Local trace formulae and scaling asymptotics in Toeplitz quantization, II

In the spectral theory of positive elliptic operators, an important role is played by certain smoothing kernels, related to the Fourier transform of the trace of a wave operator, which may be heuristically interpreted as smoothed spectral projectors asymptotically drifting to the right of the spectrum. In the setting of Toeplitz quantization, we consider analogues of these, where the wave operator is replaced by the Hardy space compression of a linearized Hamiltonian flow, possibly composed with a family of zeroth order Toeplitz operators. We study the local asymptotics of these smoothing kernels, and specifically how they concentrate on the fixed loci of the linearized dynamics.Comment: Typos corrected. Slight expository change

Improved CMB anisotropy constraints on primordial magnetic fields from the post-recombination ionization history

We investigate the impact of a stochastic background of Primordial Magnetic Fields (PMF) generated before recombination on the ionization history of the Universe and on the Cosmic Microwave Background radiation (CMB). Pre-recombination PMFs are dissipated during recombination and reionization via decaying MHD turbulence and ambipolar diffusion. This modifies the local matter and electron temperatures and thus affects the ionization history and Thomson visibility function. We use this effect to constrain PMFs described by a spectrum of power-law type, extending our previous study (based on a scale-invariant spectrum) to arbitrary spectral index. We derive upper bounds on the integrated amplitude of PMFs due to the separate effect of ambipolar diffusion and MHD decaying turbulence and their combination. We show that ambipolar diffusion is relevant for $n_{\rm B}>0$ whereas for $n_{\rm B}<0$ MHD turbulence is more important. The bound marginalized over the spectral index on the integrated amplitude of PMFs with a sharp cut-off is $\sqrt{\langle B^2 \rangle}<0.83$ nG. We discuss the quantitative relevance of the assumptions on the damping mechanism and the comparison with previous bounds.Comment: 11 pages, 21 figures. Minor updates to match the published versio

Local trace formulae and scaling asymptotics in Toeplitz quantization

A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of symmetries on quantizable compact symplectic manifolds. The local trace formula involves certain scaling asymptotics along the clean fixed locus of the Hamiltonian flow of the symbol, reminiscent of the scaling asymptotics of the equivariant components of the Szeg\"o kernel along the diagonal

The genome sequence of Podospora anserina, a classic model fungus

The genome sequence of the coprophilous fungus Podospora anserina shows both typical ascomycete features and how this species is adapted to its specialized environment

Nonlinear behaviour of self-excited microcantilevers in viscous fluids

Microcantilevers are increasingly being used to create sensitive sensors for rheology and mass sensing at the micro- and nano-scale. When operating in viscous liquids, the low quality factor of such resonant structures, translating to poor signal-to-noise ratio, is often manipulated by exploiting feedback strategies. However, the presence of feedback introduces poorly-understood dynamical behaviours that may severely degrade the sensor performance and reliability. In this paper, the dynamical behaviour of self-excited microcantilevers vibrating in viscous fluids is characterized experimentally and two complementary modelling approaches are proposed to explain and predict the behaviour of the closed-loop system. In particular, the delay introduced in the feedback loop is shown to cause surprising non-linear phenomena consisting of shifts and sudden-jumps of the oscillation frequency. The proposed dynamical models also suggest strategies for controlling such undesired phenomena

Case Histories Paper: Jackup Rig Spud Can Penetration: A 6,000 Ton Load Test

One of the most exciting geotechnical problems for the offshore engineer is the prediction of mobile jack-up rig spud can penetration. Jack-up drilling rigs are used to drill offshore oil and gas wells in water depths up to about 100 m. The rigs are supported by circular “spud can” foundations fitted at the end of extendable platform legs. Upon arrival to the site the jack-up extends the legs to the sea floor and self-elevates out of the water. This action forces the spud cans into the seabed until soil capacity is attained. Prior to jacking the rig out of the water, a geotechnical borehole is made from the rig to verify soil conditions and estimate bearing capacity and leg penetration. The geotechnical engineer makes predictions of foundation capacity in real time; the predictions are then verified by the actual behavior of the footing under the 6,000 ton preload. This paper presents experience with bearing capacity predictions versus field measurements from over 15 offshore sites. Relatively simple closed form bearing capacity formulas are shown to provide good predictions for real behavior of these large scale foundations

The Institute of Archaeology & Siegfried H. Horn Museum Newsletter Volume 27.4

Spring Study Tour, Paul J. Ray, Jr. Tappy Lecture, Carrie Rhodes Drehem Archive, Paola Paoletti Random Surveyhttps://digitalcommons.andrews.edu/iaham-news/1028/thumbnail.jp

Population genetic structure of the parasite Anisakis simplex (s. s.) collected in Clupea harengus L. from North East Atlantic fishing grounds

The Atlantic herring is a schooling, pelagic species that inhabits both sides of the North Atlantic Ocean. Herring stock identification is usually based on several approaches, including fish meristic characters, population genetic analysis and the use of parasite species composition. A total of 654 Anisakis spp. larvae collected from herring of four fishing grounds in the Norwegian Sea, Baltic Sea, North Sea, and the English Channel off the French coast, was identified to species level using diagnostic allozymes and sequence analysis of EF1 α−1 nDNA and the mtDNA cox2 genes. Population genetic differentiation of Anisakis simplex (s. s.) among the different fishing areas was estimated, at the intraspecific level, on the basis of mtDNA cox2 sequences analysis. Spatial comparison based on molecular variance analysis and Fst values was performed for the collected specimens (among regions). Haplotype network construction showed relevant differences in haplotype frequencies between samples of A. simplex (s. s.) from the different geographical areas. Results indicate a genetic sub-structuring of A. simplex (s. s.) obtained from herring in different areas, with the population from the Norwegian Sea being the most differentiated one, and with North Sea and Baltic Sea populations being most similar. The population genetic structure of A. simplex (s. s.) was in accordance with the herring population genetic structure throughout the host’s geographical range in the NE Atlantic. Results suggest that mtDNA cox2 is a suitable genetic marker for A. simplex (s. s.) population genetic structure analysis and a valuable tool to elucidate the herring stock structure in the NE Atlantic Ocean