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Determining Lyapunov Exponents from a Time Series
 Physica
, 1985
"... We present the first algorithms that allow the estimation of nonnegative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of n ..."
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We present the first algorithms that allow the estimation of nonnegative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of nearby orbits in phase space. A system with one or more positive Lyapunov exponents is defined to be chaotic. Our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems: we monitor the longterm growth rate of small volume elements in an attractor. The method is tested on model systems with known Lyapunov spectra, and applied to data for the BelousovZhabotinskii reaction and CouetteTaylor flow. Contents 1.
Gas transport across an air/water interface populated by capillary waves, Phys
 Fluids
, 1999
"... An experimental study of gas transport across an air/water interface, populated by a field of standing capillary waves is presented. The experiments were conducted in a small tank containing distilled water, enriched with carbon dioxide. The capillary waves were of the Faraday type, generated by pr ..."
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An experimental study of gas transport across an air/water interface, populated by a field of standing capillary waves is presented. The experiments were conducted in a small tank containing distilled water, enriched with carbon dioxide. The capillary waves were of the Faraday type, generated by providing a small vertical vibration to the water tank. The frequency of excitation was varied from 200 to 400 Hz, giving wavelengths from 3.62 to 2.26 mm ͑linear estimate͒. The gas transport rate across the interface increased by almost two orders of magnitude as the wave slope was increased from zero to slightly above 0.2 m/m. A unique aspect of these experiments is that capillary waves were isolated from the obfuscating effects of turbulence, aerosol generation, and other phenomena typically present in wind/wave tunnel experiments. Consequently the large enhancement in gas transfer was due to the effects of capillary waves alone, demonstrating their importance in gas exchange processes. The maximum mass transfer coefficients obtained in these experiments are not achieved in typical wind/wave tunnel experiments below wind speeds of 10 m/s.
B.: Modal interactions in dynamical and structural systems
 Appl. Mech. Rev
, 1989
"... We review theoretical and experimental studies of the influence of modal interactions on the nonlinear response of harmonically excited structural and dynamical systems. In particular, we discuss the response of pendulums, ships, rings, shells, arches, beam structures, surface waves, and the simil ..."
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Cited by 9 (1 self)
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We review theoretical and experimental studies of the influence of modal interactions on the nonlinear response of harmonically excited structural and dynamical systems. In particular, we discuss the response of pendulums, ships, rings, shells, arches, beam structures, surface waves, and the similarities in the qualitative behavior of these systems. The systems are characterized by quadratic nonlinearities which may lead to twotoone and combination autoparametric resonances. These resonances give rise to a coupling between the modes involved in the resonance leading to nonlinear periodic, quasiperiodic, and chaotic motions. 1. INTRODUCTION 1.1 Onetoone Internal
PATTERN SELECTION FOR FARADAY WAVES IN AN INCOMPRESSIBLE VISCOUS FLUID ∗
"... Abstract. When a layer of fluid is oscillated up and down with a sufficiently large amplitude, patterns form on the surface, a phenomenon first observed by Faraday. A wide variety of such patterns have been observed from regular squares and hexagons to superlattice and quasipatterns and more exotic ..."
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Abstract. When a layer of fluid is oscillated up and down with a sufficiently large amplitude, patterns form on the surface, a phenomenon first observed by Faraday. A wide variety of such patterns have been observed from regular squares and hexagons to superlattice and quasipatterns and more exotic patterns such as oscillons. Previous work has investigated the mechanisms of pattern selection using the tools of symmetry and bifurcation theory. The hypotheses produced by these generic arguments have been tested against an equation derived by Zhang and Viñals in the weakly viscous and large depth limit. However, in contrast, many of the experiments use shallow viscous layers of fluid to counteract the presence of high frequency weakly damped modes that can make patterns hard to observe. Here we develop a weakly nonlinear analysis of the full Navier–Stokes equations for the twofrequency excitation Faraday experiment. The problem is formulated for general depth, although results are presented only for the infinite depth limit. We focus on a few particular cases where detailed experimental results exist and compare our analytical results with the experimental observations. Good agreement with the experimental results is found. Key words. Faraday waves, superlattice patterns, weakly nonlinear analysis AMS subject classification. 37N10 DOI. 10.1137/050639223 1. Introduction. Waves
unknown title
, 1997
"... Mode competition in a system of two parametrically driven pendulums; the role of symmetry ..."
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Mode competition in a system of two parametrically driven pendulums; the role of symmetry
NorthHolland, Amsterdam CHARACTERIZATION OF HYDRODYNAMIC STRANGE ATrRACTORS
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"... Dynamics of counterpropagating waves in parametrically forced, large aspect ratio, nearly conservative systems with nonzero detuning ..."
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Dynamics of counterpropagating waves in parametrically forced, large aspect ratio, nearly conservative systems with nonzero detuning
Fluid Dynamics Research 33 (2003) 113–140 Dynamics of counterpropagating waves in parametrically forced, large aspect ratio, nearly conservative systems with
, 2002
"... nonzero detuning ..."
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Under consideration for publication in J. Fluid Mech. 1 Numerical simulation of supersquare patterns in Faraday waves
"... (Received?; revised?; accepted?.) We report the first simulations of the Faraday instability using the full threedimensional NavierStokes equations in domains much larger than the characteristic wavelength of the pattern. We use a massively parallel code based on a hybrid FrontTracking/Levelset ..."
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(Received?; revised?; accepted?.) We report the first simulations of the Faraday instability using the full threedimensional NavierStokes equations in domains much larger than the characteristic wavelength of the pattern. We use a massively parallel code based on a hybrid FrontTracking/Levelset algorithm for Lagrangian tracking of arbitrarily deformable phase interfaces. Simulations performed in square and cylindrical domains yield complex patterns. In particular, a superlatticelike pattern similar to those of [Douady & Fauve, Europhys. Lett. 6, 221226 (1988); Douady, J. Fluid Mech. 221, 383409 (1990)] is observed. The pattern consists of the superposition of two square superlattices. We conjecture that such patterns are widespread if the square container is large compared to the critical wavelength. In the cylinder, pentagonal cells near the outer wall allow a squarewave pattern to be accommodated in the center. 1.
Certified by................
, 1996
"... This study is focused on the complex dynamics of the mobile gates designed to span the three inlets of the Venice Lagoon for flood protection (the "acqua alta " phenomenon). In calm weather the gates rest horizontally on the seabed, while in stormy weather they are raised by buoyancy so t ..."
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This study is focused on the complex dynamics of the mobile gates designed to span the three inlets of the Venice Lagoon for flood protection (the "acqua alta " phenomenon). In calm weather the gates rest horizontally on the seabed, while in stormy weather they are raised by buoyancy so to act as a dam for keeping the high water outside the lagoon. Previous laboratory experiments with sinusoidal waves incident normally to a gate array have shown the presence of a resonant subharmonic response in which neighboring gates oscillate out of phase in a variety of ways. Linear and nonlinear theories are developed here and compared with the laboratory experiments of Tran(1996) The linear theory predicts the eigenfrequencies and eigenmodes as functions of the geometry of the gates and channel characteristics at which this phenomenon occurs. The nonlinear theory yields an evolution equation of the StuartLandau type for the amplitude of the resonated eigenmode. Viscous dissipation effects are systematically included in the perturbation theory. The theoretical results, which show bifurcations