Director Field Configurations around a Spherical Particle in a Nematic Liquid Crystal

We study the director field around a spherical particle immersed in a uniformly aligned nematic liquid crystal and assume that the molecules prefer a homeotropic orientation at the surface of the particle. Three structures are possible: a dipole, a Saturn-ring, and a surface-ring configuration, which we investigate by numerically minimizing the Frank free energy supplemented by a magnetic-field and a surface term. In the dipole configuration, which is the absolutely stable structure for micron-size particles and sufficiently strong surface anchoring, a twist transition is found and analyzed. We show that a transition from the dipole to the Saturn ring configuration is induced by either decreasing the particle size or by applying a magnetic field. The effect of metastability and the occurence of hysteresis in connection with a magnetic field are discussed. The surface-ring configuration appears when the surface-anchoring strength W is reduced. It is also favored by a large saddle-splay constant K_24. A comparison with recent experiments by Poulin et al. gives a lower bound for W, i.e., W > 0.6 erg/cm^2 for the interface of water and pentylcyanobiphenyl (5CB) in the presence of the surfactant sodium dodecyl sulfate.Comment: 11 pages, Revtex, 16 eps figures, submitted to Eur. Phys. J.

Indefiniteness and Specificity in Old Italian Texts

Object of this study is the marking of nominal indefiniteness in Old Italian, more precisely Old Tuscan texts, in three collections of novellas

Self-consistent tomography of the state-measurement Gram matrix

State and measurement tomography make assumptions about the experimental states or measurements. These assumptions are often not justified because state preparation and measurement errors are unavoidable in practice. Here we describe how the Gram matrix associated with the states and measurement operators can be estimated via semidefinite programming if the states and the measurements are so called globally completable. This is for instance the case if the unknown measurements are known to be projective and non-degenerate. The computed Gram matrix determines the states, and the measurement operators uniquely up to simultaneous rotations in the space of Hermitian matrices. We prove the reliability of the proposed method in the limit of a large number of independent measurement repetitions.Comment: We have completely rewritten the first version because new results from arXiv:1209.6499 allowed to significantly clearify the first submission. We have added some reference