Free-standing films of twist grain boundary TGBA and UTGBC* liquid crystals studied by fluorescence confocal polarizing microscopy

The director structures, meniscus profile, and defects in free-standing films of the twist grain boundary TGB_A and UTGB_C* liquid crystals were studied. The films were characterized by a combination of polarizing microscopy and fluorescence confocal polarizing microscopy. Five principal regions of meniscus were distinguished. When film thickness in the meniscus is much smaller then the TGB pitch, there is no difference between the free-standing films of TGB and ordinary smectic A liquid crystals. When the film thickness is larger than the TGB pitch, filamentary texture is observed. The 3D director pattern of the filaments are similar to the ground state director fields of TGB_A and UTGB_C* liquid crystals. In the intermediate thickness region of the meniscus, when the film thickness and TGB pitch are commensurate, a unique radial pattern is observed. Based on the fluorescence confocal polarizing microscopy studies of the director field, we propose a model for the 3D director structure in this part of the meniscus.     

Sectionally Semicomplemented Distributive Nearlattices

A nearlattice S is a meet semilattice together with the property that any two elements possessing a common upper bound have a supremum. Here the authors have introduced the notion of sectionally semicomplemented distributive nearlattices and given several characterizations of them. The skeleton SCon(S) of Con(S), the congruence lattice, consists of all those nearlattice congruences which are the pseudocomplements of members of Con(S). The relationship between skeletal congruences and kernel of skeletal congruences leads to numerous characterizations of sectionally semicomplemented distributive nearlattices and semiboolean algebras. For example we prove, for a distributive nearlattice S with 0, the following conditions are equivalent:

Parity-breaking phase transition in tangentially anchored nematic drops

Summary The existence of the parity-breaking phase transition between untwisted and twisted bipolar structures of the tangentially anchored spherical nematic drops has been shown experimentally. Twisted structures behave like the optically active objects in spite of the nonactivity of nematic and isotropic matrix themselves. Temperature dependences of the order parameter (twist angle) have been determined for the drops of 8 CB and 8 OCB. It has been shown that these dependences are very similar to that observed in usual second-order phase transition. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Precision measurement of neutrino oscillation parameters at INO-ICAL detector

A magnetized Iron CALorimeter (ICAL) detector at the India-based neutrino observatory (INO) is used to study neutrino oscillation sensitivity using atmospheric muon neutrino source. The ICAL detector will be able to detect muon tracks and hadron showers produced by neutrino interactions with the iron target. We have performed precision measurement analysis for the atmospheric neutrino oscillation parameters with the muon neutrino events, generated by Monte Carlo NUANCE event generator. A marginalized χ² analysis based on reconstructed neutrino energy and muon zenith angle binning scheme has been performed to determine the sensitivity for the atmospheric neutrino mixing parameters, \(\sin ^{2}\theta _{23}\) and \(| {\Delta } m^{2}_{23}|\).     

Thermodielectric bistability in dual frequency nematic liquid crystal

We report on a thermodielectric bistability in dual frequency nematic liquid crystals (LCs) caused by the anisotropic nature of dielectric heating and director reorientation in an electric field. The bistability is a result of the positive feedback loop: director reorientation --> anisotropic dielectric heating --> dielectric anisotrophy --> director reorientation. We demonstrate both experimentally and theoretically that two states with different temperature and director orientation, namely, a cold planar state and a hot homeotropic state coexist in a LC cell for a certain frequency and amplitude range of the applied voltage.     

Coefficient estimates of negative powers and inverse coefficients for certain starlike functions

For ?1≤B<A≤1, let \(\mathcal {S}^{*}(A,B)\) denote the class of normalized analytic functions \(f(z)= z+{\sum }_{n=2}^{\infty }a_{n} z^{n}\) in |z|<1 which satisfy the subordination relation z f ^′(z)/f(z)?(1 + A z)/(1 + B z) and Σ^?(A,B) be the corresponding class of meromorphic functions in |z|>1. For \(f\in \mathcal {S}^{*}(A,B)\) and λ>0, we shall estimate the absolute value of the Taylor coefficients a _n (?λ,f) of the analytic function (f(z)/z)^?λ . Using this we shall determine the coefficient estimate for inverses of functions in the classes \(\mathcal {S}^{*}(A,B)\) and Σ^?(A,B).