Self-similar vortex reconnection

As shown by Crow in 1970, the evolution of two almost parallel vortex filaments with opposite circulation exhibits a long-wave instability. Ultimately, the symmetric mode increases its amplitude reconnecting both filaments and ending into the formation of an almost periodic structure of vortex rings. This is a universal process, which appears in a wide range of scales: from the vortex trails behind an airplane to a microscopic scale of superfluids and Bose–Einstein condensates. In this paper, I will focus on the vortex reconnection for the latter case by employing Gross–Pitaevskii theory. Essentially, I focus on the well-known laws of interaction and motion of vortex filaments. By means of numerical simulations, as well as theoretically, I show that a self-similar finite-time dynamics manifests near the reconnection time. A self-similar profile is selected showing excellent agreement with numerical simulations.     

Patterns and supersolids

In the frame of the Gross–Pitaevskii equation with a non-local interaction term we study the crystallization induced by the non-local interaction and its connection with the theory of supersolids. The crystallization is well understood as the search of a ground-state of a certain energy functional, and uses the techniques of pattern-formation in the weak (but finite) amplitude limit. In two space dimensions an hexagonal pattern is displayed, however, in three space dimensions density modulation displays an hexagonal-close-packing or hcp structure. We derive, using the technique of homogenization, an effective Lagrangian that provides the long-wave slow dynamics for the local density variations, the global wavefunction phase, and for the crystal deformation. As a classical crystal, our supersolid displays shear and compression waves for the elastic deformations, however the later are coupled with the wave function phase and the local density. Finally the system presents the quite remarkable property of non-classical rotational inertia (NCRI) under rotation. Indeed under an uniform slow rotation the effective moment of inertia is less than the one of a classical rigid body.     

Superfluid density in a two-dimensional model of supersolid

We study in 2-dimensions the superfluid density of periodically modulated states in the framework of the mean-field Gross-Pitaevskiǐ model of a quantum solid. We obtain a full agreement for the superfluid fraction between a semi-theoretical approach and direct numerical simulations. As in 1-dimension, the superfluid density decreases exponentially with the amplitude of the particle interaction. We discuss the case when defects are present in this modulated structure. In the case of isolated defects (e.g. dislocations) the superfluid density only shows small changes. Finally, we report an increase of the superfluid fraction up to 50% in the case of extended macroscopical defects. We show also that this excess of superfluid fraction depends on the length of the complex network of grain boundaries in the system.     

Electrokinetics in extremely bimodal suspensions

Prompted by the results obtained by Mantegazza et al. [Nature Physics 1 (2005) 103], where the electric birefringence of suspensions of elongated particles was strikingly affected by the presence of a sea of very small (size ratio lower than 10:1) colloidal spheres, we have undertaken an investigation of other electrokinetic phenomena in suspensions containing various relative concentrations of large (Teflon or polystyrene latex) and small (nanometer-sized silica spheres) colloids. We have determined the quantities that might be greatly affected by the size distribution of the particles, mainly in the presence of ac electric fields, since the response of the suspensions will show very characteristic relaxations, dominated in principle by the size of the particles. In this work, we report on measurements of the dielectric dispersion of mixed particles as a function of the concentration, ionic strength, and field frequency. The results indicate that the response is not just a simple combination of those obtained with suspensions of the individual particles, and in fact the presence of even small amounts of the small particles affects considerably the frequency response of the suspensions.