Critical behavior of light in mode-locked lasers

Light is shown to exhibit critical and tricritical behavior in passively mode-locked lasers with externally injected pulses. It is a first and unique example of critical phenomena in a one-dimensional many-body light-mode system. The phase diagrams consist of regimes with continuous wave, driven parapulses, spontaneous pulses via mode condensation, and heterogeneous pulses, separated by phase transition lines that terminate with critical or tricritical points. Enhanced non-Gaussian fluctuations and collective dynamics are present at the critical and tricritical points, showing a mode system analog of the critical opalescence phenomenon. The critical exponents are calculated and shown to comply with the mean field theory, which is rigorous in the light system.     

Faraday rotation in a two-dimensional photonic crystal with a magneto-optic defect

We study the magneto-optic (MO) Faraday rotation in a two-dimensional square-lattice photonic crystal with a central MO defect layer in the optical wavelength range. We show that when a TM plane wave is incident upon a photonic crystal, an enhancement of Faraday rotation takes place in a region where a resonance peak appears in the photonic bandgap. In this region the mode conversion is high.     

Cu-catalyzed asymmetric allylic alkylations of aromatic and aliphatic phosphates with alkylzinc reagents. An effective method for enantioselective synthesis of tertiary and quaternary carbons

Efficient enantioselective Cu-catalyzed allylic alkylations of aromatic and aliphatic allylic phosphates bearing di- and trisubstituted olefins are disclosed. Enantioselective C-C bond forming reactions are promoted in the presence of 10 mol % readily available chiral amino acid-based ligand (5 steps, 40% overall yield synthesis) and 5 mol % (CuOTf)2 x C6H6. Reactions deliver tertiary and quaternary stereogenic carbon centers regioselectively and in 78-96% ee. Data regarding the effect of variations in ligand structure on the efficiency and enantioselectivity of the alkylation process, as well as a mechanistic working model, are presented. The suggested model involves a dual role for the chiral Cu complex: association of the Cu(I) center to the olefin is facilitated by a two-point binding between the carbonyl of the ligand's amide terminus and the P=O of the substrate.     

Real-time 2D NMR identification of analytes undergoing continuous chromatographic separation

We have recently proposed and demonstrated an approach that enables the acquisition of multidimensional nuclear magnetic resonance (NMR) spectra within a single scan. A promising application opened up by this new accelerated form of data acquisition concerns the possibility of monitoring in real time the chemical nature of analytes subject to a continuous flow. The present paper illustrates such potential, with the real-time acquisition of a series of 2D 1H NMR spectra arising from a mixture of compounds subject to a continuous liquid chromatography (LC) separation. This real-time 2D NMR identification of chemicals eluted minutes apart under usual LC-NMR conditions differs from the way in which LC-2D NMR has hitherto been carried out, which relies on stopped-flow modes of operations whereby fractions are first collected and then subject to individual, aliquot-by-aliquot analyses. The real-time LC-2D NMR experiment hereby introduced can be implemented in a straightforward manner using modern commercial LC-NMR hardware, thus opening up immediate possibilities in high-throughput characterizations of complex molecules.     

Quantitative optical imaging of the pharmacokinetics of fluorescent-specific antibodies to tumor markers through tissuelike turbid media

Fluorescent optical imaging of tumors deep within tissue depends on specific binding of antibodies to the tumors' surface markers. These fluorescent antibodies propagating in the vicinity of the tumor can be attached to and (or) diffused away from it. We illustrate application of a new tool, based on the random-walk theory in turbid media, for extracting the pharmacokinetics of these fluorescent antibodies by data deconvolution, excluding the effect of upper turbid tissue layers.     

Microscopic visualization of alamethicin incorporation into model membrane monolayers

Lipid interactions and cooperative assembly properties are fundamental determinants for the action of antimicrobial membrane-active peptides. Here we analyze the interactions and aggregation properties of alamethicin, an antimicrobial pore-forming peptide, with films formed at the air/water interface. Surface-area/pressure isotherms, Brewster angle microscopy, and fluorescence-confocal microscopy provided detailed information on the morphologies and structural properties of the peptide and its effect on the film components. The pressure-area analysis and microscopy experiments facilitated unprecedented visualization of the structural consequences of alamethicin association at the air/water interface, with pure phospholipid films, and within mixed phospholipid/polydiacetylene (PDA) films. The analysis exposed the kinetic features and the interplay between the peptide aggregates and film constituents. In particular, the results demonstrate the use of phospholipid/PDA film assemblies for studying membrane-peptide association and interactions within two-dimensional films.     

Chiral Ru-based complexes for asymmetric olefin metathesis: enhancement of catalyst activity through steric and electronic modifications

Design, synthesis, characterization, and catalytic activity of six enantiomerically pure Ru-based metathesis catalysts are disclosed (3a-3f). The new chiral catalysts were prepared through steric and electronic alterations of the parent catalyst system (3). The present studies indicate that the effect of structural modifications of chiral complex 3 does not always correspond to those of the related achiral complexes. The present findings illustrate that modified Ru complexes (3e and 3f) deliver reactivity levels that are more than 2 orders of magnitude higher than 3. Reactivity and physical data are provided that shed light on the origin of activity differences. Some members of the new generation of chiral Ru catalysts promote asymmetric ring-opening (AROM) and ring-closing (ARCM) metatheses that cannot be effected by the first generation chiral catalyst (3).     

An enantiomerically pure adamantylimido molybdenum alkylidene complex. An effective new catalyst for enantioselective olefin metathesis

An enantiomerically pure Mo-based complex that bears an alkylimido ligand is prepared and characterized through NMR spectroscopy and X-ray analysis. Mo complex 4 is the only reported chiral alkylimido catalyst; all previous chiral complexes are arylimido systems. These studies show that the chiral Mo catalyst exists exclusively as the syn isomer and that it offers unique reactivity and selectivity profiles in asymmetric olefin metathesis.     

Enantioselective synthesis of propargylamines through Zr-catalyzed addition of mixed alkynylzinc reagents to arylimines

[reaction: see text] Addition of mixed alkynylzinc reagents to various arylimines is catalyzed by chiral amino acid-based ligand 1 and Zr(Oi-Pr)(4).HOi-Pr to afford chiral propargylamines in up to 90% ee. Oxidative removal of the o-anisidyl group affords the free amine, which can then be acylated.     

Thin points for Brownian motion

Let Θ(x,r) denote the occupation measure of the ball of radius r centered at x for Brownian motion {W_t}_0≤t≤1 in . We prove that for any analytic set E in [0,1], we have

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, where dim_P(E) is the packing dimension of E. We deduce that for any a≥1, the Hausdorff dimension of the set of “thin points” x for which

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, is almost surely 2−2/a; this is the correct scaling to obtain a nondegenerate “multifractal spectrum” for the “thin” part of Brownian occupation measure. The methods of this paper differ considerably from those of our work on Brownian thick points, due to the high degree of correlation in the present case. To prove our results, we establish general criteria for determining which deterministic sets are hit by random fractals of ‘limsup type' in the presence of long-range correlations. The hitting criteria then yield lower bounds on Hausdorff dimension. This refines previous work of Khoshnevisan, Xiao and the second author, that required decay of correlations.