Vortex transmutation

Using group theory arguments and numerical simulations, we demonstrate the possibility of changing the vorticity or topological charge of an individual vortex by means of the action of a system possessing a discrete rotational symmetry of finite order. We establish on theoretical grounds a "transmutation pass" determining the conditions for this phenomenon to occur and numerically analyze it in the context of two-dimensional optical lattices. An analogous approach is applicable to the problems of Bose-Einstein condensates in periodic potentials.     

Fano resonance in quadratic waveguide arrays

We study resonant light scattering in arrays of channel optical waveguides in which tunable quadratic non-linearity is introduced as nonlinear defects by periodic poling of single (or several) waveguides in the array. We describe novel features of wave scattering that can be observed in this structure and show that it is a good candidate for observation of Fano resonance in nonlinear optics.     

Efficient methods for the synthesis of 2-hydroxyphenazine based on the Pd-catalyzed N-arylation of aryl bromides

[reaction: see text] Substituted diphenylamines can be synthesized by Pd(0)-catalyzed N-arylation using o-nitroanilines and nitro-substituted aryl bromides for a substrate. Cyclization of the diphenylamines by various methods, including the intramolecular Pd(0)-catalyzed N-arylation, produces 2-methoxyphenazine which can easily be deprotected to give 2-hydroxyphenazine. This phenazine is required to synthesize methanophenazine, a novel redoxactive cofactor isolated from methanogenic archaea.     

Surface light-scattering at the air-liquid interface: from newtonian to viscoelastic polymer solutions

The dynamics of the liquid-air interface of aqueous solutions of a tensioactive triblock copolymer (Pluronic F-68) has been studied using surface quasielastic light scattering over a broad range of concentrations and temperatures. Ancillary surface tension and bulk rheometry data have been obtained for the same system. The results show that the classical theoretical spectrum for monolayers on a Newtonian fluid can be applied only for concentrations below 4.10(-2) mM. For concentrations above c = 14 mM a clear peak centered at zero frequency appears in the spectrum. This feature is incompatible with the classical theoretical spectrum. The SQELS spectra have been described in terms of the theory of Wang and Huang [Wang, C. H.; Huang, Q. R. J. Chem. Phys. 1997, 107, 5898] considering that the loss modulus of the concentrated solutions shows the existence of two relaxation modes even at low frequencies. The theory is able to explain the existence of a peak centered at zero frequency in the spectra, and the theoretical spectra point out the existence of an elastic peak together with the capillary one. There is a reasonable agreement between the relaxation times and the product Gtau obtained from the fits of the SQELS spectra to the theory of Wang and Huang and those obtained from bulk rheology.     

The rank of a commutative cancellative semigroup

Summary For a commutative cancellative semigroup S, we define the rank of S intrinsically. This definition implies that the rank of S equals the usual rank of its group of quotients. We also characterize the rank in terms of embeddability into a rational vector space of the greatest power cancellative image of S.