Little Tots, Forget - Me - Nots : Motion Song For A Group Of Children

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A geometric perspective on the τ\tau-cluster morphism category

We show how the $\tau$-cluster morphism category may be defined in terms of the wall-and-chamber structure of an algebra. This geometric perspective leads to a simplified proof that the category is well-defined.Comment: 20 pages, 5 figures. Comments welcome! v2: added a little more discussio

Capillary deformations of bendable films

We address the partial wetting of liquid drops on ultrathin solid sheets resting on a deformable foundation. Considering the membrane limit of sheets that can relax compression through wrinkling at negligible energetic cost, we revisit the classical theory for the contact of liquid drops on solids. Our calculations and experiments show that the liquid-solid-vapor contact angle is modified from the Young angle, even though the elastic bulk modulus (E) of the sheet is so large that the ratio between the surface tension γ and E is of molecular size. This finding establishes a new type of “soft capillarity” that stems from the bendability of thin elastic bodies rather than from material softness. We also show that the size of the wrinkle pattern that emerges in the sheet is fully predictable, thus resolving a puzzle noticed in several previous attempts to model “drop-on-a-floating-sheet” experiments, and enabling a reliable usage of this setup for the metrology of ultrathin films

Liquid Transport Due to Light Scattering

Using experiments and theory, we show that light scattering by inhomogeneities in the index of refraction of a fluid can drive a large-scale flow. The experiment uses a near-critical, phase-separated liquid, which experiences large fluctuations in its index of refraction. A laser beam traversing the liquid produces a large-scale deformation of the interface and can cause a liquid jet to form. We demonstrate that the deformation is produced by a scattering-induced flow by obtaining good agreements between the measured deformations and those calculated assuming this mechanism.Comment: 4 pages, 5 figures, submitted to Physical Review Letters v2: Edited based on comments from referee

A circular order on edge-coloured trees and RNA m-diagrams

We study a circular order on labelled, m-edge-coloured trees with k vertices, and show that the set of such trees with a fixed circular order is in bijection with the set of RNA m-diagrams of degree k, combinatorial objects which can be regarded as RNA secondary structures of a certain kind. We enumerate these sets and show that the set of trees with a fixed circular order can be characterized as an equivalence class for the transitive closure of an operation which, in the case m=3, arises as an induction in the context of interval exchange transformations.Comment: 15 pages, 7 figures. New title. Shortened version, presenting the results more efficientl

A geometric perspective on the ττ-cluster morphism category

We show how the $\tau$-cluster morphism category may be defined in terms of the wall-and-chamber structure of an algebra. This geometric perspective leads to a simplified proof that the category is well-defined

The geometry of Brauer graph algebras and cluster mutations.

In this paper we establish a connection between ribbon graphs and Brauer graphs. As a result, we show that a compact oriented surface with marked points gives rise to a unique Brauer graph algebra up to derived equivalence. In the case of a disc with marked points we show that a dual construction in terms of dual graphs exists. The rotation of a diagonal in an m-angulation gives rise to a Whitehead move in the dual graph, and we explicitly construct a tilting complex on the related Brauer graph algebras reflecting this geometrical move

Nanoscale atomic waveguides with suspended carbon nanotubes

We propose an experimentally viable setup for the realization of one-dimensional ultracold atom gases in a nanoscale magnetic waveguide formed by single doubly-clamped suspended carbon nanotubes. We show that all common decoherence and atom loss mechanisms are small guaranteeing a stable operation of the trap. Since the extremely large current densities in carbon nanotubes are spatially homogeneous, our proposed architecture allows to overcome the problem of fragmentation of the atom cloud. Adding a second nanowire allows to create a double-well potential with a moderate tunneling barrier which is desired for tunneling and interference experiments with the advantage of tunneling distances being in the nanometer regime.Comment: Replaced with the published version, 7 pages, 3 figure

Impact of a Viscous Liquid Drop

We simulate the impact of a viscous liquid drop onto a smooth dry solid surface. As in experiments, when ambient air effects are negligible, impact flattens the falling drop without producing a splash. The no-slip boundary condition at the wall produces a boundary layer inside the liquid. Later, the flattening surface of the drop traces out the boundary layer. As a result, the eventual shape of the drop is a "pancake" of uniform thickness except at the rim, where surface tension effects are significant. The thickness of the pancake is simply the height where the drop surface first collides with the boundary layer.Comment: 5 pages, 3 figures, submitted to Physical Review Letter