A divergent approach to highly substituted benzothiepinones and to 2,3-dihydrothieno[2,3-b]thiopyran-4-ones

The radical addition-transfer of S-(2-fluoro-phenacyl)xanthates can be used to construct rapidly benzothiepinones, including libraries of complex aza-bridged derivatives, and highly functionalized 2,3-dihydrothieno[2,3-b]thiopyran-4-ones.     

Pattern Densities in Non-Frozen Planar Dimer Models

In this paper, we introduce a family of observables for the dimer model on a bi-periodic bipartite planar graph, called pattern density fields. We study the scaling limit of these objects for non-frozen Gibbs measures of the dimer model, and prove that they converge to a linear combination of a derivative of the Gaussian massless free field and an independent white noise.     

Random Skew Plane Partitions with a Piecewise Periodic Back Wall

Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes. In the present work, we consider the limit of large random skew plane partitions where the inner boundary approaches a piecewise linear curve with non-lattice slopes, describing the limit shape and the local fluctuations in various regions. This analysis is fairly similar to that in Okounkov and Reshetikhin (Commun Math Phys 269:571–609, 2007), but we do find some new behavior. For instance, the boundary of the limit shape is now a single smooth (not algebraic) curve, whereas the boundary in Okounkov and Reshetikhin (Commun Math Phys 269:571–609, 2007) is singular. We also observe the bead process introduced in Boutillier (Ann Probab 37(1):107–142, 2009) appearing in the asymptotics at the top of the limit shape.     

Non-Colliding Paths in the Honeycomb Dimer Model and the Dyson Process

In this paper we describe a natural family of random non-intersecting discrete paths in the dimer model on the honeycomb lattice. We show that when the dimer model is going to freeze, this family of paths, after a proper rescaling, converges to the extended sine process, obtained traditionally as the limit of the Dyson model when the number of particles goes to infinity.     

On the structure of transparent water and oil dispersions stabilized by polymeric emulsifiers

Summary An investigation has been made of transparent oil-water dispersions stabilized by amphiphilic polymeric substances. The samples are well-defined polyethylene oxide — polystyrene graft copolymers with various lengths of backbone and side chains. The domain for existence of microemulsions and the phase diagrams were determined turbidimetrically by titration with 2-propanol for water/toluene/graft copolymer systems. Results are generalized to several amphilic copolymers of different chemical structure using various polar oils. A behavior markedly different is observed depending on whether soaps or copolymers are used for these systems. In particular, polymeric microemulsions form only when there is a mutual solubility for the ternary solvent mixture. A simple model is proposed, based on particles which consist of two concentric spheres having a PS part solvated by toluene and a PEO part by water, the continuous medium being composed of the ternary solvent mixture at mutual solubility. The size of the particles was determined by light scattering spectroscopy.

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Zusammenfassung Transparente, durch amphiphile Polymere stabilisierte Öl-Wasserstreuungen wurden untersucht. Die Proben bestehen aus modellartigen Polyäthylenoxyd-Polystyrol-Pfropfcopolymeren mit verschiedenen Haupt- und Seitenkettenlängen. Wir haben den Bereich der Mikroemulsionbildung und die Phasendiagramme durch Titration der Wasser/Toluol/Pfropfcopolymeren mit 2-Propanol bestimmt. Die allgemeine Gültigkeit der Ergebnisse wurde an mehreren amphiphilen Copolymeren mit verschiedenen chemischen Zusammensetzungen und in verschiedenen Ölen probiert. Ganz verschiedenes Verhalten wurde festgestellt —je nachdem ob Seifen oder Copolymere angewendet wurden. Insbesondere bilden sich Polymermikroemulsionen nur, wenn eine gegenseitige Löslichkeit in den ternären Mischsystemen besteht. Ein einfaches Modell aus zwei konzentrischen Kugeln wird vorgeschlagen: Die eine Kugel besteht aus toluolgequollenem Polystyrol, die andere aus wassergequollenem Polyäthylenoxyd. Die kontinuierliche Phase wird dargestellt durch das ternäre Lösungsmittelsystem. Die Partikelgrößen wurden mit Lichtstreuung bestimmt.

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With 7 figures and 5 tables     

Martin Boundary of Killed Random Walks on Isoradial Graphs

Potential Analysis - We consider killed planar random walks on isoradial graphs. Contrary to the lattice case, isoradial graphs are not translation invariant, do not admit any group structure and...     

Optimization and Characterization of InGaAsN/GaAs Quantum-well Ridge Laser Diodes for High Frequency Operation

Optimization and characterization of multiple InGaAsN/GaAs quantum-well laser diodes for high frequency operation are reported. From the modelling of the dilute nitride quantum well, we investigate how to design the structure to achieve a high frequency operation. The gain characteristics are optimized by incorporating the minimum amount of nitrogen in the well to obtain the emission at 1.3 μm with a low transparency density and a high differential gain. We show that the number of wells must be adjusted to three to benefit of the best compromise between the threshold current and the differential gain. The effects of the cavity losses on the dynamic characteristics are evaluated and demonstrate the interest for high cavity losses to reach high relaxation frequency despite a lower characteristic temperature. An optimized structure has been realized and exhibits an emission at 1.34 μm with a transparency current density of 642 A/cm² and a characteristic temperature T₀ ~ 80 K. Dynamic properties for ridge devices are evaluated from relative intensity noise measurements and small-signal modulation. A relaxation frequency as high as 7.4 GHz and a 9.7 GHz small-signal bandwidth are reported. We demonstrate transmission up to 10 Gb/s at 25°C without penalty and bit error floor.