Parametric forcing of waves with a nonmonotonic dispersion relation: Domain structures in ferrofluids

Abstract

Surface waves on ferrofluids exposed to a dc-magnetic field exhibit a nonmonotonic dispersion relation. The effect of a parametric driving on such waves is studied within suitable coupled Ginzburg-Landau equations. Due to the non-monotonicity the neutral curve for the excitation of standing waves can have up to three minima. The stability of the waves with respect to long-wave perturbations is determined via a phase-diffusion equation. It shows that the band of stable wave numbers can split up into two or three sub-bands. The resulting competition between the wave numbers corresponding to the respective sub-bands leads quite naturally to patterns consisting of multiple domains of standing waves which differ in their wave number. The coarsening dynamics of such domain structures is addressed.October 28, 2018 05.45.+b, 05.90.+m, 47.20. Tg

Surface Wave Assisted Self-Assembly of Multidomain Magnetic Structures

“…The mechanism of parametrically driven surface waves in these experiments is similar to the one reported earlier for ferrofluids [16,17]. A major difference, however, is the fact that the dominant response of a ferrofluid to external vertical magnetic driving comes at half frequency, as does that found in vibrated water and sand layers (harmonic response was reported for the free surface of a ferrofluid driven with the parallel ac magnetic field [18]).…”

Parametrically Excited Surface Waves in Magnetic Fluids: Observation of Domain Structures

“…A separation of the surface wave into different phases has recently been predicted for parametrically excited surface waves [4]. This intriguing result is due to a non-monotonic dispersion relation for surface waves, which means that up to three different wave numbers can be excited with one single driving frequency.…”

Superlattice, Rhombus, Square, and Hexagonal Standing Waves in Magnetically Driven Ferrofluid Surface

“…At this point, we note that a recent theoretical study has shown that parametrically driven surface waves on ferrofluids can be unstable to multiple spatial modes simultaneously [10]. Here, the existence of multiple unstable modes originates from the non-monotonic dispersion relation of ferrofluids.…”

“…In our experiments, coexisting domains with different wavevectors are only observed in bistable regions. In order to check the feasibility of this hypothesis, we have extended the earlier theoretical study by Raitt and Riecke [10] to two-dimensional space and have found a parameter regime in which well defined rhombic patterns are globally stable [14]. Recently, Lifshitz and Petrich have also demonstrated the existence of a stable rhombic pattern in a generic model system containing two unstable spatial modes [15].…”

“…The other reason is that ferrofluid exposed to a magnetic field can exhibit a non-monotonic dispersion relation [9]. Due to the nonmonotonicity the neural stability curve for the excitation of standing waves can have multiple minima [10,11], thus, several spatial modes can be excited simultaneously.…”