Monte Carlo Study of Slot-waveguide Liquid Crystal Phase Shifters

Abstract

We present detailed Monte Carlo simulations of a simple model of a nematic liquid crystal slot waveguide shifter, investigating the effect of an applied electric external field. The simulations are based on the Lebwohl-Lasher lattice spin model with boundary conditions chosen to mimic the planar alignment as in Silicon Organic Hybrid waveguides and the homeotropic anchoring appropriate for Polydimethylsiloxane polymer walls. The external field is modeled by adding a term to the Hamiltonian which describes its coupling to the mesogenic molecules. We have investigated the effect of the external field on the optical transmission and the ordering across the cell.     

Bounds for complete elliptic integrals of the first kind

In this note by using some elementary computations we present some new sharp lower and upper bounds for the complete elliptic integrals of the first kind. These results improve some known bounds in the literature and are deduced from the well-known Wallis inequality, which has been studied extensively in the last 10 years.     

A Kantorovich-type analysis of Broyden’s method using recurrent functions

We provide a semilocal convergence analysis for Broyden’s method for approximating locally unique solutions of nonlinear operator equations. Using the majorant principle we show that under the same or weaker hypotheses, in combination with our new idea of recurrent functions, we can find weaker sufficient conditions for the convergence of Broyden’s method as well as finer error bounds on the distances involved, and a more precise information on the location of the solution than before (Broyden, Math. Comput. 19:577–593, 1965; Chen, Ann. Inst. Stat. Math. 42:387–401, 1990; Dennis, Nonlinear Functional Analysis and Applications, pp. 425–472, Academic Press, San Diego, 1971; Li and Fukushima, Ann. Oper. Res. 103:71–97, 2001). Numerical examples are also provided involving polynomial, integral, and differential equations.     

Corrigendum to “(p,1)-total labelling of graphs” [Discrete Math. 308 (2008) 496–513]

We give a corrected proof of Proposition 51 of the paper cited in the title.     

Biocompatibility of nitrogen-doped multiwalled carbon nanotubes with murine fibroblasts and human hematopoietic stem cells

Journal of Nanoparticle Research - Workers are increasingly exposed to nanoparticles, mostly via inhalation. Respiratory protection is recommended as an additional control measure. Particulate...     

Exciton Interactions,Excimer Formation,and [2π+2π] Photodimerization in Nonconjugated Curcuminoid-BF2 Dimers

We describe the synthesis of a series of covalently linked dimers of quadrupolar curcuminoid-BF₂ dyes and the detailed investigation of their solvent-dependent spectroscopic and photophysical properties. In solvents of low polarity, intramolecular folding induces the formation of aggregated chromophores, the UV/Vis absorption spectra of which display the optical signature characteristic of weakly-coupled H-aggregates. The extent of folding and, in turn, of ground-state aggregation is strongly dependent on the nature of the flexible linker. Steady-state and time-resolved fluorescence emission spectroscopies show that the Frenkel exciton relaxes into a fluorescent symmetrical excimer state with a long lifetime. Furthermore, our in-depth studies show that a weakly emitting excimer lies on the pathway toward a photocyclomer. Two-dimensional ¹H NMR spectroscopy and density functional theory (DFT) allowed the structure of the photoproduct to be established. To our knowledge, this represents the first example of a [2π+2π] photodimerization of the curcuminoid chromophore.     

Hartogs-Bochner type theorem in projective space

We prove the following Hartogs-Bochner type theorem: Let M be a connected C² hypersurface of P_n(C) (n≥2) which divides P_n(C) in two connected open sets Ω₁ and Ω₂. Suppose that M has at most one open CR orbit. Then there exists i∈{1,2} such that C¹ CR functions defined on M extends holomorphically to Ω _i . Supported by the TMR network.