Superlattice Patterns in Vertically Oscillated Rayleigh-Bénard Convection

Rogers, Jeffrey L.; Schatz, Michael F.; Brausch, Oliver; Pesch, Werner

doi:10.1103/physrevlett.85.4281

Cited by 65 publications

(48 citation statements)

References 19 publications

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“…We obtained expressions for the critical forcing acceleration and wave number, and analyzed them to elucidate the role played by the secondary forcing component. We also were able to identify the most important frequency components in the unstable eigenmode in terms of the integers m and n. We then analyzed the expression for the (23), with frequency components (m, n, p, q) = (8,9,11,13). For this calculation, the m = 8 forcing component dominates, but we are near a "quad-critical" point so that the other three frequency components are strong.…”

Section: Discussionmentioning

confidence: 99%

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Resonances and superlattice pattern stabilization in two-frequency forced Faraday waves

Topaz

Silber

2002

Physica D: Nonlinear Phenomena

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We investigate the role weakly damped modes play in the selection of Faraday wave patterns forced with rationally-related frequency components mω and nω. We use symmetry considerations to argue for the special importance of the weakly damped modes oscillating with twice the frequency of the critical mode, and those oscillating primarily with the "difference frequency" |n − m|ω and the "sum frequency" (n+m)ω. We then perform a weakly nonlinear analysis using equations of Zhang and Viñals [1] which apply to small-amplitude waves on weakly inviscid, semi-infinite fluid layers. For weak damping and forcing and one-dimensional waves, we perform a perturbation expansion through fourth order which yields analytical expressions for onset parameters and the cubic bifurcation coefficient that determines wave amplitude as a function of forcing near onset. For stronger damping and forcing we numerically compute these same parameters, as well as the cubic cross-coupling coefficient for competing waves travelling at an angle θ relative to each other. The resonance effects predicted by symmetry are borne out in the perturbation results for one spatial dimension, and are supported by the numerical results in two dimensions. The difference frequency resonance plays a key role in stabilizing superlattice patterns of the SL-I type observed by Kudrolli, Pier and Gollub [2].

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Section: Discussionmentioning

confidence: 99%

“…Related equations forż 2 ,ẇ 1 ,ẇ 2 , andẇ 3 can be obtained from the discrete spatial symmetries (12) and (13). The δG m w 1 term in (15) is the usual parametric forcing term.…”

Section: Determination Of Important Resonances For Weak Damping and Fmentioning

confidence: 99%

Resonances and superlattice pattern stabilization in two-frequency forced Faraday waves

Topaz

Silber

2002

Physica D: Nonlinear Phenomena

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“…[84][85][86] Porém, estruturas quadradas mostraram--se com um pequeno tempo de vida quando removida a perturbação, retornando para o padrão labiríntico. 87 A emergência de padrões quadrados tem sido observada numa variedade de experimentos em sistemas fora do estado de equilíbrio termodinâmico, como as ondas de Faraday, 88,89 convecções de Marangoni-Nérnard 90-92 e RayleighBérnard, [93][94][95][96] além das descargas de barreiras dielétricas, 97 mas dificilmente são observadas em sistemas de reação-difusão.…”

Section: Figura 3 Esquema Genérico Que Representa a Emergência Dos Punclassified

Turing Patterns in Chemical Systems

Nagao¹,

Varela²

2016

Química Nova

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publicado na web em 18/02/2016 TURING PATTERNS IN CHEMICAL SYSTEMS. Spontaneous pattern formation in reaction-diffusion systems was theoretically proposed by Alan M. Turing in 1952. His breakthrough conceptions of chemical self-organization were able to explain how patterns emerge in nature and the symmetry breaking, which are of utmost importance, for instance, in the context of origin of life. Along with the experimental observations in the Belousov-Zhabotinsky reaction and the development of the nonequilibrium thermodynamics by Prigogine and co-workers, Turing predictions are considered the foundation of the field of Nonlinear Chemical Dynamics. This review aims to describe the basis of Turing structures with their consequent scientific achievements and to provide future directions in the development of this field. Keywords: Turing patterns; self-organization; nonlinear dynamics; pattern formation; oscillations. INTRODUÇÃOA prevalência de padrões auto-organizados em seres vivos é um resultado característico da seleção natural.1 Ao longo do tempo, o padrão que melhor se adapta ao ambiente externo é selecionado e transmitido para as gerações seguintes. Pode-se citar como um exemplo recorrente desta estruturação, a formação de moléculas de ácido desoxirribonucleico (deoxyribonucleic acid, DNA) capazes de carregar informações codificadas estritamente necessárias para a concepção de estruturas complexas em escala supramolecular. 2A autorreplicação dessas moléculas é regida por uma maquinaria reprodutiva de divisão celular que, em determinadas condições, desencadeia um processo de diferenciação e, consequentemente, um conjunto de células ou órgãos com funcionalidades específicas. Este desenvolvimento celular seletivo é conhecido por morfogênese. A primeira descrição químico-matemática desse processo foi formulada por Turing em 1952 em seu trabalho: The Chemical Basis of Morphogenesis. 3Alan Mathison Turing (23/06/1912 -7/06/1954) foi um matemá-tico britânico e criptoanalista conhecido sobretudo pela fundação da ciência da computação, criando o conceito de algoritmo e computação com a "Máquina de Turing".6 Trabalhou durante a Segunda Guerra Mundial à serviço do comando militar britânico no Government Code and Cypher School em Bletchley Park como decifrador de mensagens encriptadas por uma máquina desenvolvida pelos alemães chamada de "Enigma". Além da sua contribuição na ciência da computação, outro grande legado foi concebido dois anos antes do seu falecimento.Turing acreditava que padrões complexos encontrados em diversos aspectos na natureza poderiam ser descritos por meio da combinação de leis físicas simples. Basicamente, ele sugere que a formação desses padrões é regida pelo acoplamento entre os parâ-metros cinéticos da reação com fenômenos de transporte de massa de espécies químicas presentes no meio reacional. Essa descrição, ainda que simplificada, serviu como um passo inicial importante para o melhor entendimento da segregação espontânea de espécies químicas ao longo do espaço observada em diversos sistema...

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“…Recently, it has been reported that multiple frequency forcing on the granular layer yields superlattice patterns [7]. Similar patterns have been studied in Faraday waves [20], driven ferrofluid surfaces [21], nonlinear optics [22], Turing patterns [23] and Rayleigh-Benard convection [24]. As in the single frequency forcing [3], the important variables determining patterns are expected to be the free-flight times and contact times.…”

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confidence: 96%

Square to stripe transition and superlattice patterns in vertically oscillated granular layers

Park

Moon

2002

Phys. Rev. E

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We investigated the physical mechanism for the pattern transition from square lattice to stripes, which appears in vertically oscillating granular layers. We present a continuum model to show that the transition depends on the competition between inertial force and local saturation of transport. By introducing multiple free-flight times, this model further enables us to analyze the formation of superlattices as well as hexagonal lattices

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Superlattice Patterns in Vertically Oscillated Rayleigh-Bénard Convection

Cited by 65 publications

References 19 publications

Resonances and superlattice pattern stabilization in two-frequency forced Faraday waves

Resonances and superlattice pattern stabilization in two-frequency forced Faraday waves

Turing Patterns in Chemical Systems

Square to stripe transition and superlattice patterns in vertically oscillated granular layers

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