Scaling asymptotics for quantized Hamiltonian flows

In recent years, the near diagonal asymptotics of the equivariant components of the Szeg\"{o} kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of this theme, here we consider the local scaling asymptotics of the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically how they concentrate on the graph of the underlying classical map

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

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

Propagating and evanescent internal waves in a deep ocean model

We present experimental and computational studies of the propagation of internal waves in a stratified fluid with an exponential density profile that models the deep ocean. The buoyancy frequency profile $N(z)$ (proportional to the square root of the density gradient) varies smoothly by more than an order of magnitude over the fluid depth, as is common in the deep ocean. The nonuniform stratification is characterized by a turning depth $z_c$, where $N(z_c)$ is equal to the wave frequency $\omega$ and $N(z < z_c) < \omega$. Internal waves reflect from the turning depth and become evanescent below the turning depth. The energy flux below the turning depth is shown to decay exponentially with a decay constant given by $k_c$, which is the horizontal wavenumber at the turning depth. The viscous decay of the vertical velocity amplitude of the incoming and reflected waves above the turning depth agree within a few percent with a previously untested theory for a fluid of arbitrary stratification [Kistovich and Chashechkin, J. App. Mech. Tech. Phys. 39, 729-737 (1998)].Comment: 13 pages, 4 figures, 4 table

Explicit characterization of the identity configuration in an Abelian Sandpile Model

Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the square lattice, in different geometries, and a variant with directed edges. Cylinders, through their extra symmetry, allow an easy determination of the identity, which is a homogeneous function. The directed variant on square geometry shows a remarkable exact structure, asymptotically self-similar.Comment: 11 pages, 8 figure

Machine learning for gravitational-wave detection: surrogate Wiener filtering for the prediction and optimized cancellation of Newtonian noise at Virgo

The cancellation of noise from terrestrial gravity fluctuations, also known as Newtonian noise (NN), in gravitational-wave detectors is a formidable challenge. Gravity fluctuations result from density perturbations associated with environmental fields, e.g., seismic and acoustic fields, which are characterized by complex spatial correlations. Measurements of these fields necessarily provide incomplete information, and the question is how to make optimal use of available information for the design of a noise-cancellation system. In this paper, we present a machine-learning approach to calculate a surrogate model of a Wiener filter. The model is used to calculate optimal configurations of seismometer arrays for a varying number of sensors, which is the missing keystone for the design of NN cancellation systems. The optimization results indicate that efficient noise cancellation can be achieved even for complex seismic fields with relatively few seismometers provided that they are deployed in optimal configurations. In the form presented here, the optimization method can be applied to all current and future gravitational-wave detectors located at the surface and with minor modifications also to future underground detectors

Infection levels and species diversity of ascaridoid nematodes in Atlantic cod, Gadus morhua, are correlated with geographic area and fish size

Atlantic cod (Gadus morhua) is among the most important commercial fish species on the world market. Its infection by ascaridoid nematodes has long been known, Pseudoterranova even being named cod worm. In the present study, 755 individuals were sampled in the Barents, Baltic and North Seas during 2012–2014. Prevalences for Anisakis in whole fish and in fillets in the different fishing areas varied from 16 to 100% and from 12 to 90% respectively. Abundance was also greatly influenced by the sampling area. Generalized additive model results indicate higher numbers of Anisakis in the North Sea, even after the larger body size was accounted for. Numbers and prevalence of Anisakis were positively related to fish length or weight. The prevalence of parasites in whole fish and in fillets was also influenced by the season, with the spring displaying a peak for the prevalence in whole fish and, at the same time, a drop for the prevalence in fillets. Whereas 46% of cod had Anisakis larvae in their fillets, the majority (39%) had parasites mainly in the ventral part of the fillet and only 12% had parasites in their dorsal part. This observation is of importance for the processing of the fish. Indeed, the trimming of the ventral part of the cod fillet would allow the almost total elimination of ascaridoids except for cod from the Baltic Sea where there was no difference between the dorsal and the ventral part. The presence of other ascaridoid genera was also noticeable in some areas. For Pseudoterranova, the highest prevalence (45%) in whole fish was observed in the Northern North Sea, whereas the other areas had prevalences between 3 and 16%. Contracaecum was present in every commercial size cod sampled in the Baltic Sea with an intensity of up to 96 worms but no Contracaecum was isolated from the Central North Sea. Non-zoonotic Hysterothylacium was absent from the Baltic Sea but with a prevalence of 83% in the Barents and the Northern North Sea. A subsample of worms was identified with genetic-molecular tools and assigned to the species A. simplex (s.s.), A. pegreffii, P. decipiens (s.s.), P. krabbei, C. osculatum and H. aduncum. In addition to high prevalence and abundance values, the cod sampled in this study presented a diversity of ascaridoid nematodes with a majority of fish displaying a co-infection. Out of 295 whole infected fish, 269 were co-infected by at least 2 genera

Drilling polymeric matrix composites

This chapter presents the basics of drilling of polymeric matrix composites (PMCs). PMCs are becoming widely used in the manufacturing of products where a high mechanical strength must be accompanied by a low weight. However, the machining of PMCs implies coping with problems that are not encountered when machining other materials. Drilling is a particularly critical operation for PMCs laminates because the large concentrated forces generated can lead to widespread damage. This damage causes aesthetic problems but, more importantly, may compromise the mechanical properties of the finished part