More ergodic billiards with an infinite cusp

In a previous paper (nlin.CD/0107041) the following class of billiards was studied: For $f: [0, +\infty) \longrightarrow (0, +\infty)$ convex, sufficiently smooth, and vanishing at infinity, let the billiard table be defined by $Q$, the planar domain delimited by the positive $x$-semiaxis, the positive $y$-semiaxis, and the graph of $f$. For a large class of $f$ we proved that the billiard map was hyperbolic. Furthermore we gave an example of a family of $f$ that makes this map ergodic. Here we extend the latter result to a much wider class of functions.Comment: 13 pages, 4 figure

Magnetometer suitable for Earth field measurement based on transient atomic response

We describe the development of a simple atomic magnetometer using $^{87}$Rb vapor suitable for Earth magnetic field monitoring. The magnetometer is based on time-domain determination of the transient precession frequency of the atomic alignment around the measured field. A sensitivity of 1.5 nT/$\sqrt{Hz}$ is demonstrated on the measurement of the Earth magnetic field in the laboratory. We discuss the different parameters determining the magnetometer precision and accuracy and predict a sensitivity of 30 pT/$\sqrt{Hz}$Comment: 6 pages, 5 figure

Sub-Doppler resonances in the back-scattered light from random porous media infused with Rb vapor

We report on the observation of sub-Doppler resonances on the back-scattered light from a random porous glass medium with rubidium vapor filling its interstices. The sub-Doppler spectral lines are the consequence of saturated absorption where the incident laser beam saturates the atomic medium and the back-scattered light probes it. Some specificities of the observed spectra reflect the transient atomic evolution under confinement inside the pores. Simplicity, robustness and potential miniaturization are appealing features of this system as a spectroscopic reference.Comment: 6 pages, 4 figure

Escape Orbits for Non-Compact Flat Billiards

It is proven that, under some conditions on $f$, the non-compact flat billiard $\Omega = \{ (x,y) \in \R_0^{+} \times \R_0^{+};\ 0\le y \le f(x) \}$ has no orbits going {\em directly} to $+\infty$. The relevance of such sufficient conditions is discussed.Comment: 9 pages, LaTeX, 3 postscript figures available at http://www.princeton.edu/~marco/papers/ . Minor changes since previously posted version. Submitted to 'Chaos

Comparative fragility methods for seismic assessment of masonry buildings located in Muccia (Italy)

The current paper focuses on a sector of the historic centre of Muccia, in the district of Macerata (Italy), affected by the seismic sequence that involved Central Italy in 2016. The main goal is comparison, in terms of fragility curves, among two vulnerability assessment methodologies (empirical and mechanical). The study area has been structurally and typologically identified according to the Building Typology Matrix (BTM). Physical vulnerability analysis of the urban-sector was performed through application of an index-based method, specifically for masonry building aggregates. An isolated masonry building, damaged after the seismic sequences, has been selected as a case study. For the assessed building, empirical fragility curves are presented according to Guagenti & Petrini’s correlation law. Furthermore, a numerical model has been set up by using the macro-element approach, which has allowed to perform non-linear static analyses. Mechanical properties of masonry were defined according to the New Technical Codes for Constructions (NTC18), assuming a limited knowledge level (LC1). Refined mechanical fragility functions have been derived and compared to the empirical ones. Analysis results have shown that the empirical method tends to overestimate by 5% and 10% the expected damage for slight and moderate thresholds. For PGA values greater than 0,3 g the damage levels decreased by 30% and 20%, with reference to the near collapse and collapse conditions, respectively

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of R^d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called `quenched random Lorentz tube'. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.Comment: Final version for J. Stat. Phys., 18 pages, 4 figure

Numerical model upgrading of a historical masonry building damaged during the 2016 Italian earthquakes: the case study of the Podestà palace in Montelupone (Italy)

In October 2016, two major earthquakes occurred in Marche region in the Centre of Italy, causing widespread damage. The epicentre of the second one struck Norcia, Visso and Accumoli and a lot of damages to cultural heritage were done in the cities of Tolentino, San Severino, Camerino, Matelica, Macerata and Montelupone, where are located the Podesta` Palace and the Civic Tower investigated in this paper. The main aim of this research is the determination of modal properties of these historical masonry constructions using experimental and numerical studies. The experimental analysis was based on ambient vibration survey, while numerical analysis was based on finite element analysis with solid elements. The results of the experimental study were used to tune the numerical model of the structure. As the most doubtful parameters, the modulus of elasticity of the masonry and the interaction among structural parts were adjusted to achieve the experimental results with numerical model by simple operations. Obtaining good consistency between the experimental and numerical analyses, the study revealed the actual dynamic properties of the damaged palace

Theoretical study of dark resonances in micro-metric thin cells

We investigate theoretically dark resonance spectroscopy for a dilute atomic vapor confined in a thin (micro-metric) cell. We identify the physical parameters characterizing the spectra and study their influence. We focus on a Hanle-type situation, with an optical irradiation under normal incidence and resonant with the atomic transition. The dark resonance spectrum is predicted to combine broad wings with a sharp maximum at line-center, that can be singled out when detecting a derivative of the dark resonance spectrum. This narrow signal derivative, shown to broaden only sub-linearly with the cell length, is a signature of the contribution of atoms slow enough to fly between the cell windows in a time as long as the characteristic ground state optical pumping time. We suggest that this dark resonance spectroscopy in micro-metric thin cells could be a suitable tool for probing the effective velocity distribution in the thin cell arising from the atomic desorption processes, and notably to identify the limiting factors affecting desorption under a grazing incidence.Comment: 12 pages, 11 figures theoretical articl