There is no continuous projection from the measurable functions on the square onto the measurable functions on the interval

It is proved that the space of functions constant on vertical lines is not complemented in the space of all measurable functions on the unit square (with the topology of convergence in measure). The analogous results is proved for the space of all measurable functions on the product of two probability spaces, one of which is atomless. This research was partially supported by National Science Foundation grant N.S.F. GP 28577.     

Drag reduction in bubbly Taylor-Couette turbulence

In Taylor-Couette flow the total energy dissipation rate and therefore the drag can be determined by measuring the torque on the system. We do so for Reynolds numbers between Re=7 x 10(4) and Re=10(6) after having injected (i) small bubbles (R=1 mm) up to a volume concentration of alpha=5% and (ii) buoyant particles (rhop/rhol=0.14) of comparable volume concentration. In case (i) we observe a crossover from little drag reduction at smaller Re to strong drag reduction up to 20% at Re=10(6). In case (ii) we observe at most little drag reduction throughout. Several theoretical models for bubbly drag reduction are discussed in view of our findings.     

Strongly accelerated and humidity-independent drying of nanochannels induced by sharp corners

Measurements are shown indicating that the drying rate of nanochannels can be enhanced by up to 3 orders of magnitude relative to drying by vapor diffusion, and that the drying rate is independent of the relative humidity of the environment up to a relative humidity of more than 90%. Micromachined Pyrex glass nanochannels of 72 nm height and with sharp corners (corner angles 7 degrees) were used. Available theory shows that the sharp corners function as a low-resistance pathway for liquid water, siphoning (wicking) the water to a location close to the channel exit before it evaporates. The described phenomena are of importance for the understanding of drying processes in industry and agriculture. The introduction of sharp corners or grooves can furthermore be beneficial for the functioning of microheat pipes and capillary-pumped loops.     

Femtosecond optical vortices in air

We examine the robustness of ultrashort optical vortices propagating freely in the atmosphere. We first approximate the stability regions of femtosecond spinning pulses as a function of their topological charge. Next, we numerically demonstrate that atmospheric optical vortices are capable of conveying high power levels in air over hundreds of meters before they break up into filaments.     

Interaction of femtosecond light filaments with obscurants in aerosols

The interaction of ultrashort laser pulses with opaque droplets in the atmosphere is examined numerically. Intense filaments resulting from the balance between self-focusing and ionization of air molecules are shown to be robust against obscurants sized up to 2/3 of the filament diameter. (3D+1)-dimensional numerical simulations confirm recent experimental data [F. Courvoisier et al., Appl. Phys. Lett. 83, 213 (2003)]. The filament is rapidly rebuilt with minimal loss of energy over a few cm after the interaction region. The replenishment of the pulse mainly proceeds from the nonlinear attractor responsible for the formation of a spatial soliton modeling the filament core.     

Stereochemical variations on the colchicine motif. Peracid oxidation of thiocolchicone. Synthesis, conformation and inhibition of microtubule assembly

When 7-oxodesacetamidothiocolchicine (1) was treated with various peroxides in order to afford a Baeyer-Villiger rearrangement, a complex mixture of products was formed, which included the sulfoxide, (2) and sulfone, (3). When peracetic acid was used two additional products were formed; a C-ring lactone (4) and a ring-contracted allocolchicine derivative (5). The sulfoxide (2) was semi-preparatively resolved into enantiomers by chromatography on microcrystalline triacetylcellulose. Rotational barriers around the A-C pivot bond of, and were determined by dynamic 1H NMR analysis. The compounds, and exhibit moderate inhibition of tubulin polymerization, according to in vitro turbidity studies, whereas was inactive.     

A simple approach to sensor discovery and fabrication on self-assembled monolayers on glass

Self-assembled monolayers (SAMs) on glass were used as a platform to sequentially deposit fluorophores and small molecules for ion sensing. The preorganization provided by the surface avoids the need for complex receptor design, allowing for a combinatorial approach to sensing systems based on small molecules. The resulting libraries are easily measured and show varied responses to a series of both cations and anions. This technology is transferable from the macro- to the microscale both via microcontact printing (microCP), where the fluorophore is printed onto a glass surface, and via direct attachment of the fluorophore to microchannel walls. The ease of miniaturization of this technology may make the generation of a wide variety of simple yet efficient microarrays possible.