Low symmetry patterns on magnetic fluids

Friedrichs, R.

doi:10.1103/physreve.66.066215

Cited by 14 publications

(14 citation statements)

References 22 publications

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“…The open squares (circles) mark the data for an increase (decrease) ofB, respectively. The hysteresis is characteristic for a subcritical bifurcation, which has been predicted for the transition from ridges to stretched hexagons [2]. Next we describe the amplitude A H ≡ A H 0 of the hexagons after the secondary bifurcation at ǫ S = (B 2 − B 2 S )/B 2 P .…”

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confidence: 72%

“…The angular dependence observed in the experiment, is quantitatively described by taking into account the nonlinear magnetization. In addition we measured the backward bifurcation to hexagons, which has been predicted by an energy variational method [2]. A full quantitative agreement with these predictions can not be expected, because the theory is restricted to permeabilities µ r < 1.4, while we had to use µ r = 2.11 to avoid huge fields.…”

mentioning

confidence: 86%

“…This situation is structurally unstable, however: The smallest distortion of this symmetry acts as a singular perturbation and will lead to a qualitatively different instability, namely a primary bifurcation to a stripe like pattern. A specific example has recently been calculated in detail [2] for a magnetic fluid [3]. In the ideal isotropic system, hexagons will occur under the influence of a magnetic field which is perfectly normal with respect to the fluid surface [4].…”

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confidence: 99%

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Hexagons become the secondary pattern if symmetry is broken

et al. 2005

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Pattern formation on the free surface of a magnetic fluid subjected to a magnetic field is investigated experimentally. By tilting the magnetic field, the symmetry can be broken in a controllable manner. When increasing the amplitude of the tilted field, the flat surface gives way to liquid ridges. A further increase results in a hysteretic transition to a pattern of stretched hexagons. The instabilities are detected by means of a linear array of magnetic Hall sensors and compared with theoretical predictions.

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confidence: 72%

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confidence: 86%

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confidence: 99%

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Hexagons become the secondary pattern if symmetry is broken

et al. 2005

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“…In systems with a strong axial anisotropy, such as in nematic liquid crystals, this rotational symmetry is broken [41,42,43,44] and hexagonal convection patterns do not occur. Thus the interplay between different broken symmetries, such as the broken up-down symmetry with a weak anisotropy, leads to an interesting competition between stripe and hexagonal patterns as has been shown recently [45,46,47].…”

Section: Introductionmentioning

confidence: 81%

Stripe-hexagon competition in forced pattern-forming systems with broken up-down symmetry

et al. 2005

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We investigate the response of two-dimensional pattern-forming systems with a broken up-down symmetry, such as chemical reactions, to spatially resonant forcing and propose related experiments. The nonlinear behavior immediately above threshold is analyzed in terms of amplitude equations suggested for a 1:2 and 1:1 ratio between the wavelength of the spatial periodic forcing and the wavelength of the pattern of the respective system. Both sets of coupled amplitude equations are derived by a perturbative method from the Lengyel-Epstein model describing a chemical reaction showing Turing patterns, which gives us the opportunity to relate the generic response scenarios to a specific pattern-forming system. The nonlinear competition between stripe patterns and distorted hexagons is explored and their range of existence, stability, and coexistence is determined. Whereas without modulations hexagonal patterns are always preferred near onset of pattern formation, single-mode solutions (stripes) are favored close to threshold for modulation amplitudes beyond some critical value. Hence distorted hexagons only occur in a finite range of the control parameter and their interval of existence shrinks to zero with increasing values of the modulation amplitude. Furthermore, depending on the modulation amplitude, the transition between stripes and distorted hexagons is either subcritical or supercritical.

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“…Another approach 14) considers a static regime, where only the normal stress boundary condition is considered for the nonlinear expansion and where a horizontal field component of the magnetic field was assumed to be strong enough to suppress two dimensional patterns. 15) The dynamics of the system has first been taken into account by Kubstrup et al 16) who used a Swift-Hohenberg model to describe fronts between hexagons and squares. This approach, however, lacks the connection of the parameters introduced in the Swift-Hohenberg equation to the material properties of the medium.…”

Section: §1 Introductionmentioning

confidence: 99%

The Amplitude Equation for the Rosensweig Instability in Magnetic Fluids and Gels

Bohlius

Pleiner

Brand

2011

Progress of Theoretical Physics

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The Rosensweig instability has a special character among the frequently discussed instabilities. One distinct property is the necessary presence of a deformable surface, and another very important fact is, that the driving force acts purely via the surface and shows no bulk effect. These properties make it rather difficult to give a correct weakly nonlinear analysis. In this paper we give a detailed derivation of the appropriate amplitude equation based on the hydrodynamic equations emphasizing the conceptually new procedures necessary to deal with the distinct properties mentioned above. First the deformable surface requires a fully dynamic treatment of the instability and the observed stationary case can be interpreted as the limiting case of a frozen-in characteristic mode. Second, the fact that the driving force is manifest in the boundary conditions, only, requires a considerable change in the formalism of weakly nonlinear bifurcation theory. To obtain the amplitude equations a combination of solubility conditions and (normal stress) boundary conditions has to be invoked in all orders of the expansions.

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Low symmetry patterns on magnetic fluids

Cited by 14 publications

References 22 publications

Hexagons become the secondary pattern if symmetry is broken

Hexagons become the secondary pattern if symmetry is broken

Stripe-hexagon competition in forced pattern-forming systems with broken up-down symmetry

The Amplitude Equation for the Rosensweig Instability in Magnetic Fluids and Gels

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