Influences of supercell termination and lateral row number on the determination of slow light properties of photonic crystal waveguides

We systematically analyze the effects of the use of an inaccurate supercell termination and an insufficient supercell size of plane-wave expansion method on the dispersion and the slow light properties of the photonic crystal waveguides. The inattentive use of supercells of photonic crystal waveguides appeared in the literature is found to be yielding errors in the dispersion and slow light characteristics of the fundamental guided mode of photonic crystal waveguides. In addition, extra modes appear in the photonic band gap of the photonic crystal waveguide due to inaccurate supercell termination. By examining the field distribution of the modes, the extra modes can be determined and removed from the band diagram. The dispersion, group index and bandwidth characteristics are observed to be less affecting from inaccurate supercell termination as the number of rows adjacent to the waveguide increases. Moreover, the dispersion and the group index-frequency curves of the fundamental guided mode of correctly terminated supercells are found to be converging as the lateral row number along the line-defect is increased.     

Uniform 1-cochains and genuine laminations

We construct a pair of transverse genuine laminations on an atoroidal 3-manifold admitting a transversely orientable uniform 1-cochain. The laminations are induced by the uniform 1-cochain and they are the straightening of the coarse laminations defined by Calegari, by using minimal surface techniques. Moreover, when we collapse these laminations, we get a topological pseudo-Anosov flow, as defined by Mosher.     

Thermally curable polyvinylchloride via click chemistry

Novel side‐chain benzoxazine functional polyvinylchloride (PVC‐Benzoxazine) was synthesized by using “Click Chemistry” strategy. First, approximately 10% of chloro groups of PVC were converted to azido groups by using NaN₃ in N,N‐dimethylformamide. Propargyl benzoxazine was prepared independently by a ring closure reaction between p‐propargyloxy aniline, paraformaldehyde, and phenol. Finally, azidofunctionalized PVC was coupled to propargyl benzoxazine with high efficiency by click chemistry. The spectral and thermal analysis confirmed the presence of benzoxazine functionality in the resulting polymer. It is shown that PVC containing benzoxazine undergoes thermally activated curing in the absence of any catalyst forming PVC thermoset with high thermal stability. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3512–3518, 2008     

Duplex strand formation using alternating copolymers

The regular arrangement of complementary diaminopyridine-thymine (DAP-THY) on alternating copolymers permits cooperative binding events and the effective formation of well-controlled micrometre-scale aggregates.     

Polyglycidol Based Amphiphilic Double‐Comb Copolymers and Their Self‐Association in Aqueous Solution

Herein, we report synthesis and self‐association properties of amphiphilic double‐comb polymers with polyglycidol backbones. First, a bifunctional polyglycidol precursor is synthesized via monomer activated anionic polymerization. Next, two efficient and orthogonal polymer analogous reactions are carried out for grafting hydrophilic oligoethylene glycol side chains and hydrophobic linear aliphatic side‐chains. The polymers are analyzed by means of NMR, GPC, and DSC. From the DSC analysis of the bulk samples it is evident that aliphatic side chains segregate from the polar backbone and thus crystallize. Furthermore, in aqueous media the double‐comb polymers spontaneously self‐assemble to form a multilayer structure. The present results pave a way to tailor and design amphiphilic polymers based on glycidols. Major advantages are spontaneous self‐assembly in water and the possibility to form onion polymersomes relevant to encapsulation.

     

Mean convex hulls and least area disks spanning extreme curves

We show that for any extreme curve in a 3-manifold M, there exist a canonical mean convex hull containing all least area disks spanning the curve. Similar result is true for asymptotic case in such that for any asymptotic curve , there is a canonical mean convex hull containing all minimal planes spanning Γ. Applying this to quasi-Fuchsian manifolds, we show that for any quasi-Fuchsian manifold, there exist a canonical mean convex core capturing all essential minimal surfaces. On the other hand, we also show that for a generic C³-smooth curve in the boundary of C³-smooth mean convex domain in ℝ³, there exist a unique least area disk spanning the curve.     

Kinetics of facile bilayer island formation at low temperature: Ag/NiAl(110)

Facile nucleation and growth of bilayer Ag(110) islands on NiAl(110) is observed by STM for Ag deposition at temperatures as low as 127 K. Density functional theory analysis for supported Ag films determines adatom adsorption energies (which favor bilayer islands), interaction energies, and diffusion barriers. Analysis of an atomistic lattice-gas model incorporating these energies elucidates the role of strongly anisotropic interactions in enabling the upward mass transport needed for bilayer island formation.