Björling type problems for elastic surfaces

In this survey we address the Bj"orling problem for various classes of surfaces associated to the Euler--Lagrange equation of the Helfrich elastic energy subject to volume and area constraints

Closed trajectories of a particle model on null curves in anti-de Sitter 3-space

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur

A clock network for geodesy and fundamental science

Leveraging the unrivaled performance of optical clocks in applications in fundamental physics beyond the standard model, in geo-sciences, and in astronomy requires comparing the frequency of distant optical clocks truthfully. Meeting this requirement, we report on the first comparison and agreement of fully independent optical clocks separated by 700 km being only limited by the uncertainties of the clocks themselves. This is achieved by a phase-coherent optical frequency transfer via a 1415 km long telecom fiber link that enables substantially better precision than classical means of frequency transfer. The fractional precision in comparing the optical clocks of three parts in $10^{17}$ was reached after only 1000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than with any other existing frequency transfer method. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.Comment: 14 pages, 3 figures, 1 tabl

Brownian force noise from molecular collisions and the sensitivity of advanced gravitational wave observatories

We present an analysis of Brownian force noise from residual gas damping of reference test masses as a fundamental sensitivity limit in small force experiments. The resulting acceleration noise increases significantly when the distance of the test mass to the surrounding experimental apparatus is smaller than the dimension of the test mass itself. For the Advanced LIGO interferometric gravitational wave observatory, where the relevant test mass is a suspended 340 mm diameter cylindrical end mirror, the force noise power is increased by roughly a factor 40 by the presence of a similarly shaped reaction mass at a nominal separation of 5 mm. The force noise, of order 20 fN\rthz\ for $2 \times 10^{-6}$ Pa of residual H$_2$ gas, rivals quantum optical fluctuations as the dominant noise source between 10 and 30 Hz. We present here a numerical and analytical analysis for the gas damping force noise for Advanced LIGO, backed up by experimental evidence from several recent measurements. Finally, we discuss the impact of residual gas damping on the gravitational wave sensitivity and possible mitigation strategies.Comment: 13 pages with 9 figures (fixed typos found in proofs

Yield and nutrient uptake of soybean cultivars under intensive cropping systems.

Sustainable agricultural systems are necessary to improve soybean [Glycine max (L.) Merr.] seed yield and to increase nutrient use efficiency. Intensification of agricultural systems is an important tool to increase farmers? profitability in the Cerrado region (Brazil), where soybean is rotated with corn in the same growing season. However, this intensification requires soybean cultivar with short growing periods which is achieved by indeterminate soybean cultivars. There is a lack of information regarding the nutrient uptake by soybean cultivars under intensive agricultural systems in the Cerrado. We sought to investigate soybean biomass production and soybean seed yield of determinate and indeterminate soybean cultivars. We also aimed to quantify the amounts of nutrients taken up by soybean biomass and seeds. Field research was conducted to evaluate 17 soybean cultivars commonly grown by farmers, and we considered the determinate and indeterminate soybean growth habit. Nutrient uptake and aboveground soybean biomass were higher under shorter soybean growth and development cycles. Nitrogen, phosphorus and potassium extraction in modern cultivars was higher than in cultivars used in past decades. Nutrient use efficiency was higher in determinate soybean cultivars than in indeterminate soybean cultivars

Sub-femto-g free fall for space-based gravitational wave observatories: LISA pathfinder results

We report the first results of the LISA Pathfinder in-flight experiment. The results demonstrate that two free-falling reference test masses, such as those needed for a space-based gravitational wave observatory like LISA, can be put in free fall with a relative acceleration noise with a square root of the power spectral density of 5.2 ± 0.1 fm s−2/√Hz or (0.54 ± 0.01) × 10−15 g/√Hz, with g the standard gravity, for frequencies between 0.7 and 20 mHz. This value is lower than the LISA Pathfinder requirement by more than a factor 5 and within a factor 1.25 of the requirement for the LISA mission, and is compatible with Brownian noise from viscous damping due to the residual gas surrounding the test masses. Above 60 mHz the acceleration noise is dominated by interferometer displacement readout noise at a level of (34.8 ± 0.3) fm/√Hz, about 2 orders of magnitude better than requirements. At f ≤ 0.5 mHz we observe a low-frequency tail that stays below 12 fm s−2/√Hz down to 0.1 mHz. This performance would allow for a space-based gravitational wave observatory with a sensitivity close to what was originally foreseen for LISA

State space modelling and data analysis exercises in LISA Pathfinder

LISA Pathfinder is a mission planned by the European Space Agency to test the key technologies that will allow the detection of gravitational waves in space. The instrument on-board, the LISA Technology package, will undergo an exhaustive campaign of calibrations and noise characterisation campaigns in order to fully describe the noise model. Data analysis plays an important role in the mission and for that reason the data analysis team has been developing a toolbox which contains all the functionalities required during operations. In this contribution we give an overview of recent activities, focusing on the improvements in the modelling of the instrument and in the data analysis campaigns performed both with real and simulated data.Comment: Plenary talk presented at the 9th International LISA Symposium, 21-25 May 2012, Pari

Quantum cascade laser frequency stabilisation at the sub-Hz level

Quantum Cascade Lasers (QCL) are increasingly being used to probe the mid-infrared "molecular fingerprint" region. This prompted efforts towards improving their spectral performance, in order to reach ever-higher resolution and precision. Here, we report the stabilisation of a QCL onto an optical frequency comb. We demonstrate a relative stability and accuracy of 2x10-15 and 10-14, respectively. The comb is stabilised to a remote near-infrared ultra-stable laser referenced to frequency primary standards, whose signal is transferred via an optical fibre link. The stability and frequency traceability of our QCL exceed those demonstrated so far by two orders of magnitude. As a demonstration of its capability, we then use it to perform high-resolution molecular spectroscopy. We measure absorption frequencies with an 8x10-13 relative uncertainty. This confirms the potential of this setup for ultra-high precision measurements with molecules, such as our ongoing effort towards testing the parity symmetry by probing chiral species

Pain management procedures used by dental and maxillofacial surgeons: an investigation with special regard to odontalgia

BACKGROUND: Little is known about the procedures used by German dental and maxillofacial surgeons treating patients suffering from chronic orofacial pain (COP). This study aimed to evaluate the ambulatory management of COP. METHODS: Using a standardized questionnaire we collected data of dental and maxillofacial surgeons treating patients with COP. Therapists described variables as patients' demographics, chronic pain disorders and their aetiologies, own diagnostic and treatment principles during a period of 3 months. RESULTS: Although only 13.5% of the 520 addressed therapists returned completely evaluable questionnaires, 985 patients with COP could be identified. An orofacial pain syndrome named atypical odontalgia (17.0 %) was frequent. Although those patients revealed signs of chronification, pain therapists were rarely involved (12.5%). For assessing pain the use of Analogue Scales (7%) or interventional diagnostics (4.6%) was uncommon. Despite the fact that surgical procedures are cofactors of COP therapists preferred further surgery (41.9%) and neglected the prescription of analgesics (15.7%). However, most therapists self-evaluated the efficacy of their pain management as good (69.7 %). CONCLUSION: Often ambulatory dental and maxillofacial surgeons do not follow guidelines for COP management despite a high prevalence of severe orofacial pain syndromes