Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of $N$ fluids with arbitrary viscosities, thicknesses, densities, and surface tension
s in both the Stokes regime and for the full Navier--Stokes problem. Generalizing previous work by Tomotika (N=2), Stone & Brenner (N=3, equal viscosities) and others, we present a full linear stability analysis of the growth modes and rates, reducing the system to a linear generalized eigenproblem in the Stokes case. Furthermore, we demonstrate by Plateau-style geometrical arguments that only axisymmetric instabilities need be considered. We show that the N=3 case is already sufficient to obtain several interesting phenomena: limiting cases of thin shells or low shell viscosity that reduce to N=2 problems, and a system with competing breakup processes at very different length scales. The latter is demonstrated with full 3-dimensional Stokes-flow simulations. Many $N > 3$ cases remain to be explored, and as a first step we discuss two illustrative $N to infty$ cases, an alternating-layer structure and a geometry with a continuously varying viscosity.
Recent experimental observations have demonstrated interesting instability phenomenon during thermal drawing of microstructured glass/polymer fibers, and these observations motivate us to examine surface-tension-driven instabilities in concentric cyl
indrical shells of viscous fluids. In this paper, we focus on a single instability mechanism: classical capillary instabilities in the form of radial fluctuations, solving the full Navier--Stokes equations numerically. In equal-viscosity cases where an analytical linear theory is available, we compare to the full numerical solution and delineate the regime in which the linear theory is valid. We also consider unequal-viscosity situations (similar to experiments) in which there is no published linear theory, and explain the numerical results with a simple asymptotic analysis. These results are then applied to experimental thermal drawing systems. We show that the observed instabilities are consistent with radial-fluctuation analysis, but cannot be predicted by radial fluctuations alone---an additional mechanism is required. We show how radial fluctuations alone, however, can be used to analyze various candidate material systems for thermal drawing, clearly ruling out some possibilities while suggesting others that have not yet been considered in experiments.
Excited states of $^{38}_{17}$Cl$_{21}$ were populated in grazing reactions during the interaction of a beam of $^{36}_{16}$S$_{20}$ ions of energy 215 MeV with a $^{208}_{82}$Pb$_{126}$ target. The combination of the PRISMA magnetic spectrometer and
the CLARA $gamma$-ray detector array was used to identify the reaction fragments and to detect their decay via $gamma$-ray emission. A level scheme for $^{38}$Cl is presented with tentative spin and parity assignments. The level scheme is discussed within the context of the systematics of neighboring nuclei and is compared with the results of state-of-the-art shell model calculations.
A set of exact closed-form Bloch-state solutions to the stationary Gross-Pitaevskii equation are obtained for a Bose-Einstein condensate in a one-dimensional periodic array of quantum wells, i.e. a square-well periodic potential. We use these exact s
olutions to comprehensively study the Bloch band, the compressibility, effective mass and the speed of sound as functions of both the potential depth and interatomic interaction. According to our study, a periodic array of quantum wells is more analytically tractable than the sinusoidal potential and allows an easier experimental realization than the Kronig-Penney potential, therefore providing a useful theoretical model for understanding Bose-Einstein condensates in a periodic potential.
The speed of sound of a Bose-Einstein condensate in an optical lattice is studied both analytically and numerically in all three dimensions. Our investigation shows that the sound speed depends strongly on the strength of the lattice. In the one-dime
nsional case, the speed of sound falls monotonically with increasing lattice strength. The dependence on lattice strength becomes much richer in two and three dimensions. In the two-dimensional case, when the interaction is weak, the sound speed first increases then decreases as the lattice strength increases. For the three dimensional lattice, the sound speed can even oscillate with the lattice strength. These rich behaviors can be understood in terms of compressibility and effective mass. Our analytical results at the limit of weak lattices also offer an interesting perspective to the understanding: they show the lattice component perpendicular to the sound propagation increases the sound speed while the lattice components parallel to the propagation decreases the sound speed. The various dependence of the sound speed on the lattice strength is the result of this competition.
