Centerlines of regions in the sphere

Given a region U in the 2-sphere S such that the boundary of U contains at least two points, let D(U) be the collection of open circular disks (called maximal disks) in U whose boundary meets the boundary of U in at least two points and let U₂ be the collection of all regions U⊂S such that for each D∈D(U), D meets the boundary of U in at most two points. In this paper we study geometric properties of regions U∈U₂. We show for such U that the centerline (i.e., the set of centers of maximal disks) is always a smooth, connected 1-manifold. We also show that the boundary of U has at most two components and, if it has exactly two components, then the boundary is locally connected.These results are related the set of points E(X,Y) which are equidistant to two disjoint closed sets X and Y. In particular we investigate when the equidistant set is a 1-manifold.     

Fabrication of Kidney Proximal Tubule Grafts Using Biofunctionalized Electrospun Polymer Scaffolds

The increasing prevalence of end‐stage renal disease and persistent shortage of donor organs call for alternative therapies for kidney patients. Dialysis remains an inferior treatment as clearance of large and protein‐bound waste products depends on active tubular secretion. Biofabricated tissues could make a valuable contribution, but kidneys are highly intricate and multifunctional organs. Depending on the therapeutic objective, suitable cell sources and scaffolds must be selected. This study provides a proof‐of‐concept for stand‐alone kidney tubule grafts with suitable mechanical properties for future implantation purposes. Porous tubular nanofiber scaffolds are fabricated by electrospinning 12%, 16%, and 20% poly‐ε‐caprolactone (PCL) v/w (chloroform and dimethylformamide, 1:3) around 0.7 mm needle templates. The resulting scaffolds consist of 92%, 69%, and 54% nanofibers compared to microfibers, respectively. After biofunctionalization with L‐3,4‐dihydroxyphenylalanine and collagen IV, 10 × 10⁶ proximal tubule cells per mL are injected and cultured until experimental readout. A human‐derived cell model can bridge all fiber‐to‐fiber distances to form a monolayer, whereas small‐sized murine cells form monolayers on dense nanofiber meshes only. Fabricated constructs remain viable for at least 3 weeks and maintain functionality as shown by inhibitor‐sensitive transport activity, which suggests clearance capacity for both negatively and positively charged solutes.     

Resistive transitions in Nb/Cu0.41Ni0.59/Nb trilayers

The superconducting phase transition in Nb/Cu_0.41Ni_0.59/Nb trilayers, with superconducting (S) Nb and ferromagnetic (F) Cu_0.41Ni_0.59, has been experimentally studied as a function of the F-layer thickness by measuring the temperature dependence of the electrical resistance R(T). It is shown that the shape and the width of the R(T) curves depends on the Cu_0.41Ni_0.59 thickness, in particular in the regime where π is the coupling between the S layers, which can be expected. To explain the data, we developed a qualitative model which makes the interconnection between the superconducting phase transition and the 0 to π transition in SFS structures are more evident. The text was submitted by the authors in English.     

STM imaging of flux line arrangements in the peak effect regime

We present the results of a study of vortex arrangements in the peak-effect regime of 2H-NbSe2 by scanning tunneling microscopy. By slowly increasing the temperature in a constant magnetic field, we observed a sharp transition from collective vortex motion to positional fluctuations of individual vortices at the temperature which coincides with the onset of the peak effect in ac susceptibility. We conclude that the peak effect is a disorder driven transition, with the pinning energy winning against the elastic energy.     

On analytic design of loudspeaker arrays with uniform radiation characteristics

Some notes on analytical derived loudspeaker arrays with uniform radiation characteristics are presented. The array coefficients are derived via analytical means and compared with so-called maximal flat sequences known from telecommunications and information theory. It appears that the newly derived array, i.e., the quadratic phase array, has a higher efficiency than the Bessel array and a flatter response than the Barker array. The method discussed admits generalization to the design of arrays with desired nonuniform radiating characteristics.     

Hydrodynamics of droplet coalescence

We study droplet coalescence in a molecular system with a variable viscosity and a colloid-polymer mixture with an ultralow surface tension. When either the viscosity is large or the surface tension is small enough, we observe that the opening of the liquid bridge initially proceeds at a constant speed set by the capillary velocity. In the first system we show that inertial effects become dominant at a Reynolds number of about 1.5+/- 0.5 and the neck then grows as the square root of time. In the second system we show that decreasing the surface tension by a factor of 10(5) opens the way to a more complete understanding of the hydrodynamics involved.