A cohomological approach to Ruelle-Pollicott resonances and speed of mixing of Anosov diffeomorphisms

Given a transitive Anosov diffeomorphism on a closed manifold it is known that, for smooth enough observables, the system is mixing w.r.t. the measure of maximal entropy. Therefore, it makes sense to investigate the speed of decay of correlations and to look for the so-called Ruelle-Pollicott resonances, in order to determine a complete asymptotics for the decay of correlations. In this thesis we are able to find the first terms of that asymptotics and to prove an estimate for the speed of decaying of correlations. The proof is based on a surprising connection between the action of a transfer operator on suitable anisotropic Banach spaces of currents and the action induced by the Anosov map on the de Rham cohomology.

Second law analysis and simulation techniques for the energy optimization of buildings

The research activity described in this thesis is focused mainly on the study of finite-element techniques applied to thermo-fluid dynamic problems of plant components and on the study of dynamic simulation techniques applied to integrated building design in order to enhance the energy performance of the building. The first part of this doctorate thesis is a broad dissertation on second law analysis of thermodynamic processes with the purpose of including the issue of the energy efficiency of buildings within a wider cultural context which is usually not considered by professionals in the energy sector. In particular, the first chapter includes, a rigorous scheme for the deduction of the expressions for molar exergy and molar flow exergy of pure chemical fuels. The study shows that molar exergy and molar flow exergy coincide when the temperature and pressure of the fuel are equal to those of the environment in which the combustion reaction takes place. A simple method to determine the Gibbs free energy for non-standard values of the temperature and pressure of the environment is then clarified. For hydrogen, carbon dioxide, and several hydrocarbons, the dependence of the molar exergy on the temperature and relative humidity of the environment is reported, together with an evaluation of molar exergy and molar flow exergy when the temperature and pressure of the fuel are different from those of the environment. As an application of second law analysis, a comparison of the thermodynamic efficiency of a condensing boiler and of a heat pump is also reported. The second chapter presents a study of borehole heat exchangers, that is, a polyethylene piping network buried in the soil which allows a ground-coupled heat pump to exchange heat with the ground. After a brief overview of low-enthalpy geothermal plants, an apparatus designed and assembled by the author to carry out thermal response tests is presented. Data obtained by means of in situ thermal response tests are reported and evaluated by means of a finite-element simulation method, implemented through the software package COMSOL Multyphysics. The simulation method allows the determination of the precise value of the effective thermal properties of the ground and of the grout, which are essential for the design of borehole heat exchangers. In addition to the study of a single plant component, namely the borehole heat exchanger, in the third chapter is presented a thorough process for the plant design of a zero carbon building complex. The plant is composed of: 1) a ground-coupled heat pump system for space heating and cooling, with electricity supplied by photovoltaic solar collectors; 2) air dehumidifiers; 3) thermal solar collectors to match 70% of domestic hot water energy use, and a wood pellet boiler for the remaining domestic hot water energy use and for exceptional winter peaks. This chapter includes the design methodology adopted: 1) dynamic simulation of the building complex with the software package TRNSYS for evaluating the energy requirements of the building complex; 2) ground-coupled heat pumps modelled by means of TRNSYS; and 3) evaluation of the total length of the borehole heat exchanger by an iterative method developed by the author. An economic feasibility and an exergy analysis of the proposed plant, compared with two other plants, are reported. The exergy analysis was performed by considering the embodied energy of the components of each plant and the exergy loss during the functioning of the plants.

Numerical modelling and structural optimization of multifunctional maritime structures aimed to protect harbours and produce energy

The main objective of this PhD thesis is to optimize a specific multifunctional maritime structure for harbour protection and energy production, named Overtopping Breakwater for Energy Conversion (OBREC), developed by the team of the University of Campania. This device is provided with a sloping plate followed by a unique reservoir, which is linked with the machine room (where the energy conversion occurs) by means of a pipe passing through the crown wall, provided with a parapet on top of it. Therefore, the potential energy of the overtopping waves, collected inside the reservoir located above the still water level, is then converted by means of low – head turbines. In order to improve the understanding of the wave – structure interactions with OBREC, several methodologies have been used and combined together: i. analysis of recent experimental campaigns on wave overtopping discharges and pressures at the crown wall on small – scale OBREC cross sections, carried out in other laboratories by the team of the University of Campania; ii. new experiments on cross sections similar to the OBREC device, planned and carried out in the hydraulic lab at the University of Bologna in the framework of this PhD work; iii. numerical modelling with a 1 – phase incompressible fluid model IH – 2VOF, developed by the University of Cantabria, and with a 2 – phase incompressible fluid model OpenFOAM, both available from the literature; iv. numerical modelling with a new 2 – phase compressible fluid model developed in the OpenFOAM environment within this PhD work; v. analysis of the data gained from the monitoring of the OBREC prototype installation.

Statistical properties of Radio Halos and the re-acceleration model

Galaxy clusters occupy a special position in the cosmic hierarchy as they are the largest bound structures in the Universe. There is now general agreement on a hierarchical picture for the formation of cosmic structures, in which galaxy clusters are supposed to form by accretion of matter and merging between smaller units. During merger events, shocks are driven by the gravity of the dark matter in the diffuse barionic component, which is heated up to the observed temperature. Radio and hard-X ray observations have discovered non-thermal components mixed with the thermal Intra Cluster Medium (ICM) and this is of great importance as it calls for a “revision” of the physics of the ICM. The bulk of present information comes from the radio observations which discovered an increasing number of Mpcsized emissions from the ICM, Radio Halos (at the cluster center) and Radio Relics (at the cluster periphery). These sources are due to synchrotron emission from ultra relativistic electrons diffusing through µG turbulent magnetic fields. Radio Halos are the most spectacular evidence of non-thermal components in the ICM and understanding the origin and evolution of these sources represents one of the most challenging goal of the theory of the ICM. Cluster mergers are the most energetic events in the Universe and a fraction of the energy dissipated during these mergers could be channelled into the amplification of the magnetic fields and into the acceleration of high energy particles via shocks and turbulence driven by these mergers. Present observations of Radio Halos (and possibly of hard X-rays) can be best interpreted in terms of the reacceleration scenario in which MHD turbulence injected during these cluster mergers re-accelerates high energy particles in the ICM. The physics involved in this scenario is very complex and model details are difficult to test, however this model clearly predicts some simple properties of Radio Halos (and resulting IC emission in the hard X-ray band) which are almost independent of the details of the adopted physics. In particular in the re-acceleration scenario MHD turbulence is injected and dissipated during cluster mergers and thus Radio Halos (and also the resulting hard X-ray IC emission) should be transient phenomena (with a typical lifetime <» 1 Gyr) associated with dynamically disturbed clusters. The physics of the re-acceleration scenario should produce an unavoidable cut-off in the spectrum of the re-accelerated electrons, which is due to the balance between turbulent acceleration and radiative losses. The energy at which this cut-off occurs, and thus the maximum frequency at which synchrotron radiation is produced, depends essentially on the efficiency of the acceleration mechanism so that observations at high frequencies are expected to catch only the most efficient phenomena while, in principle, low frequency radio surveys may found these phenomena much common in the Universe. These basic properties should leave an important imprint in the statistical properties of Radio Halos (and of non-thermal phenomena in general) which, however, have not been addressed yet by present modellings. The main focus of this PhD thesis is to calculate, for the first time, the expected statistics of Radio Halos in the context of the re-acceleration scenario. In particular, we shall address the following main questions: • Is it possible to model “self-consistently” the evolution of these sources together with that of the parent clusters? • How the occurrence of Radio Halos is expected to change with cluster mass and to evolve with redshift? How the efficiency to catch Radio Halos in galaxy clusters changes with the observing radio frequency? • How many Radio Halos are expected to form in the Universe? At which redshift is expected the bulk of these sources? • Is it possible to reproduce in the re-acceleration scenario the observed occurrence and number of Radio Halos in the Universe and the observed correlations between thermal and non-thermal properties of galaxy clusters? • Is it possible to constrain the magnetic field intensity and profile in galaxy clusters and the energetic of turbulence in the ICM from the comparison between model expectations and observations? Several astrophysical ingredients are necessary to model the evolution and statistical properties of Radio Halos in the context of re-acceleration model and to address the points given above. For these reason we deserve some space in this PhD thesis to review the important aspects of the physics of the ICM which are of interest to catch our goals. In Chapt. 1 we discuss the physics of galaxy clusters, and in particular, the clusters formation process; in Chapt. 2 we review the main observational properties of non-thermal components in the ICM; and in Chapt. 3 we focus on the physics of magnetic field and of particle acceleration in galaxy clusters. As a relevant application, the theory of Alfv´enic particle acceleration is applied in Chapt. 4 where we report the most important results from calculations we have done in the framework of the re-acceleration scenario. In this Chapter we show that a fraction of the energy of fluid turbulence driven in the ICM by the cluster mergers can be channelled into the injection of Alfv´en waves at small scales and that these waves can efficiently re-accelerate particles and trigger Radio Halos and hard X-ray emission. The main part of this PhD work, the calculation of the statistical properties of Radio Halos and non-thermal phenomena as expected in the context of the re-acceleration model and their comparison with observations, is presented in Chapts.5, 6, 7 and 8. In Chapt.5 we present a first approach to semi-analytical calculations of statistical properties of giant Radio Halos. The main goal of this Chapter is to model cluster formation, the injection of turbulence in the ICM and the resulting particle acceleration process. We adopt the semi–analytic extended Press & Schechter (PS) theory to follow the formation of a large synthetic population of galaxy clusters and assume that during a merger a fraction of the PdV work done by the infalling subclusters in passing through the most massive one is injected in the form of magnetosonic waves. Then the processes of stochastic acceleration of the relativistic electrons by these waves and the properties of the ensuing synchrotron (Radio Halos) and inverse Compton (IC, hard X-ray) emission of merging clusters are computed under the assumption of a constant rms average magnetic field strength in emitting volume. The main finding of these calculations is that giant Radio Halos are naturally expected only in the more massive clusters, and that the expected fraction of clusters with Radio Halos is consistent with the observed one. In Chapt. 6 we extend the previous calculations by including a scaling of the magnetic field strength with cluster mass. The inclusion of this scaling allows us to derive the expected correlations between the synchrotron radio power of Radio Halos and the X-ray properties (T, LX) and mass of the hosting clusters. For the first time, we show that these correlations, calculated in the context of the re-acceleration model, are consistent with the observed ones for typical µG strengths of the average B intensity in massive clusters. The calculations presented in this Chapter allow us to derive the evolution of the probability to form Radio Halos as a function of the cluster mass and redshift. The most relevant finding presented in this Chapter is that the luminosity functions of giant Radio Halos at 1.4 GHz are expected to peak around a radio power » 1024 W/Hz and to flatten (or cut-off) at lower radio powers because of the decrease of the electron re-acceleration efficiency in smaller galaxy clusters. In Chapt. 6 we also derive the expected number counts of Radio Halos and compare them with available observations: we claim that » 100 Radio Halos in the Universe can be observed at 1.4 GHz with deep surveys, while more than 1000 Radio Halos are expected to be discovered in the next future by LOFAR at 150 MHz. This is the first (and so far unique) model expectation for the number counts of Radio Halos at lower frequency and allows to design future radio surveys. Based on the results of Chapt. 6, in Chapt.7 we present a work in progress on a “revision” of the occurrence of Radio Halos. We combine past results from the NVSS radio survey (z » 0.05 − 0.2) with our ongoing GMRT Radio Halos Pointed Observations of 50 X-ray luminous galaxy clusters (at z » 0.2−0.4) and discuss the possibility to test our model expectations with the number counts of Radio Halos at z » 0.05 − 0.4. The most relevant limitation in the calculations presented in Chapt. 5 and 6 is the assumption of an “averaged” size of Radio Halos independently of their radio luminosity and of the mass of the parent clusters. This assumption cannot be released in the context of the PS formalism used to describe the formation process of clusters, while a more detailed analysis of the physics of cluster mergers and of the injection process of turbulence in the ICM would require an approach based on numerical (possible MHD) simulations of a very large volume of the Universe which is however well beyond the aim of this PhD thesis. On the other hand, in Chapt.8 we report our discovery of novel correlations between the size (RH) of Radio Halos and their radio power and between RH and the cluster mass within the Radio Halo region, MH. In particular this last “geometrical” MH − RH correlation allows us to “observationally” overcome the limitation of the “average” size of Radio Halos. Thus in this Chapter, by making use of this “geometrical” correlation and of a simplified form of the re-acceleration model based on the results of Chapt. 5 and 6 we are able to discuss expected correlations between the synchrotron power and the thermal cluster quantities relative to the radio emitting region. This is a new powerful tool of investigation and we show that all the observed correlations (PR − RH, PR − MH, PR − T, PR − LX, . . . ) now become well understood in the context of the re-acceleration model. In addition, we find that observationally the size of Radio Halos scales non-linearly with the virial radius of the parent cluster, and this immediately means that the fraction of the cluster volume which is radio emitting increases with cluster mass and thus that the non-thermal component in clusters is not self-similar.

Petrology and geochemistry of Lipari Island (Aeolian archipelago): constraints on magma genesis and evolution

A full set of geochemical and Sr, Nd and Pb isotope data both on bulk-rock and mineral samples is provided for volcanic rocks representative of the whole stratigraphic succession of Lipari Island in the Aeolian archipelago. These data, together with petrographic observations and melt/fluid inclusion investigations from the literature, give outlines on the petrogenesis and evolution of magmas through the magmatic and eruptive history of Lipari. This is the result of nine successive Eruptive Epochs developing between 271 ka and historical times, as derived from recentmost volcanological and stratigraphic studies, combined with available radiometric ages and correlation of tephra layers and marine terrace deposits. These Eruptive Epochs are characterized by distinctive vents partly overlapping in space and time, mostly under control of the main regional tectonic trends (NNW-SSE, N-S and minor E-W). A large variety of lava flows, scoriaceous deposits, lava domes, coulees and pyroclastics are emplaced, ranging in composition through time from calcalkaline (CA) and high-K (HKCA) basaltic andesites to rhyolites. CA and HKCA basaltic andesitic to dacitic magmas were erupted between 271 and 81 ka (Eruptive Epochs 1-6) from volcanic edifices located along the western coast of the island (and subordinately the eastern Monterosa) and the M.Chirica and M.S.Angelo stratocones. These mafic to intermediate magmas mainly evolved through AFC and RAFC processes, involving fractionation of mafic phases, assimilation of wall rocks and mixing with newly injected mafic magmas. Following a 40 ka-long period of volcanic quiescence, the rhyolitic magmas were lately erupted from eruptive vents located in the southern and north-eastern sectors of Lipari between 40 ka and historical times (Eruptive Epochs 7-9). They are suggested to derive from the previous mafic to intermediate melts through AFC processes. During the early phases of rhyolitic magmatism (Eruptive Epochs 7-8), enclaves-rich rocks and banded pumices, ranging in composition from HKCA dacites to low-SiO2 rhyolites were erupted, representing the products of magma mixing between fresh mafic magmas and the fractionated rhyolitic melts. The interaction of mantle-derived magmas with the crust represents an essential process during the whole magmatic hystory of Lipari, and is responsible for the wide range of observed geochemical and isotopic variations. The crustal contribution was particularly important during the intermediate phases of activity of Lipari when the cordierite-bearing lavas were erupted from the M. S.Angelo volcano (Eruptive Epoch 5, 105 ka). These lavas are interpreted as the result of mixing and subsequent hybridization of mantle-derived magmas, akin to the ones characterizing the older phases of activity of Lipari (Eruptive Epochs 1-4), and crustal anatectic melts derived from dehydration-melting reactions of metapelites in the lower crust. A comparison between the adjacent islands of Lipari and Vulcano outlines that their mafic to intermediate magmas seem to be genetically connected and derive from a similar mantle source affected by different degrees of partial melting (and variable extent of crustal assimilation) producing either the CA magmas of Lipari (higher degrees) or the HKCA to SHO magmas of Vulcano (lower degrees). On a regional scale, the most primitive rocks (SiO2<56%, MgO>3.5%) of Lipari, Vulcano, Salina and Filicudi are suggested to derive from a similar MORB-like source, variably metasomatized by aqueous fluids coming from the slab and subordinately by the additions of sediments.

Measurements of ttbar Differential Cross Section at the ATLAS Experiment in pp Collisions at sqrt(s)=7TeV and sqrt(s)=8TeV

This PhD thesis presents two measurements of differential production cross section of top and anti-top pairs tt ̅ decaying in a lepton+jets final state. The normalize cross section is measured as a function of the top transverse momentum and the tt ̅ mass, transverse momentum and rapidity using the full 2011 proton-proton (pp) ATLAS data taking at a center of mass energy of √s=7 TeV and corresponding to an integrated luminosity of L=4.6 〖fb〗^(-1). The cross section is also measured at the particle level as a function of the hadronic top transverse momentum for highly energetic events using the full 2012 data taking at √s=8 TeV and with L=20 〖fb〗^(-1). The measured spectra are fully corrected for detector efficiency and resolution effects and are compared to several theoretical predictions showing a quite good agreement, depending on different spectra.

Toward a Magnitude Scale for Low Frequency Seismicity The LP energy for Campi Flegrei caldera

The energy released during a seismic crisis in volcanic areas is strictly related to the physical processes in the volcanic structure. In particular Long Period seismicity, that seems to be related to the oscillation of a fluid-filled crack (Chouet , 1996, Chouet, 2003, McNutt, 2005), can precedes or accompanies an eruption. The present doctoral thesis is focused on the study of the LP seismicity recorded in the Campi Flegrei volcano (Campania, Italy) during the October 2006 crisis. Campi Flegrei Caldera is an active caldera; the combination of an active magmatic system and a dense populated area make the Campi Flegrei a critical volcano. The source dynamic of LP seismicity is thought to be very different from the other kind of seismicity ( Tectonic or Volcano Tectonic): it’s characterized by a time sustained source and a low content in frequency. This features implies that the duration–magnitude, that is commonly used for VT events and sometimes for LPs as well, is unadapted for LP magnitude evaluation. The main goal of this doctoral work was to develop a method for the determination of the magnitude for the LP seismicity; it’s based on the comparison of the energy of VT event and LP event, linking the energy to the VT moment magnitude. So the magnitude of the LP event would be the moment magnitude of a VT event with the same energy of the LP. We applied this method to the LP data-set recorded at Campi Flegrei caldera in 2006, to an LP data-set of Colima volcano recorded in 2005 – 2006 and for an event recorded at Etna volcano. Experimenting this method to lots of waveforms recorded at different volcanoes we tested its easy applicability and consequently its usefulness in the routinely and in the quasi-real time work of a volcanological observatory.