A quantitative central limit theorem for linear statistics of random matrix eigenvalues

It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost $1/n$ can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein's method of exchangeable pairs.Comment: Title modified; main result stated under slightly weaker conditions; accepted for publication in the Journal of Theoretical Probabilit

Nesting attempts and success of Arctic-breeding geese can be derived with high precision from accelerometry and GPS-tracking

Abstract Sensors, such as accelerometers, in tracking devices allow for detailed bio-logging to understand animal behaviour, even in remote places where direct observation is difficult. To study breeding in birds remotely, one needs to understand how to recognise a breeding event from tracking data, and ideally validate this by direct observation. We tagged 49 adult female pink-footed geese (Anser brachyrhynchus) with transmitter neckbands in Finland in spring of 2018 and 2019, and in Svalbard in summer 2018, and validated inferences from tracking by field observations of nesting sites and family status in 2018–2020 (54 spring–summer tracks). We estimated nesting locations by taking the median coordinates of GPS-fixes at which the goose was motionless (overall dynamic body acceleration, ODBA    75% of time within 50 m of the nest, because nest site attendances steeply increased within one day to above this threshold. Nesting duration (number of consecutive days with  >  75% nest site attendance) ranged between 3 and 44 days (n  =  28), but was 30–34 days in confirmed successful nests (n = 9). The prolonged nesting of 39–44 days (n = 3) suggested incubation on unhatchable egg(s). Nest losses before hatching time occurred mostly in day 3–10 and 23–29 of nesting, periods with an increased frequency of nest site recesses. As alternative method, allowing for non-simultaneous GPS and accelerometer data, we show that nesting days were classified with 98.6% success by two general characteristics of breeding: low body motion (daily median ODBA) and low geographic mobility (daily SD of latitude). Median coordinates on nesting days approached real nest sites closely (within 0.8–3.6 m, n  =  6). When considering only geographic mobility (allowing for GPS data only) nesting locations were similarly accurate, but some short nesting attempts were undetected and non-breeding tracks misclassified. We show that nesting attempts, as short as 3 days, and nesting success can be detected remotely with good precision using GPS-tracking and accelerometry. Our method may be generalised to other (precocial) bird species with similar incubation behaviour

The National Ignition Facility: The world's largest optical system

The National Ignition Facility (NIF), a 192-beam fusion laser, is presently under construction at the Lawrence Livermore National Laboratory with an expected completion in 2008. The facility contains 7,456 meter-scale optics for amplification, beam steering, vacuum barriers, focusing, polarization rotation, and wavelength conversion. A multiphase program was put in place to increase the monthly optical manufacturing rate by up to 20x while simultaneously reducing cost by up to 3x through a sub-scale development, full-scale facilitization, and a pilot production phase. Currently 80% of the optics are complete with over 50% installed. In order to manufacture the high quality optics at desired manufacturing rate of over 100 precision optics per month, new more deterministic advanced fabrication technologies had to be employed over those used to manufacture previous fusion lasers

Comparison of Simulator Wear Measured by Gravimetric vs Optical Surface Methods for Two Million Cycles

Understanding wear mechanisms are key for better implants Critical to the success of the simulation Small amount of metal wear can have catastrophic effects in the patient such as heavy metal poisoning or deterioration of the bone/implant interface leading to implant failure Difficult to measure in heavy hard-on-hard implants (metal-on-metal or ceramic-on-ceramic) May have only fractions of a milligram of wear on a 200 g component At the limit of detection of even high-end balances when the component is 200 g and the change in weight is on the order of 0.000 1 grams Here we compare the standard gravimetric wear estimate with A non-contact 3D optical profiling method at each weighing stop A coordinate measuring machine (CMM) at the beginning and end of the ru

Numerical simulation of exciton dynamics in Cu2O at ultra low temperatures within a potential trap

We have studied theoretically the relaxation behaviour of excitons in cuprous oxide (Cu2O) at ultra low temperatures when excitons are confined within a potential trap by solving numerically the Boltzmann equation. As relaxation processes, we have included in this paper deformation potential phonon scattering, radiative and non-radiative decay and Auger decay. The relaxation kinetics has been analysed for temperatures in the range between 0.3K and 5K. Under the action of deformation potential phonon scattering only, we find for temperatures above 0.5K that the excitons reach local equilibrium with the lattice i.e. that the effective local temperature is coming down to bath temperature, while below 0.5K a non-thermal energy distribution remains. Interestingly, for all temperatures the global spatial distribution of excitons does not reach the equilibrium distribution, but stays at a much higher effective temperature. If we include further a finite lifetime of the excitons and the two-particle Auger decay, we find that both the local and the global effective temperature are not coming down to bath temperature. In the first case we find a Bose-Einstein condensation (BEC) to occur for all temperatures in the investigated range. Comparing our results with the thermal equilibrium case, we find that BEC occurs for a significantly higher number of excitons in the trap. This effect could be related to the higher global temperature, which requires an increased number of excitons within the trap to observe the BEC. In case of Auger decay, we do not find at any temperature a BEC due to the heating of the exciton gas

Gain spectroscopy of a type-II VECSEL chip

Using optical pump-white light probe spectroscopy the gain dynamics is investigated for a VECSEL chip which is based on a type-II heterostructure. The active region the chip consists of a GaAs/(GaIn)As/Ga(AsSb)/(GaIn)As/GaAs multiple quantum well. For this structure, a fully microscopic theory predicts a modal room temperature gain at a wavelength of 1170 nm, which is confirmed by experimental spectra. The results show a gain buildup on the type-II chip which is delayed relative to that of a type-I chip. This slower gain dynamics is attributed to a diminished cooling rate arising from reduced electron-hole scattering.Comment: 4 pages, 4 figure

Excitonic Photoluminescence in Semiconductor Quantum Wells: Plasma versus Excitons

Time-resolved photoluminescence spectra after nonresonant excitation show a distinct 1s resonance, independent of the existence of bound excitons. A microscopic analysis identifies excitonic and electron-hole plasma contributions. For low temperatures and low densities the excitonic emission is extremely sensitive to even minute optically active exciton populations making it possible to extract a phase diagram for incoherent excitonic populations.Comment: 9 pages, 4 figure

Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings

Hafnium-silica multilayer mirrors and polarizers were deposited by e-beam evaporation onto BK7 glass substrates. The mirrors and polarizers were coated for operation at 1053 nm at 45{degree} and at Brewster`s angle (56{degree}), respectively. They were tested with a single 3-ns laser pulse. Morphology of the laser-induced damage was characterized by optical and scanning electron microscopy. Four distinct damage morphologies were found: pits, flatbottom pits, scalds, and delaminates. The pits and flat bottom pits (<30{mu}m dia) were detected at lower fluences (as low as 5 J/cm{sup 2}). The pits seemed to result from ejection of nodular defects by causing local enhancement of the electric field. Scalds and delaminates could be observed at higher fluences (above 13 J/cm{sup 2}) and seemed to result from the formation of plasmas on the surface. These damage types often originated at pits and were less than 300 {mu}m diameter; their size increased almost linearly with fluence. Finally, effects of the damage on the beam (reflectivity degradation and phase modulations) were measured