Effects of disorder in pattern formation

Abstract. Linear stability analysis of fully developed axisymmetric steady and spatially modulated Taylor-Couette flow is carried out in the narrow-gap limit. The inner cylinder is sinusoidally modulated and rotating, while the outer cylinder is straight and at rest. The modulation amplitude is assumed to be small, and the base steady flow is determined using a regular perturbation expansion of the flow field coupled to a variable-step finite-difference scheme. The disturbance flow equations are derived within the framework of Floquet theory and solved using a nonlinear two-point boundary-value approach. In contrast to unforced Taylor-Couette flow, only vortical base flow is possible in the forced case. It is found that the forcing tends to generally destabilize the base flow, especially around the critical point. Both the critical Taylor number and wavenumber are found to decrease essentially linearly with modulation amplitude.

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“…Clearly, solution (21) indicates that the base modulated flow at α = 0 is the same as that corresponding to the flow between straight cylinders. …”

Section: Resultsmentioning

confidence: 99%

Effect of weak geometrical forcing on the stability of Taylor-vortex flow

Pan

Khayat

2008

J. Phys.: Conf. Ser.

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“…Therefore one expects in such cases a spatially varying mobility of proteins embedded in the membrane. How this heterogeneity affects the formation of patterns is another interesting question as has been investigated for other model systems [52,53,54,55,56]. A detailed analysis of all these questions may be given in forthcoming works.…”

Section: Discussionmentioning

confidence: 99%

Publisher's Note: Hexagonal, square, and stripe patterns of the ion channel density in biomembranes [Phys. Rev. E75, 016202 (2007)]

Hilt¹,

Zimmermann²

2007

Phys. Rev. E

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Transmembrane ion flow through channel proteins undergoing density fluctuations may cause lateral gradients of the electrical potential across the membrane giving rise to electrophoresis of charged channels. A model for the dynamics of the channel density and the voltage drop across the membrane (cable equation) coupled to a binding-release reaction with the cell skeleton (P. Fromherz and W. Zimmerman, Phys. Rev. E 51, R1659 (1995)) is analyzed in one and two spatial dimensions. Due to the binding release reaction spatially periodic modulations of the channel density with a finite wave number are favored at the onset of pattern formation, whereby the wave number decreases with the kinetic rate of the binding-release reaction. In a two-dimensional extended membrane hexagonal modulations of the ion channel density are preferred in a large range of parameters. The stability diagrams of the periodic patterns near threshold are calculated and in addition the equations of motion in the limit of a slow binding-release kinetics are derived.

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“…Essentially the same approach was applied also to some other equations, describing the pattern-forming systems (see, e.g. [19]). …”

Section: (5)mentioning

confidence: 99%

The ?Frozen In? Fluctuations in Systems with Non-Conserved Order Parameter

Mchedlov-Petrossyan

Abysov

Давыдов

et al. 1998

phys. stat. sol. (b)

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An early time kinetics of a system with non-conserved order parameter quenched into unstable two-phase region of the phase diagram is considered. The process of phase separation under the influence of random inhomogeneities of the phenomenological coefficient in the Ginzburg-Landautype equation of motion is studied. The combined effect of this`frozen-in' (time-independent) fluctuations and persistent thermal fluctuations on the structure factor is discussed. The classical Lifshits-Allen-Cahn law is reproduced, however, in the limit of applicability (in time) of the present analysis.

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Effects of disorder in pattern formation

Cited by 33 publications

References 15 publications

Effect of weak geometrical forcing on the stability of Taylor-vortex flow

Effect of weak geometrical forcing on the stability of Taylor-vortex flow

Publisher's Note: Hexagonal, square, and stripe patterns of the ion channel density in biomembranes [Phys. Rev. E75, 016202 (2007)]

The ?Frozen In? Fluctuations in Systems with Non-Conserved Order Parameter

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