Undulation instability in stripe domain structures of « bubble » material

Sornette, Didier

doi:10.1051/jphys:01987004801015100

Cited by 52 publications

(25 citation statements)

References 8 publications

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“…In the variational case the patterns stabilize and uniform arrays of stripes on either side of a domain wall tend to make an angle close to 60 with the boundary. This is reminiscent of patterns generated in ferroauids [3] and magnetic bubble material [4]. Conversely, when the dynamics is nonvariational the patterns do not appear to settle down and arrays of uniform stripes have less well defined boundaries.…”

Section: A Prologuementioning

confidence: 92%

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Pattern formation in the presence of symmetries

Gunaratne

Ouyang

Swinney³

1994

Phys. Rev. E

191

142

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We present a detailed theoretical study of pattern formation in planar continua with translational, rotational, and reflection symmetry. The theoretical predictions are tested in experiments on a quasitwo-dimensional reaction-diffusion system. Spatial patterns form in a chlorite-iodide-malonic acid reaction in a thin gel layer reactor that is sandwiched between two continuously refreshed reservoirs of reagents; thus, the system can be maintained inde6nitely in a well-defined nonequilibrium state. This physical system satis6es, to a very good approximation, the Euclidean symmetries assumed in the theory. The theoretical analysis, developed in the amplitude equation formalism, is a spatiotemporal extension of the normal form. The analysis is identical to the Newell-Whitehead-Segel theory [J. Fluid Mech. 38, 203 (1969); 38, 279 (1969)] at the lowest order in perturbation, but has the advantage that it exactly preserves the Euclidean symmetries of the physical system. Our equations can be derived by a suitable modification of the perturbation expansion, as shown for two variations of the Swift-Hohenberg equation [Phys. Rev. A 15, 319 (1977)]. Our analysis is complementary to the Cross-Newell approach [Physica D 10, 299 (1984)] to the study of pattern formation and is equivalent to it in the common domain of applicability. Our analysis yields a rotationally invariant generalization of the phase equation of Pomeau and Manneville [J. Phys. Lett. 40, L609 (1979)]. The theory predicts the existence of stable rhombic arrays with qualitative details that should be system independent. Our experiments in the reaction-diffusion system yield patterns in good accord with the predictions. Finally, we consider consequences of resonances between the basic modes of a hexagonal pattern and compare the results of the analysis with experiments.

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Section: A Prologuementioning

confidence: 92%

“…A wide array of controlled experimental systems, including chemical reactions [1], Rayleigh-Benard convection [2], ferrofluids [3], and magnetic bubble material [4], have been used to study pattern formation. Figure 1 shows some patterns we have obtained in experiments on a reaction-di8'usion system.…”

Section: A Prologuementioning

confidence: 99%

Pattern formation in the presence of symmetries

Gunaratne

Ouyang

Swinney³

1994

Phys. Rev. E

191

142

View full text Add to dashboard Cite

show abstract

“…It is important to point out that a lack of noise does not necessarily imply zero temperature, and that this situation is similar in spirit to the experimental realizations for ferrimagnetic films. For lamellar patterns, experiments 5,6,8,9 and previous theoretical 40,41 considerations show that, outside of the small critical region, temperature fluctuations are irrelevant and the only role of temperature is to modulate the characteristic period (analogously to the parameter R). The same is true for the bubble patterns, where the coercive friction associated with microscopic roughness suppresses the effects of any thermal fluctuations.…”

Section: Introductionmentioning

confidence: 97%

New and Exotic Self-Organized Patterns for Modulated Nanoscale Systems

2005

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The self-assembled domain patterns of modulated systems are the result of competing short-range attractive and long-range repulsive interactions found in diverse physical and chemical systems. From an application point of view, there is considerable interest in these domain patterns, as they form templates suitable for the fabrication of nanostructures. In this work we have generated a variety of new and exotic patterns, which represent either metastable or glassy states. These patterns arise as a compromise between the required equilibrium modulation period and the strain resulting from topologically constrained trajectories in phase space that effectively preclude the equilibrium configuration.

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“…Expanding the local component to quadratic order in the fluctuation field u, it can be written in Fourier space as [19,22,25] …”

mentioning

confidence: 99%

Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions

2015

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We study two dimensional stripe forming systems with competing repulsive interactions decaying as r(-α). We derive an effective Hamiltonian with a short-range part and a generalized dipolar interaction which depends on the exponent α. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for α<2 long-range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When α≥2 no long-range order is possible, but a phase transition in the Kosterlitz-Thouless universality class is still present. These two different critical scenarios should be observed in experimentally relevant two dimensional systems like electronic liquids (α=1) and dipolar magnetic films (α=3). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results.

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Undulation instability in stripe domain structures of « bubble » material

Abstract: Résumé. 2014

Cited by 52 publications

References 8 publications

Pattern formation in the presence of symmetries

Pattern formation in the presence of symmetries

New and Exotic Self-Organized Patterns for Modulated Nanoscale Systems

Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions

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