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

Effective Forchheimer Coefficient for Layered Porous Media

Inertial flow in porous media, governed by the Forchheimer equation, is affected by domain heterogeneity at the field scale. We propose a method to derive formulae of the effective Forchheimer coefficient with application to a perfectly stratified medium. Consider uniform flow under a constant pressure gradient Delta P/L in a layered permeability field with a given probability distribution. The local Forchheimer coefficient beta is related to the local permeability k via the relation beta = a/k(c), where a > 0 being a constant and c is an element of [0, 2]. Under ergodicity, an effective value of beta is derived for flow (i) perpendicular and (ii) parallel to layers. Expressions for effective Forchheimer coefficient, beta(e), generalize previous formulations for discrete permeability variations. Closed-form beta(e) expressions are derived for flow perpendicular to layers and under two limit cases, F << 1 and F >> 1, for flow parallel to layering, with F a Forchheimer number depending on the pressure gradient. For F of order unity, beta(e) is obtained numerically: when realistic values of Delta P/L and a are adopted, beta(e) approaches the results valid for the high Forchheimer approximation. Further, beta(e) increases with heterogeneity, with values always larger than those it would take if the beta - k relationship was applied to the mean permeability; it increases (decreases) with increasing (decreasing) exponent c for flow perpendicular (parallel) to layers. beta(e) is also moderately sensitive to the permeability distribution, and is larger for the gamma than for the lognormal distribution

PROVISIONAL MEASURES IN INTERNATIONAL INVESTMENT ARBITRATION

The thesis deals with provisional measures in one of the fastest-growing areas of public international law, namely international investment law and arbitration. Since to the best of my knowledge no monograph has ever been devoted thereto, my task in structuring this dissertation was at the same time easy (I was completely free to choose) and difficult (there was no extensive study to which I could refer). Moreover, the fact that this topic is a moving target, as I demonstrated in my study, rendered my task more complicated and fascinating. Therefore, this thesis constitutes a very personal endeavour, since it aims at representing the current state of my topic as it appeared to me throughout these three years. After presenting the investment framework with a broad angle (Chapter one), the analysis proceeds through the adoption of a differentiated approach: in Chapter two I firstly draw on the history of the interpretation and application of provisional measures in inter-State and State-private international adjudication (Section one) and, secondly, address these measures from a comparative perspective inscribed in public international law adjudication (Section two). Indeed, in my opinion the choice of comparing the arbitral provisional power in international investment arbitration and international commercial arbitration would have been a wrong one, for two series of reasons, which can be briefly summarised as follows: - The sovereign nature of one of the parties determines a fundamental difference between the two frameworks, causing that group of disputes to be inscribed in public international law adjudication, which merely share with international commercial arbitration the dispute settlement tool; - As a corollary, contrary to international commercial arbitral case law, investment arbitral case law is perfectly able to influence (and to be influenced by) consolidation, divergence and development of public international law, constituting one of its sources under the terms of Art. 38 (1) lett. d) of the ICJ Statute. Chapter three is devoted to the current state of provisional measures in international investment arbitration. Section one addresses their specific features, namely legal force and exclusive / concurrent jurisdiction to rule upon them. Thereafter, Section two focuses on conditions, purposes and atypicalness of recourse thereto (in the effort to describe the picture of the arbitral default rules as they emerge from case law), whereas Section three sets some aspects of treatification and contractualisation of provisional measures. Chapter four discusses the rules applicable to the implementation of these measures, considering voluntary compliance, non-compliance and its consequences, finally the options available to the addressee in order to oppose their application. My thesis concludes with some remarks on the role of consent, namely on the possibility for the parties to amend such default rules - through treatification and contractualisation of provisional measures - before their potential dispute occurs. Thus, they are able to tailor the latter to their needs, and particularly to their bargaining power before the investment is carried out in the host State, so as to increase legal security in that respect

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

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

Modal parameters identification with environmental tests and advanced numerical analyses for masonry bell towers: a meaningful case study

Abstract In the first part, a dynamic monitoring for non-destructive evaluation of heritage structures is discussed with reference to a case study, namely the Pomposa Abbey belfry, located in the Ferrara Province (Italy). The main dynamic parameters constitute an important reference to define an advanced numerical model, discussed in the second part, based on Non-Smooth Contact Dynamics (NSCD) method. Schematised as a system of rigid blocks undergoing frictional sliding and plastic impacts, the tower has exhibited complex dynamics, because of both geometrical nonlinearity and the non-smooth nature of the contact laws. First, harmonic oscillations have been applied to the basement of the tower and a systematic parametric study has been conducted, aimed at correlating the system vulnerability to the values of amplitude and frequency of the assigned excitation corroborated by the dynamic identification results. In addition, numerical analyses have been done to highlight the effects of the friction coefficient and of the blocks geometries on the dynamics, in particular on the collapse modes. Finally, a study of the tower stability against seismic excitations has been addressed and 3D simulations have been performed with a real earthquake

iconic crumbling of the clock tower in amatrice after 2016 central italy seismic sequence advanced numerical insight

Abstract The present paper investigates from an advanced numerical point of view the progressive damage of the Amatrice (Rieti, Italy) civic clock tower, after a long sequence of strong earthquakes that struck central Italy in 2016. Two advanced numerical models are here utilised to have an insight into the modalities of progressive damage and the behaviour of the structure under strong non-linear dynamic excitations, namely a Non-Smooth Contact Dynamics (NSCD) and a FE Concrete Damage Plasticity (CDP) models. In both cases, a full 3D detailed discretization is adopted. From the numerical results, both the role played by the actual geometries and the insufficient resistance of the constituent materials are envisaged, showing a good match with actual crack patterns observed after the seismic sequence

Proceedings of the EYCN Symposium – 1st Edition

The 1st edition of the EYCN Symposium is the scientific event organized by the Italian Chemical Society and the European Young Chemists’ Network within the XIII EYCN Delegate Assembly. This symposium is fully devoted to young researchers, such as MSc and PhD students, post-doc fellows and young researchers in companies. All the disciplines of Chemistry are covered: analytical, physical, industrial, organic, inorganic, theoretical, pharmaceutical, biological, environmental, macromolecular and electrochemistry

On infinite-volume mixing

In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be relevant, at least for extended systems with a direct physical interpretation. We discuss the pros and cons of a few mathematical definitions that can be devised, testing them on a prototypical class of infinite measure-preserving dynamical systems, namely, the random walks.Comment: 34 pages, final version accepted by Communications in Mathematical Physics (some changes in Sect. 3 -- Prop. 3.1 in previous version was partially incorrect

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