Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall

The locomotion of microorganisms and tiny artificial swimmers is governed by low-Reynolds-number hydrodynamics, where viscous effects dominate and inertial effects are negligible. While the theory of low-Reynolds-number locomotion is well studied for unbounded fluid domains, the presence of a boundary has a significant influence on the swimmer’s trajectories and poses problems of dynamic stability of its motion. In this paper we consider a simple theoretical model of a microswimmer near a wall, study its dynamics, and analyze the stability of its motion. We highlight the underlying geometric structure of the dynamics, and establish a relation between the reversing symmetry of the system and existence and stability of periodic and steady solutions of motion near the wall. The results are demonstrated by numerical simulations and validated by motion experiments with macroscale robotic swimmer prototypes

Progenitor constraints on the Type-Ia supernova SN2011fe from pre-explosion Hubble Space Telescope HeII narrow-band observations

We present Hubble Space Telescope (HST) imaging observations of the site of the Type-Ia supernova SN2011fe in the nearby galaxy M101, obtained about one year prior to the event, in a narrow band centred on the HeII 4686 \AA{} emission line. In a "single-degenerate" progenitor scenario, the hard photon flux from an accreting white dwarf (WD), burning hydrogen on its surface over $\sim1$ Myr should, in principle, create a HeIII Str\"{o}mgren sphere or shell surrounding the WD. Depending on the WD luminosity, the interstellar density, and the velocity of an outflow from the WD, the HeIII region could appear unresolved, extended, or as a ring, with a range of possible surface brightnesses. We find no trace of HeII 4686 \AA{} line emission in the HST data. Using simulations, we set $2\sigma$ upper limits on the HeII 4686 \AA{} luminosity of $L_{\rm HeII} < 3.4 \times 10^{34}$ erg s$^{-1}$ for a point source, corresponding to an emission region of radius $r < 1.8$ pc. The upper limit for an extended source is $L_{\rm HeII} < 1.7 \times 10^{35}$ erg s$^{-1}$, corresponding to an extended region with $r\sim11$ pc. The largest detectable shell, given an interstellar-medium density of 1 cm$^{-3}$, has a radius of $\sim6$ pc. Our results argue against the presence, within the $\sim10^5$ yr prior to the explosion, of a supersoft X-ray source of luminosity $L_{\rm bol} \ge 3 \times 10^{37}$ erg s$^{-1}$, or of a super-Eddington accreting WD that produces an outflowing wind capable of producing cavities with radii of 2-6 pc.Comment: Accepted by MNRAS Letters; revised version following referee report and readers' comment

Deep Functional Maps: Structured Prediction for Dense Shape Correspondence

We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input shapes. We propose a paradigm shift and design a structured prediction model in the space of functional maps, linear operators that provide a compact representation of the correspondence. We model the learning process via a deep residual network which takes dense descriptor fields defined on two shapes as input, and outputs a soft map between the two given objects. The resulting correspondence is shown to be accurate on several challenging benchmarks comprising multiple categories, synthetic models, real scans with acquisition artifacts, topological noise, and partiality.Comment: Accepted for publication at ICCV 201