Pattern formation in large domains

Rucklidge, Alastair M.

doi:10.1098/rsta.2003.1267

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…As the excitation amplitude increases, the physical appearance of additional capillary wave modes is known to occur. Moreover, the two-dimensional and strongly curved fluid surface permits many more capillary wave modes due to three-wave resonant interaction that is perhaps best explained by Chen and Viñals 30 and Rucklidge 31 who showed the formation of patterns similar to capillary waves appearing on temporal scales remarkably different than that of the excitation signal. Moreover, the two-dimensional and strongly curved fluid surface permits many more capillary wave modes due to three-wave resonant interaction that is perhaps best explained by Chen and Viñals 30 and Rucklidge 31 who showed the formation of patterns similar to capillary waves appearing on temporal scales remarkably different than that of the excitation signal.…”

Section: Introductionmentioning

confidence: 98%

Capillary wave motion excited by high frequency surface acoustic waves

et al. 2010

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This paper presents a numerical and experimental study of capillary wave motion excited by high frequency surface acoustic waves ͑SAWs͒. The objective of this study is to provide insight into the dynamic behavior of the fluid free surface and its dependence on the excitation amplitude. A two-dimensional numerical model that couples the motion of the piezoelectric substrate to a thin liquid layer atop the substrate is constructed. A perturbation method, in the limit of small-amplitude acoustic waves, is used to decompose the equations governing fluid motion to resolve the widely differing time scales associated with the high frequency excitation. While this model focuses on the free surface dynamics in the low-amplitude flow regime, the experimental study focuses on the high-amplitude flow regime. Transformation of time series data from both experiments and simulations into the frequency domain reveals that, in the low-amplitude regime, a fundamental resonant frequency and a superharmonic frequency are found in the frequency spectra. The former is found to be identical to that of the applied SAW, and the free surface displacement magnitude is comparable to that of the substrate displacement. Our numerical results also confirm previous speculation that the separation distance between two displacement antinodal points on the free surface is ␦ St Ϸ SAW / 2 for a film and ␦ St Ϸ f / 2 for a drop, where SAW and f denote the SAW wavelength and the acoustic wavelength in the fluid, respectively. Finally, in the high-amplitude regime, strong nonlinearities shift the acoustic energy to a lower frequency than that of the SAW; this low-frequency broadband response, quite contrary to the subharmonic half-frequency capillary wave excitation predicted by the classical linear or weakly nonlinear Faraday theories, is supported by a scaling analysis of the momentum equations.

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Section: Introductionmentioning

confidence: 98%

Capillary wave motion excited by high frequency surface acoustic waves

et al. 2010

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“…We suggest that the hard squares represent a superlattice structure where several wave vectors interact to suppress the ZZ instability. Such superlattices, which often represent quasiperiodic structures, have been of considerable interest recently [26,27]. They have been investigated experimentally, in particular, in the Faraday instability in cells with aspect ratio below about 50 [28].…”

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confidence: 99%

Isotropic Convection Scenarios in an Anisotropic Fluid

et al. 2004

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We study a new variant of electroconvection using a homeotropically aligned nematic liquid crystal. The novelty of this system is a direct transition to roll- or square-type patterns controlled by the frequency of the applied voltage with a rich crossover scenario and strong influence of the zigzag instability even at onset. From the weakly nonlinear theory and simulations of an adapted Swift-Hohenberg model one can understand essential features of the phase diagram. In particular we find a quasiperiodic pattern with square symmetry.

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“…Rhombic patterns were found to appear to be natural at the primary instability in the form of a bicritical point. Under two-frequency parametric excitation, Rucklidge [342] considered pattern formation in large domains with an attention to QPs, where the appearance of small divisors causes the standard theoretical method to fail. The symmetry-based approach developed by Tse et al [343] was used by Rucklidge et al [344] to analyze three observed spatial period-multiplying transitions from an initial hexagonal pattern.…”

Section: Two-frequency Parametric Excitation It Is Believed That Edwmentioning

confidence: 99%

Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems

Ibrahim

2015

Journal of Fluids Engineering

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Liquid parametric sloshing, known also as Faraday waves, has been a long standing subject of interest. The development of the theory of Faraday waves has witnessed a number of controversies regarding the analytical treatment of sloshing modal equations and modes competition. One of the significant contributions is that the energy is transferred from lower to higher harmonics and the nonlinear coupling generated static components in the temporal Fourier spectrum, leading to a contribution of a nonoscillating permanent sinusoidal deformed surface state. This article presents an overview of different problems of Faraday waves. These include the boundary value problem of liquid parametric sloshing, the influence of damping and surfactants on the stability and response of the free surface, the weakly nonlinear parametric and autoparametric sloshing dynamics, and breaking waves under high parametric excitation level. An overview of the physics of Faraday wave competition together with pattern formation under single-, two-, three-, and multifrequency parametric excitation will be presented. Significant effort was made in order to understand and predict the pattern selection using analytical and numerical tools. Mechanisms for selecting the main frequency responses that are different from the first subharmonic one were identified in the literature. Nontraditional sources of parametric excitation and Faraday waves of ferromagnetic films and ferrofluids will be briefly discussed. Under random parametric excitation and g-jitter, the behavior of Faraday waves is described in terms of stochastic stability modes and spectral density function.

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Pattern formation in large domains

Cited by 4 publications

References 15 publications

Capillary wave motion excited by high frequency surface acoustic waves

Capillary wave motion excited by high frequency surface acoustic waves

Isotropic Convection Scenarios in an Anisotropic Fluid

Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems

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