Optimal mistuning for enhanced aeroelastic stability of transonic fans

An inverse design procedure was developed for the design of a mistuned rotor. The design requirements are that the stability margin of the eigenvalues of the aeroelastic system be greater than or equal to some minimum stability margin, and that the mass added to each blade be positive. The objective was to achieve these requirements with a minimal amount of mistuning. Hence, the problem was posed as a constrained optimization problem. The constrained minimization problem was solved by the technique of mathematical programming via augmented Lagrangians. The unconstrained minimization phase of this technique was solved by the variable metric method. The bladed disk was modelled as being composed of a rigid disk mounted on a rigid shaft. Each of the blades were modelled with a single tosional degree of freedom

Yang-Mills theory and the Segal-Bargmann transform

We use a variant of the classical Segal-Bargmann transform to understand the canonical quantization of Yang-Mills theory on a space-time cylinder. This transform gives a rigorous way to make sense of the Hamiltonian on the gauge-invariant subspace. Our results are a rigorous version of the widely accepted notion that on the gauge-invariant subspace the Hamiltonian should reduce to the Laplacian on the compact structure group. We show that the infinite-dimensional classical Segal-Bargmann transform for the space of connections, when restricted to the gauge-invariant subspace, becomes the generalized Segal-Bargmann transform for the the structure group

Analysis of the origin of Aufeis feed-water on the arctic slope of Alaska

The origin of water feeding large aufeis fields (overflow river ice) on the Arctic Slope of Alaska is analyzed. Field measurements of two large aufeis fields on the eastern Arctic Slope were taken during July of 1978 and 1979. Measurements of aufeis extent and distribution were made using LANDSAT Multispectral Scanner Subsystem (MSS) satellite data from 1973 through 1979. In addition, ice cores were analyzed in the laboratory. Results of the field and laboratory studies indicate that the water derived from aufeis melt water has a chemical composition different from the adjacent upstream river water. Large aufeis fields are found in association with springs and faults thus indicating a subterranean origin of the feed water. In addition, the maximum extent of large aufeis fields was not found to follow meteorological patterns which would only be expected if the origin of the feed water were local. It is concluded that extent of large aufeis in a given river channel on the Arctic Slope is controlled by discharge from reservoirs of groundwater. It seems probable that precipitation passes into limestone aquifers in the Brooks Range, through an interconnecting system of subterranean fractures in calcareous rocks and ultimately discharges into alluvial sediments on the coastal plain to form aufeis. It is speculated that only small aufeis patches are affected by local meteorological parameters in the months just prior to aufeis formation

The Bargmann representation for the quantum mechanics on a sphere

The Bargmann representation is constructed corresponding to the coherent states for a particle on a sphere introduced in: K. Kowalski and J. Rembielinski, J. Phys. A: Math. Gen. 33, 6035 (2000). The connection is discussed between the introduced formalism and the standard approach based on the Hilbert space of square integrable functions on a sphere S^2.Comment: LaTe

Physical Education or Playtime: which is more effective at promoting physical activity in primary school children?

Background School physical education (PE) and playtime provide important opportunities for physical activity (PA). However, little research has assessed PA during primary school PE using accelerometry or compared PA during different lesson types. There is also a lack of research comparing PA during PE and playtime, despite suggestions that playtime promotes more PA. The primary aim of this study was to determine which types of PE lesson are most facilitative of PA. The secondary aim was to determine whether children are more active during PE or playtime. Methods Descriptive and fitness data were assessed in 20 children aged 8-9years from a single school. Over eight consecutive weeks PA was assessed during PE lessons, which were classified as either team games or movement activities. At the mid-week of data collection playtime PA was also assessed. PA was assessed using accelerometry and the percentage of time spent in moderate to vigorous PA (MVPA) calculated. Paired t-tests were used to compare MVPA during movement lessons and team games lessons and during PE and playtime. Results Children spent 9.5% of PE lessons in MVPA and engaged in significantly more MVPA during team games (P < 0.001). MVPA was also significantly higher during PE than playtime (P < 0.01). Conclusions Children do not engage in sufficient PA during PE, but are most active during team games lessons; whilst PA during playtime is lower than PE. Interventions to increase PA during both PE and playtime are therefore required. PE interventions should target games lessons as they dominate the curriculum, encourage most PA and present the greatest potential for change. Playtime interventions should encourage participation in active games through the provision of playground equipment and markings

The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces

We prove the Makeenko-Migdal equation for two-dimensional Euclidean Yang-Mills theory on an arbitrary compact surface, possibly with boundary. In particular, we show that two of the proofs given by the first, third, and fourth authors for the plane case extend essentially without change to compact surfaces.Comment: Final version, minor typographical corrections. To appear in Comm. Math. Phy