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## Dynamical analysis of turbulence in fusion plasmas and nonlinear waves

Fonte: ELSEVIER SCIENCE BV; AMSTERDAM
Publicador: ELSEVIER SCIENCE BV; AMSTERDAM

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

66.21%

#TURBULENCE#FLUIDS#PLASMAS#NONLINEAR WAVES#CHAOS#TOKAMAKS#ACTION PRINCIPLE FORMULATIONS#SELF-SUSTAINING PROCESS#SCRAPE-OFF LAYER#EDGE TURBULENCE#DRIFT WAVES

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)

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/09/2013

Relevância na Pesquisa

56.22%

#Physics - Fluid Dynamics#Condensed Matter - Other Condensed Matter#Nonlinear Sciences - Chaotic Dynamics#Physics - Classical Physics

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)

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## Nonequilibrium chaos of disordered nonlinear waves

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/06/2013

Relevância na Pesquisa

56.06%

#Nonlinear Sciences - Chaotic Dynamics#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Statistical Mechanics

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/04/1999

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

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

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## Nonlinear Waves in Disordered Diatomic Granular Chains

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.2%

#Nonlinear Sciences - Pattern Formation and Solitons#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Materials Science#Condensed Matter - Statistical Mechanics#Nonlinear Sciences - Chaotic Dynamics

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)

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/08/2012

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.

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## Anderson localization or nonlinear waves? A matter of probability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/08/2011

Relevância na Pesquisa

56.13%

#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Other Condensed Matter#Nonlinear Sciences - Chaotic Dynamics#Nonlinear Sciences - Pattern Formation and Solitons

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

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## Universal subdiffusion of nonlinear waves in two dimensions with disorder

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/03/2012

Relevância na Pesquisa

56.13%

#Nonlinear Sciences - Chaotic Dynamics#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Other Condensed Matter

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/01/2012

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.

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/08/2010

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...

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## Simulation of strong nonlinear waves with vectorial lattice Boltzmann schemes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/01/2014

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

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## Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/02/2003

Relevância na Pesquisa

56.26%

#Condensed Matter - Statistical Mechanics#Nonlinear Sciences - Chaotic Dynamics#Nonlinear Sciences - Pattern Formation and Solitons

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/02/2014

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.

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## Localized nonlinear waves in a two-mode nonlinear fiber

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/01/2015

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/07/2013

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.

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/12/2011

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

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## Nonlinear Waves in Lattices: Past, Present, Future

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/09/2010

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

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## Generation and Propagation of Nonlinear Waves in Travelling Wave Tubes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/06/2005

Relevância na Pesquisa

56.2%

#Physics - Accelerator Physics#Nonlinear Sciences - Pattern Formation and Solitons#Physics - Plasma Physics

The generation and evolution of nonlinear waves in microwave amplifiers such
as travelling wave tubes, free electron lasers and klystrons have been studied.
The analysis is based on the hydrodynamic and field equations for the
self-consistent evolution of the beam density distribution, the current
velocity and the electromagnetic fields. A system of coupled nonlinear
Schr\"{o}dinger equations for the slowly varying amplitudes of interacting
beam-density waves has been derived. Under the approximation of an isolated
mode neglecting the effect of the rest of the modes, this system reduces to a
single nonlinear Schr\"{o}dinger equation for that particular mode.; Comment: 6 pages, No figures

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## Two-dimensional Nonlinear Optically-induced Photonic Lattices in Photorefractive Crystals

Fonte: SPIE - The International Society for Optical Engineering
Publicador: SPIE - The International Society for Optical Engineering

Tipo: Conference paper

Relevância na Pesquisa

56.24%

#Keywords: Anisotropy#Phase modulation#Photorefractive materials#Solitons#Nonlinear waves#Optically-induced photonic lattices#Photorefractive medium#Soliton arrays#Nonlinear optics Nonlinear waves#Optically-induced photonic lattices#Photorefractive medium

We study theoretically and generate experimentally two-dimensional nonlinear optically-induced photonic lattices with periodic phase modulation of different geometries in a photorefractive medium, including the periodic nonlinear waves with an internal energy flow or vortex lattices. We demonstrate that the light-induced periodically modulated nonlinear refractive index is highly anisotropic and nonlocal, and it depends on the orientation of a two-dimensional lattice relative to the crystal axis. We discuss stability of such optically-induced photonic two-dimensional structures and demonstrate experimentally their waveguiding properties.

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