Bekki-Nozaki Amplitude Holes in Hydrothermal Nonlinear Waves

Burguete, Javier; Chaté, Hugues; Daviaud, François; Mukolobwiez, Nathalie

doi:10.1103/physrevlett.82.3252

Cited by 56 publications

(40 citation statements)

References 25 publications

(31 reference statements)

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“…Once screen image is recorded with a CCD camera, it is digitalized and processed in a computer, obtaining both two-dimensional photographs and spatio-temporal diagrams. Space and time Fourier transforms and complex demodulation techniques are used to extract the spatio-temporal behavior of the patterns (see details in [8] and references therein). We have determined in this way the hydrodynamic characteristics of the patterns.…”

Section: Methodsmentioning

confidence: 99%

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One-dimensional dynamics in locally heated liquid layers

Burguete

Maza

Mancini

2003

Physica D: Nonlinear Phenomena

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Recent results on one-dimensional patterns in locally heated experiments are presented. A fluid layer is heated locally by a nearly one-dimensional heater, and subjected to both horizontal and vertical temperature gradients. Depending on the fluid depth and on the temperature difference established across the layer different convective regimes appear. When a very small temperature gradient is applied a basic convective state appears. It consists of two big rolls parallel to the heater and filling the convective cell. A primary instability in the homogeneous basic flow gives rise to a one-dimensional cellular stationary pattern. For higher values of the control parameters, time-dependent patterns appear through a secondary instability. Various regimes are analyzed: oscillations, traveling waves and alternating patterns. The hydrodynamic characteristics of these patterns are provided. Local temperature measurements allows to describe the physical mechanisms responsible for the instabilities. The similarities and discrepancies of the experimental data with some theoretical models are provided.

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Section: Methodsmentioning

confidence: 99%

“…In particular, a complex Ginzburg-Landau model is able to reproduce a grate number of the experimental results (see for example [8,9] and references therein).…”

Section: Introductionmentioning

confidence: 99%

One-dimensional dynamics in locally heated liquid layers

Burguete

Maza

Mancini

2003

Physica D: Nonlinear Phenomena

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“…Calculations anticipated results that in many cases have been after confirmed in experiments, as the "hole" type solutions [22,23]. More recently, another group of numerical studies with Ginzburg-Landau equations including higher order non-linearities (quintic) like in ref.…”

Section: Introductionmentioning

confidence: 98%

Localized structures in convective experiments

Burguete

Mancini

2014

Eur. Phys. J. Spec. Top.

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Abstract. In this work we review localized structures appearing in thermo-convective experiments performed in extended (large "aspect ratio") fluid layers. After a brief general review (not exhaustive), we focus on some results obtained in pure fluids in a Bénard -Marangoni system with non-homogeneous heating where some structures of this kind appear. The experimental results are compared in reference to the most classical observed in binary mixtures experiments or simulations. In the Bénard-Marangoni experiment we present the stability diagram where localized structures appear and the typical situations where these local mechanisms have been studied experimentally. Some new experimental results are also included.

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“…1(b) its temporal evolution. In this parameter region, the amplitude pattern is composed of characteristic hole structures that move around the system randomly (defect turbulence [1][2][3][4][23][24][25][26] ). On the other hand, the NCGL is a system of CGL oscillators coupled through a nonlocal mean field weighted by a kernel that decreases exponentially with distance.…”

Section: -4mentioning

confidence: 99%

Independent Component Analysis of Spatiotemporal Chaos

Asano

Nakao

2005

J. Phys. Soc. Jpn.

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Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear oscillators are analyzed using independent component analysis (ICA). For diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth amplitude patterns, ICA extracts localized one-humped basis vectors that reflect the characteristic hole structures of the system, and for nonlocally coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns, ICA extracts localized basis vectors with characteristic gap structures. Statistics of the decomposed signals also provide insight into the complex dynamics of the spatiotemporal chaos.KEYWORDS: coupled oscillators, spatiotemporal chaos, signal processing, feature extraction Spatiotemporal chaos (STC) arising from interaction between autonomous elements is ubiquitous in nonequilibrium dissipative systems such as fluid flows and chemical reactions.1-4 It is generally difficult to reduce the complex behavior of strongly coupled systems to the individual dynamics of the component elements, so we must employ collective modes of the system for description. For example, we employ various types of bases in the description of fluids, e.g. Fourier basis, wavelet basis, or eigenfunctions of linearized evolution equations, which represent flow modes such as waves, vortices, and convections. [1][2][3][4][5][6][7] In this case, the observer needs to subjectively choose which basis to use depending on the situation.On the other hand, there also exist methods of constructing basis functions objectively from statistical properties of the system by some criterion, without explicitly fixing them. A representative method is the principal component analysis (PCA) or the Karhunen-Loéve expansion, 5-17 which is a standard method in multivariate analysis. PCA has already been employed in analyzing STC, for example, to truncate its evolution equation or to estimate its degree of freedom.13-17 However, as we show below, when PCA is applied to STC, spatially delocalized bases are typically extracted, which are not appropriate for describing local field structures. Particularly, when the system has translational symmetry, it can be proven that PCA extracts the Fourier basis itself. Therefore, some statistical method that can objectively and compactly capture the complex field structures is desirable.In this letter, we apply independent component analysis (ICA) to STC. ICA is a recently developed method of statistical signal processing, which attempts to decompose observed mixed signals into maximally independent signals. [8][9][10][11][12] It is known that the ICA basis gives an information-theoretically efficient representation of multivariate signals. [8][9][10][11][12] We analyze STC exhibited by two types of coupled nonlinear oscillators, namely, locally (diffusively) coupled complex Ginzburg-Landau oscillators (LCGL), 1-4 and nonlocally coupled complex * Corresponding author: nakao@ton.scphys.kyoto-u.ac.jpGinzburg-Landau oscillators (NCGL), [18][19][20][21][22] and assess the utility of I...

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Bekki-Nozaki Amplitude Holes in Hydrothermal Nonlinear Waves

Cited by 56 publications

References 25 publications

One-dimensional dynamics in locally heated liquid layers

One-dimensional dynamics in locally heated liquid layers

Localized structures in convective experiments

Independent Component Analysis of Spatiotemporal Chaos

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