Surface Waves on a Semi-toroidal Water Ring

We study the dynamics of surface waves on a semi-toroidal ring of water that is excited by vertical vibration. We create this specific fluid volume by patterning a glass plate with a hydrophobic coating, which confines the fluid to a precise geometric region. To excite the system, the supporting plate is vibrated up and down, thus accelerating and decelerating the fluid ring along its toroidal axis. When the driving acceleration is sufficiently high, the surface develops a standing wave, and at yet larger accelerations, a traveling wave emerges. We also explore frequency dependencies and other geometric shapes of confinement

Linear oscillations of a compressible hemispherical bubble on a solid substrate

The linear natural and forced oscillations of a hemispherical bubble on a solid substrate are under theoretical consideration. The contact line dynamics is taken into account with the Hocking condition, which eventually leads to interaction of the shape and volume oscillations. Resonant phenomena, mostly pronounced for the bubble with the fixed contact line or with the fixed contact angle, are found out. The limiting case of weakly compressible bubble is studied. The general criterion identifying whether the compressibility of a bubble can be neglected is obtained.Comment: new slightly extended version with some minor changes, added journal reference and DOI information; 12 pages, 8 figures, published in Physics of Fluid

Exploration of finite dimensional Kac algebras and lattices of intermediate subfactors of irreducible inclusions

We study the four infinite families KA(n), KB(n), KD(n), KQ(n) of finite dimensional Hopf (in fact Kac) algebras constructed respectively by A. Masuoka and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of coideal subalgebras. We reduce the study to KD(n) by proving that the others are isomorphic to KD(n), its dual, or an index 2 subalgebra of KD(2n). We derive many examples of lattices of intermediate subfactors of the inclusions of depth 2 associated to those Kac algebras, as well as the corresponding principal graphs, which is the original motivation. Along the way, we extend some general results on the Galois correspondence for depth 2 inclusions, and develop some tools and algorithms for the study of twisted group algebras and their lattices of coideal subalgebras. This research was driven by heavy computer exploration, whose tools and methodology we further describe.Comment: v1: 84 pages, 13 figures, submitted. v2: 94 pages, 15 figures, added connections with Masuoka's families KA and KB, description of K3 in KD(n), lattices for KD(8) and KD(15). v3: 93 pages, 15 figures, proven lattice for KD(6), misc improvements, accepted for publication in Journal of Algebra and Its Application

Open string theory and planar algebras

In this note we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real rational functions. These moduli spaces appear naturally in the formulation of open string theory on the projective line. We also show two geometric ways to obtain planar algebras from real algebraic geometry, one based on string topology and one on Gromov-Witten theory. In particular, through the well known relation between planar algebras and subfactors, these results establish a connection between open string theory, real algebraic geometry, and subfactors of von Neumann algebras.Comment: 13 pages, LaTeX, 7 eps figure

Theoretical and Experimental Study of the Vibration of Axisymmetric Viscous Liquid Bridges

n this paper the dynamics of axisymmetric liquid columns held by capillary forces between two circular, concentric, solid disks is considered. The problem has been solved by using a one‐dimensional model known in the literature as the Cosserat model, which includes viscosity effects, where the axial velocity is considered constant in each section of the liquid bridge. The dynamic response of the bridge to an excitation consisting of a small‐amplitude vibration of the supporting disks has been solved by linearizing the Cosserat model. It has been assumed that such excitation is harmonic so that the analysis has been performed in the frequency domain. The particular case of a cylindrical liquid bridge has been analytically studied and the transfer function has been calculated in the cases of oscillation of both disks (either in phase or in counterphase) or only of one of them. The resolution of the general formulation for a noncylindrical liquid bridge has been numerically made by using an implicit finite difference method. In this case, the influence of the volume of the liquid column and of the residual gravity level on the first resonance has been studied, and the results compared, for the inviscid case, with other potential models, both one and three dimensional. To demonstrate the usefulness of this theoretical model in predicting the vibrational behavior of axisymmetric viscous liquid bridges, some experiments have been performed by using the neutral buoyancy technique (also known as the Plateau technique) to simulate reduced gravity conditions, with good agreement between the results of the model and experiments

Evolutionary Mechanisms of Long-Term Genome Diversification Associated With Niche Partitioning in Marine Picocyanobacteria.

Marine picocyanobacteria of the genera Prochlorococcus and Synechococcus are the most abundant photosynthetic organisms on Earth, an ecological success thought to be linked to the differential partitioning of distinct ecotypes into specific ecological niches. However, the underlying processes that governed the diversification of these microorganisms and the appearance of niche-related phenotypic traits are just starting to be elucidated. Here, by comparing 81 genomes, including 34 new Synechococcus, we explored the evolutionary processes that shaped the genomic diversity of picocyanobacteria. Time-calibration of a core-protein tree showed that gene gain/loss occurred at an unexpectedly low rate between the different lineages, with for instance 5.6 genes gained per million years (My) for the major Synechococcus lineage (sub-cluster 5.1), among which only 0.71/My have been fixed in the long term. Gene content comparisons revealed a number of candidates involved in nutrient adaptation, a large proportion of which are located in genomic islands shared between either closely or more distantly related strains, as identified using an original network construction approach. Interestingly, strains representative of the different ecotypes co-occurring in phosphorus-depleted waters (Synechococcus clades III, WPC1, and sub-cluster 5.3) were shown to display different adaptation strategies to this limitation. In contrast, we found few genes potentially involved in adaptation to temperature when comparing cold and warm thermotypes. Indeed, comparison of core protein sequences highlighted variants specific to cold thermotypes, notably involved in carotenoid biosynthesis and the oxidative stress response, revealing that long-term adaptation to thermal niches relies on amino acid substitutions rather than on gene content variation. Altogether, this study not only deciphers the respective roles of gene gains/losses and sequence variation but also uncovers numerous gene candidates likely involved in niche partitioning of two key members of the marine phytoplankton