Azimuthally polarized spatial dark solitons: exact solutions of Maxwell's equations in a Kerr medium

Spatial Kerr solitons, typically associated with the standard paraxial nonlinear Schro dinger equation, are shown to exist to all nonparaxial orders as exact solutions of Maxwell's equations in the presence of the vectorial Kerr effect. More precisely, we prove the existence of azimuthally polarized, spatial, dark soliton solutions of Maxwell's equations, while exact linearly polarized (2 + 1)D solitons do not exist. Our ab initio approach predicts the existence of dark solitons up to an upper value of the maximum field amplitude, corresponding to a minimum soliton width of about one-fourth of the wavelength.     

Nonparaxial dark solitons in optical Kerr media

We show that the nonlinear equation that describes nonparaxial Kerr propagation, together with the already reported bright-soliton solutions, admits of (1 + 1)D dark-soliton solutions. Unlike their paraxial counterparts, dark solitons can be excited only if their asymptotic normalized intensity u2infinity is below 3/7; their width becomes constant when u2infinity approaches this value.     

Measurement of the generalized polarizabilities of the proton in virtual Compton scattering at Q2=0.92 and 1.76 GeV2

We report a virtual Compton scattering study of the proton at low c.m. energies. We have determined the structure functions P(LL)-P(TT)/epsilon and P(LT), and the electric and magnetic generalized polarizabilities (GPs) alpha(E)(Q2) and beta(M)(Q2) at momentum transfer Q(2)=0.92 and 1.76 GeV2. The electric GP shows a strong falloff with Q2, and its global behavior does not follow a simple dipole form. The magnetic GP shows a rise and then a falloff; this can be interpreted as the dominance of a long-distance diamagnetic pion cloud at low Q2, compensated at higher Q2 by a paramagnetic contribution from piN intermediate states.     

Topological origin of the phase transition in a model of DNA denaturation

The hypothesis that phase transitions originate from some topological change of the critical level hypersurface of the potential energy receives direct evident support by our study of the Bishop-Peyrard model of DNA thermal denaturation.     

D-branes on Calabi–Yau Manifolds and Superpotentials

We show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this Calabi-Yau.Louis Michel Professor     

One-pot synthesis of cyanuric acid-bridged porphyrin-porphyrin dyads

Stepwise amination of cyanuric chloride (1) with 5-(4-aminophenyl)-10,15,20-triphenylporphyrin (2) and/or its zinc(II) complex (3) enables the synthesis of porphyrin-porphyrin dyads with predetermined free base-free base forms or free base-zinc and zinc-zinc metalation states. Furthermore, the use of aminopropyl-silanized silica gel as a scavenger for unwanted byproducts allowed the one-pot synthesis of title porphyrin compounds in high yield and purity with minimum use of preparative column chromatography.     

Oxidative coupling of 17beta-estradiol: inventory of oligomer products and configuration assignment of atropoisomeric c4-linked biphenyl-type dimers and trimers

The oxidation chemistry of 17beta-estradiol (1) is of central relevance to the nongenomic effects of estrogens and offers valuable prospects in the search for novel steroidal scaffolds of academic and industrial interest. Herein, we report the results of a detailed investigation into the nature of the oligomer products formed by phenolic oxidation of 1. Of the oxidants tested, the peroxidase/H2O2 system proved to be the most effective in inducing conversion of 1 to a complex mixture of oligomer species. Repeated chromatographic fractionation followed by extensive 2D NMR and mass spectrometric analysis allowed identification of a series of phenolic coupling products comprising, besides the C2-symmetric dimers 2 and 3, a 2,4' dimer (4), two O-linked dimers (5, 6), and the novel trimers 7-9. All 4-linked biphenyl-type oligomers, i.e., 3 and 7-9, occurred as couples of atropoisomers, reflecting steric hindrance at biphenyl linkages. For all atropoisomers, absolute configuration was established by the exciton chirality method and the interconversion energy was determined by dynamic NMR. These results provide the first systematic inventory of oxidative coupling products of 1 and lay the foundation for future studies aimed to develop novel estrogen derivatives based on oligomeric scaffolds.