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.     

Ultimate state of thermal convection

The ultimate regime of thermal convection, the so-called Kraichnan regime [R. H. Kraichnan, Phys. Fluids 5, 1374 (1962)]], hitherto has been elusive. Here numerical evidence for that regime is presented by performing simulations of the bulk of turbulence only, eliminating the thermal and kinetic boundary layers and replacing them with periodic boundary conditions.     

Nonnegatively Curved Metrics on S 2 × ℝ2

We classify the complete metrics of nonnegative sectional curvature on M ² × ², where M ² is any compact 2-manifold.     

Solvability of second-order left-invariant differential operators on the Heisenberg group satisfying a cone condition

We discuss local solvability of operators of the form where theV _j are left-invariant vector fields on the Heisenberg group such that [V _j ,V _j+n ]=U for 1≤j≤n andA=(a _jk )=A ₁+iA ₂ is a complex symmetric matrix satisfying the “cone condition” |A ₂|≤CA ₁. The authors acknowledge the support for this work by the European Commission through the European HCM-program “Fourier Analysis” and the TMR network “Harmonic Analysis”.     

Local solvability for positive combinations of generalized sub-Laplacians on the Heisenberg group

As one step in a program to understand local solvability of complex coefficient second order differential operators on the Heisenberg group in a complete way, solvability of operators of the form , where the leading term is a ``positive combination of generalized and degenerate generalized sub-Laplacians', has been studied in a recent article by M. Peloso, F. Ricci and the first-named author (J. Reine Angew Math. 513 (1999)). It was shown that there exists a discrete set of ``critical' values , such that solvability holds for . The case remained open, and it is the purpose of this note to close this gap. Our results extend corresponding results in another article by the above-mentioned authors (J. Funct. Anal. 148 (1997)), by means of an even simplified approach which should allow for further generalizations.

     

Uptake of magnetic nanoparticles into cells for cell tracking

A challenge for future applications in nanotechnology is the functional integration of nano-sized materials into cellular structures. Here we investigated superparamagnetic Fe₃O₄ iron oxide nanoparticles coated with a lipid bilayer for uptake into cells and for targeting subcellular compartments. It was found that magnetic nanoparticles (MNPs) are effectively taken up into cells and make cells acquire magnetic activity. Biotin-conjugated MNPs were further functionalized by binding of the fluorescent tag streptavidin–fluorescein isothiocyanate (FITC) and, following uptake into cells, shown to confer magnetic activity and fluorescence labeling. Such FITC-MNPs were localized in the lysosomal compartment of cells which suggests a receptor-mediated uptake mechanism.     

Short range order in the isotropic phase of antiferroelectric liquid crystals

Optical activity measurements in the isotropic phase of two antiferroelectric liquid crystal systems in which the chirality can be varied reveal unusual behaviour of the short range order. In one system the phase sequence as the chirality is increased is smectic A, smectic C^*_A, and smectic Q. In the other system the phase sequence is smectic C^*, smectic C^*_A, and smectic Q as the chirality is increased. The short range order of the isotropic phase behaves similarly for these systems, showing mean field behaviour at low chirality and far above the phase transition, but deviating from this behaviour significantly as the chirality is increased and the phase transition is approached. These optical activity results indicate how different is the short range order in the isotropic phase for these antiferroelectric liquid crystal systems and demonstrates the crucial role played by chirality. Past theoretical work that includes smecticlike fluctuations in the calculation of short range order in the isotropic phase is capable of qualitatively explaining these results.