Cluster structure and the first-order phase transition in dipolar systems

The Monte Carlo technique is used to simulate a 3D dipolar hard-sphere system. The spatial and magnetic structure of clusters formed by magnetic dipolar interactions in zero applied field is investigated. It is shown that the many-particle clusters are characterized by a quasi-spherical shape, extremely small magnetic moments, and a fractal dimension close to three. These clusters are regarded as nuclei of a new concentrated isotropic phase. The numerical simulation of the first-order phase transition has been realized which allows us to find the interface between two coexisting phases. It has been found that the dipole-dipole and steric interactions are sufficient to separate the system into two phases with low and high concentrations of particles. The introduction of any additional attraction potential is not required. The phase diagram of dipolar system in zero applied field has been obtained. The simulation results are in qualitative agreement with the predictions of some analytical models

Surface instabilities of ferrofluids

We report on recent progress in understanding the formation of surface protuberances on a planar layer of ferrofluid in a magnetic field oriented normally to the surface. This normal field or Rosensweig instability can be tackled by a linear and a nonlinear description. In the linear regime of small amplitudes we focus on the wave number of maximal growth, its corresponding growth rate and the oscillatory decay of metastable pattern, accessible via a pulse technique. A quantitative comparison of measurements with predictions of the linear stability analysis is performed, whereby the viscosity and the finite depth of the liquid layer are taken into account. In the nonlinear regime the fully developed peak pattern can be predicted by a minimization of the free energy and by numerics employing the finite element method. For a comparison with the results of both methods, the three-dimensional surface profile is recorded by a radioscopic measurement technique. In the bistable regime of the flat and patterned state we generate localized states (ferrosolitons) which are recovered in analytical and numerical model descriptions. For higher fields an inverse hysteretic transition from hexagonal to square planforms is measured. % Via a horizontal field component the symmetry can be broken in the experiment, resulting in liquid ridges and distorted hexagons, as predicted by theory. Replacing ferrofluid by ferrogel also an elastic energy contribution has to be taken into account for a proper model description, yielding a linear shift of the threshold and an increased bistability range. Parametric excitation in combination with magnetic fields is widening the horizon of pattern formation even further. For the mono-spike oscillator harmonic and subharmonic response as well as deterministic chaos is observed and modeled. In a ring of spikes the formation of domains of different wavelengths and spatio-temporal intermittency is quantitatively studied. For an extended layer of ferrofluid we predict that a stabilizing horizontal field counteracted by vertical vibrations will result in oblique rolls with preselected orientation