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.

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.

Finanza Imprenditoriale: Teoria del Portafoglio e Costo del Capitale

This thesis focuses on the limits that may prevent an entrepreneur from maximizing her value, and the benefits of diversification in reducing her cost of capital. After reviewing all relevant literature dealing with the differences between traditional corporate finance and entrepreneurial finance, we focus on the biases occurring when traditional finance techniques are applied to the entrepreneurial context. In particular, using the portfolio theory framework, we determine the degree of under-diversification of entrepreneurs. Borrowing the methodology developed by Kerins et al. (2004), we test a model for the cost of capital according to the firms' industry and the entrepreneur's wealth commitment to the firm. This model takes three market inputs (standard deviation of market returns, expected return of the market, and risk-free rate), and two firm-specific inputs (standard deviation of the firm returns and correlation between firm and market returns) as parameters, and returns an appropriate cost of capital as an output. We determine the expected market return and the risk-free rate according to the huge literature on the market risk premium. As for the market return volatility, it is estimated considering a GARCH specification for the market index returns. Furthermore, we assume that the firm-specific inputs can be obtained considering new-listed firms similar in risk to the firm we are evaluating. After we form a database including all the data needed for our analysis, we perform an empirical investigation to understand how much of the firm's total risk depends on market risk, and which explanatory variables can explain it. Our results show that cost of capital declines as the level of entrepreneur's commitment decreases. Therefore, maximizing the value for the entrepreneur depends on the fraction of entrepreneur's wealth invested in the firm and the fraction she sells to outside investors. These results are interesting both for entrepreneurs and policy makers: the former can benefit from an unbiased model for their valuation; the latter can obtain some guidelines to overcome the recent financial market crisis.

Theoretical and Experimental Study of the Magnetic Separation of Pollutants from Wastewater

This Thesys reports the study of a HGMS (High GradientMagnetic Separation) process for the treatment of industrialwastewaters that considers an assisted chemical-physical pre-treatment for the removal of heavy metals through the bound by adsorption with added iron-oxide particulate matter (hematite). The considered filter, constituted by ferromagnetic stainless steel wool and permanent magnets, is studied with a new approach based on a statistical analysis that requires the study of the trajectories of the particles. Experimental activity on a laboratory device has been carried out in order to test the model.

Study of apoptotic deletion mediated by Bifidobacterium longum with construction of recombinant strains for Serpin encoding gene and phenotypes comparison in a pig cell model

The first part of the research project of the Co-Advisorship Ph.D Thesis was aimed to select the best Bifidobacterium longum strains suitable to set the basis of our study. We were looking for strains with the abilities to colonize the intestinal mucosa and with good adhesion capacities, so that we can test these strains to investigate their ability to induce apoptosis in “damaged” intestinal cells. Adhesion and apoptosis are the two process that we want to study to better understand the role of an adhesion protein that we have previously identified and that have top scores homologies with the recent serpin encoding gene identified in B. longum by Nestlè researchers. Bifidobacterium longum is a probiotic, known for its beneficial effects to the human gut and even for its immunomodulatory and antitumor activities. Recently, many studies have stressed out the intimate relation between probiotic bacteria and the GIT mucosa and their influence on human cellular homeostasis. We focused on the apoptotic deletion of cancer cells induced by B. longum. This has been valued in vitro, performing the incubation of three B.longum strains with enterocyte-like Caco- 2 cells, to evidence DNA fragmentation, a cornerstone of apoptosis. The three strains tested were defined for their adhesion properties using adhesion and autoaggregation assays. These features are considered necessary to select a probiotic strain. The three strains named B12, B18 and B2990 resulted respectively: “strong adherent”, “adherent” and “non adherent”. Then, bacteria were incubated with Caco-2 cells to investigate apoptotic deletion. Cocultures of Caco-2 cells with B. longum resulted positive in DNA fragmentation test, only when adherent strains were used (B12 and B18). These results indicate that the interaction with adherent B. longum can induce apoptotic deletion of Caco-2 cells, suggesting a role in cellular homeostasis of the gastrointestinal tract and in restoring the ecology of damaged colon tissues. These results were used to keep on researching and the strains tested were used as recipient of recombinant techniques aimed to originate new B.longum strains with enhanced capacity of apoptotic induction in “damaged” intestinal cells. To achieve this new goal it was decided to clone the serpin encoding gene of B. longum, so that we can understand its role in adhesion and apoptosis induction. Bifidobacterium longum has immunostimulant activity that in vitro can lead to apoptotic response of Caco-2 cell line. It secretes a hypothetical eukaryotic type serpin protein, which could be involved in this kind of deletion of damaged cells. We had previously characterised a protein that has homologies with the hypothetical serpin of B. longum (DD087853). In order to create Bifidobacterium serpin transformants, a B. longum cosmid library was screened with a PCR protocol using specific primers for serpin gene. After fragment extraction, the insert named S1 was sub-cloned into pRM2, an Escherichia coli - Bifidobacterium shuttle vector, to construct pRM3. Several protocols for B. longum transformation were performed and the best efficiency was obtained using MRS medium and raffinose. Finally bacterial cell supernatants were tested in a dotblot assay to detect antigens presence against anti-antitrypsin polyclonal antibody. The best signal was produced by one starin that has been renamed B. longum BLKS 7. Our research study was aimed to generate transformants able to over express serpin encoding gene, so that we can have the tools for a further study on bacterial apoptotic induction of Caco-2 cell line. After that we have originated new trasformants the next step to do was to test transformants abilities when exposed to an intestinal cell model. In fact, this part of the project was achieved in the Department of Biochemistry of the Medical Faculty of the University of Maribor, guest of the abroad supervisor of the Co-Advisorship Doctoral Thesis: Prof. Avrelija Cencic. In this study we examined the probiotic ability of some bacterial strains using intestinal cells from a 6 years old pig. The use of intestinal mammalian cells is essential to study this symbiosis and a functional cell model mimics a polarised epithelium in which enterocytes are separated by tight junctions. In this list of strains we have included the Bifidobacterium longum BKS7 transformant strain that we have previously originated; in order to compare its abilities. B. longum B12 wild type and B. longum BKS7 transformant and eight Lactobacillus strains of different sources were co-cultured with porcine small intestine epithelial cells (PSI C1) and porcine blood monocytes (PoM2) in Transwell filter inserts. The strains, including Lb. gasseri, Lb. fermentum, Lb. reuterii, Lb. plantarum and unidentified Lactobacillus from kenyan maasai milk and tanzanian coffee, were assayed for activation of cell lines, measuring nitric oxide by Griess reaction, H202 by tetramethylbenzidine reaction and O2 - by cytochrome C reduction. Cytotoxic effect by crystal violet staining and induction on metabolic activity by MTT cell proliferation assay were tested too. Transepithelial electrical resistance (TER) of polarised PSI C1 was measured during 48 hours co-culture. TER, used to observe epithelium permeability, decrease during pathogenesis and tissue becomes permeable to ion passive flow lowering epithelial barrier function. Probiotics can prevent or restore increased permeability. Lastly, dot-blot was achieved against Interleukin-6 of treated cells supernatants. The metabolic activity of PoM2 and PSI C1 increased slightly after co-culture not affecting mitochondrial functions. No strain was cytotoxic over PSI C1 and PoM2 and no cell activation was observed, as measured by the release of NO2, H202 and O2 - by PoM2 and PSI C1. During coculture TER of polarised PSI C1 was two-fold higher comparing with constant TER (~3000 ) of untreated cells. TER raise generated by bacteria maintains a low permeability of the epithelium. During treatment Interleukin-6 was detected in cell supernatants at several time points, confirming immunostimulant activity. All results were obtained using Lactobacillus paracasei Shirota e Carnobacterium divergens as controls. In conclusion we can state that both the list of putative probiotic bacteria and our new transformant strain of B. longum are not harmful when exposed to intestinal cells and could be selected as probiotics, because can strengthen epithelial barrier function and stimulate nonspecific immunity of intestinal cells on a pig cell model. Indeed, we have found out that none of the strains tested that have good adhesion abilities presents citotoxicity to the intestinal cells and that non of the strains tested can induce cell lines to produce high level of ROS, neither NO2. Moreover we have assayed even the capacity of producing certain citokynes that are correlated with immune response. The detection of Interleukin-6 was assayed in all our samples, including B.longum transformant BKS 7 strain, this result indicates that these bacteria can induce a non specific immune response in the intestinal cells. In fact, when we assayed the presence of Interferon-gamma in cells supernatant after bacterial exposure, we have no positive signals, that means that there is no activation of a specific immune response, thus confirming that these bacteria are not recognize as pathogen by the intestinal cells and are certainly not harmful for intestinal cells. The most important result is the measure of Trans Epithelial Electric Resistance that have shown how the intestinal barrier function get strengthen when cells are exposed to bacteria, due to a reduction of the epithelium permeability. We have now a new strain of B. longum that will be used for further studies above the mechanism of apoptotic induction to “damaged cells” and above the process of “restoring ecology”. This strain will be the basis to originate new transformant strains for Serpin encoding gene that must have better performance and shall be used one day even in clinical cases as in “gene therapy” for cancer treatment and prevention.

Crashworthiness and composite materials: development of an experimental test method for the energy absorption determination and implementation of the relative numerical model

In this PhD thesis the crashworthiness topic is studied with the perspective of the development of a small-scale experimental test able to characterize a material in terms of energy absorption. The material properties obtained are then used to validate a nu- merical model of the experimental test itself. Consequently, the numerical model, calibrated on the specific ma- terial, can be extended to more complex structures and used to simulate their energy absorption behavior. The experimental activity started at University of Washington in Seattle, WA (USA) and continued at Second Faculty of Engi- neering, University of Bologna, Forl`ı (Italy), where the numerical model for the simulation of the experimental test was implemented and optimized.

General effective medium model for the complex permittivity extraction with an open-ended coaxial probe in presence of a multilayer material under test

The work presented in this thesis is focused on the open-ended coaxial-probe frequency-domain reflectometry technique for complex permittivity measurement at microwave frequencies of dispersive dielectric multilayer materials. An effective dielectric model is introduced and validated to extend the applicability of this technique to multilayer materials in on-line system context. In addition, the thesis presents: 1) a numerical study regarding the imperfectness of the contact at the probe-material interface, 2) a review of the available models and techniques, 3) a new classification of the extraction schemes with guidelines on how they can be used to improve the overall performance of the probe according to the problem requirements.