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Dynamical analysis of turbulence in fusion plasmas and nonlinear waves

Viana, Ricardo Luiz; Lopes, Sergio Roberto; Caldas, Ibere Luiz; Szezech Junior, Jose Danilo; Guimarães Filho, Zwinglio de Oliveira; Lima, Gustavo Zampier dos Santos; Galuzio, Paulo Paneque; Batista, Antonio Marcos; Kuznetsov, Yurii; Nascimento, Ivan Cunh
Fonte: ELSEVIER SCIENCE BV; AMSTERDAM Publicador: ELSEVIER SCIENCE BV; AMSTERDAM
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.21%
Turbulence is one of the key problems of classical physics, and it has been the object of intense research in the last decades in a large spectrum of problems involving fluids, plasmas, and waves. In order to review some advances in theoretical and experimental investigations on turbulence a mini-symposium on this subject was organized in the Dynamics Days South America 2010 Conference. The main goal of this mini-symposium was to present recent developments in both fundamental aspects and dynamical analysis of turbulence in nonlinear waves and fusion plasmas. In this paper we present a summary of the works presented at this mini-symposium. Among the questions to be addressed were the onset and control of turbulence and spatio-temporal chaos. (C) 2011 Elsevier B. V. All rights reserved.; FAPESP; FAPESP; CNPq; CNPq; CAPES; CAPES; Fundacao Araucarias; Fundacao Araucarias; RNF-CNEN (Brazilian Fusion Network); RNFCNEN (Brazilian Fusion Network)

Nonlinear waves on the surface of a fluid covered by an elastic sheet

Deike, Luc; Bacri, Jean-Claude; Falcon, Eric
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.22%
We experimentally study linear and nonlinear waves on the surface of a fluid covered by an elastic sheet where both tension and flexural waves take place. An optical method is used to obtain the full space-time wave field, and the dispersion relation of waves. When the forcing is increased, a significant nonlinear shift of the dispersion relation is observed. We show that this shift is due to an additional tension of the sheet induced by the transverse motion of a fundamental mode of the sheet. When the system is subjected to a random noise forcing at large scale, a regime of hydro-elastic wave turbulence is observed with a power-law spectrum of the scale in disagreement with the wave turbulence prediction. We show that the separation between relevant time scales is well satisfied at each scale of the turbulent cascade as expected theoretically. The wave field anisotropy, and finite size effects are also quantified and are not at the origin of the discrepancy. Finally, the dissipation is found to occur at all scales of the cascade contrary to the theoretical hypothesis, and could thus explain this disagreement.; Comment: Journal of Fluid Mechanics (2013)

Nonequilibrium chaos of disordered nonlinear waves

Skokos, Charalampos; Gkolias, Ioannis; Flach, Sergej
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.06%
Do nonlinear waves destroy Anderson localization? Computational and experimental studies yield subdiffusive nonequilibrium wave packet spreading. Chaotic dynamics and phase decoherence assumptions are used for explaining the data. We perform a quantitative analysis of the nonequilibrium chaos assumption, and compute the time dependence of main chaos indicators - Lyapunov exponents and deviation vector distributions. We find a slowing down of chaotic dynamics, which does not cross over into regular dynamics up to the largest observed time scales, still being fast enough to allow for a thermalization of the spreading wave packet. Strongly localized chaotic spots meander through the system as time evolves. Our findings confirm for the first time that nonequilibrium chaos and phase decoherence persist, fueling the prediction of a complete delocalization.; Comment: 5 pages, 5 figures

Nonlinear waves, differential resultant, computer algebra and completely integrable dynamical systems

Kostov, N. A.; Kostova, Z. T.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.18%
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer algebra such differential resultant and others.; Comment: 33 pages, no figures

Chaotic behaviour of nonlinear waves and solitons of perturbed Korteweg - de Vries equation

Blyuss, K. B.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.22%
This paper considers properties of nonlinear waves and solitons of Korteweg-de Vries equation in the presence of external perturbation. For time-periodic hamiltonian perturbation the width of the stochastic layer is calculated. The conclusions about chaotic behaviour in long-period waves and solitons are inferred. Obtained theoretical results find experimental confirmation in experiments with the propagation of ion-acoustic waves in plasma.; Comment: 7 pages, LaTeX, 2 Postscript figures, submitted to Reports on Mathematical Physics

Nonlinear Waves in Disordered Diatomic Granular Chains

Ponson, Laurent; Boechler, Nicholas; Lai, Yi Ming; Porter, Mason A.; Kevrekidis, P. G.; Daraio, Chiara
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.2%
We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin", so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: In low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatio-temporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for such a transition. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.; Comment: 10 pages, 8 figures (some with multiple parts), to appear in Physical Review E; summary of changes: new title, one new figure, additional discussion of several points (including both background and results)

Interactions among different types of nonlinear waves described by the Kadomtsev-Petviashvili Equation

Cheng, Xue-Ping; Chen, Chun-Li; Lou, Sen-Yue
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.31%
In nonlinear physics, the interactions among solitons are well studied thanks to the multiple soliton solutions can be obtained by various effective methods. However, it is very difficult to study interactions among different types of nonlinear waves such as the solitons (or solitary waves), the cnoidal periodic waves and Painlev\'e waves. In this paper, the nonlocal symmetries related to the Darboux transformations (DT) of the Kadomtsev-Petviashvili (KP) equation is localized after imbedding the original system to an enlarged one. Then the DT is used to find the corresponding group invariant solutions such that interaction solutions among different types of nonlinear waves can be found. It is shown that starting from a Boussinesq wave or a KdV-type wave, which are two basic reductions of the KP equation, the essential and unique role of the DT is to add an additional soliton.

Anderson localization or nonlinear waves? A matter of probability

Ivanchenko, M. V.; Laptyeva, T. V.; Flach, S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.13%
In linear disordered systems Anderson localization makes any wave packet stay localized for all times. Its fate in nonlinear disordered systems is under intense theoretical debate and experimental study. We resolve this dispute showing that at any small but finite nonlinearity (energy) value there is a finite probability for Anderson localization to break up and propagating nonlinear waves to take over. It increases with nonlinearity (energy) and reaches unity at a certain threshold, determined by the initial wave packet size. Moreover, the spreading probability stays finite also in the limit of infinite packet size at fixed total energy. These results are generalized to higher dimensions as well.; Comment: 4 pages, 3 figures

Universal subdiffusion of nonlinear waves in two dimensions with disorder

Laptyeva, T. V.; Bodyfelt, J. D.; Flach, S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.13%
We follow the dynamics of nonlinear waves in two-dimensional disordered lattices with tunable nonlinearity. In the absence of nonlinear terms Anderson localization traps the packet in space. For the nonlinear case a destruction of Anderson localization is found. The packet spreads subdiffusively, and its second moment grows in time asymptotically as $t^\alpha$. We perform fine statistical averaging and test theoretical predictions for $\alpha$. Along with a precise confirmation of the predictions in [Chemical Physics \textbf{375}, 548 (2010)], we also find potentially long lasting intermediate deviations due to a growing number of surface resonances of the wave packet.; Comment: 6 pages, 6 figures, 1 table

Equation for three-dimensional nonlinear waves in liquid with gas bubbles

Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.3%
Nonlinear waves in a liquid containing gas bubbles are considered in the three-dimensional case. Nonlinear evolution equation is given for description of long nonlinear pressure waves. It is shown that in the general case the equation is not integrable. Some exact solutions for the nonlinear evolution equation are presented. Application of the Hirota method is illustrated for finding multi-soliton solutions for the nonintegrable evolution equation in the three-dimensional case. The stability of the one-dimensional solitary waves is investigated. It is shown that the one-dimensional solitary waves are stable to transverse perturbations.

Nonlinear waves in Newton's cradle and the discrete p-Schroedinger equation

James, Guillaume
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.3%
We study nonlinear waves in Newton's cradle, a classical mechanical system consisting of a chain of beads attached to linear pendula and interacting nonlinearly via Hertz's contact forces. We formally derive a spatially discrete modulation equation, for small amplitude nonlinear waves consisting of slow modulations of time-periodic linear oscillations. The fully-nonlinear and unilateral interactions between beads yield a nonstandard modulation equation that we call the discrete p-Schroedinger (DpS) equation. It consists of a spatial discretization of a generalized Schroedinger equation with p-Laplacian, with fractional p>2 depending on the exponent of Hertz's contact force. We show that the DpS equation admits explicit periodic travelling wave solutions, and numerically find a plethora of standing wave solutions given by the orbits of a discrete map, in particular spatially localized breather solutions. Using a modified Lyapunov-Schmidt technique, we prove the existence of exact periodic travelling waves in the chain of beads, close to the small amplitude modulated waves given by the DpS equation. Using numerical simulations, we show that the DpS equation captures several other important features of the dynamics in the weakly nonlinear regime...

Simulation of strong nonlinear waves with vectorial lattice Boltzmann schemes

Dubois, François
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.06%
We show that an hyperbolic system with a mathematical entropy can be discretized with vectorial lattice Boltzmann schemes with the methodology of kinetic representation of the dual entropy. We test this approach for the shallow water equations in one and two space dimensions. We obtain interesting results for a shock tube, reflection of a shock wave and unstationary two-dimensional propagation. This contribution shows the ability of vectorial lattice Boltzmann schemes to simulate strong nonlinear waves in unstationary situations.; Comment: 12 pages

Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media

Brusch, Lutz; Torcini, Alessandro; Baer, Markus
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.26%
Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example, where waves originate from a source exhibiting a back-and-forth movement in radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves (superspiral''). Using the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonous growth or decay as well as saturation of these modulations away from the source depending on the perturbation frequency. Our findings allow a consistent interpretation of recent experimental observations concerning superspirals and their decay to spatio-temporal chaos.; Comment: 4 pages, 4 figures

Nonlinear waves in networks: a simple approach using the sine--Gordon equation

Caputo, Jean-Guy; Dutykh, Denys
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.18%
To study the propagation of nonlinear waves across Y-- and T--type junctions, we consider the 2D sine--Gordon equation as a model and study the dynamics of kinks and breathers in such geometries. The comparison of the energies reveals that the angle of the fork plays no role. Motivated by this, we introduce a 1D effective equation whose solutions agree well with the 2D simulations for kink and breather solutions. For branches of equal width, breather crossing occurs approximately when $v > 1 - \omega$, where $v$ is the breather celerity and $\omega$ is its frequency. We then characterize the breathers in the two upper branches by estimating their velocity and frequency. These new breathers are slower than the initial breather and up-shifted in frequency. In perspective, this study could be generalized to more complex nonlinear waves.

Localized nonlinear waves in a two-mode nonlinear fiber

Zhao, Li-Chen; Liu, Jie
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.3%
We find that diverse nonlinear waves, such as soliton, Akhmediev breather, and rogue waves (RWs), can emerge and interplay with each other in a two-mode coupled system. It provides a good platform to study interaction between different kinds of nonlinear waves. In particular, we obtain dark RWs analytically for the first time in the coupled system, and find that two RWs can appear in the temporal-spatial distribution. Possible ways to observe these nonlinear waves are discussed.; Comment: 8 pages, 8 figures

Extended equation for description of nonlinear waves in liquid with gas bubbles

Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.35%
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for long weakly nonlinear waves taking into consideration liquid viscosity, inter--phase heat transfer and surface tension. Additional conditions for the parameters of the equation are determined for integrability of the mathematical model. The transformation for linearization of the nonlinear equation is presented too. Some exact solutions of the nonlinear equation are found for integrable and non--integrable cases. The nonlinear waves described by the nonlinear equation are numerically investigated.

Nonlinear waves in bubbly liquids with consideration for viscosity and heat transfer

Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.32%
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order for describing nonlinear waves in gas-liquid mixtures are derived. Exact solutions of these nonlinear evolution equations are found. Properties of nonlinear waves in a liquid with gas bubbles are discussed.; Comment: Physics Letters A, Volume 374, Issues 19-20, Pages 2011-2016

Nonlinear Waves in Lattices: Past, Present, Future

Kevrekidis, P. G.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.13%
In the present work, we attempt a brief summary of various areas where nonlinear waves have been emerging in the phenomenology of lattice dynamical systems. These areas include nonlinear optics, atomic physics, mechanical systems, electrical lattices, nonlinear metamaterials, plasma dynamics and granular crystals. We give some of the recent developments in each one of these areas and speculate on some of the potentially interesting directions for future study.; Comment: 35 pages, 3 figures, brief review to appear in IMA Journal of Applied Mathematics

Generation and Propagation of Nonlinear Waves in Travelling Wave Tubes

Tzenov, Stephan I.
Tipo: Artigo de Revista Científica