Numerical study of domain coarsening in anisotropic stripe patterns

Boyer, Denis

doi:10.1103/physreve.69.066111

Cited by 16 publications

(34 citation statements)

References 27 publications

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“…These results remain largely unexplained theoretically. A first numerical study [34] based on a potential anisotropic Swift-Hohenberg equation for oblique stripes [36] reproduced the decay of the dislocation density but predicted a much faster ordering in the y direction than observed experimentally.…”

Section: Introductionmentioning

confidence: 89%

Coarsening in potential and nonpotential models of oblique stripe patterns

Gomez-Solano

Boyer

2007

Phys. Rev. E

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We study the coarsening of two-dimensional oblique stripe patterns by numerically solving potential and nonpotential anisotropic Swift-Hohenberg equations. Close to onset, all models exhibit isotropic coarsening with a single characteristic length scale growing in time as t1/2. Further from onset, the characteristic lengths along the preferred directions x and ŷ grow with different exponents, close to 1/3 and 1/2, respectively. In this regime, one-dimensional dynamical scaling relations hold. We draw an analogy between this problem and model A in a stationary, modulated external field. For deep quenches, nonpotential effects produce a complicated dislocation dynamics that can lead to either arrested or faster-than-power-law growth, depending on the model considered. In the arrested case, small isolated domains shrink down to a finite size and fail to disappear. A comparison with available experimental results for electroconvection in nematics is presented.

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Section: Introductionmentioning

confidence: 89%

Coarsening in potential and nonpotential models of oblique stripe patterns

Gomez-Solano

Boyer

2007

Phys. Rev. E

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“…Moving from the field variables to the discrete particle variables is not straightforward. In most defect studies, one resorts to various approximate methods to estimate the locations and velocity of defects by following their trajectories [13,19,22].…”

Section: A Locating and Tracking Of Defectsmentioning

confidence: 99%

“…In addition, dislocations often coexist and interact with other kinds of defects such as disinclinations and grain boundaries, which makes it harder to study in isolation. For this reason, phase ordering is much more difficult to study in isotropic stripe phases and polycrystalline phases, then in anisotropic stripes and single crystals where only dislocations are present [18,19].…”

Section: Introductionmentioning

confidence: 99%

Anisotropic velocity statistics of topological defects under shear flow

2012

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We report numerical results on the velocity statistics of topological defects during the dynamics of phase ordering and non-relaxational evolution assisted by an external shear flow. We propose a numerically efficient tracking method for finding the position and velocity of defects, and apply it to vortices in a uniform field and dislocations in anisotropic stripe patterns. During relaxational dynamics, the distribution function of the velocity fluctuations is characterized by a dynamical scaling with a scaling function that has a robust algebraic tail with an inverse cube power law. This is characteristic to defects of codimension two, e.g. point defects in two dimensions and filaments in three dimensions, regardless of whether the motion is isotropic (as for vortices) or highly anisotropic (as for dislocations). However, the anisotropic dislocation motion leads to anisotropic statistical properties when the interaction between defects and their motion is influenced by the presence of an external shear flow transverse to the stripe orientation.

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“…The formation of spatially periodic patterns in a wide variety of media driven far from equilibrium continues to attract a great deal of attention from experiment, simulations, and theory [1,2,3,4,5,6,7,8,9,10,11,12,13]. For patterns in fluids, many important advances have relied on careful experiments with samples possessing a very high degree of spatial homogeneity in the material properties and the external control parameters.…”

Section: Introductionmentioning

confidence: 99%

Amplitude modulation and relaxation-oscillation of counterpropagating rolls within a broken-symmetry laser-induced electroconvection strip

2006

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We report a liquid-crystal pattern-formation experiment in which we break the lateral (translational) symmetry of a nematic medium with a laser-induced thermal gradient. The work is motivated by an improved measurement (reported here) of the temperature dependence of the electroconvection threshold voltage in planar-nematic 4-methoxybenzylidene-4-butylaniline (MBBA). In contrast with other broken-symmetry-pattern studies that report a uniform drift, we observe a strip of counterpropagating rolls that collide at a sink point, and a strong temporally periodic amplitude modulation within a width of 3-4 rolls about the sink point. The time dependence of the amplitude at a fixed position is periodic but displays a nonsinusoidal relaxation-oscillation profile. After reporting experimental results based on spacetime contours and wavenumber profiles, along with a measurement of the change in the drift frequency with applied voltage at a fixed control parameter, we propose some potential guidelines for a theoretical model based on saddle-point solutions for Eckhaus-unstable states and coupled complex Ginzburg-Landau equations. Published in PRE 73, 036317 (2006).

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Numerical study of domain coarsening in anisotropic stripe patterns

Cited by 16 publications

References 27 publications

Coarsening in potential and nonpotential models of oblique stripe patterns

Coarsening in potential and nonpotential models of oblique stripe patterns

Anisotropic velocity statistics of topological defects under shear flow

Amplitude modulation and relaxation-oscillation of counterpropagating rolls within a broken-symmetry laser-induced electroconvection strip

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