Relative entropy and hydrodynamics of Ginzburg-Landau models

We prove the hydrodynamic limit of Ginzburg-Landau models by considering relative entropy and its rate of change with respect to local Gibbs states. This provides a new understanding of the role played by relative entropy in the hydrodynamics of interacting particle systems.Work partially supported by U.S. National Science Foundation Grant. DMS-8806731 and Army Grant ARO-DAAL 03-88-K-0047.     

Regularity ofp-energy minimizing maps andp-superstrongly unstable indices

We derive the first and the second variational formulas forp-energy functional on maps between Riemannian manifolds, obtain a Bochner formula with related estimates and discuss Liouville-type theorems and the regularity ofp-minimizers. In particular, via an extrinsic average variational method,p-superstrongly unstable manifolds and indices are found and their role in the regularity theory is established.     

Gradient estimates,Harnack inequalities and estimates for heat kernels of the sum of squares of vector fields

Research partially supported by NSF grant no. DMS-87-04209 and DMS-90-04062     

An efficient synthesis of an alphavbeta3 antagonist

A practical preparation of an alpha(v)beta(3) antagonist is reported. The antagonist consists of three key components, a tetrahydronaphthyridine moiety, a beta-alanine moiety, and a central imidazolidone moiety. The tetrahydronaphthyridine component was prepared using two different methods, both of which relied on variations of the Friedl?nder reaction to establish the desired regiochemistry. The beta-alanine component was prepared using Davies' asymmetric 1,4-addition methodology as the key stereo-defining step. The central imidazolidone portion was created from these two components using an effective three-step cyclization protocol. Thus, a highly convergent process for the drug candidate was defined.     

1,3-dialkylimidazolium-based room-temperature ionic liquids as background electrolyte and coating material in aqueous capillary electrophoresis

The 1-ethyl-3-methylimidazolium (EMIM) cation was found to have constant mobility of 4.5 x 10(-4) cm2 V(-1) s(-1) over the pH range of 3 to 11. The electroosmotic flow of bare silica capillary was reversed by the covalently bonded room-temperature ionic liquid (RTIL) coating. With run buffer of 5 mM EMIM (pH 8.5), NH4+ in human urine was separated from the K+ matrix and was detected to be 0.37 +/- 0.012%. K+, Na+, Li+, Ca2+, Mg2+ and Ba2+ were baseline separated in RTIL-coated capillary with run buffer of 10 mM EMIMOH-acetic acid at pH 5, and the concentration of the above ions in a red wine were detected to be 907, 27.9, 0, 71.0, 83.4 and 31.1 microg/ml, respectively. The RTIL-coated capillary showed stable electroosmotic flow for at least 80 h in the run buffer.     

Electrophoresis of DNA in ionic liquid coated capillary

An ionic liquid (IL) coated capillary was prepared and investigated for DNA separation. The electroosmotic flow of the capillary was reversed between pH 4.5 and 9. Below 900 base pairs the larger DNA fragment suffered more retardation in the IL coated capillary due to the increasing charge density of the fragment with size. In the presence of 4% hydroxyethylcellulose, the phiX174 DNA-Hae III digest fragments were baseline separated in both IL- and polyacrylamide-coated capillary except for the fragments of 271 and 281 base pairs; while the analysis time was shorter in the IL-coated capillary. Our experiments indicated that the IL-coated capillary could work stably in the run buffer for at least 96 h with no notable deterioration in performance.     

Transient resonance Raman and density functional theory investigation of the 4-acetamidophenylnitrenium ion

This paper reports a transient resonance Raman and density functional theory study of the 4-acetamidophenylnitrenium ion in a mostly aqueous solvent. The transient Raman bands combined with results from density functional theory calculations indicate that the spectrum should be assigned to the singlet state of the 4-acetamidophenylnitrenium ion. The 4-acetamidophenylnitrenium ion was found to have a substantial iminocyclohexadienyl character comparable to previously studied para-phenyl-substituted phenylnitrenium ions and noticeable charge on both the acetamido and nitrenium moieties. The structure and properties of the 4-acetamidophenylnitrenium ion are compared to those of other arylnitrenium ions. We briefly discuss the chemical reactivity and selectivity of the para-acetamido-substituted phenylnitrenium ions compared to para-phenyl- or para-alkoxy-substituted phenylnitrenium ions.     

Equivalences between isolated hypersurface singularities

Research by this author supported in part by N.S.F. Grant No. DMS-84114477     

Energy extraction of Porro resonator in Pockels cell Q-switch operation

Deviation of a practical Pockels cell Q-switch bias voltage from the ideal bias value significantly affects the extraction of useful output energy. The losses of two practical bias voltages are calculated and the properly rotated angle towards the right-hand side prism of the Porro resonator is determined to simulate the different losses. The losses are due to deviation of the Q-switch bias voltage from the ideal value. It not only degrades the useful output energy, but introduces a useless energy loss in the reverse output direction. For the different losses of these two practical Pockels cell bias voltages, the useful output energy difference is about 30%. The useful output energy and lost energy ratios of the two equivalent loss configurations are 0.54 and 0.89, respectively. These ratios agreed quite well with the theoretical results.