structure occurs, which is affected by the higher-order terms and frequency detuning. (vi) Interaction between the two Akhmediev-like breathers or two Kuznetsov-Ma-like solitons shows the different patterns with different ratios of the relative modulation frequencies, while the interaction area induced by the two breathers looks like a higher-order rogue wave.
Strongly nonlinear waves in capillary electrophoresis
NASA Astrophysics Data System (ADS)
Chen, Zhen; Ghosal, Sandip
2012-05-01
In capillary electrophoresis, sample ions migrate along a microcapillary filled with a background electrolyte under the influence of an applied electric field. If the sample concentration is sufficiently high, the electrical conductivity in the sample zone could differ significantly from the background. Under such conditions, the local migration velocity of sample ions becomes concentration-dependent, resulting in a nonlinear wave that exhibits shocklike features. If the nonlinearity is weak, the sample concentration profile, under certain simplifying assumptions, can be shown to obey Burgers’ equation [Ghosal and Chen, Bull. Math. Biol.BMTBAP0092-824010.1007/s11538-010-9527-2 72, 2047 (2010)], which has an exact analytical solution for arbitrary initial condition. In this paper, we use a numerical method to study the problem in the more general case where the sample concentration is not small in comparison to the concentration of background ions. In the case of low concentrations, the numerical results agree with the weakly nonlinear theory presented earlier, but at high concentrations, the wave evolves in a way that is qualitatively different.
NASA Astrophysics Data System (ADS)
Chefranov, Sergey; Chefranov, Alexander
2016-04-01
Linear hydrodynamic stability theory for the Hagen-Poiseuille (HP) flow yields a conclusion of infinitely large threshold Reynolds number, Re, value. This contradiction to the observation data is bypassed using assumption of the HP flow instability having hard type and possible for sufficiently high-amplitude disturbances. HP flow disturbance evolution is considered by nonlinear hydrodynamic stability theory. Similar is the case of the plane Couette (PC) flow. For the plane Poiseuille (PP) flow, linear theory just quantitatively does not agree with experimental data defining the threshold Reynolds number Re= 5772 ( S. A. Orszag, 1971), more than five-fold exceeding however the value observed, Re=1080 (S. J. Davies, C. M. White, 1928). In the present work, we show that the linear stability theory conclusions for the HP and PC on stability for any Reynolds number and evidently too high threshold Reynolds number estimate for the PP flow are related with the traditional use of the disturbance representation assuming the possibility of separation of the longitudinal (along the flow direction) variable from the other spatial variables. We show that if to refuse from this traditional form, conclusions on the linear instability for the HP and PC flows may be obtained for finite Reynolds numbers (for the HP flow, for Re>704, and for the PC flow, for Re>139). Also, we fit the linear stability theory conclusion on the PP flow to the experimental data by getting an estimate of the minimal threshold Reynolds number as Re=1040. We also get agreement of the minimal threshold Reynolds number estimate for PC with the experimental data of S. Bottin, et.al., 1997, where the laminar PC flow stability threshold is Re = 150. Rogue waves excitation mechanism in oppositely directed currents due to the PC flow linear instability is discussed. Results of the new linear hydrodynamic stability theory for the HP, PP, and PC flows are published in the following papers: 1. S.G. Chefranov, A
NASA Astrophysics Data System (ADS)
Yang, Yunqing; Yan, Zhenya; Malomed, Boris A.
2015-10-01
We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schrödinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel equations. We present continuous-wave (CW) solutions and conditions for their modulation instability in the framework of this model. Applying the Darboux transformation to the CW input, novel first- and second-order RW solutions of the FONLS equation are analytically found. In particular, trajectories of motion of peaks and depressions of profiles of the first- and second-order RWs are produced by means of analytical and numerical methods. The solutions also include newly found rational and W-shaped one- and two-soliton modes. The results predict the corresponding dynamical phenomena in extended models of nonlinear fiber optics and other physically relevant integrable systems.
Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves
NASA Astrophysics Data System (ADS)
El, G. A.; Khamis, E. G.; Tovbis, A.
2016-09-01
We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.
Yang, Yunqing; Yan, Zhenya; Malomed, Boris A
2015-10-01
We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schrödinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel equations. We present continuous-wave (CW) solutions and conditions for their modulation instability in the framework of this model. Applying the Darboux transformation to the CW input, novel first- and second-order RW solutions of the FONLS equation are analytically found. In particular, trajectories of motion of peaks and depressions of profiles of the first- and second-order RWs are produced by means of analytical and numerical methods. The solutions also include newly found rational and W-shaped one- and two-soliton modes. The results predict the corresponding dynamical phenomena in extended models of nonlinear fiber optics and other physically relevant integrable systems. PMID:26520078
Numerical simulation of the resonantly excited capillary-gravity waves
NASA Astrophysics Data System (ADS)
Hanazaki, Hideshi; Hirata, Motonori; Okino, Shinya
2015-11-01
Capillary gravity waves excited by an obstacle are investigated by a direct numerical simulation. In the flow without capillary effects, it is well known that large-amplitude upstream advancing solitary waves are generated periodically under the resonant condition, i.e., when the phase velocity of the long surface waves and the mean flow velocity agrees. With capillary effects, solutions of the Euler equations show the generation of very short waves further upstream of the solitary waves and also in the depression region downstream of the obstacle. The overall characteristics of these waves agree with the solutions of the forced fifth-order KdV equation, while the weakly nonlinear theory generally overestimates the wavelength of the short waves.
The role of capillary waves in two-fluid atomization
NASA Astrophysics Data System (ADS)
Tsai, Shirley C.; Luu, Patrick; Childs, Paul; Teshome, Asseged; Tsai, Chen S.
1997-10-01
A mechanistic study of two-fluid atomization has been carried out using a new spray technique called ultrasound-modulated two-fluid (UMTF) atomization. This technique is based on resonance between the liquid capillary waves generated by ultrasound and those generated by high-velocity air. Specifically, capillary waves are established on the surface of a liquid jet as it issues from a coaxial two-fluid atomizer, the nozzle tip of which vibrates at the same frequency as the ultrasound while the frequency of the capillary waves is only half of the ultrasound frequency. As these capillary waves travel downstream in the direction of air flow, their amplitude is further amplified by the air flowing around them. Atomization occurs when the wave amplitude becomes too great to maintain wave stability; the resulting drop sizes are proportional to the wavelength of the resonant capillary waves which is determined by the harmonic frequency of the ultrasound in accordance with the Kelvin equation. Theoretical calculations of the amplitude growth rate are based on two models of temporal instability of wind-generated capillary waves: Taylor's dispersion relation and Jeffreys' one-parameter (sheltering factor) model. Good agreements between the theoretical predictions by these models and the experimental results of how drop-size and size distributions are influenced by air velocity and surface tension led to the conclusion that Taylor-mode breakup of capillary waves plays a very important role in two-fluid atomization. Furthermore, all peak drop diameters can be accounted for by the harmonic frequencies of the ultrasound. Hence, it is further concluded that secondary atomization is negligible in co-flow two-fluid atomization of a water jet at air velocities up to 170 m/s and air-to-water mass ratio up to 5.6. In addition, uniform drops with diameters predetermined by the ultrasound frequency can be accomplished by adjusting the air velocity.
Vishnu Priya, N; Senthilvelan, M; Lakshmanan, M
2013-08-01
We present explicit forms of general breather (GB), Akhmediev breather (AB), Ma soliton (MS), and rogue wave (RW) solutions of the two-component nonlinear Schrödinger (NLS) equation, namely Manakov equation. We derive these solutions through two different routes. In the forward route, we first construct a suitable periodic envelope soliton solution to this model from which we derive GB, AB, MS, and RW solutions. We then consider the RW solution as the starting point and derive AB, MS, and GB in the reverse direction. The second approach has not been illustrated so far for the two component NLS equation. Our results show that the above rational solutions of the Manakov system can be derived from the standard scalar nonlinear Schrödinger equation with a modified nonlinearity parameter. Through this two-way approach we establish a broader understanding of these rational solutions, which will be of interest in a variety of situations. PMID:24032912
Non-Condensable Gas Absorption by Capillary Waves
NASA Astrophysics Data System (ADS)
Andre, Matthieu A.; Bardet, Philippe M.
2013-03-01
Oceans and atmosphere are constantly exchanging heat and mass; this has a direct consequence on the climate. While these exchanges are inherently multi-scales, in non-breaking waves the smallest scales strongly govern the transfer rates at the ocean-atmosphere interface. The present experimental study aims at characterizing and quantifying the exchanges of non-condensable gas at a sub-millimeter scale, in the presence of capillary waves. In oceans, capillaries are generated by high winds and are also present on the forward face of short gravity waves. Capillary waves are thus present over a large fraction of the ocean surface, but their effect on interphase phenomena is little known. In the experiment, 2D capillary waves are generated by the relaxation of a shear layer at the surface of a laminar water slab jet. Wave profile is measured with Planar Laser Induced Fluorescence (PLIF) and 2D velocity field of the water below the surface is resolved with Particle Image Velocimetry (PIV). Special optical arrangements coupled with high speed imaging allow 0.1 mm- and 0.1 ms- resolution. These data reveal the interaction of vorticity and free surface in the formation and evolution of capillaries. The effect of the capillaries on the transfer of oxygen from the ambient air to anoxic water is measured with another PLIF system. In this diagnostic, dissolved oxygen concentration field is indirectly measured using fluorescence quenching of Pyrenebutyric Acid (PBA). The three measurements performed simultaneously -surface profile, velocity field, and oxygen concentration- give deep physical insights into oxygen transfer mechanisms under capillary waves.
Nonlocal resonances in weak turbulence of gravity-capillary waves.
Aubourg, Quentin; Mordant, Nicolas
2015-04-10
We report a laboratory investigation of weak turbulence of water surface waves in the gravity-capillary crossover. By using time-space-resolved profilometry and a bicoherence analysis, we observe that the nonlinear processes involve three-wave resonant interactions. By studying the solutions of the resonance conditions, we show that the nonlinear interaction is dominantly one dimensional and involves collinear wave vectors. Furthermore, taking into account the spectral widening due to weak nonlinearity explains why nonlocal interactions are possible between a gravity wave and high-frequency capillary ones. We observe also that nonlinear three-wave coupling is possible among gravity waves, and we raise the question of the relevance of this mechanism for oceanic waves. PMID:25910127
A Simple Theory of Capillary-Gravity Wave Turbulence
NASA Technical Reports Server (NTRS)
Glazman, Roman E.
1995-01-01
Employing a recently proposed 'multi-wave interaction' theory, inertial spectra of capillary gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear inertia gravity waves) intractable by small-perturbation techniques, even in the weak-turbulence limit. The analytical solution obtained in the present work for an arbitrary degree of nonlinearity is shown to be in reasonable agreement with experimental data. The theory explains the dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves, while the appropriate (long- and short-wave) limits yield power laws corresponding to the Zakharov-Filonenko and Phillips spectra.
NASA Astrophysics Data System (ADS)
Zhang, Hai-Qiang; Chen, Jian
2016-04-01
In this paper, we study a higher-order variable coefficient nonlinear Schrödinger (NLS) equation, which plays an important role in the control of the ultrashort optical pulse propagation in nonlinear optical systems. Then, we construct a generalized Darboux transformation (GDT) for the higher-order variable coefficient NLS equation. The Nth order rogue wave solution is obtained by the iterative rule and it can be expressed by the determinant form. As application, we calculate rogue waves (RWs) from first- to fourth-order in accordance with different kinds of parameters. In particular, the dynamical properties and spatial-temporal structures of RWs are discussed and compared with Hirota equation through some figures.
El-Tantawy, S. A.; Moslem, W. M.
2014-05-15
Solitons (small-amplitude long-lived waves) collision and rogue waves (large-amplitude short-lived waves) in non-Maxwellian electron-positron-ion plasma have been investigated. For the solitons collision, the extended Poincaré-Lighthill-Kuo perturbation method is used to derive the coupled Korteweg-de Vries (KdV) equations with the quadratic nonlinearities and their corresponding phase shifts. The calculations reveal that both positive and negative polarity solitons can propagate in the present model. At critical value of plasma parameters, the coefficients of the quadratic nonlinearities disappear. Therefore, the coupled modified KdV (mKdV) equations with cubic nonlinearities and their corresponding phase shifts have been derived. The effects of the electron-to-positron temperature ratio, the ion-to-electron temperature ratio, the positron-to-ion concentration, and the nonextensive parameter on the colliding solitons profiles and their corresponding phase shifts are examined. Moreover, generation of ion-acoustic rogue waves from small-amplitude initial perturbations in plasmas is studied in the framework of the mKdV equation. The properties of the ion-acoustic rogue waves are examined within a nonlinear Schrödinger equation (NLSE) that has been derived from the mKdV equation. The dependence of the rogue wave profile on the relevant physical parameters has been investigated. Furthermore, it is found that the NLSE that has been derived from the KdV equation cannot support the propagation of rogue waves.
A Simple Theory of Capillary-Gravity Wave Turbulence
NASA Technical Reports Server (NTRS)
Glazman, Roman E.
1993-01-01
Employing a recently proposed 'multi-wave interaction' theory [JFM, 243, 623-625], spectra of capillary-gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The resultant absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear Rossby waves) intractable by small-perturbation techniques, even in the weak turbulence limit. The analytical solution obtained in the present work is shown to be in good agreement with experimental data. Its low- and high-frequency limits yield power-laws characterizing spectra of purely gravity and capillary waves, respectively. In the limits of weak and strong linearity, these reduce of the Zakharov-Filonenko and Phillips spectra, respectively.
NASA Astrophysics Data System (ADS)
Chen, Pengzhen; Wang, Xiaoqing; Liu, Li; Chong, Jinsong
2016-06-01
According to Bragg theory, capillary waves are the predominant scatterers of high-frequency band (such as Ka-band) microwave radiation from the surface of the ocean. Therefore, understanding the modulation mechanism of capillary waves is an important foundation for interpreting high-frequency microwave remote sensing images of the surface of the sea. In our experiments, we discovered that modulations of capillary waves are significantly larger than the values predicted by the classical theory. Further, analysis shows that the difference in restoring force results in an inflection point while the phase velocity changes from gravity waves region to capillary waves region, and this results in the capillary waves being able to resonate with gravity waves when the phase velocity of the gravity waves is equal to the group velocity of the capillary waves. Consequently, we propose a coupling modulation model in which the current modulates the capillary wave indirectly by modulating the resonant gravity waves, and the modulation of the former is approximated by that of the latter. This model very effectively explains the results discovered in our experiments. Further, based on Bragg scattering theory and this coupling modulation model, we simulate the modulation of normalized radar cross section (NRCS) of typical internal waves and show that the high-frequency bands are superior to the low-frequency bands because of their greater modulation of NRCS and better radiometric resolution. This result provides new support for choice of radar band for observation of wave-current modulation oceanic phenomena such as internal waves, fronts, and shears.
Capillary waves in the subcritical nonlinear Schroedinger equation
Kozyreff, G.
2010-01-15
We expand recent results on the nonlinear Schroedinger equation with cubic-quintic nonlinearity to show that some solutions are described by the Bernoulli equation in the presence of surface tension. As a consequence, capillary waves are predicted and found numerically at the interface between regions of large and low amplitude.
NASA Astrophysics Data System (ADS)
Tiofack, C. G. L.; Coulibaly, S.; Taki, M.; De Bièvre, S.; Dujardin, G.
2015-10-01
It is shown that sufficiently large periodic modulations in the coefficients of a nonlinear Schrödinger equation can drastically impact the spatial shape of the Peregrine soliton solutions: they can develop multiple compression points of the same amplitude, rather than only a single one, as in the spatially homogeneous focusing nonlinear Schrödinger equation. The additional compression points are generated in pairs forming a comblike structure. The number of additional pairs depends on the amplitude of the modulation but not on its wavelength, which controls their separation distance. The dynamics and characteristics of these generalized Peregrine solitons are analytically described in the case of a completely integrable modulation. A numerical investigation shows that their main properties persist in nonintegrable situations, where no exact analytical expression of the generalized Peregrine soliton is available. Our predictions are in good agreement with numerical findings for an interesting specific case of an experimentally realizable periodically dispersion modulated photonic crystal fiber. Our results therefore pave the way for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in the wide class of physical systems modeled by the nonlinear Schrödinger equation.
Quantum Capillary Waves at the Superfluid—Mott-Insulator Interface
NASA Astrophysics Data System (ADS)
Rath, Steffen Patrick; Spivak, Boris; Zwerger, Wilhelm
2011-10-01
We discuss quantum fluctuations of the interface between a superfluid and a Mott-insulating state of ultracold atoms in a trap. The fluctuations of the boundary are due to a new type of surface modes, whose spectrum is similar—but not identical—to classical capillary waves. The corresponding quantum capillary length sets the scale for the penetration of the superfluid into the Mott-insulating regime by the proximity effect and may be on the order of several lattice spacings. It determines the typical magnitude of the interface width due to quantum fluctuations, which may be inferred from single-site imaging of ultracold atoms in an optical lattice.
A Cascade Model of Wave Turbulence with Applications to Surface Gravity and Capillary Waves
NASA Technical Reports Server (NTRS)
Glazman, Roman E.
1993-01-01
A heuristic approach to the derivation of power spectra of wave motion is described and applied to capillary waves. The case of gravity waves studied earlier is briefly reviewed. In contract to the previous studies, the nonlinearity of the wave motion is not required to be small, and the mean number of resonantly interacting wave harmonics is not limited to a smallest possible number (which is 4 for gravity waves on a deep fluid and 3 for capillary waves). The main external parameter of the problem is the input flux Q of the wave energy related to the mean wind velocity. Depending on its value, wave spectra take various forms---from that corresponding to the weak-turbulence limit to that corresponding to the saturated (Phillips') wave spectra...
Thermal capillary waves in colloid polymer mixtures in water
NASA Astrophysics Data System (ADS)
Jamie, E. A. G.; Davies, G. J.; Howe, M. D.; Dullens, R. P. A.; Aarts, D. G. A. L.
2008-12-01
We develop two colloid-polymer mixtures in water and study their phase and interface behaviour by means of confocal scanning laser microscopy. The systems consist either of silica or of poly(methylmethacrylate) particles, fluorescently labelled, with, as the polymer, xanthan. The fluid-fluid phase separation can be clearly followed in time and, depending on the concentrations and system details, we observe coarsening either of a bicontinuous spinodal structure or of a suspension of colloid-rich droplets. After phase separation has completed, we study the thermal capillary waves at the fluid-fluid interface. We construct correlation functions and compare with capillary wave theory. Finally, we demonstrate that these colloid-polymer systems are compatible with microfluidics.
Polymer Surface Melting Mediated by Capillary Waves
NASA Astrophysics Data System (ADS)
Herminghaus, Stephan; Seemann, Ralf; Landfester, Katharina
2004-07-01
Nuclear magnetic resonance investigations of atactic polystyrene emulsions yield direct evidence that the polymer surface exhibits a rather well-defined molten layer. Its thickness d grows continuously as the temperature is increased towards the bulk glass transition, according to d∝(Tg-T)-1. This is precisely what was recently predicted by a simple continuum model considering viscoelastic surface waves. Furthermore, this model is capable of explaining the frequently reported depression of the glass transition temperature in thin polymer films, and thus suggests a quite simple mechanism to underlie all these effects.
Capillary Wave Dynamics of Thin Polymer Films over Submerged Nanostructures
Alvine, Kyle J.; Dai, Yeling; Ro, Hyun W.; Narayanan, Suresh; Sandy, Alec; Soles, Christopher L.; Shpyrko, Oleg G.
2012-11-13
The surface dynamics of thin molten polystyrene films supported by nanoscale periodic silicon line-space gratings were investigated with x-ray photon correlation spectroscopy. Surface dynamics over these nanostructures exhibit high directional anisotropy above certain length scales, as compared to surface dynamics over flat substrates. A cutoff length scale in the dynamics perpendicular to the grooves is observed. This marks a transition from standard over-damped capillary wave behavior to suppressed dynamics due to substrate interactions.
Three-wave interactions in a gravity-capillary range of wind waves
NASA Astrophysics Data System (ADS)
Kosnik, M.; Dulov, V.; Kudryavtsev, V.
2009-04-01
The effects of three-wave interactions on forming of short wind waves spectrum are investigated. Wavenumber spectrum in gravity-capillary and capillary range is found as a result of evolution of initial arbitrary spectrum under the influence of assigned sources of kinetic equation. Three-wave interactions are taken into account using exact collision integral without any additional assumptions simplifying a problem. Model validity is proved by reproducing Zaharov & Filonenko (1967) theoretical spectra describing the "energy equipartition" and "inertial interval" cases. Numerical calculations show that the main role of three-wave interactions consists in energy transfer from short gravity waves to waves of smaller lengths. The prominent feature of most of resulting spectra is a dip on curvature spectrum in the vicinity of phase speed minimum. Wind forcing, viscous dissipation and mechanism of generation of parasitic capillaries are considered in a number of calculations using parameterization for corresponding sources by Kudryavtsev, Makin, Chapron, 1999. The necessity of additional nonlinear dissipation terms in kinetic equation for short gravity and capillary waves is revealed. The results of calculation with this realistic parameterization of kinetic equation sources show that, when accounted, nonlinear dissipation and parasitic capillaries terms play much more significant part in capillary range than wave-wave interactions. The latter are important only in phase speed minimum area where the typical dip remains at the same wavenumber in all numerical experiments. This work was supported by the EU under the projects INTAS 05-1000008-8014, INTAS/ESA 06-1000025-9264 and Contract # SST5 CT 2006 031001 (MONRUK) of FP6.
Rogue events in the group velocity horizon
Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Mahnke, Christoph; Mitschke, Fedor; Steinmeyer, Günter
2012-01-01
The concept of rogue waves arises from a mysterious and potentially calamitous phenomenon of oceanic surfaces. There is mounting evidence that they are actually commonplace in a variety of different physical settings. A set of defining criteria has been advanced; this set is of great generality and therefore applicable to a wide class of systems. The question arises naturally whether there are generic mechanisms responsible for extreme events in different systems. Here we argue that under suitable circumstances nonlinear interaction between weak and strong waves results in intermittent giant waves with all the signatures of rogue waves. To obtain these circumstances only a few basic conditions must be met. Then reflection of waves at the so-called group-velocity horizon occurs. The connection between rogue waves and event horizons, seemingly unrelated physical phenomena, is identified as a feature common in many different physical systems. PMID:23152941
Spatiotemporal measurement of surfactant distribution on gravity-capillary waves
NASA Astrophysics Data System (ADS)
Strickland, Stephen; Shearer, Michael; Daniels, Karen
2015-11-01
Materials adsorbed to the surface of a fluid - for instance, crude oil, biogenic slicks, or industrial/medical surfactants - will move in response to surface waves. Due to the difficulty of non-invasive measurement of the spatial distribution of a molecular monolayer, little is known about the dynamics that couple the surface waves and the evolving density field. We report measurements of the spatiotemporal dynamics of the density field of an insoluble surfactant driven by gravity-capillary waves in a shallow cylindrical container. Standing Faraday waves and traveling waves generated by the meniscus are superimposed to create a non-trivial surfactant density field. We measure both the height field of the surface using moire-imaging and the density field of the surfactant via the fluorescence of NBD-tagged phosphatidylcholine. Through phase-averaging stroboscopically-acquired images of the density field, we determine that the surfactant accumulates on the leading edge of the traveling meniscus waves and in the troughs of the standing Faraday waves. We fit the spatiotemporal variations in the two fields and report measurements of the wavenumbers as well as a temporal phase shift between the two fields. These measurements suggest that longitudinal waves contribute to the dynamics. Funded by NSF grant DMS-0968258.
Regularity for steady periodic capillary water waves with vorticity.
Henry, David
2012-04-13
In the following, we prove new regularity results for two-dimensional steady periodic capillary water waves with vorticity, in the absence of stagnation points. Firstly, we prove that if the vorticity function has a Hölder-continuous first derivative, then the free surface is a smooth curve and the streamlines beneath the surface will be real analytic. Furthermore, once we assume that the vorticity function is real analytic, it will follow that the wave surface profile is itself also analytic. A particular case of this result includes irrotational fluid flow where the vorticity is zero. The property of the streamlines being analytic allows us to gain physical insight into small-amplitude waves by justifying a power-series approach. PMID:22393112
NASA Astrophysics Data System (ADS)
Gao, Zhe; Gao, Yi-Tian; Su, Chuan-Qi; Wang, Qi-Min; Mao, Bing-Qing
2016-01-01
Under investigation in this article is a generalised nonlinear Schrödinger-Maxwell-Bloch system for the picosecond optical pulse propagation in an inhomogeneous erbium-doped silica optical fibre. Lax pair, conservation laws, Darboux transformation, and generalised Darboux transformation for the system are constructed; with the one- and two-soliton solutions, the first- and second-order rogue waves given. Soliton propagation is discussed. Nonlinear tunneling effect on the solitons and rogue waves are investigated. We find that (i) the detuning of the atomic transition frequency from the optical pulse frequency affects the velocity of the pulse when the detuning is small, (ii) nonlinear tunneling effect does not affect the energy redistribution of the soliton interaction, (iii) dispersion barrier/well has an effect on the soliton velocity, whereas nonlinear well/barrier does not, (iv) nonlinear well/barrier could amplify/compress the solitons or rogue waves in a smoother manner than the dispersion barrier/well, and (v) dispersion barrier could "attract" the nearby rogue waves, whereas the dispersion well has a repulsive effect on them.
Liu, Meng; Cai, Ze-Rong; Hu, Song; Luo, Ai-Ping; Zhao, Chu-Jun; Zhang, Han; Xu, Wen-Cheng; Luo, Zhi-Chao
2015-10-15
We reported on the generation of dissipative rogue waves (DRWs) induced by long-range chaotic multi-pulse interactions in a fiber laser based on a topological insulator (TI)-deposited microfiber photonic device. By virtue of the simultaneous saturable absorption effect and high nonlinearity provided by the TI-deposited microfiber, a localized, chaotic multi-pulse wave packet with strong long-range nonlinear interactions could be obtained, which gives rise to the formation of DRWs. The results might enhance the understanding of DRWs in optical systems, and further demonstrated that the TI-deposited microfiber could be considered as an excellent photonic device with both saturable absorption and highly nonlinear effects for the application field of nonlinear optics. PMID:26469615
Experimental study of three-wave interactions among capillary-gravity surface waves
NASA Astrophysics Data System (ADS)
Haudin, Florence; Cazaubiel, Annette; Deike, Luc; Jamin, Timothée; Falcon, Eric; Berhanu, Michael
2016-04-01
In propagating wave systems, three- or four-wave resonant interactions constitute a classical nonlinear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface waves in a closed laboratory tank. We generate two crossing wave trains and we study their interaction. Using two optical methods, a local one (laser doppler vibrometry) and a spatiotemporal one (diffusive light photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wave number. Furthermore, by focusing on the stationary regime and by taking into account viscous dissipation, we directly estimate the growth rate of the resonant mode. The latter is then compared to the predictions of the weakly nonlinear triadic resonance interaction theory. The obtained results confirm qualitatively and extend previous experimental results obtained only for collinear wave trains. Finally, we discuss the relevance of three-wave interaction mechanisms in recent experiments studying gravity-capillary turbulence.
Thermally excited capillary waves at vapor/liquid interfaces of water-alcohol mixtures
Vaknin, David; Bu, Wei; Sung, Jaeho; Jeon, Yoonnam; Kim, Doseok
2009-02-02
The density profiles of liquid/vapor interfaces of water–alcohol (methanol, ethanol and propanol) mixtures were studied by surface-sensitive synchrotron x-ray scattering techniques. X-ray reflectivity and diffuse scattering measurements, from the pure and mixed liquids, were analyzed in the framework of capillary wave theory to address the characteristic length scales of the intrinsic roughness and the shortest capillary wavelength (alternatively, the upper wavevector cutoff in capillary wave theory). Our results establish that the intrinsic roughness is dominated by average interatomic distances. The extracted effective upper wavevector cutoff indicates capillary wave theory breaks down at distances of the order of bulk correlation lengths.
Wave drag due to generation of capillary-gravity surface waves
NASA Astrophysics Data System (ADS)
Burghelea, Teodor; Steinberg, Victor
2002-11-01
The onset of the wave resistance via the generation of capillary-gravity waves by a small object moving with a velocity V is investigated experimentally. Due to the existence of a minimum phase velocity Vc for surface waves, the problem is similar to the generation of rotons in superfluid helium near their minimum. In both cases, waves or rotons are produced at V>Vc due to Cherenkov radiation. We find that the transition to the wave drag state is continuous: in the vicinity of the bifurcation the wave resistance force is proportional to (V-Vc) for various fluids. This observation contradicts the theory of Raphaël and de Gennes. We also find that the reduced wave drag force for different fluids and different ball size may be scaled in such a way that all the data collapse on a single curve. The capillary-gravity wave pattern and the shape of the wave-generating region are investigated both experimentally and theoretically. Good agreement between the theory and the experimental data is found in this case.
Rogue run-up events at the North Sea coast
NASA Astrophysics Data System (ADS)
Didenkulova, Ira; Blossier, Brice; Daly, Christopher; Herbst, Gabriel; Senichev, Dmitry; Winter, Christian
2015-04-01
On the 1st of January, 1995, the Statoil-operated "Draupner" platform located in the North Sea recorded the so-called "New Year wave". Since then, rogue waves have been the topic of active scientific discussions and investigations. Waves of extreme height appearing randomly at the sea surface have been measured in both deep and shallow waters and have been involved in a number of ship accidents. Nowadays rogue waves are frequently recorded all over the world with several different instruments (range finders installed on offshore platforms, deployed buoys, radars including SAR, etc.). Rogue wave also occur at the coast, where they appear as either sudden flooding of coastal areas or high splashes over steep banks or sea walls. These waves are especially dangerous for beach users and lead regularly to human injuries and fatalities. Despite numerous reports of human accidents, coastal rogue waves have not yet been recorded experimentally. In this paper we discuss the recording of rogue wave events at German North Sea coasts by using high-resolution beach cameras. The recorded rogue waves are observed during different tide levels and different weather conditions. Possible mechanisms of their generation are discussed.
Capillary freak waves in He-II as a manifestation of discrete wave turbulent regime
NASA Astrophysics Data System (ADS)
Kartashova, Elena
2010-05-01
Two fundamental findings of the modern theory of wave turbulence are • existence of Kolmogorov-Zakharov power energy spectra (KZ-spectra) in k-space, [1], and • existence of 'gaps" in KZ-spectra corresponding to the resonance clustering, [2]. Accordingly, three wave turbulent regimes can be singled out: kinetic (described by wave kinetic equations and KZ-spectra, in random phase approximation, [3]); discrete (described by a few dynamical systems, with coherent phases corresponding to resonance conditions, [4]); mesoscopic (where kinetic and discrete evolution of the wave field coexist, [5]). We present an explanation of freak waves appearance in capillary waves in He-II, [6], as a manifestation of discrete wave turbulent regime. Implications of these results for other wave systems are briefly discussed. References [1] V. E. Zakharov and N. N. Filonenko. Weak turbulence of capillary waves. Appl. Mech. Tech. Phys. 4 (1967), 500-15. [2] E. Kartashova. A model of laminated turbulence. JETP Lett., 83 (2006), 341-45. [3] V. E. Zakharov, V. S. L'vov and G. Falkovich. Kolmogorov Spectra of Turbulence (Series in Nonlinear Dynamics, Springer-Verlag, New York, 1992). [4] E. Kartashova. Discrete wave turbulence. EPL 87 (2009), 44001-1-5. [5] V. E. Zakharov, A. O. Korotkevich, A. N. Pushkarev and A. I. Dyachenko. Mesoscopic wave turbulence. JETP Lett. 82 (2005), 487-91. [6] L. V. Abdurakhimov, Y. M. Brazhnikov, G. V. Kolmakov and A. A. Levchenko. Study of high-frequency edge of turbulent cascade on the surface of He-II. J. Phys.: Conf. Ser. 150 (2009) (3): 032001.
Laser probe for measuring 2-D wave slope spectra of ocean capillary waves
NASA Technical Reports Server (NTRS)
Palm, C. S.; Anderson, R. C.; Reece, A. M.
1977-01-01
A laser-optical instrument for use in determining the two-dimensional wave-slope spectrum of ocean capillary waves is described. The instrument measures up to a 35-deg tip angle of the surface normal by measuring the position of a refracted laser beam directed vertically upward through a water surface. A telescope, a continuous two-dimensional Schottky barrier photodiode, and a pair of analog dividers render the signals independent of water height and insensitive to laser-beam intensity fluctuations. Calibration is performed entirely in the laboratory before field use. Sample records and wave-slope spectra are shown for one-dimensional wave-tank tests and for two-dimensional ocean tests. These are presented along with comparison spectra for calm and choppy water conditions. A mechanical wave follower was used to adjust the instrument position in the presence of large ocean swell and tides.
Diffusing light photography of solitons and capillary-wave turbulence
Wright, W.; Budak, R.; Putterman, S. )
1994-11-01
The attenuation of light propagating through a slab of water (containing a dilute concentration of polyballs) is approximately proportional to its thickness. Application of this insight to the local elevation of a fluid surface has enabled us to use photography to determine the instantaneous global topography of the surface of a fluid in motion. Use of diffusing light enables us to obtain images that are free of the caustics which plague shadowgraphs. Applications include breather solitons and wave turbulence which results from the nonlinear interaction of a broadband spectrum of high amplitude surface ripples. Measurements indicate that as the amplitude of excitation of the surface of water is increased the wave number of the capillary motion displays a transition to a broadband spectrum. The temporal response of a single pixel yields the power spectrum of the surface height as a function of frequency [ital f].'' The numerous harmonics which can be seen at low amplitude merge at high amplitude into a broadband spectrum which goes as 1/[ital f][sup 3]. This technique should permit the measurement of turbulent parameters which go beyond the purported range of current theories. [Work supported by US DOE Division of Engineering and Geophysics and NASA Microgravity.
NASA Astrophysics Data System (ADS)
Ball, Philip
2015-07-01
Once thought to be the stuff of exaggeration by seafaring folk, we now know that giant “rogue” waves that soar to heights of up to 30 m really do occur at sea. But scientists can't yet agree on why they happen, as Philip Ball reports.
Capillary waves in an inhomogeneous three-layer liquid with a free surface
NASA Astrophysics Data System (ADS)
Shiryaeva, S. O.; Grigor'ev, A. I.; Zav'yalov, D. A.
2016-06-01
In the domain of capillary waves, a bicubic dispersion relation is derived and analyzed for surface and internal capillary-gravitational waves in a three-layer liquid with a free surface. It is shown that the ratio of the internal wave amplitudes to the surface wave amplitudes is fairly large if the trivial condition of a "homogeneous liquid" is discarded. The amplitude ratio between the internal waves themselves (generated at different interfaces) may be both greater and smaller than unity depending on the physical parameters of the system. Specifically, it strongly depends on the densities of the layers and their thicknesses.
NASA Astrophysics Data System (ADS)
Anisimov, V. N.; Kozolupenko, A. P.; Sebrant, A. Yu
1988-12-01
An experimental investigation was made of the plasma transparency to heating radiation in capillaries when absorption waves propagated in these capillaries as a result of interaction with a CO2 laser pulse of 5-μs duration. When the length of the capillary was in excess of 20 mm, total absorption of the radiation by the plasma was observed at air pressures of 1-100 kPa. When the capillary length was 12 mm, a partial recovery of the transparency took place. A comparison was made with the dynamics and recovery of the plasma transparency when breakdown of air took place near the free surface.
Stability of capillary-gravity interfacial waves between two bounded fluids
NASA Astrophysics Data System (ADS)
Christodoulides, Paul; Dias, Frédéric
1995-12-01
Two-dimensional periodic capillary-gravity waves at the interface between two bounded fluids of different densities are considered. Based on a variational formulation, the relation between wave frequency and wave amplitude is obtained through a weakly nonlinear analysis. All classes of space-periodic waves are studied: traveling and standing waves as well as a degenerate class of mixed waves. As opposed to water waves, mixed interfacial waves exist even for pure gravity waves. The stability of traveling and standing waves with respect to three-dimensional modulations is then studied. By using the method of multiple scales, Davey-Stewartson-type equations are obtained. A detailed stability analysis is performed in three cases: pure gravity waves, capillary-gravity waves when one layer is infinitely deep, and capillary-gravity waves when both layers are infinitely deep. The main results for oblique (i.e., combined longitudinal and transverse) modulations reveal a mostly stabilizing effect of the density ratio for traveling waves and a destabilizing effect for standing waves.
On the physical mechanism of front-back asymmetry of nonlinear gravity-capillary waves
NASA Astrophysics Data System (ADS)
Dosaev, Alexander; Troitskaya, Yulia; Shrira, Victor
2016-04-01
In nature wind waves of all scales are asymmetric both with respect to the horizontal and vertical axes. The front-back (or fore-aft asymmetry), i.e. the asymmetry with respect to the vertical axis, manifests itself in steeper front slopes. Although it can be important for remote sensing of sea surface and wave field interaction with wind, especially for the waves of gravity-capillary range, at present the understanding of physical mechanisms causing the gravity-capillary waves asymmetry and its dependence on parameters is very poor; there has been no study dedicated to this problem. Here we address this gap. The decimetre-range water waves in many respects essentially differ from the waves of other ranges: wind forcing is stronger, steep waves develop a characteristic pattern of capillary ripples on their forward slopes. These 'parasitic capillaries', generated by a narrow pressure distribution associated with an underlying longer wave' crest, remain quasi-stationary with regard to the longer wave. The train of capillaries is localised on the front slope and decays towards the trough. We investigate the nature of the asymmetry of such waves by extensive numerical simulations of the Euler equations employing the method of conformal mapping for two-dimensional potential flow and taking into account wave generation by wind and dissipation due to molecular viscosity. We examine the role of various factors contributing to the wave profile asymmetry: wind pumping, viscous stresses, the Reynolds stresses caused by ripples and found the latter to be by far the most important. It is the lop-sided ripple distribution which leads to noticeable fore-aft asymmetry of the mean wave profile. We also found how the asymmetry depends on wavelength, steepness, wind and viscosity, which enables us to parametrize these dependencies for applications in microwave remote sensing and wave generation.
Capillary-gravity waves on a liquid film of arbitrary depth: analysis of the wave resistance.
Wędołowski, Karol; Napiórkowski, Marek
2013-10-01
We discuss the wave resistance in the case of an externally perturbed viscous liquid film of arbitrary thickness. Emphasis is placed on the dependence of the wave resistance on the film thickness H, the length scale b characterizing the external perturbation, and its velocity V. In particular, the effectiveness of the mechanisms of capillary-gravity waves and the viscous dissipation localized in the vicinity of the perturbation are compared and discussed as functions of H and V. We show that, in general, the wave resistance is a nonmonotonous function of H with a maximum whose amplitude and position depend on b and V. In the case of small H the wave resistance depends on a parameter S proportional V/H(3). We find three different regimes of this parameter in which the wave resistance behaves like S(r) with the exponent r equal to 1, 1/3, and -1. These results are also obtained independently within the thin liquid film approximation. This allows us to assess the range of validity of the thin liquid film approximation in various cases, in particular its dependence on the perturbation length scale b. PMID:24229283
An investigation of the modulation of capillary and short gravity waves in the open ocean
NASA Technical Reports Server (NTRS)
Evans, D. D.; Shemdin, O. H.
1980-01-01
A preliminary investigation of the modulation of capillary and gravity waves by long ocean waves is described. A pressure transducer is used to obtain water surface displacements, and a high-response laser-optical system is used to detect short-wave slopes. Analytical techniques are developed to account for the orbital motion of long waves. The local mean squared wave slope is found to be maximum leeward of the long-wave crests. For the long waves studied here and for short waves from 1 cm to 1 m, the longer a short-wave component is, the more leeward its maximum tends to occur. Also, the shortest waves tend to modulate least. The modulation of short waves is found to be strong enough to be an important component of the synthetic aperture radar image formation mechanism for long ocean waves.
Capillary Dynamics of Elastic-Wave-Enhanced Two-Phase Flow in Porous Media
NASA Astrophysics Data System (ADS)
Hilpert, Markus; Guo, Chunyan; Katz, Joseph
2006-05-01
Elastic waves may enhance two-phase flow in porous media. We investigate the role and dynamics of capillary forces during the enhancement process. We present a theory that allows us to estimate the response of trapped nonwetting phase blobs to variable frequency excitation. According to this theory capillary trapped oil blobs may exhibit resonance, depending on the properties of the fluids and the pore space. Using this theory we estimate the resonant frequencies of crude oil and gasoline blobs in sphere packings. We will also present experimental evidence showing that capillary trapped liquid blobs exhibit resonance.
Confining capillary waves to control aerosol droplet size from surface acoustic wave nebulisation
NASA Astrophysics Data System (ADS)
Nazarzadeh, Elijah; Reboud, Julien; Wilson, Rab; Cooper, Jonathan M.
Aerosols play a significant role in targeted delivery of medication through inhalation of drugs in a droplet form to the lungs. Delivery and targeting efficiencies are mainly linked to the droplet size, leading to a high demand for devices that can produce aerosols with controlled sizes in the range of 1 to 5 μm. Here we focus on enabling the control of the droplet size of a liquid sample nebulised using surface acoustic wave (SAW) generated by interdigitated transducers on a piezoelectric substrate (lithium niobate). The formation of droplets was monitored through a high-speed camera (600,000 fps) and the sizes measured using laser diffraction (Spraytec, Malvern Ltd). Results show a wide droplet size distribution (between 0.8 and 400 μm), while visual observation (at fast frame rates) revealed that the large droplets (>100 μm) are ejected due to large capillary waves (80 to 300 μm) formed at the free surface of liquid due to leakage of acoustic radiation of the SAWs, as discussed in previous literature (Qi et al. Phys Fluids, 2008). To negate this effect, we show that a modulated structure, specifically with feature sizes, typically 200 μm, prevents formation of large capillary waves by reducing the degrees of freedom of the system, enabling us to obtain a mean droplet size within the optimum range for drug delivery (<10 μm). This work was supported by an EPSRC grant (EP/K027611/1) and an ERC Advanced Investigator Award (340117-Biophononics).
NASA Astrophysics Data System (ADS)
Lehle, H.; Oettel, M.
2008-10-01
We analyze the effective potential for nanoparticles trapped at a fluid interface within a simple model which incorporates surface and line tensions as well as a thermal average over interface fluctuations (capillary waves). For a single colloid, a reduced steepness of the potential well hindering movements out of the interface plane compared to rigid interface models is observed, and an instability of the capillary wave partition sum in the case of negative line tensions is pointed out. For two colloids, averaging over the capillary waves leads to an effective Casimir-type interaction which is long ranged, power-like in the inverse distance, but whose power sensitively depends on possible restrictions of the colloid degrees of freedom. A nonzero line tension leads to changes in the magnitude but not in the functional form of the effective potential asymptotics.
Acoustic microfluidics: Capillary waves and vortex currents in a spherical fluid drop
NASA Astrophysics Data System (ADS)
Lebedev-Stepanov, P. V.; Rudenko, O. V.
2016-07-01
We calculate the radiation forces in a spherical drop lying on a solid substrate. The forces form as a result of the action of a capillary wave on a fluid as it propagates along the free spherical surface. We study the structure of acoustic currents excited by the radiation forces.
Gravity capillary waves in fluid layers under normal electric fields.
Papageorgiou, Demetrios T; Petropoulos, Peter G; Vanden-Broeck, Jean-Marc
2005-11-01
We study the formation and dynamics of interfacial waves on a perfect dielectric ideal fluid layer of finite depth, wetting a solid wall, when the region above the fluid is hydrodynamically passive but has constant permittivity, for example, air. The wall is held at a constant electric potential and a second electrode having a different potential is placed parallel to the wall and infinitely far from it. In the unperturbed state the interface is flat and the normal horizontally uniform electric field is piecewise constant in the liquid and air. We derive a system of long wave nonlinear evolution equations valid for interfacial amplitudes as large as the unperturbed layer depth and which retain gravity, surface tension and electric field effects. It is shown that for given physical parameters there exists a critical value of the voltage potential difference between electrodes, below which the system is dispersive and above which a band of unstable waves is possible centered around a finite wavenumber. In the former case nonlinear traveling waves are calculated and their stability is studied, while in the latter case the instability leads to thinning of the layer with the interface touching down in finite time. A similarity solution of the second kind is found to be dominant near the singularity, and the scaling exponents are determined using analysis and computations. PMID:16383611
Acoustic wave detection of chemical species electrokinetically transported within a capillary tube.
Li, Paul C H; Prasad, Ronald
2003-06-01
For the first time, we report the acoustic wave detection of chemical species being transported in a capillary tube to a region where acoustic coupling occurs. The measured parameter was a change in phase, which was originally only attributed to a change in solution density as the analyte passed by the detection region. Accordingly, we report the detection of change in phase as various chemical species (e.g. Cy5 dye, Cy5-derivatized glycine and underivatized glycine) were introduced into and migrated along a capillary tube through electrokinetic processes. To improve detection sensitivity, we modified various experimental parameters, such as run buffer concentration, capillary wall thickness and transducer frequency. Although acoustic wave detection was feasible, the peak width and detection limit were inadequate as compared to conventional detection methods for HPLC or CE. Nevertheless, the effects of various physical and chemical relaxation processes on acoustic wave absorption were discussed, and this has shed some light on explaining some observations, which cannot be explained by density differences alone. Accordingly, the acoustic wave method is suggested to investigate these processes, as studied in ultrasonic relaxation spectroscopy, in a flow system. PMID:12866892
Hamiltonian structure for rotational capillary waves in stratified flows
NASA Astrophysics Data System (ADS)
Martin, Calin Iulian
2016-07-01
We show that the governing equations of two-dimensional water waves driven by surface tension propagating over two-layered stratified flows admit a Hamiltonian formulation. Moreover, the underlying flows that we consider here, have piecewise constant distribution of vorticity, the jump in vorticity being located along the interface separating the fluid of bigger density at the bottom from the lighter fluid adjacent to the free surface.
Maxwell, Eric J; Tong, William G
2016-05-01
An ultrasensitive label-free antibody-free detection method for malachite green and crystal violet is presented using nonlinear laser wave-mixing spectroscopy and capillary zone electrophoresis. Wave-mixing spectroscopy provides a sensitive absorption-based detection method for trace analytes. This is accomplished by forming dynamic gratings within a sample cell, which diffracts light to create a coherent laser-like signal beam with high optical efficiency and high signal-to-noise ratio. A cubic dependence on laser power and square dependence on analyte concentration make wave mixing sensitive enough to detect molecules in their native form without the use of fluorescent labels for signal enhancement. A 532 nm laser and a 635 nm laser were used for malachite green and crystal violet sample excitation. The use of two lasers of different wavelengths allows the method to simultaneously detect both analytes. Selectivity is obtained through the capillary zone electrophoresis separation, which results in characteristic migration times. Measurement in capillary zone electrophoresis resulted in a limit of detection of 6.9 × 10(-10)M (2.5 × 10(-19) mol) for crystal violet and 8.3 × 10(-11)M (3.0 × 10(-20) mol) for malachite green at S/N of 2. PMID:26998858
Silicon surface periodic structures produced by plasma flow induced capillary waves
Dojcinovic, I. P.; Kuraica, M. M.; Obradovic, B. M.; Puric, J.
2006-08-14
Silicon single crystal surface modification by the action of nitrogen quasistationary compression plasma flow generated by a magnetoplasma compressor is studied. It has been found that highly oriented silicon periodic cylindrical shape structures are produced during a single pulse surface treatment. The periodical structure formation can be related to the driven capillary waves quenched during fast cooling and resolidification phase of the plasma flow interaction with silicon surface. These waves are induced on the liquid silicon surface due to the compression plasma flow intrinsic oscillations.
Water Surface Currents, Short Gravity-Capillary Waves and Radar Backscatter
NASA Technical Reports Server (NTRS)
Atakturk, Serhad S.; Katsaros, Kristina B.
1993-01-01
Despite their importance for air-sea interaction and microwave remote sensing of the ocean surface, intrinsic properties of short gravity-capillary waves are not well established. This is largely due to water surface currents and their effects on the direct measurements of wave parameters conducted at a fixed point. Frequencies of small scale waves propagating on a surface which itself is in motion, are subject to Doppler shifts. Hence, the high frequency tail of the wave spectra obtained from such temporal observations is smeared. Conversion of this smeared measured-frequency spectra to intrinsic-frequency (or wavenumber) spectra requires corrections for the Doppler shifts. Such attempts in the past have not been very successful in particular when field data were used. This becomes evident if the amplitude modulation of short waves by underlying long waves is considered. Microwave radar studies show that the amplitude of a short wave component attains its maximum value near the crests and its minimum in the troughs of the long waves. Doppler-shifted wave data yield similar results but much larger in modulation magnitude, as expected. In general, Doppler shift corrections reduce the modulation magnitude. Overcorrection may result in a negligible modulation or even in a strong modulation with the maximum amplitude in the wave troughs. The latter situation is clearly contradictory to our visual observations as well as the radar results and imply that the advection by currents is overestimated. In this study, a differential-advection approach is used in which small scale waves are advected by the currents evaluated not at the free surface, but at a depth proportional to their wavelengths. Applicability of this approach is verified by the excellent agreement in phase and magnitude of short-wave modulation between results based on radar and on wave-gauge measurements conducted on a lake.
Experimental investigations of capillary effects on nonlinear free-surface waves
NASA Astrophysics Data System (ADS)
Diorio, James D.
This thesis presents the results of three experiments on various aspects of the effects of surface tension on nonlinear free-surface waves. The first two experiments focus on capillary effects on the breaking of short-wavelength gravity waves, a problem of interest in areas of physical oceanography and remote sensing. The third experiment is concerned with the bifurcation of solitary capillary-gravity waves, a problem that is relevant in the study of nonlinear, dispersive wave systems. In the first set of experiments, streamwise profile measurements were made of spilling breakers at the point of incipient breaking. Both wind-waves and mechanically generated waves were investigated in this study, with gravity wavelengths in the range of 10--120 cm. Although it has been previously argued that the crest shape is dependent only on the surface tension, the results reported herein are to the contrary as several geometrical parameters used to describe the crest change significantly with the wavelength. However, the non-dimensional crest shape is self-similar, with two-shape parameters that depend on a measure of the local wave slope. This self-similarity persists over the entire range of wavelengths and breaker conditions measured, indicating a universal behavior in the near-crest dynamics that is independent of the method used to generate the wave. The measured wave slope is found to be related to the wave growth rate and phase-speed prior to breaking, a result that contributes towards the development of a breaking criterion for unsteady capillary-gravity waves. The second set of experiments examines the cross-stream surface structure in the turbulent breaking zone generated by short-wavelength breakers. Waves in this study were generated using a mechanical wedge and ranged in wavelength from 80--120 cm. To isolate the effects of surface tension on the flow, the important experimental parameters were adjusted to produce Froude-scaled, dispersively-focused wave packets
Interfacial free energy of the NaCl crystal-melt interface from capillary wave fluctuations.
Benet, Jorge; MacDowell, Luis G; Sanz, Eduardo
2015-04-01
In this work we study, by means of molecular dynamics simulations, the solid-liquid interface of NaCl under coexistence conditions. By analysing capillary waves, we obtain the stiffness for different orientations of the solid and calculate the interfacial free energy by expanding the dependency of the interfacial free energy with the solid orientation in terms of cubic harmonics. We obtain an average value for the solid-fluid interfacial free energy of 89 ± 6 mN m(-1) that is consistent with previous results based on the measure of nucleation free energy barriers [Valeriani et al., J. Chem. Phys. 122, 194501 (2005)]. We analyse the influence of the simulation setup on interfacial properties and find that facets prepared as an elongated rectangular stripe give the same results as those prepared as squares for all cases but the 111 face. For some crystal orientations, we observe at small wave-vectors a behaviour not consistent with capillary wave theory and show that this behavior does not depend on the simulation setup. PMID:25854257
Capillary waves on the surface of a droplet falling into a liquid
NASA Astrophysics Data System (ADS)
Chashechkin, Yu. D.; Ilinykh, A. Yu.
2015-12-01
In a laboratory pool, the fine structure of flows arising from the primary contact of freely falling droplet with a liquid at rest is investigated by the methods of macrophotography and high-speed videotaping. Primary attention is paid to visualization of short capillary waves on the droplet surface formed from the impact of small splashes. The angular positions of the trajectories of splashes determine the values of the surface-tension coefficients of the liquids of the droplet and the accepting environment. The conditions under which the splashes hit the droplet surface are determined.
NASA Astrophysics Data System (ADS)
Albers, Bettina
2016-06-01
It is well known that the capillary pressure curve of partially saturated soils exhibits a hysteresis. For the same degree of saturation it has different values depending on the initial state of the soil, thus for drying of a wet soil or wetting of a dry soil. The influence of these different values of the capillary pressure on the propagation of sound waves is studied by use of a linear hyperbolic model. Even if the model does not contain a hysteresis operator, the effect of hysteresis in the capillary pressure curve is accounted for. In order to obtain the limits of phase speeds and attenuations for the two processes the correspondent values for main drying and main wetting are inserted into the model separately. This is done for two examples of soils, namely for Del Monte sand and for a silt loam both filled by an air-water mixture. The wave analysis reveals four waves: one transversal wave and three longitudinal waves. The waves which are driven by the immiscible pore fluids are influenced by the hysteresis in the capillary pressure curve while the waves which are mainly driven by the solid are not.
Spatiotemporal rogue events in optical multiple filamentation.
Birkholz, Simon; Nibbering, Erik T J; Brée, Carsten; Skupin, Stefan; Demircan, Ayhan; Genty, Goëry; Steinmeyer, Günter
2013-12-13
The transient appearance of bright spots in the beam profile of optical filaments formed in xenon is experimentally investigated. Fluence profiles are recorded with high-speed optical cameras at the kilohertz repetition rate of the laser source. A statistical analysis reveals a thresholdlike appearance of heavy-tailed fluence distributions together with the transition from single to multiple filamentation. The multifilament scenario exhibits near-exponential probability density functions, with extreme events exceeding the significant wave height by more than a factor of 10. The extreme events are isolated in space and in time. The macroscopic origin of these experimentally observed heavy-tail statistics is shown to be local refractive index variations inside the nonlinear medium, induced by multiphoton absorption and subsequent plasma thermalization. Microscopically, mergers between filament strings appear to play a decisive role in the observed rogue wave statistics. PMID:24483663
Spatiotemporal Rogue Events in Optical Multiple Filamentation
NASA Astrophysics Data System (ADS)
Birkholz, Simon; Nibbering, Erik T. J.; Brée, Carsten; Skupin, Stefan; Demircan, Ayhan; Genty, Goëry; Steinmeyer, Günter
2013-12-01
The transient appearance of bright spots in the beam profile of optical filaments formed in xenon is experimentally investigated. Fluence profiles are recorded with high-speed optical cameras at the kilohertz repetition rate of the laser source. A statistical analysis reveals a thresholdlike appearance of heavy-tailed fluence distributions together with the transition from single to multiple filamentation. The multifilament scenario exhibits near-exponential probability density functions, with extreme events exceeding the significant wave height by more than a factor of 10. The extreme events are isolated in space and in time. The macroscopic origin of these experimentally observed heavy-tail statistics is shown to be local refractive index variations inside the nonlinear medium, induced by multiphoton absorption and subsequent plasma thermalization. Microscopically, mergers between filament strings appear to play a decisive role in the observed rogue wave statistics.
Asymmetric Directional Multicast for Capillary Machine-to-Machine Using mmWave Communications.
Kwon, Jung-Hyok; Kim, Eui-Jik
2016-01-01
The huge demand for high data rate machine-to-machine (M2M) services has led to the use of millimeter Wave (mmWave) band communications with support for a multi-Gbps data rate through the use of directional antennas. However, unnecessary sector switching in multicast transmissions with directional antennas results in a long delay, and consequently a low throughput. We propose asymmetric directional multicast (ADM) for capillary M2M to address this problem in mmWave communications. ADM provides asymmetric sectorization that is optimized for the irregular deployment pattern of mulicast group members. In ADM, an M2M gateway builds up asymmetric sectors with a beamwidth of a different size to cover all multicast group members with the minimum number of directional transmissions. The performance of ADM under various simulation environments is evaluated through a comparison with legacy mmWave multicast. The results of the simulation indicate that ADM achieves a better performance in terms of the transmission sectors, the transmission time, and the aggregate throughput when compared with the legacy multicast method. PMID:27077859
Growth of gravity-capillary waves in countercurrent air/water turbulence
NASA Astrophysics Data System (ADS)
Soldati, Alfredo; Zonta, Francesco; Onorato, Miguel
2015-11-01
We use Direct Numerical Simulation (DNS) of the Navier Stokes equations to analyze the dynamics of the interface between air and water when both phases are driven by opposite pressure gradients (countercurrent configuration). The Reynolds number (Reτ), the Weber number (We) and the Froude number (Fr) fully describe the physical problem. We examine the problem of the transient growth of interface waves for different combinations of physical parameters. Keeping Reτ constant and varying We and Fr , we show that, in the initial stages of the wave generation process, the amplitude of the interface elevation η grows in time as η ~t 2 / 5 . Wavenumber spectra, E (kx) , of the surface elevation in the capillary range are in good agreement with the prediction of the Wave Turbulence Theory. Finally, the wave-induced modification of the average wind and current velocity profiles will be addressed. Support from Regione Autonoma Friuli Venezia Giulia under grant PAR FSC 2007/2013 is gratefully acknowledged.
Asymmetric Directional Multicast for Capillary Machine-to-Machine Using mmWave Communications
Kwon, Jung-Hyok; Kim, Eui-Jik
2016-01-01
The huge demand for high data rate machine-to-machine (M2M) services has led to the use of millimeter Wave (mmWave) band communications with support for a multi-Gbps data rate through the use of directional antennas. However, unnecessary sector switching in multicast transmissions with directional antennas results in a long delay, and consequently a low throughput. We propose asymmetric directional multicast (ADM) for capillary M2M to address this problem in mmWave communications. ADM provides asymmetric sectorization that is optimized for the irregular deployment pattern of mulicast group members. In ADM, an M2M gateway builds up asymmetric sectors with a beamwidth of a different size to cover all multicast group members with the minimum number of directional transmissions. The performance of ADM under various simulation environments is evaluated through a comparison with legacy mmWave multicast. The results of the simulation indicate that ADM achieves a better performance in terms of the transmission sectors, the transmission time, and the aggregate throughput when compared with the legacy multicast method. PMID:27077859
Capillary Waves at Liquid/Vapor Interfaces: A Molecular Dynamics Simulation
Sides, Scott W.; Grest, Gary S.; Lacasse, Martin-D.
1999-07-16
Evidence for capillary waves at a liquid/vapor interface are presented from extensive molecular dynamics simulations of a system containing up to 1.24 million Lennard-Jones particles. Careful measurements show that the total interfacial width depends logarithmically on L{sub {parallel}}, the length of the simulation cell parallel to the interface, as predicted theoretically. The strength of the divergence of the interfacial width on L{sub {parallel}} depends inversely on the surface tension {gamma}. This allows us to measure {gamma} two ways since {gamma} can also be obtained from the difference in the pressure parallel and perpendicular to the interface. These two independent measures of {gamma} agree provided that the interfacial order parameter profile is fit to an error function and not a hyperbolic tangent, as often assumed. We explore why these two common fitting functions give different results for {gamma}.
Laboratory investigation of damping of gravity-capillary waves on the surface of turbulized liquid
NASA Astrophysics Data System (ADS)
Ermakov, S. A.; Kapustin, I. A.; Shomina, O. V.
2014-03-01
Investigation of damping of gravity-capillary waves (GCWs) in the presence of turbulence is a classical hydrodynamic problem which has important geophysical applications, one of which is related with the problem of forming a radar and optical image of a ship wake on wavy water surface. In this work a new method for the laboratory study of surface wave damping in turbulized liquid is described and the results are presented. The damping of standing GCWs by turbulence on the water surface in a tank mounted on a vibration table is studied. GCWs and turbulence are excited using a two-frequency mode of vibration table oscillations. A high-frequency small amplitude signal is used for parametric GCW excitation; a low-frequency large amplitude signal is used for generating turbulence due to water flowing through a fixed perforated grid submerged into the tank. The coefficient of GCW damping is determined by measured threshold of parametric excitation of the waves; turbulence characteristics are determined by the PIV and PTV techniques. Dependences of GCW damping coefficients on their frequency at different turbulence intensities are obtained, estimates for turbulent viscosity are presented, and a comparison with empirical models proposed earlier is performed.
The local structure factor near an interface; beyond extended capillary-wave models
NASA Astrophysics Data System (ADS)
Parry, A. O.; Rascón, C.; Evans, R.
2016-06-01
We investigate the local structure factor S (zq) at a free liquid–gas interface in systems with short-ranged intermolecular forces and determine the corrections to the leading-order, capillary-wave-like, Goldstone mode divergence of S (zq) known to occur for parallel (i.e. measured along the interface) wavevectors q\\to 0 . We show from explicit solution of the inhomogeneous Ornstein–Zernike equation that for distances z far from the interface, where the profile decays exponentially, S (zq) splits unambiguously into bulk and interfacial contributions. On each side of the interface, the interfacial contributions can be characterised by distinct liquid and gas wavevector dependent surface tensions, {σ l}(q) and {σg}(q) , which are determined solely by the bulk two-body and three-body direct correlation functions. At high temperatures, the wavevector dependence simplifies and is determined almost entirely by the appropriate bulk structure factor, leading to positive rigidity coefficients. Our predictions are confirmed by explicit calculation of S (zq) within square-gradient theory and the Sullivan model. The results for the latter predict a striking temperature dependence for {σ l}(q) and {σg}(q) , and have implications for fluctuation effects. Our results account quantitatively for the findings of a recent very extensive simulation study by Höfling and Dietrich of the total structure factor in the interfacial region, in a system with a cut-off Lennard-Jones potential, in sharp contrast to extended capillary-wave models which failed completely to describe the simulation results.
The local structure factor near an interface; beyond extended capillary-wave models.
Parry, A O; Rascón, C; Evans, R
2016-06-22
We investigate the local structure factor S (z;q) at a free liquid-gas interface in systems with short-ranged intermolecular forces and determine the corrections to the leading-order, capillary-wave-like, Goldstone mode divergence of S (z;q) known to occur for parallel (i.e. measured along the interface) wavevectors [Formula: see text]. We show from explicit solution of the inhomogeneous Ornstein-Zernike equation that for distances z far from the interface, where the profile decays exponentially, S (z;q) splits unambiguously into bulk and interfacial contributions. On each side of the interface, the interfacial contributions can be characterised by distinct liquid and gas wavevector dependent surface tensions, [Formula: see text] and [Formula: see text], which are determined solely by the bulk two-body and three-body direct correlation functions. At high temperatures, the wavevector dependence simplifies and is determined almost entirely by the appropriate bulk structure factor, leading to positive rigidity coefficients. Our predictions are confirmed by explicit calculation of S (z;q) within square-gradient theory and the Sullivan model. The results for the latter predict a striking temperature dependence for [Formula: see text] and [Formula: see text], and have implications for fluctuation effects. Our results account quantitatively for the findings of a recent very extensive simulation study by Höfling and Dietrich of the total structure factor in the interfacial region, in a system with a cut-off Lennard-Jones potential, in sharp contrast to extended capillary-wave models which failed completely to describe the simulation results. PMID:27115774
Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional.
Chacón, Enrique; Tarazona, Pedro
2016-06-22
We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers. PMID:27115912
Capillary wave Hamiltonian for the Landau–Ginzburg–Wilson density functional
NASA Astrophysics Data System (ADS)
Chacón, Enrique; Tarazona, Pedro
2016-06-01
We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau–Ginzburg–Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.
Slow Modulations of Periodic Waves in Hamiltonian PDEs, with Application to Capillary Fluids
NASA Astrophysics Data System (ADS)
Benzoni-Gavage, S.; Noble, P.; Rodrigues, L. M.
2014-08-01
Since its elaboration by Whitham almost 50 years ago, modulation theory has been known to be closely related to the stability of periodic traveling waves. However, it is only recently that this relationship has been elucidated and that fully nonlinear results have been obtained. These only concern dissipative systems though: reaction-diffusion systems were first considered by Doelman et al. (Mem Am Math Soc 199(934):viii+105, 2009), and viscous systems of conservation laws have been addressed by Johnson et al. (Invent Math, 2013). Here, only nondissipative models are considered, and a most basic question is investigated, namely, the expected link between the hyperbolicity of modulated equations and the spectral stability of periodic traveling waves to sideband perturbations. This is done first in an abstract Hamiltonian framework, which encompasses a number of dispersive models, in particular the well-known (generalized) Korteweg-de Vries equation and the less known Euler-Korteweg system, in both Eulerian coordinates and Lagrangian coordinates. The latter is itself an abstract framework for several models arising in water wave theory, superfluidity, and quantum hydrodynamics. As regards its application to compressible capillary fluids, attention is paid here to untangle the interplay between traveling waves/modulation equations in Eulerian coordinates and those in Lagrangian coordinates. In the most general setting, it is proved that the hyperbolicity of modulated equations is indeed necessary for the spectral stability of periodic traveling waves. This extends earlier results by Serre (Commun Partial Differ Equ 30(1-3):259-282, 2005), Oh and Zumbrun (Arch Ration Mech Anal 166(2):99-166, 2003), and Johnson et al. (Phys D 239(23-24):2057-2065, 2010). In addition, reduced necessary conditions are obtained in the small-amplitude limit. Then numerical investigations are carried out for the modulated equations of the Euler-Korteweg system with two types of "pressure
Roots and Rogues in German Child Language
ERIC Educational Resources Information Center
Duffield, Nigel
2008-01-01
This article is concerned with the proper characterization of subject omission at a particular stage in German child language. It focuses on post-verbal null subjects in finite clauses, here termed Rogues. It is argued that the statistically significant presence of Rogues, in conjunction with their distinct developmental profile, speaks against a…
Damage Caused by the Rogue Trustee
ERIC Educational Resources Information Center
O'Banion, Terry
2009-01-01
Fifty-nine community college presidents and chancellors in 16 states report on the damage caused by rogue trustees. While the damage to presidents, other trustees, and faculty and staff is alarming, the damage these trustees cause the college suggests that the rogue trustee may be the single most destructive force ever to plague an educational…
Nickerson, Stella; Frost, Denzil S; Phelan, Harrison; Dai, Lenore L
2013-12-01
We have studied the calculation of surface and interfacial tension for a variety of liquid-vapor and liquid-liquid interfaces using molecular dynamics (MD) simulations. Because of the inherently small scale of MD systems, large pressure fluctuations can cause imprecise calculations of surface tension using the pressure tensor route. The capillary wave method exhibited improved precision and stability throughout all of the simulated systems in this study. In order to implement this method, the interface was defined by fitting an error function to the density profile. However, full mapping of the interface from coordinate files produced enhanced accuracy. Upon increasing the system size, both methods exhibited higher precision, although the capillary wave method was still more reliable. PMID:24122780
NASA Astrophysics Data System (ADS)
de Poyferré, Thibault; Nguyen, Quang-Huy
2016-07-01
We consider the gravity-capillary waves in any dimension and in fluid domains with general bottoms. Using the paradifferential reduction established in [19], we prove Strichartz estimates for solutions to this problem, at a low regularity level such that initially, the velocity field can be non-Lipschitz up to the free surface. We then use those estimates to solve the Cauchy problem at this level of regularity.
Contours of slope as a measure of gravity-capillary wind waves
NASA Astrophysics Data System (ADS)
Cox, C. S.; Zhang, X.
2012-12-01
Contours of both x and y components of water surface slopes can be generated optically. Two horizontal arrays of thin, linear lamps placed a few meters below the water surface are photographed from above. One array, consisting of a group of colored y-parallel lamps produces contours of x-slope. The value of each contour is recognized by its color. The other array, of x -parallel lamps produces contours of y-slope. When the two arrays are pulsed alternately and photographed by a fast camera, the full structure and evolution of the water surface shape can be monitored. In order to register capillaries down to one or two millimeter wavelengths the light pulses must be as short as 200 micro seconds to avoid smearing Adequate light intensity in such short pulses is generated by a row of high intensity light emitting diodes in each linear lamp. LEDs are advantageous because several different colored types are available. permitting many different contours to be generated. When each emitter has a narrow wavelength range, problems from light dispersion and differential color absorption in the water are avoided. In analyzing the photographs, correct identification of the color in the image of each contour is essential. Color sensing cameras have only the three color coordinates, red, green and blue. It is useful to identify each colored contour image by a unit vector in the 3-space of RGB for comparison with the array of expected values. This enables recognition of the most probable color and an estimate of probable error of the choice. If the probable error is large, the contour can then be discarded because of uncertainty of its value.. The conversion from a small number of contours to a continuous representation of the water surface shape is in theory perfect for a band limited spectrum of waves, but in practice inaccuracies, even at the pixel level, in the location of contours produce errors. The spacing of contours of slope is determined by the physical spacing between
Understanding the influence of capillary waves on solvation at the liquid-vapor interface
NASA Astrophysics Data System (ADS)
Rane, Kaustubh; van der Vegt, Nico F. A.
2016-03-01
This work investigates the question if surface capillary waves (CWs) affect interfacial solvation thermodynamic properties that determine the propensity of small molecules toward the liquid-vapor interface. We focus on (1) the evaluation of these properties from molecular simulations in a practical manner and (2) understanding them from the perspective of theories in solvation thermodynamics, especially solvent reorganization effects. Concerning the former objective, we propose a computational method that exploits the relationship between an external field acting on the liquid-vapor interface and the magnitude of CWs. The system considered contains the solvent, an externally applied field (f) and the solute molecule fixed at a particular location. The magnitude of f is selected to induce changes in CWs. The difference between the solvation free energies computed in the presence and in the absence of f is then shown to quantify the contribution of CWs to interfacial solvation. We describe the implementation of this method in the canonical ensemble by using a Lennard-Jones solvent and a non-ionic solute. Results are shown for three types of solutes that differ in the nature of short-ranged repulsive (hard-core) interactions. Overall, we observe that CWs have a negligible or very small effect on the interfacial solvation free energy of a solute molecule fixed near the liquid-vapor interface for the above systems. We also explain how the effects of pinning or dampening of CWs caused by a fixed solute are effectively compensated and do not contribute to the solvation free energy.
NASA Astrophysics Data System (ADS)
Diorio, J. D.; Watkins, N.; Zuech, J.; Duncan, J. H.
2008-11-01
There have been several recent numerical investigations that have shown the existence of three-dimensional nonlinear solitary surface wave patterns that propagate with speeds less than the minimum wave phase speed prescribed by linear theory (23 cm/s for clean water). In the present study, wave patterns were generated by translating a small-diameter region of high pressure across a water surface. The high-pressure region was created by forcing air through a small-diameter vertically oriented tube attached to a carriage that propelled it horizontally at speeds near 23 cm/s. The wave pattern was measured with a cinematic LIF technique. It was found that a steady solitary wave pattern can exist at speeds below the linear-theory minimum phase speed, while for speeds above the minimum, a pattern of gravity-capillary waves was produced. The solitary wave pattern, which only appeared when the pressure forcing was large, dissipated rapidly when the forcing was turned off. The streamwise dimension of the solitary wave was much smaller than the transverse dimension.
NASA Technical Reports Server (NTRS)
Long, S. R.; Huang, N. E.
1976-01-01
A new laser device has been used to make direct wave-slope measurements in the capillary-gravity range. Owing to the design principles, the digital nature of the system and the use of a laser beam as a probe, the earlier problems of intensity variations and meniscus effects were avoided. Using this new technique, wave-slope spectra both down and across the channel were obtained for different wind conditions, along with corresponding mean-square slope values. Comparisons are made with existing data. The results indicate that a quasi-equilibrium state may exist for each wind speed and that it increases in intensity with increasing wind, which may imply an asymptotic nature for the equilibrium-range coefficient. From the data, two significant frictional velocities, 17.5 and 31 cm/s respectively, are identified as critical values for different ranges of wave development.
NASA Astrophysics Data System (ADS)
Masnadi, N.; Duncan, J. H.
2012-11-01
The non-linear response of a water free surface to a localized pressure distribution moving at constant speed just below the minimum phase speed (Cmin ~ 23 cm/s) of gravity-capillary waves is studied experimentally in a long tank. The pressure distribution is generated by blowing air onto the water surface via a vertically oriented 2-mm-ID tube that is mounted on an instrument carriage that is in turn set to move along the tank at constant speeds between 20 and 23 cm/s. A cinematic light refraction method is used to obtain quantitative measurements of the surface deformation pattern behind the air jet. At towing speeds just below Cmin, an unsteady V-shaped wave pattern appears behind the pressure source. From observations of the wave pattern evolution, it is found that localized depressions are generated near the pressure source and propagate in pairs along the two arms of the V-shaped pattern. These are eventually shed from the tips of the pattern and rapidly decay. Measurements of the evolution of the speed of these localized depression patterns are compared to existing measurements of the speeds of steady three-dimensional solitary gravity-capillary waves (lumps) that appear behind the pressure source at even lower towing speeds. Supported by the National Science Foundation Division of Ocean Sciences.
MacDowell, Luis G; Benet, Jorge; Katcho, Nebil A; Palanco, Jose M G
2014-04-01
In this paper we review simulation and experimental studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial Hamiltonian Model. We discuss recent simulation results that reveal a film-height-dependent surface tension not accounted for in the classical Interfacial Hamiltonian Model. We show how this observation may be explained bottom-up from sound principles of statistical thermodynamics and discuss some of its implications. PMID:24351859
NASA Astrophysics Data System (ADS)
Tarigan, Hendra J.
2008-09-01
Backscattered He-Ne laser light from a side illuminated fluid-filled fused silica capillary tube generates a series of fringes when viewed in an imaging plane. The light intensity variation as a function of scattering angle constitutes a waveform, which contains hills and valleys. Geometrical Optics and Wave Theories, simultaneously, are employed to model the waveforms and quantify the index of refraction of fluid in the capillary tube.
Bolognesi, Guido; Saito, Yuki; Tyler, Arwen I I; Ward, Andrew D; Bain, Colin D; Ces, Oscar
2016-04-19
Measurements of the ultralow interfacial tension and surfactant film bending rigidity for micron-sized heptane droplets in bis(2-ethylhexyl) sodium sulfosuccinate-NaCl aqueous solutions were performed in a microfluidic device through the analysis of thermally driven droplet interface fluctuations. The Fourier spectrum of the stochastic droplet interface displacement was measured through bright-field video microscopy and a contour analysis technique. The droplet interfacial tension, together with the surfactant film bending rigidity, was obtained by fitting the experimental results to the prediction of a capillary wave model. Compared to existing methods for ultralow interfacial tension measurements, this contactless, nondestructive, all-optical approach has several advantages, such as fast measurement, easy implementation, cost-effectiveness, reduced amount of liquids, and integration into lab-on-a-chip devices. PMID:26982629
... Why do capillary hemangiomas on the eyelids cause vision problems? Capillary Hemangiomas of the eyelid can cause ... a capillary hemangioma in the eye socket cause vision problems? A capillary hemangioma in the eye socket ( ...
78 FR 60375 - Rogue Valley Terminal Railroad Corporation-Corporate Family Transaction Exemption
Federal Register 2010, 2011, 2012, 2013, 2014
2013-10-01
... TRANSPORTATION Surface Transportation Board Rogue Valley Terminal Railroad Corporation--Corporate Family Transaction Exemption Rogue Valley Terminal Railroad Corporation (Rogue Valley),\\1\\ a Class III rail carrier... White City Terminal & Utility Co. (WCTU) and was indirectly controlled by Berkshire Hathaway...
Strategies for Dealing with Rogue Trustees
ERIC Educational Resources Information Center
O'Banion, Terry
2009-01-01
In the two previous articles in this three-part series the author reported on the motivations and damage caused by rogue trustees. The articles are based on a study of 59 community college CEOs from 16 different states. In this final article the author addresses the strategies that presidents and their board chairs have used to curtail the…
NASA Astrophysics Data System (ADS)
Masnadi, Naeem; Cho, Yeunwoo; Duncan, James H.; Akylas, Triantaphyllos
2015-11-01
The non-linear response of a water free surface to a pressure source moving at speeds near the minimum speed of linear gravity-capillary waves (Cmin ~ 23 cm/s) is investigated with experiments and theory. In the experiments, waves are generated by a vertically oriented air-jet that moves at a constant speed over the water surface in a long tank. The 3-D surface shape behind the air-jet is measured using a cinematic refraction-based technique combined with an LIF technique. At towing speeds just below Cmin, an unsteady pattern is formed where localized depressions periodically appear in pairs and move away from the source along the arms of a downstream V-shaped pattern. This behavior is analogous to the periodic shedding of solitary waves upstream of a source moving at the maximum wave speed in shallow water. The gravity-capillary depressions are rapidly damped by viscosity and their speed-amplitude characteristics closely match those from inviscid calculations of gravity-capillary lumps. The shedding frequency of the lumps in the present experiments increases with both increasing towing speed and air-flow rate. Predictions of this behavior using a model equation that incorporates damping and a quadratic nonlinearity are in good agreement with the experiments. The partial support of the National Science Foundation under grant OCE0751853 is gratefully acknowledged.
NASA Astrophysics Data System (ADS)
Seo, Jongmin; García-Mayoral, Ricardo; Mani, Ali
2015-11-01
Superhydrophobic surfaces under liquid flow can produce significant slip, and thus drag reduction, when they entrap gas bubbles within their roughness elements. Our work aims to explore the onset mechanism to the failure of drag reduction by superhydrophobic surfaces when they are exposed to turbulent boundary layers. We focus on the effect of finite surface tension to the dynamic response of deformable interfaces between overlying water flow and the gas pockets. To this end, we conduct direct numerical simulations of turbulent flows over superhydrophobic surfaces allowing deformable gas-liquid interface. DNS results show that spanwise-coherent, upstream-traveling waves develop on the gas-liquid interface as a result of its interactions with turbulence. We study the nature and scaling of the upstream-traveling waves through semi-analytical modeling. We will show that the traveling waves are well described by a Weber number based on the slip velocity at the interface. In higher Weber number, the stability of gas pocket decreases as the amplitude of interface deformation and the magnitude of pressure fluctuations are augmented. Supported by Office of Naval Research and the Kwanjeong Educational Scholarship Foundation.
Warner, M.
1988-10-15
Rapid instrumental methods for performing electrophoretic separations in capillary tubes have recently been developed, making capillary electrophoresis one of the most exciting new techniques available to analytical chemists. This article discusses detection methods, applications, and the future of capillary electrophoresis.
... using capillary blood sampling. Disadvantages to capillary blood sampling include: Only a limited amount of blood can be drawn using this method. The procedure has some risks (see below). Capillary ...
33 CFR 80.1310 - Rogue River, OR.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 33 Navigation and Navigable Waters 1 2010-07-01 2010-07-01 false Rogue River, OR. 80.1310 Section 80.1310 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY INTERNATIONAL NAVIGATION RULES COLREGS DEMARCATION LINES Thirteenth District § 80.1310 Rogue River, OR. A line drawn...
Wang, Lei; Zhu, Yu-Jie; Qi, Feng-Hua; Li, Min; Guo, Rui
2015-06-01
In this paper, the nonautonomous Lenells-Fokas (LF) model is investigated. The modulational instability analysis of the solutions with variable coefficients in the presence of a small perturbation is studied. Higher-order soliton, breather, earthwormon, and rogue wave solutions of the nonautonomous LF model are derived via the n-fold variable-coefficient Darboux transformation. The solitons and earthwormons display the elastic collisions. It is found that the nonautonomous LF model admits the higher-order periodic rogue waves, composite rogue waves (rogue wave pair), and oscillating rogue waves, whose dynamics can be controlled by the inhomogeneous nonlinear parameters. Based on the second-order rogue wave, a diamond structure consisting of four first-order rogue waves is observed. In addition, the semirational solutions (the mixed rational-exponential solutions) of the nonautonomous LF model are obtained, which can be used to describe the interactions between the rogue waves and breathers. Our results could be helpful for the design of experiments in the optical fiber communications. PMID:26117105
Axisymmetric capillary waves on thin annular liquid sheets. II. Spatial development
NASA Astrophysics Data System (ADS)
Mehring, C.; Sirignano, W. A.
2000-06-01
The forced motion of semi-infinite axisymmetric thin inviscid annular liquid sheets, exiting from a nozzle or atomizer into a surrounding void under zero gravity but with constant gas-core pressure is analyzed by means of the reduced-dimension approach described in C. Mehring and W. A. Sirignano [Phys. Fluids 12, 1417 (2000)]. Linear analytical time-dependent ("limit-cycle") solutions to the pure boundary-value problem are presented as well as linear and nonlinear numerical (transient) solutions to the mixed boundary- and initial-value problem of initially undisturbed sheets harmonically forced at the orifice or nozzle exit. Group velocities for the six independent solutions to the linear boundary-value problem are used to determine the location of boundary conditions. Numerical simulations of the linear transient problem are employed to validate these predictions. Parameter studies on sheet breakup and collapse lengths as well as on breakup and collapse times are reported. The dependence on modulation frequency, modulated disturbance amplitude, Weber number, and annular radius is presented for various cases of the mixed problem, i.e., for linearly or nonlinearly stable and unstable, dilationally or sinusoidally forced sheets. Nonlinear effects often have significant effects on breakup times and lengths or on collapse times and lengths. Nonlinear wave forms can deviate substantially from linear predictions resulting in major impacts on the size of the rings and shells that will remain after breakup.
Haselberg, Rob; van der Sneppen, Lineke; Ariese, Freek; Ubachs, Wim; Gooijer, Cees; de Jong, Gerhardus J; Somsen, Govert W
2009-12-15
Protein adsorption to silica surfaces is a notorious problem in analytical separations. Evanescent-wave cavity ring-down spectroscopy (EW-CRDS) and capillary electrophoresis (CE) were employed to investigate the capability of positively charged polymer coatings to minimize the adsorption of basic proteins. Adsorption of cytochrome c (cyt c) to silica coated with a single layer of polybrene (PB), or a triple layer of PB, dextran sulfate (DS), and PB, was studied and compared to bare silica. Direct analysis of silica surfaces by EW-CRDS revealed that both coatings effectively reduce irreversible protein adsorption. Significant adsorption was observed only for protein concentrations above 400 microM, whereas the PB-DS-PB coating was shown to be most effective and stable. CE analyses of cyt c were performed with and without the respective coatings applied to the fused-silica capillary wall. Monitoring of the electroosmotic flow and protein peak areas indicated a strong reduction of irreversible protein adsorption by the positively charged coatings. Determination of the electrophoretic mobility and peak width of cyt c revealed reversible protein adsorption to the PB coating. It is concluded that the combination of results from EW-CRDS and CE provides highly useful information on the adsorptive characteristics of bare and coated silica surfaces toward basic proteins. PMID:19921852
Simulation of Arrhythmogenic Effect of Rogue RyRs in Failing Heart by Using a Coupled Model
Lu, Luyao; Xia, Ling; Zhu, Xiuwei
2012-01-01
Cardiac cells with heart failure are usually characterized by impairment of Ca2+ handling with smaller SR Ca2+ store and high risk of triggered activities. In this study, we developed a coupled model by integrating the spatiotemporal Ca2+ reaction-diffusion system into the cellular electrophysiological model. With the coupled model, the subcellular Ca2+ dynamics and global cellular electrophysiology could be simultaneously traced. The proposed coupled model was then applied to study the effects of rogue RyRs on Ca2+ cycling and membrane potential in failing heart. The simulation results suggested that, in the presence of rogue RyRs, Ca2+ dynamics is unstable and Ca2+ waves are prone to be initiated spontaneously. These release events would elevate the membrane potential substantially which might induce delayed afterdepolarizations or triggered action potentials. Moreover, the variation of membrane potential depolarization is indicated to be dependent on the distribution density of rogue RyR channels. This study provides a new possible arrhythmogenic mechanism for heart failure from subcellular to cellular level. PMID:23056145
Functional description of signal processing in the Rogue GPS receiver
NASA Technical Reports Server (NTRS)
Thomas, J. B.
1988-01-01
Over the past year, two Rogue GPS prototype receivers have been assembled and successfully subjected to a variety of laboratory and field tests. A functional description is presented of signal processing in the Rogue receiver, tracing the signal from RF input to the output values of group delay, phase, and data bits. The receiver can track up to eight satellites, without time multiplexing among satellites or channels, simultaneously measuring both group delay and phase for each of three channels (L1-C/A, L1-P, L2-P). The Rogue signal processing described requires generation of the code for all three channels. Receiver functional design, which emphasized accuracy, reliability, flexibility, and dynamic capability, is summarized. A detailed functional description of signal processing is presented, including C/A-channel and P-channel processing, carrier-aided averaging of group delays, checks for cycle slips, acquistion, and distinctive features.