Symmetric vortices for two-component Ginzburg-Landau systems

We study Ginzburg--Landau equations for a complex vector order parameter Psi=(psi_+,psi_-). We consider symmetric (equivariant) vortex solutions in the plane R^2 with given degrees n_\pm, and prove existence, uniqueness, and asymptotic behavior of solutions for large r. We also consider the monotonicity properties of solutions, and exhibit parameter ranges in which both vortex profiles |psi_+|, |psi_i| are monotone, as well as parameter regimes where one component is non-monotone. The qualitative results are obtained by means of a sub- and supersolution construction and a comparison theorem for elliptic systems.Comment: 32 page

Thermosonic flip chip interconnection using electroplated copper column arrays

Published versio

Regioselective Formation of α-Vinylpyrroles from the Ruthenium-Catalyzed Coupling Reaction of Pyrroles and Terminal Alkynes Involving C–H Bond Activation

The cationic ruthenium catalyst Ru3(CO)12/NH4PF6 was found to be highly effective for the intermolecular coupling reaction of pyrroles and terminal alkynes to give gem-selective α-vinylpyrroles. The carbon isotope effect on the α-pyrrole carbon and the Hammett correlation from a series of para-substituted N-arylpyrroles (ρ = −0.90) indicate a rate-limiting C−C bond formation step of the coupling reaction

Scope and Mechanistic Investigations on the Solvent-Controlled Regio- and Stereoselective Formation of Enol Esters from the Ruthenium-Catalyzed Coupling Reaction of Terminal Alkynes and Carboxylic Acids

The ruthenium-hydride complex (PCy3)2(CO)RuHCl was found to be a highly effective catalyst for the alkyne-to-carboxylic acid coupling reaction to give synthetically useful enol ester products. A strong solvent effect was observed for the ruthenium catalyst in modulating the activity and selectivity; the coupling reaction in CH2Cl2 led to the regioselective formation of gem-enol ester products, while the stereoselective formation of (Z)-enol esters was obtained in THF. The coupling reaction was found to be strongly inhibited by PCy3. The coupling reaction of both PhCO2H/PhC≡CD and PhCO2D/PhC≡CH led to extensive deuterium incorporation on the vinyl positions of the enol ester products. An opposite Hammett value was observed when the correlation of a series of para-substituted p-X-C6H4CO2H (X = OMe, CH3, H, CF3, CN) with phenylacetylene was examined in CDCl3 (ρ = +0.30) and THF (ρ = −0.68). Catalytically relevant Ru-carboxylate and -vinylidene-carboxylate complexes, (PCy3)2(CO)(Cl)Ru(κ2-O2CC6H4-p-OMe) and (PCy3)2(CO)(Cl)RuC(═CHPh)O2CC6H4-p-OMe, were isolated, and the structure of both complexes was completely established by X-ray crystallography. A detailed mechanism of the coupling reaction involving a rate-limiting C−O bond formation step was proposed on the basis of these kinetic and structural studies. The regioselective formation of the gem-enol ester products in CH2Cl2 was rationalized by a direct migratory insertion of the terminal alkyne via a Ru-carboxylate species, whereas the stereoselective formation of (Z)-enol ester products in THF was explained by invoking a Ru-vinylidene species

Simple Theoretical Models for Resonant Cold Atom Interactions

Magnetically tunable scattering resonances have been used with great success for precise control of s-wave scattering lengths in ultracold atomic collisions. We describe relatively simple yet quite powerful analytic treatments of such resonances based on the analytic properties of the van der Waals long range potential. This theory can be used to characterize a number of properties of specific resonances that have been used successfully in various experiments with $^{87}$Rb, $^{85}$Rb, $^{40}$K, and $^{6}$Li. Optical Feshbach resonances are also possible and may be practical with narrow intercombination line photoassociative transitions in species like Sr and Yb.Comment: To be published in the Proceedings of the 20th International Conference on Atomic Physics, held in Innsbruck, Austria, July 200

Modeling and analysis of the variability of the water cycle in the upper Rio Grande basin at high resolution

Estimating the water budgets in a small-scale basin is a challenge, especially in the mountainous western United States, where the terrain is complex and observational data in the mountain areas are sparse. This manuscript reports on research that downscaled 5-yr (1999-2004) hydrometeorological fields over the upper Rio Grande basin from a 2.5° NCEP-NCAR reanalysis to a 4-km local scale using a regional climate model [fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5), version 3]. The model can reproduce the terrain-related precipitation distribution - the trend of diurnal, seasonal, and interannual precipitation variability - although poor snow simulation caused it to overestimate precipitation and evapotranspiration in the cold season. The outcomes from the coupled model are also comparable to offline Variable Infiltration Capacity (VIC) and Land Data Assimilation System (LDAS)/Mosaic land surface simulations that are driven by observed and/or analyzed surface meteorological data. © 2007 American Meteorological Society

Modeling intraseasonal features of 2004 North American monsoon precipitation

This study examines the capabilities and limitations of the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5) in predicting the precipitation and circulation features that accompanied the 2004 North American monsoon (NAM). When the model is reinitialized every 5 days to restrain the growth of modeling errors, its results for precipitation checked at subseasonal time scales (not for individual rainfall events) become comparable with ground- and satellite-based observations as well as with the NAM's diagnostic characteristics. The modeled monthly precipitation illustrates the evolution patterns of monsoon rainfall, although it underestimates the rainfall amount and coverage area in comparison with observations. The modeled daily precipitation shows the transition from dry to wet episodes on the monsoon onset day over the Arizona-New Mexico region, and the multiday heavy rainfall (>1 mm day-1) and dry periods after the onset. All these modeling predictions agree with observed variations. The model also accurately simulated the onset and ending dates of four major moisture surges over the Gulf of California during the 2004 monsoon season. The model reproduced the strong diurnal variability of the NAM precipitation, but did not predict the observed diurnal feature of the precipitation peak's shift from the mountains to the coast during local afternoon to late night. In general, the model is able to reproduce the major, critical patterns and dynamic variations of the NAM rainfall at intraseasonal time scales, but still includes errors in precipitation quantity, pattern, and timing. The numerical study suggests that these errors are due largely to deficiencies in the model's cumulus convective parameterization scheme, which is responsible for the model's precipitation generation. © 2007 American Meteorological Society