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.

Development of musculoskeletal models for the design and the pre-clinical validation of hip resurfacing prosthesis

Background. The surgical treatment of dysfunctional hips is a severe condition for the patient and a costly therapy for the public health. Hip resurfacing techniques seem to hold the promise of various advantages over traditional THR, with particular attention to young and active patients. Although the lesson provided in the past by many branches of engineering is that success in designing competitive products can be achieved only by predicting the possible scenario of failure, to date the understanding of the implant quality is poorly pre-clinically addressed. Thus revision is the only delayed and reliable end point for assessment. The aim of the present work was to model the musculoskeletal system so as to develop a protocol for predicting failure of hip resurfacing prosthesis. Methods. Preliminary studies validated the technique for the generation of subject specific finite element (FE) models of long bones from Computed Thomography data. The proposed protocol consisted in the numerical analysis of the prosthesis biomechanics by deterministic and statistic studies so as to assess the risk of biomechanical failure on the different operative conditions the implant might face in a population of interest during various activities of daily living. Physiological conditions were defined including the variability of the anatomy, bone densitometry, surgery uncertainties and published boundary conditions at the hip. The protocol was tested by analysing a successful design on the market and a new prototype of a resurfacing prosthesis. Results. The intrinsic accuracy of models on bone stress predictions (RMSE < 10%) was aligned to the current state of the art in this field. The accuracy of prediction on the bone-prosthesis contact mechanics was also excellent (< 0.001 mm). The sensitivity of models prediction to uncertainties on modelling parameter was found below 8.4%. The analysis of the successful design resulted in a very good agreement with published retrospective studies. The geometry optimisation of the new prototype lead to a final design with a low risk of failure. The statistical analysis confirmed the minimal risk of the optimised design over the entire population of interest. The performances of the optimised design showed a significant improvement with respect to the first prototype (+35%). Limitations. On the authors opinion the major limitation of this study is on boundary conditions. The muscular forces and the hip joint reaction were derived from the few data available in the literature, which can be considered significant but hardly representative of the entire variability of boundary conditions the implant might face over the patients population. This moved the focus of the research on modelling the musculoskeletal system; the ongoing activity is to develop subject-specific musculoskeletal models of the lower limb from medical images. Conclusions. The developed protocol was able to accurately predict known clinical outcomes when applied to a well-established device and, to support the design optimisation phase providing important information on critical characteristics of the patients when applied to a new prosthesis. The presented approach does have a relevant generality that would allow the extension of the protocol to a large set of orthopaedic scenarios with minor changes. Hence, a failure mode analysis criterion can be considered a suitable tool in developing new orthopaedic devices.

A mixed methods inquiry into the political economy of agriculture and rural areas in Lebanon

The present work, then, is concerned with the forgotten elements of the Lebanese economy, agriculture and rural development. It investigates the main problematic which arose from these forgotten components, in particular the structure of the agricultural sector, production technology, income distribution, poverty, food security, territorial development and local livelihood strategies. It will do so using quantitative Computable General Equilibrium (CGE) modeling and a qualitative phenomenological case study analysis, both embedded in a critical review of the historical development of the political economy of Lebanon, and a structural analysis of its economy. The research shows that under-development in Lebanese rural areas is not due to lack of resources, but rather is the consequence of political choices. It further suggests that agriculture – in both its mainstream conventional and its innovative locally initiated forms of production – still represents important potential for inducing economic growth and development. In order to do so, Lebanon has to take full advantage of its human and territorial capital, by developing a rural development strategy based on two parallel sets of actions: one directed toward the support of local rural development initiatives, and the other directed toward intensive form of production. In addition to its economic returns, such a strategy would promote social and political stability.

Strategy as a matter of beliefs: the recorded music industry reinventing itself by rethinking itself

Managerial and organizational cognition studies the ways cognitions of managers in groups, organizations and industries shape their strategies and actions. Cognitions refer to simplified representations of managers’ internal and external environments, necessary to cope with the rich, ambiguous information requirements that characterize strategy making. Despite the important achievements in the field, many unresolved puzzles remain as to this process, particular as to the cognitive factors that condition actors in framing a response to a discontinuity, how actors can change their models in the face of a discontinuity, and the reciprocal relation between cognition and action. I leverage on the recent case of the recorded music industry in the face of the digital technology to study these issues, through a strategy-oriented study of the way early response to the discontinuity was constructed and of the subsequent evolution of this response. Through a longitudinal historical and cognitive analysis of actions and cognitions at both the industry and firm-level during the period in which the response took place (1999-2010), I gain important insights on the way historical beliefs in the industry shaped early response to the digital disruption, on the role of outsiders in promoting change through renewed vision about important issues, and on the reciprocal relationship between cognitive and strategic change.

Solutions to common issues in widefield microscopy: vignetting, mosaicing and depth of focus

In this thesis we have developed solutions to common issues regarding widefield microscopes, facing the problem of the intensity inhomogeneity of an image and dealing with two strong limitations: the impossibility of acquiring either high detailed images representative of whole samples or deep 3D objects. First, we cope with the problem of the non-uniform distribution of the light signal inside a single image, named vignetting. In particular we proposed, for both light and fluorescent microscopy, non-parametric multi-image based methods, where the vignetting function is estimated directly from the sample without requiring any prior information. After getting flat-field corrected images, we studied how to fix the problem related to the limitation of the field of view of the camera, so to be able to acquire large areas at high magnification. To this purpose, we developed mosaicing techniques capable to work on-line. Starting from a set of overlapping images manually acquired, we validated a fast registration approach to accurately stitch together the images. Finally, we worked to virtually extend the field of view of the camera in the third dimension, with the purpose of reconstructing a single image completely in focus, stemming from objects having a relevant depth or being displaced in different focus planes. After studying the existing approaches for extending the depth of focus of the microscope, we proposed a general method that does not require any prior information. In order to compare the outcome of existing methods, different standard metrics are commonly used in literature. However, no metric is available to compare different methods in real cases. First, we validated a metric able to rank the methods as the Universal Quality Index does, but without needing any reference ground truth. Second, we proved that the approach we developed performs better in both synthetic and real cases.

Automatic Deployment of Applications in the Cloud

In distributed systems like clouds or service oriented frameworks, applications are typically assembled by deploying and connecting a large number of heterogeneous software components, spanning from fine-grained packages to coarse-grained complex services. The complexity of such systems requires a rich set of techniques and tools to support the automation of their deployment process. By relying on a formal model of components, a technique is devised for computing the sequence of actions allowing the deployment of a desired configuration. An efficient algorithm, working in polynomial time, is described and proven to be sound and complete. Finally, a prototype tool implementing the proposed algorithm has been developed. Experimental results support the adoption of this novel approach in real life scenarios.