Hydrodynamic friction of fakir-like super-hydrophobic surfaces

A fluid droplet located on a super-hydrophobic surface makes contact with the surface only at small isolated regions, and is mostly in contact with the surrounding air. As a result, a fluid in motion near such a surface experiences very low friction, and super-hydrophobic surfaces display strong drag-reduction in the laminar regime. Here we consider theoretically a super-hydrophobic surface composed of circular posts (so called fakir geometry) located on a planar rectangular lattice. Using a superposition of point forces with suitably spatially-dependent strength, we derive the effective surface slip length for a planar shear flow on such a fakir surface as the solution to an infinite series of linear equations. In the asymptotic limit of small surface coverage by the posts, the series can be interpreted as Riemann sums, and the slip length can be obtained analytically. For posts on a square lattice, our analytical results are in excellent quantitative agreement with previous numerical computations

Which canonical algebras are derived equivalent to incidence algebras of posets?

We give a full description of all the canonical algebras over an algebraically closed field that are derived equivalent to incidence algebras of finite posets. These are the canonical algebras whose number of weights is either 2 or 3.Comment: 8 pages; slight revision; to appear in Comm. Algebr

Finite-size effects in intracellular microrheology

We propose a model to explain finite-size effects in intracellular microrheology observed in experiments. The constrained dynamics of the particles in the intracellular medium, treated as a viscoelastic medium, is described by means of a diffusion equation in which interactions of the particles with the cytoskeleton are modelled by a harmonic force. The model reproduces the observed power-law behavior of the mean-square displacement in which the exponent depends on the ratio between particle-to-cytoskeleton-network sizes.Comment: 6 pages 2 figures. To appear in the Journal of Chemical Physic

Singular point characterization in microscopic flows

We suggest an approach to microrheology based on optical traps in order to measure fluid fluxes around singular points of fluid flows. We experimentally demonstrate this technique, applying it to the characterization of controlled flows produced by a set of birefringent spheres spinning due to the transfer of light angular momentum. Unlike the previous techniques, this method is able to distinguish between a singular point in a complex flow and the absence of flow at all; furthermore it permits us to characterize the stability of the singular point.Comment: 4 pages and 4 figure

Hydrodynamics of flagellated microswimmers near free-slip interfaces

The hydrodynamics of a flagellated microorganism is investigated when swimming close to a planar free-slip surface by means of numerical solu- tions of the Stokes equations obtained via a Boundary Element Method. Depending on the initial condition, the swimmer can either escape from the free-slip surface or collide with the boundary. Interestingly, the mi- croorganism does not exhibit a stable orbit. Independently of escape or attraction to the interface, close to a free-slip surface, the swimmer fol- lows a counter-clockwise trajectory, in agreement with experimental find- ings, [15]. The hydrodynamics is indeed modified by the free-surface. In fact, when the same swimmer moves close to a no-slip wall, a set of initial conditions exists which result in stable orbits. Moreover when moving close to a free-slip or a no-slip boundary the swimmer assumes a different orientation with respect to its trajectory. Taken together, these results contribute to shed light on the hydrodynamical behaviour of microorgan- isms close to liquid-air interfaces which are relevant for the formation of interfacial biofilms of aerobic bacteria

Critical Teaching Behaviors: What Does Good Teaching Look Like?

How can faculty and administrators identify and document evidence of “good” teaching? Defining “good” teaching as the implementation of evidence-based practices proven to foster success, we developed a Critical Teaching Behaviors framework consisting of six categories of observable behaviors: alignment, assessment, inclusive learning environment, student engagement, educational technology, and reflective practice. We will present an overview of the meta-analysis conducted to construct the framework, participants will then use the framework to reflect on their teaching practice before providing feedback on its design and usefulness in documenting effective teaching behaviors at their institutions

Partial synchronisation of stochastic oscillators through hydrodynamic coupling

Holographic optical tweezers are used to construct a static bistable optical potential energy landscape where a Brownian particle experiences restoring forces from two nearby optical traps and undergoes thermally activated transitions between the two energy minima. Hydrodynamic coupling between two such systems results in their partial synchronisation. This is interpreted as an emergence of higher mobility pathways, along which it is easier to overcome barriers to structural rearrangement.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Tilted algebras and short chains of modules

We provide an affirmative answer for the question raised almost twenty years ago concerning the characterization of tilted artin algebras by the existence of a sincere finitely generated module which is not the middle of a short chain