Cosmological perturbations in generalized theories of gravity

The first part of the thesis concerns the study of inflation in the context of a theory of gravity called "Induced Gravity" in which the gravitational coupling varies in time according to the dynamics of the very same scalar field (the "inflaton") driving inflation, while taking on the value measured today since the end of inflation. Through the analytical and numerical analysis of scalar and tensor cosmological perturbations we show that the model leads to consistent predictions for a broad variety of symmetry-breaking inflaton's potentials, once that a dimensionless parameter entering into the action is properly constrained. We also discuss the average expansion of the Universe after inflation (when the inflaton undergoes coherent oscillations about the minimum of its potential) and determine the effective equation of state. Finally, we analyze the resonant and perturbative decay of the inflaton during (p)reheating. The second part is devoted to the study of a proposal for a quantum theory of gravity dubbed "Horava-Lifshitz (HL) Gravity" which relies on power-counting renormalizability while explicitly breaking Lorentz invariance. We test a pair of variants of the theory ("projectable" and "non-projectable") on a cosmological background and with the inclusion of scalar field matter. By inspecting the quadratic action for the linear scalar cosmological perturbations we determine the actual number of propagating degrees of freedom and realize that the theory, being endowed with less symmetries than General Relativity, does admit an extra gravitational degree of freedom which is potentially unstable. More specifically, we conclude that in the case of projectable HL Gravity the extra mode is either a ghost or a tachyon, whereas in the case of non-projectable HL Gravity the extra mode can be made well-behaved for suitable choices of a pair of free dimensionless parameters and, moreover, turns out to decouple from the low-energy Physics.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

The VIMOS-VLT Deep Survey: the evolution of type-1 AGN

Quasars and AGN play an important role in many aspects of the modern cosmology. Of particular interest is the issue of the interplay between AGN activity and formation and evolution of galaxies and structures. Studies on nearby galaxies revealed that most (and possibly all) galaxy nuclei contain a super-massive black hole (SMBH) and that between a third and half of them are showing some evidence of activity (Kormendy and Richstone, 1995). The discovery of a tight relation between black holes mass and velocity dispersion of their host galaxy suggests that the evolution of the growth of SMBH and their host galaxy are linked together. In this context, studying the evolution of AGN, through the luminosity function (LF), is fundamental to constrain the theories of galaxy and SMBH formation and evolution. Recently, many theories have been developed to describe physical processes possibly responsible of a common formation scenario for galaxies and their central black hole (Volonteri et al., 2003; Springel et al., 2005a; Vittorini et al., 2005; Hopkins et al., 2006a) and an increasing number of observations in different bands are focused on collecting larger and larger quasar samples. Many issues remain however not yet fully understood. In the context of the VVDS (VIMOS-VLT Deep Survey), we collected and studied an unbiased sample of spectroscopically selected faint type-1 AGN with a unique and straightforward selection function. Indeed, the VVDS is a large, purely magnitude limited spectroscopic survey of faint objects, free of any morphological and/or color preselection. We studied the statistical properties of this sample and its evolution up to redshift z 4. Because of the contamination of the AGN light by their host galaxies at the faint magnitudes explored by our sample, we observed that a significant fraction of AGN in our sample would be missed by the UV excess and morphological criteria usually adopted for the pre-selection of optical QSO candidates. If not properly taken into account, this failure in selecting particular sub-classes of AGN could, in principle, affect some of the conclusions drawn from samples of AGN based on these selection criteria. The absence of any pre-selection in the VVDS leads us to have a very complete sample of AGN, including also objects with unusual colors and continuum shape. The VVDS AGN sample shows in fact redder colors than those expected by comparing it, for example, with the color track derived from the SDSS composite spectrum. In particular, the faintest objects have on average redder colors than the brightest ones. This can be attributed to both a large fraction of dust-reddened objects and a significant contamination from the host galaxy. We have tested these possibilities by examining the global spectral energy distribution of each object using, in addition to the U, B, V, R and I-band magnitudes, also the UV-Galex and the IR-Spitzer bands, and fitting it with a combination of AGN and galaxy emission, allowing also for the possibility of extinction of the AGN flux. We found that for 44% of our objects the contamination from the host galaxy is not negligible and this fraction decreases to 21% if we restrict the analysis to a bright subsample (M1450 <-22.15). Our estimated integral surface density at IAB < 24.0 is 500 AGN per square degree, which represents the highest surface density of a spectroscopically confirmed sample of optically selected AGN. We derived the luminosity function in B-band for 1.0 < z < 3.6 using the 1/Vmax estimator. Our data, more than one magnitude fainter than previous optical surveys, allow us to constrain the faint part of the luminosity function up to high redshift. A comparison of our data with the 2dF sample at low redshift (1 < z < 2.1) shows that the VDDS data can not be well fitted with the pure luminosity evolution (PLE) models derived by previous optically selected samples. Qualitatively, this appears to be due to the fact that our data suggest the presence of an excess of faint objects at low redshift (1.0 < z < 1.5) with respect to these models. By combining our faint VVDS sample with the large sample of bright AGN extracted from the SDSS DR3 (Richards et al., 2006b) and testing a number of different evolutionary models, we find that the model which better represents the combined luminosity functions, over a wide range of redshift and luminosity, is a luminosity dependent density evolution (LDDE) model, similar to those derived from the major Xsurveys. Such a parameterization allows the redshift of the AGN density peak to change as a function of luminosity, thus fitting the excess of faint AGN that we find at 1.0 < z < 1.5. On the basis of this model we find, for the first time from the analysis of optically selected samples, that the peak of the AGN space density shifts significantly towards lower redshift going to lower luminosity objects. The position of this peak moves from z 2.0 for MB <-26.0 to z 0.65 for -22< MB <-20. This result, already found in a number of X-ray selected samples of AGN, is consistent with a scenario of “AGN cosmic downsizing”, in which the density of more luminous AGN, possibly associated to more massive black holes, peaks earlier in the history of the Universe (i.e. at higher redshift), than that of low luminosity ones, which reaches its maximum later (i.e. at lower redshift). This behavior has since long been claimed to be present in elliptical galaxies and it is not easy to reproduce it in the hierarchical cosmogonic scenario, where more massive Dark Matter Halos (DMH) form on average later by merging of less massive halos.

Essays on the political economy of European integration

Recently, a rising interest in political and economic integration/disintegration issues has been developed in the political economy field. This growing strand of literature partly draws on traditional issues of fiscal federalism and optimum public good provision and focuses on a trade-off between the benefits of centralization, arising from economies of scale or externalities, and the costs of harmonizing policies as a consequence of the increased heterogeneity of individual preferences in an international union or in a country composed of at least two regions. This thesis stems from this strand of literature and aims to shed some light on two highly relevant aspects of the political economy of European integration. The first concerns the role of public opinion in the integration process; more precisely, how economic benefits and costs of integration shape citizens' support for European Union (EU) membership. The second is the allocation of policy competences among different levels of government: European, national and regional. Chapter 1 introduces the topics developed in this thesis by reviewing the main recent theoretical developments in the political economy analysis of integration processes. It is structured as follows. First, it briefly surveys a few relevant articles on economic theories of integration and disintegration processes (Alesina and Spolaore 1997, Bolton and Roland 1997, Alesina et al. 2000, Casella and Feinstein 2002) and discusses their relevance for the study of the impact of economic benefits and costs on public opinion attitude towards the EU. Subsequently, it explores the links existing between such political economy literature and theories of fiscal federalism, especially with regard to normative considerations concerning the optimal allocation of competences in a union. Chapter 2 firstly proposes a model of citizens’ support for membership of international unions, with explicit reference to the EU; subsequently it tests the model on a panel of EU countries. What are the factors that influence public opinion support for the European Union (EU)? In international relations theory, the idea that citizens' support for the EU depends on material benefits deriving from integration, i.e. whether European integration makes individuals economically better off (utilitarian support), has been common since the 1970s, but has never been the subject of a formal treatment (Hix 2005). A small number of studies in the 1990s have investigated econometrically the link between national economic performance and mass support for European integration (Eichenberg and Dalton 1993; Anderson and Kalthenthaler 1996), but only making informal assumptions. The main aim of Chapter 2 is thus to propose and test our model with a view to providing a more complete and theoretically grounded picture of public support for the EU. Following theories of utilitarian support, we assume that citizens are in favour of membership if they receive economic benefits from it. To develop this idea, we propose a simple political economic model drawing on the recent economic literature on integration and disintegration processes. The basic element is the existence of a trade-off between the benefits of centralisation and the costs of harmonising policies in presence of heterogeneous preferences among countries. The approach we follow is that of the recent literature on the political economy of international unions and the unification or break-up of nations (Bolton and Roland 1997, Alesina and Wacziarg 1999, Alesina et al. 2001, 2005a, to mention only the relevant). The general perspective is that unification provides returns to scale in the provision of public goods, but reduces each member state’s ability to determine its most favoured bundle of public goods. In the simple model presented in Chapter 2, support for membership of the union is increasing in the union’s average income and in the loss of efficiency stemming from being outside the union, and decreasing in a country’s average income, while increasing heterogeneity of preferences among countries points to a reduced scope of the union. Afterwards we empirically test the model with data on the EU; more precisely, we perform an econometric analysis employing a panel of member countries over time. The second part of Chapter 2 thus tries to answer the following question: does public opinion support for the EU really depend on economic factors? The findings are broadly consistent with our theoretical expectations: the conditions of the national economy, differences in income among member states and heterogeneity of preferences shape citizens’ attitude towards their country’s membership of the EU. Consequently, this analysis offers some interesting policy implications for the present debate about ratification of the European Constitution and, more generally, about how the EU could act in order to gain more support from the European public. Citizens in many member states are called to express their opinion in national referenda, which may well end up in rejection of the Constitution, as recently happened in France and the Netherlands, triggering a European-wide political crisis. These events show that nowadays understanding public attitude towards the EU is not only of academic interest, but has a strong relevance for policy-making too. Chapter 3 empirically investigates the link between European integration and regional autonomy in Italy. Over the last few decades, the double tendency towards supranationalism and regional autonomy, which has characterised some European States, has taken a very interesting form in this country, because Italy, besides being one of the founding members of the EU, also implemented a process of decentralisation during the 1970s, further strengthened by a constitutional reform in 2001. Moreover, the issue of the allocation of competences among the EU, the Member States and the regions is now especially topical. The process leading to the drafting of European Constitution (even if then it has not come into force) has attracted much attention from a constitutional political economy perspective both on a normative and positive point of view (Breuss and Eller 2004, Mueller 2005). The Italian parliament has recently passed a new thorough constitutional reform, still to be approved by citizens in a referendum, which includes, among other things, the so called “devolution”, i.e. granting the regions exclusive competence in public health care, education and local police. Following and extending the methodology proposed in a recent influential article by Alesina et al. (2005b), which only concentrated on the EU activity (treaties, legislation, and European Court of Justice’s rulings), we develop a set of quantitative indicators measuring the intensity of the legislative activity of the Italian State, the EU and the Italian regions from 1973 to 2005 in a large number of policy categories. By doing so, we seek to answer the following broad questions. Are European and regional legislations substitutes for state laws? To what extent are the competences attributed by the European treaties or the Italian Constitution actually exerted in the various policy areas? Is their exertion consistent with the normative recommendations from the economic literature about their optimum allocation among different levels of government? The main results show that, first, there seems to be a certain substitutability between EU and national legislations (even if not a very strong one), but not between regional and national ones. Second, the EU concentrates its legislative activity mainly in international trade and agriculture, whilst social policy is where the regions and the State (which is also the main actor in foreign policy) are more active. Third, at least two levels of government (in some cases all of them) are significantly involved in the legislative activity in many sectors, even where the rationale for that is, at best, very questionable, indicating that they actually share a larger number of policy tasks than that suggested by the economic theory. It appears therefore that an excessive number of competences are actually shared among different levels of government. From an economic perspective, it may well be recommended that some competences be shared, but only when the balance between scale or spillover effects and heterogeneity of preferences suggests so. When, on the contrary, too many levels of government are involved in a certain policy area, the distinction between their different responsibilities easily becomes unnecessarily blurred. This may not only leads to a slower and inefficient policy-making process, but also risks to make it too complicate to understand for citizens, who, on the contrary, should be able to know who is really responsible for a certain policy when they vote in national,local or European elections or in referenda on national or European constitutional issues.

Crustal heterogeneities and complexities of fault processes

In this work we study the relation between crustal heterogeneities and complexities in fault processes. The first kind of heterogeneity considered involves the concept of asperity. The presence of an asperity in the hypocentral region of the M = 6.5 earthquake of June 17-th, 2000 in the South Iceland Seismic Zone was invoked to explain the change of seismicity pattern before and after the mainshock: in particular, the spatial distribution of foreshock epicentres trends NW while the strike of the main fault is N 7◦ E and aftershocks trend accordingly; the foreshock depths were typically deeper than average aftershock depths. A model is devised which simulates the presence of an asperity in terms of a spherical inclusion, within a softer elastic medium in a transform domain with a deviatoric stress field imposed at remote distances (compressive NE − SW, tensile NW − SE). An isotropic compressive stress component is induced outside the asperity, in the direction of the compressive stress axis, and a tensile component in the direction of the tensile axis; as a consequence, fluid flow is inhibited in the compressive quadrants while it is favoured in tensile quadrants. Within the asperity the isotropic stress vanishes but the deviatoric stress increases substantially, without any significant change in the principal stress directions. Hydrofracture processes in the tensile quadrants and viscoelastic relaxation at depth may contribute to lower the effective rigidity of the medium surrounding the asperity. According to the present model, foreshocks may be interpreted as induced, close to the brittle-ductile transition, by high pressure fluids migrating upwards within the tensile quadrants; this process increases the deviatoric stress within the asperity which eventually fails, becoming the hypocenter of the mainshock, on the optimally oriented fault plane. In the second part of our work we study the complexities induced in fault processes by the layered structure of the crust. In the first model proposed we study the case in which fault bending takes place in a shallow layer. The problem can be addressed in terms of a deep vertical planar crack, interacting with a shallower inclined planar crack. An asymptotic study of the singular behaviour of the dislocation density at the interface reveals that the density distribution has an algebraic singularity at the interface of degree ω between -1 and 0, depending on the dip angle of the upper crack section and on the rigidity contrast between the two media. From the welded boundary condition at the interface between medium 1 and 2, a stress drop discontinuity condition is obtained which can be fulfilled if the stress drop in the upper medium is lower than required for a planar trough-going surface: as a corollary, a vertically dipping strike-slip fault at depth may cross the interface with a sedimentary layer, provided that the shallower section is suitably inclined (fault "refraction"); this results has important implications for our understanding of the complexity of the fault system in the SISZ; in particular, we may understand the observed offset of secondary surface fractures with respect to the strike direction of the seismic fault. The results of this model also suggest that further fractures can develop in the opposite quadrant and so a second model describing fault branching in the upper layer is proposed. As the previous model, this model can be applied only when the stress drop in the shallow layer is lower than the value prescribed for a vertical planar crack surface. Alternative solutions must be considered if the stress drop in the upper layer is higher than in the other layer, which may be the case when anelastic processes relax deviatoric stress in layer 2. In such a case one through-going crack cannot fulfil the welded boundary conditions and unwelding of the interface may take place. We have solved this problem within the theory of fracture mechanics, employing the boundary element method. The fault terminates against the interface in a T-shaped configuration, whose segments interact among each other: the lateral extent of the unwelded surface can be computed in terms of the main fault parameters and the stress field resulting in the shallower layer can be modelled. A wide stripe of high and nearly uniform shear stress develops above the unwelded surface, whose width is controlled by the lateral extension of unwelding. Secondary shear fractures may then open within this stripe, according to the Coulomb failure criterion, and the depth of open fractures opening in mixed mode may be computed and compared with the well studied fault complexities observed in the field. In absence of the T-shaped decollement structure, stress concentration above the seismic fault would be difficult to reconcile with observations, being much higher and narrower.

Astronomical site testing in the era of the extremely large telescopes

The quality of astronomical sites is the first step to be considered to have the best performances from the telescopes. In particular, the efficiency of large telescopes in UV, IR, radio etc. is critically dependent on atmospheric transparency. It is well known that the random optical effects induced on the light propagation by turbulent atmosphere also limit telescope’s performances. Nowadays, clear appears the importance to correlate the main atmospheric physical parameters with the optical quality reachable by large aperture telescopes. The sky quality evaluation improved with the introduction of new techniques, new instrumentations and with the understanding of the link between the meteorological (or synoptical parameters and the observational conditions thanks to the application of the theories of electromagnetic waves propagation in turbulent medias: what we actually call astroclimatology. At the present the site campaigns are evolved and are performed using the classical scheme of optical seeing properties, meteorological parameters, sky transparency, sky darkness and cloudiness. New concept are added and are related to the geophysical properties such as seismicity, microseismicity, local variability of the climate, atmospheric conditions related to the ground optical turbulence and ground wind regimes, aerosol presence, use of satellite data. The purpose of this project is to provide reliable methods to analyze the atmospheric properties that affect ground-based optical astronomical observations and to correlate them with the main atmospheric parameters generating turbulence and affecting the photometric accuracy. The first part of the research concerns the analysis and interpretation of longand short-time scale meteorological data at two of the most important astronomical sites located in very different environments: the Paranal Observatory in the Atacama Desert (Chile), and the Observatorio del Roque de Los Muchachos(ORM) located in La Palma (Canary Islands, Spain). The optical properties of airborne dust at ORM have been investigated collecting outdoor data using a ground-based dust monitor. Because of its dryness, Paranal is a suitable observatory for near-IR observations, thus the extinction properties in the spectral range 1.00-2.30 um have been investigated using an empirical method. Furthermore, this PhD research has been developed using several turbulence profilers in the selection of the site for the European Extremely Large Telescope(E-ELT). During the campaigns the properties of the turbulence at different heights at Paranal and in the sites located in northern Chile and Argentina have been studied. This given the possibility to characterize the surface layer turbulence at Paranal and its connection with local meteorological conditions.

International Agricultural Trade under Regulatory Asymmetry: An Economic Analysis of SME Export Behavior

Over the last three decades, international agricultural trade has grown significantly. Technological advances in transportation logistics and storage have created opportunities to ship anything almost anywhere. Bilateral and multilateral trade agreements have also opened new pathways to an increasingly global market place. Yet, international agricultural trade is often constrained by differences in regulatory regimes. The impact of “regulatory asymmetry” is particularly acute for small and medium sized enterprises (SMEs) that lack resources and expertise to successfully operate in markets that have substantially different regulatory structures. As governments seek to encourage the development of SMEs, policy makers often confront the critical question of what ultimately motivates SME export behavior. Specifically, there is considerable interest in understanding how SMEs confront the challenges of regulatory asymmetry. Neoclassical models of the firm generally emphasize expected profit maximization under uncertainty, however these approaches do not adequately explain the entrepreneurial decision under regulatory asymmetry. Behavioral theories of the firm offer a far richer understanding of decision making by taking into account aspirations and adaptive performance in risky environments. This paper develops an analytical framework for decision making of a single agent. Considering risk, uncertainty and opportunity cost, the analysis focuses on the export behavior response of an SME in a situation of regulatory asymmetry. Drawing on the experience of fruit processor in Muzaffarpur, India, who must consider different regulatory environments when shipping fruit treated with sulfur dioxide, the study dissects the firm-level decision using @Risk, a Monte Carlo computational tool.

Characterization of fold-related fractures in the carbonate rocks of the Cingoli anticline, northern Apennines, Italy

Thrust fault-related folds in carbonate rocks are characterized by deformation accommodated by different structures, such as joints, faults, pressure solution seams, and deformation bands. Defining the development of fracture systems related to the folding process is significant both for theoretical and practical purposes. Fracture systems are useful constrains in order to understand the kinematical evolution of the fold. Furthermore, understanding the relationships between folding and fracturing provides a noteworthy contribution for reconstructing the geodynamic and the structural evolution of the studied area. Moreover, as fold-related fractures influence fluid flow through rocks, fracture systems are relevant for energy production (geothermal studies, methane and CO2 , storage and hydrocarbon exploration), environmental and social issues (pollutant distribution, aquifer characterization). The PhD project shows results of a study carried out in a multilayer carbonate anticline characterized by different mechanical properties. The aim of this study is to understand the factors which influence the fracture formation and to define their temporal sequence during the folding process. The studied are is located in the Cingoli anticline (Northern Apennines), which is characterized by a pelagic multilayer characterized by sequences with different mechanical stratigraphies. A multi-scale analysis has been made in several outcrops located in different structural positions. This project shows that the conceptual sketches proposed in literature and the strain distribution models outline well the geometrical orientation of most of the set of fractures observed in the Cingoli anticline. On the other hand, the present work suggests the relevance of the mechanical stratigraphy in particular controlling the type of fractures formed (e.g. pressure solution seams, joints or shear fractures) and their subsequent evolution. Through a multi-scale analysis, and on the basis of the temporal relationship between fracture sets and their orientation respect layering, I also suggest a conceptual model for fracture systems formation.