Boundary Vortex Formation in Polarization-Modulated Orthogonal Smectic Liquid Crystals

We investigate the relaxation of an energy functional originated in the physics literature to study the bistability of polarization modulated orthogonal smectic phases (SmAPFmod) of bent-core molecules liquid crystals. We show that the interplay between the mixed boundary conditions and the shape of the sample results in boundary defects. We also analyze the bistable switching due to an applied electric field via gradient flow numerical simulations. Our computations reveal a novel dynamic scenario, where switching is achieved by the formation of two internal vortices

Sawtooth Profile in Smectic a Liquid Crystals

We study the de Gennes free energy for smectic A liquid crystals over S2-valued vector fields to understand the chevron (zigzag) pattern formed in the presence of an applied magnetic field. We identify a small dimensionless parameter a, and investigate the behaviors of the minimizers when the field strength is of order O (ε-1). In this regime, we show via Γ-convergence that a chevron structure where the director connects two minimum states of the sphere is favored. We also analyze the Chen-Lubensky free energy, which includes the second order gradient of the smectic order parameter, and obtain the same general behavior as for the de Gennes case. Numerical simulations illustrating the chevron structures for both energies are included. © 2016, Society for Industrial and Applied Mathematic

Switching Mechanism in the B-1revtilted Phase of Bent-Core Liquid Crystals

The B1RevTilted is a uniformly smectic tilted columnar phase in which the macroscopic polarization can be reorientated via electric field. To study the effects on the reorientation mechanism of the various physical parameters, we analyze a local, and a non-local Landau-de Gennes-type energy functional. For the case of large columnar samples, we show that both energies give the same qualitative behavior, with a relevant role played by the terms that describe the interaction between polarization and nematic directors. We also obtain existence of the L2-gradient flow in metric spaces for the full local energy

The phase transition between chiral nematic and smectic C* liquid crystals

We are interested in the liquid crystals with smectic C* phases at the lower temperature and chiral nematic phases at the higher temperature. We study the modified Chen-Lubensky model, or the covariant form of the Landau-de Gennes free energy, to investigate the phase transition between chiral nematic and smectic C* liquid crystals. First, we prove the existence of the minimizers in an admissible set consisting of order parameters [special characters omitted] and molecular directors [special characters omitted]. The splay, twist, and bend Frank constants, K 1, K2, and K3 are considered to be large based on physical observation near the smectic C* to chiral nematic phase transition. Under this hypothesis, we show that the director from the minimizer must be close to a rotation of the specific vector field. With the help of this effect from the large Frank constants, we describe the phase transition regime for these two phases when a domain [special characters omitted] is a considerably large liquid crystal region confined in two plates. The analysis is based on the eigenvalue estimates of the free energy

Measurement of the B+/B0B^+/B^0 production ratio in e+e−e^+e^- collisions at the Υ(4S)\Upsilon(4S) resonance using B→J/ψ(ℓℓ)KB \rightarrow J/\psi(\ell\ell) K decays at Belle

We measure the ratio of branching fractions for the $\Upsilon (4S)$ decays to $B^+B^-$ and $B^0\bar{B}{}^0$ using $B^+ \rightarrow J/\psi(\ell\ell) K^+$ and $B^0 \rightarrow J/\psi(\ell\ell) K^0$ samples, where $J/\psi(\ell\ell)$ stands for $J/\psi \to \ell^+\ell^-$ ($\ell = e$ or $\mu$), with $711$ fb$^{-1}$ of data collected at the $\Upsilon(4S)$ resonance with the Belle detector. We find the decay rate ratio of $\Upsilon(4S) \rightarrow B^+B^-$ over $\Upsilon(4S) \rightarrow B^0\bar{B}{}^0$ to be $1.065\pm0.012\pm 0.019 \pm 0.047$, which is the most precise measurement to date. The first and second uncertainties are statistical and systematic, respectively, and the third uncertainty is systematic due to the assumption of isospin symmetry in $B \to J/\psi(\ell\ell) K$

Measurement of the Ωc0\Omega_c^0 lifetime at Belle II

We report on a measurement of the $\Omega_c^0$ lifetime using $\Omega_c^0 \to \Omega^-\pi^+$ decays reconstructed in $e^+e^-\to c\bar{c}$ data collected by the Belle II experiment and corresponding to $207~{\rm fb^{-1}}$ of integrated luminosity. The result, $\rm\tau(\Omega_c^0)=243\pm48( stat)\pm11(syst)~fs$, agrees with recent measurements indicating that the $\Omega_c^0$ is not the shortest-lived weakly decaying charmed baryon