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

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

Santa Maria di Collemaggio Church (L’Aquila, Italy) : historical reconstruction by non-destructive testing techniques

The main goal of this work was the non-destructive testing (NDT) of an ancient fresco (15th century) preserved in the Santa Maria di Collemaggio Church (L’Aquila, Italy) and damaged after the 2009 earthquake. Active infrared thermography (IRT), near-infrared (NIR) reflectography and ultraviolet imaging (UV) were used. In addition, the state of the fresco prior to the earthquake was analyzed by electronic speckle pattern interferometry (ESPI), digital speckle correlation (DSC), raking light, tap, and chemical NDT techniques. The use of these techniques was important for the monitoring of new damages and for a comparison between the results over the years. Square heating thermography (SHT) data were processed using principal component thermography (PCT) and pulsed phase thermography (PPT) algorithms, in order to improve the defects’ signature and to reduce the impact of non-uniform heating and emissivity variations due to the painting’s pigments. A multi-analysis approach, segmentation operators and a specific data correlation method emphasize the overall study of the fresco. Furthermore, the facade and the high altar area were inspected by passive thermography and ground-penetrating radar (GPR), respectively. In the present case, the combined use of NDT techniques was useful to fill in the gaps in the construction history of the building

Test Design Methodology for Time-Domain Immunity Investigations Using Electric Near-Field Probes

This article investigates the possibility to develop time-domain immunity tests using electric near-field probes, for flexible customization of broadband input waveforms injected into specific pins of PCBs. For this purpose, a test design methodology is proposed, which is based on circuit modeling of the injection mechanism on the one hand, and on pulse design and equalization on the other hand. Two circuit models are developed. The former employs measurement/simulation data along with port-reduction techniques to model noise injection through near-field probes by means of internal induced sources. Conversely, the latter model only includes passive components and is derived starting from physical observation of the involved phenomena. Both models are compatible with circuit solvers and can be easily adapted for different traces under test. Since pulse-like noise is usually broadband, suitable stress waveforms are utilized to obtain different noise spectra. Also, in order to precisely control the shape of the waveform reaching the targeted pin, an equalization procedure is employed. These models and techniques can be easily applied to amplification systems originally designed for frequency-domain tests, thus providing a comprehensive solution for the design of broadband immunity tests in the time domain. The feasibility and accuracy of the proposed methodology are proved by full-wave simulations and measurements

Analysis of Near-Field Probing Techniques for Immunity Tests

This work experimentally investigates the performance of near-field probes as injection devices for wideband immunity tests. To this end, the coupling effectiveness and resolution of different kinds of magnetic and electric near-field probes are firstly investigated in terms of S-parameters measured with the probes placed on microstrip traces. Different test benches are set up and experimentally characterized in order to investigate the characteristics and determine the frequency response of the transfer function of a typical measurement chain for immunity verification. Finally, time-domain near-field tests employing arbitrary waveform generators are introduced, showing the feasibility of injecting customized wideband noise waveforms at specific pins

Holographic interferometry (HI), infrared Vision and X-Ray fluorescence (XRF) spectroscopy for the assessment of painted wooden statues : a new integrated approach

Wood has been routinely employed in decorative arts, as well as in sculptures and paintings (support) during the Middle Ages, because of its unique aesthetic virtues. It may safely be assumed that wood, as a material for monumental sculpture, was much more commonly employed in the mediaeval period than existing examples would seem to indicate (Bulletin of the metropolitan Museum of Art, 2013). Wood is easily obtainable; it could be carved and put in place with less difficulty than stone, it is chemically stable when dry, and its surface offers a compatible substrate for paint application. However, the use of wood is not without pitfalls, and requires an understanding of its anisotropic and hygroscopic nature. It is also dimensionally unstable and subject to deterioration by fungi and insects. Moisture-related dimensional changes are certainly among the most challenging problems in painting conservation. With the purpose of preventing important damages, the use of non-or microdestructive testing (NDT) techniques is undoubtedly of paramount interest for painted wooden statues of great value. This work has a threefold purpose: (1) to validate the effectiveness of an integrated approach using near-infrared (NIR) reflectography, square pulse thermography (SPT), and holographic interferometry (HI) techniques for discovering old repairs and/or inclusions of foreign materials in a wooden structure, (2) to confirm and approximately date the restoration carried out by x-ray fluorescence (XRF) spectroscopy and energy-dispersive x-ray spectroscopy (EDS) (that is assembled with a scanning electron microscopy—SEM) techniques, and (3) to combine into a multidisciplinary approach two quantitative NDT results coming from optical and thermographic methods. The subject of the present study was a statue named “Virgin with her Child” (XIV century), whose origins are mysterious and not properly documented

How to reveal subsurface defects in Kevlar® composite materials after an impact loading using infrared vision and optical NDT techniques?

An integrated system between infrared vision and optical non-destructive testing techniques can be considered a viable, robust and reliable approach for both aerospace manufacturing and in-service inspections. In this paper, infrared vision is applied in different spectral bands on two impacted panels made of aramid–phenolic composite by applying two different methods, respectively: (1) near and short-wave infrared reflectography and transmittography, and (2) mid-wave active infrared thermography. Furthermore, optical methods, namely digital speckle photography and holographic interferometry, are used as well to highlight the damages due to the impacts on the samples. Some techniques provide more straightforward detection capabilities than others for different defect types

Primordial magnetic fields and the HI signal from the epoch of reionization

The implication of primordial magnetic-field-induced structure formation for the HI signal from the epoch of reionization is studied. Using semi-analytic models, we compute both the density and ionization inhomogeneities in this scenario. We show that: (a) The global HI signal can only be seen in emission, unlike in the standard $\Lambda$CDM models, (b) the density perturbations induced by primordial fields, leave distinctive signatures of the magnetic field Jeans' length on the HI two-point correlation function, (c) the length scale of ionization inhomogeneities is \la 1 \rm Mpc. We find that the peak expected signal (two-point correlation function) is $\simeq 10^{-4} \rm K^2$ in the range of scales $0.5\hbox{-}3 \rm Mpc$ for magnetic field strength in the range $5 \times 10^{-10} \hbox{-}3 \times 10^{-9} \rm G$. We also discuss the detectability of the HI signal. The angular resolution of the on-going and planned radio interferometers allows one to probe only the largest magnetic field strengths that we consider. They have the sensitivity to detect the magnetic field-induced features. We show that thefuture SKA has both the angular resolution and the sensitivity to detect the magnetic field-induced signal in the entire range of magnetic field values we consider, in an integration time of one week.Comment: 19 pages, 5 figures, to appear in JCA

The colours of the Higgs boson: a study in creativity and science motivation among high-school students in Italy

AbstractWith the increasing shift from STEM to STEAM education, arts-based approaches to science teaching and learning are considered promising for aligning school science curricula with the development of twenty-first century skills, including creativity. Yet the impact of STEAM practices on student creativity and specifically on how the latter is associated with science learning outcomes have thus far received scarce empirical support. This paper contributes to this line of research by reporting on a two-wave quantitative study that examines the effect of a long-term STEAM intervention on two cognitive processes associated with creativity (act, flow) and their interrelationships with intrinsic and extrinsic components of science motivation. Using pre- and post-survey data from 175 high-school students in Italy, results show an overall positive effect of the intervention both on the act subscale of creativity and science career motivation, whereas a negative effect is found on self-efficacy. Gender differences in the above effects are also observed. Further, results provide support for the mediating role of self-efficacy in the relationship between creativity and science career motivation. Implications for the design of STEAM learning environments are discussed

Variable echo time imaging for detecting the short T2* components of the sciatic nerve: a validation study

OBJECTIVE: The aim of this study was to develop and validate an MRI protocol based on a variable echo time (vTE) sensitive to the short T2* components of the sciatic nerve. MATERIALS AND METHODS: 15 healthy subjects (M/F: 9/6; age: 21-62) were scanned at 3T targeting the sciatic nerve at the thigh bilaterally, using a dual echo variable echo time (vTE) sequence (based on a spoiled gradient echo acquisition) with echo times of 0.98/5.37 ms. Apparent T2* (aT2*) values of the sciatic nerves were calculated with a mono-exponential fit and used for data comparison. RESULTS: There were no significant differences in aT2* related to side, sex, age, and BMI, even though small differences for side were reported. Good-to-excellent repeatability and reproducibility were found for geometry of ROIs (Dice indices: intra-rater 0.68-0.7; inter-rater 0.70-0.72) and the related aT2* measures (intra-inter reader ICC 0.95-0.97; 0.66-0.85) from two different operators. Side-related signal-to-noise-ratio non-significant differences were reported, while contrast-to-noise-ratio measures were excellent both for side and echo. DISCUSSION: Our study introduces a novel MR sequence sensitive to the short T2* components of the sciatic nerve and may be used for the study of peripheral nerve disorders