Linearization of Cohomology-free Vector Fields

We study the cohomological equation for a smooth vector field on a compact manifold. We show that if the vector field is cohomology free, then it can be embedded continuously in a linear flow on an Abelian group

Beewatching: A project for monitoring bees through photos

Bees play a key role in natural and agro-ecosystems and their diversity is worldwide threatened by anthropogenic causes. Despite this, there is little awareness of the existence of the numerous species of wild bees, and the common name “bee” is very often exclusively associated with Apis mellifera. Our aim was to create a citizen science project in Italy with the following objectives: (a) raising awareness of the importance and diversity of bees, (b) obtaining data on the biology, ecology and distribution of Italian species, and (c) launching the monitoring of alien bees. The first step of the project was to create a website platform with a section containing informative datasheets of the wild bee families and of the most common bee genera present in Italy, a form to send reports of observed bees and an interactive map with all citizen’s reports. During the 2 years of the project 1086 reports were sent by 269 users, with 38 Apoidea genera reported on 190 plant genera; furthermore, 22 reports regarding the alien species Megachile sculpturalis arrived. The majority of bees (34 genera) were observed on spontaneous plants, including 115 genera native to Italy. Considering the increasing number of reports and data obtained in these first two years of the project, our objectives seem to be achieved. Future steps will be to outline the profile of beewatchers, to plan activities in a more targeted way, and also to start some sub-projects for conservation purposes

A micropillar for cavity optomechanics

We present a new micromechanical resonator designed for cavity optomechanics. We have used a micropillar geometry to obtain a high-frequency mechanical resonance with a low effective mass and a very high quality factor. We have coated a 60-$\mu$m diameter low-loss dielectric mirror on top of the pillar and are planning to use this micromirror as part of a high-finesse Fabry-Perot cavity, to laser cool the resonator down to its quantum ground state and to monitor its quantum position fluctuations by quantum-limited optical interferometry

Rayleigh scattering in fused silica samples for gravitational wave detectors

Laser interferometer gravitational wave detectors require very high optical quality test masses. We report the bulk Rayleigh scattering in high quality fused silica samples. Results show that the scattering of the high quality fused silica is similar for various grades of fused silica from Heraeus. The total integrated scattering is about 0.7 ppm cm− 1at 1064 nm wavelength, which agrees with the theoretical value calculated using known fused silica parameters. All samples show Rayleigh scattering ratio inhomogeneity of ~ 4%

2D photonic-crystal optomechanical nanoresonator

We present the optical optimization of an optomechanical device based on a suspended InP membrane patterned with a 2D near-wavelength grating (NWG) based on a 2D photonic-crystal geometry. We first identify by numerical simulation a set of geometrical parameters providing a reflectivity higher than 99.8 % over a 50-nm span. We then study the limitations induced by the finite value of the optical waist and lateral size of the NWG pattern using different numerical approaches. The NWG grating, pierced in a suspended InP 265 nm-thick membrane, is used to form a compact microcavity involving the suspended nano-membrane as end mirror. The resulting cavity has a waist size smaller than 10 $\mu$m and a finesse in the 200 range. It is used to probe the Brownian motion of the mechanical modes of the nanomembrane

Symbolic approach and induction in the Heisenberg group

We associate a homomorphism in the Heisenberg group to each hyperbolic unimodular automorphism of the free group on two generators. We show that the first return-time of some flows in "good" sections, are conjugate to niltranslations, which have the property of being self-induced.Comment: 18 page

High flux polarized gamma rays production: first measurements with a four-mirror cavity at the ATF

The next generation of e+/e- colliders will require a very intense flux of gamma rays to allow high current polarized positrons to be produced. This can be achieved by converting polarized high energy photons in polarized pairs into a target. In that context, an optical system consisting of a laser and a four-mirror passive Fabry-Perot cavity has recently been installed at the Accelerator Test Facility (ATF) at KEK to produce a high flux of polarized gamma rays by inverse Compton scattering. In this contribution, we describe the experimental system and present preliminary results. An ultra-stable four-mirror non planar geometry has been implemented to ensure the polarization of the gamma rays produced. A fiber amplifier is used to inject about 10W in the high finesse cavity with a gain of 1000. A digital feedback system is used to keep the cavity at the length required for the optimal power enhancement. Preliminary measurements show that a flux of about $4\times10^6 \gamma$/s with an average energy of about 24 MeV was generated. Several upgrades currently in progress are also described

Investigation of mechanical losses of thin silicon flexures at low temperatures

The investigation of the mechanical loss of different silicon flexures in a temperature region from 5 to 300 K is presented. The flexures have been prepared by different fabrication techniques. A lowest mechanical loss of $3\times10^{-8}$ was observed for a 130 $\mu$m thick flexure at around 10 K. While the mechanical loss follows the thermoelastic predictions down to 50 K a difference can be observed at lower temperatures for different surface treatments. This surface loss will be limiting for all applications using silicon based oscillators at low temperatures. The extraction of a surface loss parameter using different results from our measurements and other references is presented. We focused on structures that are relevant for gravitational wave detectors. The surface loss parameter $\alpha_s$ = 0.5 pm was obtained. This reveals that the surface loss of silicon is significantly lower than the surface loss of fused silica.Comment: 16 pages, 7 figure