Quantitative Derivation of the Gross‐Pitaevskii Equation

Starting from first‐principle many‐body quantum dynamics, we show that the dynamics of Bose‐Einstein condensates can be approximated by the time‐dependent nonlinear Gross‐Pitaevskii equation, giving a bound on the rate of the convergence. Initial data are constructed on the bosonic Fock space applying an appropriate Bogoliubov transformation on a coherent state with expected number of particles N. The Bogoliubov transformation plays a crucial role; it produces the correct microscopic correlations among the particles. Our analysis shows that, on the level of the one‐particle reduced density, the form of the initial data is preserved by the many‐body evolution, up to a small error that vanishes as N^?1/2 in the limit of large N.© 2015 Wiley Periodicals, Inc.     

The rheological properties of hydrogenated castor oil crystals

The present study focuses on the rheological performance of a surfactant-rich aqueous suspension containing hydrogenated castor oil (HCO) crystals. HCO can be typically crystallized in five distinct shapes: spherically shaped, irregularly shaped, star-shaped (also called rosettes), short needles, and thick or thin fibers. The effect of the differences in shape on the rheological performance is studied, and the rheological properties are compared to the behavior of other triacylglycerol’s (TAG) suspensions. A suspension of TAG crystals usually behaves as a colloidal gel wherein a colloidal gel is defined as a network of flocs, with each floc being an aggregate of smaller subunits. All of these surfactant-rich aqueous suspensions of HCO crystals behaved according to a colloidal gel in the transient regime, independent of the studied crystal shapes, except the long thin fibers at a concentration above 0.1 wt% HCO transitioning from a heterogeneous fractal rod network to a homogeneous rod network, shifting from a colloidal gel to a glass.     

Phase-only shaped laser pulses in optimal control theory: application to indirect photofragmentation dynamics in the weak-field limit

We implement phase-only shaped laser pulses within quantum optimal control theory for laser-molecule interaction. This approach is applied to the indirect photofragmentation dynamics of NaI in the weak-field limit. It is shown that optimized phase-modulated pulses with a fixed frequency distribution can substantially modify transient dissociation probabilities as well as the momentum distribution associated with the relative motion of Na and I.     

Intercalation of trioxatriangulenium ion in DNA: binding,electron transfer,x-ray crystallography,and electronic structure

Trioxatriangulenium ion (TOTA(+)) is a flat, somewhat hydrophobic compound that has a low-energy unoccupied molecular orbital. It binds to duplex DNA by intercalation with a preference for G-C base pairs. Irradiation of intercalated TOTA(+) causes charge (radical cation) injection that results in strand cleavage (after piperidine treatment) primarily at GG steps. The X-ray crystal structure of TOTA(+) intercalated in the hexameric duplex d[CGATCG](2) described here reveals that intercalation of TOTA(+) results in an unusually large extension of the helical rise of the DNA and that the orientation of TOTA(+) is sensitive to hydrogen-bonding interactions with backbone atoms of the DNA. Electronic structure calculations reveal no meaningful charge transfer from DNA to TOTA(+) because the lowest unoccupied molecular orbital of TOTA(+), (LUMO)(T), falls in the gap between the highest occupied molecular orbital, (HOMO)(D), and the (LUMO)(D) of the DNA bases. These calculations reveal the importance of backbone, water, and counterion interactions, which shift the energy levels of the bases and the intercalated TOTA(+) orbitals significantly. The calculations also show that the inserted TOTA(+) strongly polarizes the intercalation cavity where a sheet of excess electron density surrounds the TOTA(+).     

Sodiation of Arenes and Heteroarenes in Continuous Flow

The first sodiations of (hetero)arenes in continuous flow using NaDA (sodium diisopropylamide) in Me₂EtN are reported. This flow procedure enables sodiation of functionalized arenes and heteroarenes that decompose under batch‐sodiation conditions. The resulting sodiated (hetero)arenes react instantly with various electrophiles, such as ketones, aldehydes, isocyanates, alkyl bromides, and disulfides, affording polyfunctionalized (hetero)arenes in high yields. Scale‐up is possible without further optimization.