The Eckhaus and the Benjamin-Feir instability near a weakly inverted bifurcation

We investigate how the criteria for two prototype instabilities in one dimensional pattern forming systems, namely for the Eckhaus instability and for the Benjamin-Feir instability, change as one goes from a continuous bifurcation, to a spatially periodic or spatially and/or time periodic state, to the corresponding weakly inverted, i.e., hysteretic, cases. We also give the generalization to two dimensional patterns in systems with anisotropy as they arise from hydrodynamic instabilities in nematic liquid crystals

Exploding dissipative solitons in reaction-diffusion systems

We show that exploding dissipative solitons can arise in a reaction-diffusion system for a range of parameters. As a function of a vorticity parameter, we observe a sequence of transitions from oscillatory localized states via meandering dissipative soli

Magneto-optic dynamics in a ferromagnetic nematic liquid crystal

We investigate dynamic magneto-optic effects in a ferromagnetic nematic liquid crystal experimentally and theoretically. Experimentally we measure the magnetization and the phase difference of the transmitted light when an external magnetic field is applied. As a model we study the coupled dynamics of the magnetization, M, and the director field, n, associated with the liquid crystalline orientational order. We demonstrate that the experimentally studied macroscopic dynamic behavior reveals the importance of a dynamic cross-coupling between M and n. The experimental data are used to extract the value of the dissipative cross-coupling coefficient. We also make concrete predictions about how reversible cross-coupling terms between the magnetization and the director could be detected experimentally by measurements of the transmitted light intensity as well as by analyzing the azimuthal angle of the magnetization and the director out of the plane spanned by the anchoring axis and the external magnetic field. We derive the eigenmodes of the coupled system and study their relaxation rates. We show that in the usual experimental set-up used for measuring the relaxation rates of the splay-bend or twist-bend eigenmodes of a nematic liquid crystal one expects for a ferromagnetic nematic liquid crystal a mixture of at least two eigenmodes.Comment: 20 pages, 23 figures, 42 reference

Inverse Lehmann effects can be used as a microscopic pump

For cholesteric and chiral smectic liquid crystals a rotation of the helical superstructure can be induced for suitable boundary conditions for external fields such as temperature gradients and electric fields: The Lehmann effect. Here we predict that the inverse effect can lead to a pump for particles and ions on a length scale of microns: When a spatial pattern such as a phase winding pattern or a spiral is generated, for example, for a freely suspended smectic C * film, a concentration current arises. We also point out, that this concentration current is, under suitable experimental conditions, accompanied by a heat current and/or an electric current. Similar effects are expected for cholesterics, smectic F * and I * as well as for Langmuir monolayers, since all these systems share the property of macroscopic chirality

Pattern formation in ferrogels: analysis of the Rosensweig instability using the energy method,”

Abstract We present a nonlinear description of the Rosensweig instability in isotropic magnetic gels based on the energy minimizing method used by Gailitis to describe the Rosensweig instability in typical ferrofluids. We extend his discussion to media with elastic degrees of freedom, assuming the shear modulus as a perturbation to the pure fluid case. We study the relative stability of the regular planforms of stripes, squares and hexagons as a function of the elastic shear modulus