Creating ground state molecules with optical feshbach resonances in tight traps

We propose to create ultracold ground state molecules in an atomic Bose-Einstein condensate by adiabatic crossing of an optical Feshbach resonance. We envision a scheme where the laser intensity and possibly also frequency are linearly ramped over the resonance. Our calculations for (87)Rb show that for sufficiently tight traps it is possible to avoid spontaneous emission while retaining adiabaticity, and conversion efficiencies of up to 50% can be expected.     

Quick synthesis of lipid-polymer hybrid nanoparticles with low polydispersity using a single-step sonication method

Lipid-polymer hybrid nanoparticle, consisting of a hydrophobic polymeric core and a lipid monolayer shell, represents a new and promising drug delivery platform that has shown controllable particle size and surface functionality, high drug loading yield, sustained drug release profile, and excellent in vitro and in vivo stability. These lipid monolayer-coated polymeric nanoparticles are typically fabricated through a modified nanoprecipitation method, which involves sample heating, vortexing, and solvent evaporation. Herein we report a new and fast method to synthesize lipid-polymer hybrid nanoparticles with controllable and nearly uniform particle size. Using a bath sonication approach, we demonstrate that the whole hybrid nanoparticle synthesis process can be completed in about 5 min compared with a few hours for previous synthesis approaches. The size and polydispersity of the resulting nanoparticles can be readily controlled by tuning the relative concentrations of individual building components. Colloidal stability tests of the synthesized hybrid nanoparticles in PBS buffer and serum show no signs of aggregation over a period of 5 days. The present method improves the production rate of the hybrid nanoparticles by near 20-fold while not compromising the physicochemical properties of the particles. This work may facilitate the bench-to-bedside translation of lipid-polymer hybrid nanoparticles as a robust drug nanocarrier by allowing for fabricating a large amount of these nanoparticles at high production rate.     

On the maslov index

In this paper we give four definitions of Maslov index and show that they all satisfy the same system of axioms and hence are equivalent to each other. Moreover, relationships of several symplectic and differential geometric, analytic, and topological invariants (including triple Maslov indices, eta invariants, spectral flow and signatures of quadratic forms) to the Maslov index are developed and formulae relating them are given. The broad presentation is designed with a view to applications both in geometry and in analysis. © 1994 John Wiley & Sons, Inc.     

Representing homology classes by locally flat 2-spheres

We prove an existence result for topologically locally flat embeddings of 2-spheres in simply connected 4-manifolds. This topological result is deduced from a splitting theorem for pointed Hermitian modules over a cyclic group ring. A stability result for such modules is also proved. This applies to the isotopy classification of locally flat embeddings.Partially supported by the NSF.     

Improved convergence in orbital localization methods

A new method for choosing the rotation angle in the usual indirect localization procedure consisting of the iterative use of 2 × 2 rotation matrices is suggested. Calculations reported here obtaining the localized orbitals of the water molecule show this new method to converge much more quickly and to a significantly better numerical value of the localization criterion than previous methods.