Small surfaces of Willmore type in Riemannian manifolds

In this paper we investigate the properties of small surfaces of Willmore type in Riemannian manifolds. By \emph{small} surfaces we mean topological spheres contained in a geodesic ball of small enough radius. In particular, we show that if there exist such surfaces with positive mean curvature in the geodesic ball $B_r(p)$ for arbitrarily small radius $r$ around a point $p$ in the Riemannian manifold, then the scalar curvature must have a critical point at $p$. As a byproduct of our estimates we obtain a strengthened version of the non-existence result of Mondino \cite{Mondino:2008} that implies the non-existence of certain critical points of the Willmore functional in regions where the scalar curvature is non-zero.Comment: 25 pages. Minor correction

Algorithm based comparison between the integral method and harmonic analysis of the timing jitter of diode-based and solid-state pulsed laser sources

AbstractA comparison between two methods of timing jitter calculation is presented. The integral method utilizes spectral area of the single side-band (SSB) phase noise spectrum to calculate root mean square (rms) timing jitter. In contrast the harmonic analysis exploits the uppermost noise power in high harmonics to retrieve timing fluctuation. The results obtained show that a consistent timing jitter of 1.2ps is found by the integral method and harmonic analysis in gain-switched laser diodes with an external cavity scheme. A comparison of the two approaches in noise measurement of a diode-pumped Yb:KY(WO4)2 passively mode-locked laser is also shown in which both techniques give 2ps rms timing jitter

Surface Profiling of Natural Dust Devils

We present results from the first high-resolution near-surface profiles conducted on dust devil wind fields. These results are integrated with extensive geologic mapping to understand the factors that influence vortex generation and erosive efficacy

Foliations of asymptotically flat manifolds by surfaces of Willmore type

The goal of this paper is to establish the existence of a foliation of the asymptotic region of an asymptotically flat manifold with nonzero mass by surfaces which are critical points of the Willmore functional subject to an area constraint. Equivalently these surfaces are critical points of the Geroch-Hawking mass. Thus our result has applications in the theory of General Relativity

New calibration procedures for airborne turbulence measurements and accuracy of the methane fluxes during the AirMeth campaigns

Low-level flights over tundra wetlands in Alaska and Canada have been conducted during the Airborne Measurements of Methane Emissions (AirMeth) campaigns to measure turbulent methane fluxes in the atmosphere. In this paper we describe the instrumentation and new calibration procedures for the essential pressure parameters required for turbulence sensing by aircraft that exploit suitable regular measurement flight legs without the need for dedicated calibration patterns. We estimate the accuracy of the mean wind and the turbulence measurements. We show that airborne measurements of turbulent fluxes of methane and carbon dioxide using cavity ring-down spectroscopy trace gas analysers together with established turbulence equipment achieve a relative accuracy similar to that of measurements of sensible heat flux if applied during low-level flights over natural area sources. The inertial subrange of the trace gas fluctuations cannot be resolved due to insufficient high-frequency precision of the analyser, but, since this scatter is uncorrelated with the vertical wind velocity, the covariance and thus the flux are reproduced correctly. In the covariance spectra the −7∕3 drop-off in the inertial subrange can be reproduced if sufficient data are available for averaging. For convective conditions and flight legs of several tens of kilometres we estimate the flux detection limit to be about 4mgm−2d−1 for w′CH4′, 1.4gm−2d−1 for w′CO2′ and 4.2Wm−2 for the sensible heat flux

Effects of Spacecraft Landings on the Moon

The rocket exhaust of spacecraft landing on the Moon causes a number of observable effects that need to be quantified, including: disturbance of the regolith and volatiles at the landing site; damage to surrounding hardware such as the historic Apollo sites through the impingement of high-velocity ejecta; and levitation of dust after engine cutoff through as-yet unconfirmed mechanisms. While often harmful, these effects also beneficially provide insight into lunar geology and physics. Research results from the past 10 years is summarized and reviewed here

Interpreting BEC in e+e- annihilation

The usual interpretation of Bose-Einstein correlations (BEC) of identical boson pairs relates the width of the peak in the correlation function at small relative four-momentum to the spatial extent of the source of the bosons. However, in the tau-model, which successfully describes BEC in hadronic Z decay, the width of the peak is related to the temporal extent of boson emission. Some new checks on the validity of both the tau-model and the usual descriptions are presented.Comment: Talk given at XLVIII International Symposium on Multiparticle Dynamics, Singapore, 3-7 Sep. 2018. To appear in the proceeding