Probabilistic approaches in civil engineering: generation of random fields and structural identification with genetic algorithms

The inherent stochastic character of most of the physical quantities involved in engineering models has led to an always increasing interest for probabilistic analysis. Many approaches to stochastic analysis have been proposed. However, it is widely acknowledged that the only universal method available to solve accurately any kind of stochastic mechanics problem is Monte Carlo Simulation. One of the key parts in the implementation of this technique is the accurate and efficient generation of samples of the random processes and fields involved in the problem at hand. In the present thesis an original method for the simulation of homogeneous, multi-dimensional, multi-variate, non-Gaussian random fields is proposed. The algorithm has proved to be very accurate in matching both the target spectrum and the marginal probability. The computational efficiency and robustness are very good too, even when dealing with strongly non-Gaussian distributions. What is more, the resulting samples posses all the relevant, welldefined and desired properties of “translation fields”, including crossing rates and distributions of extremes. The topic of the second part of the thesis lies in the field of non-destructive parametric structural identification. Its objective is to evaluate the mechanical characteristics of constituent bars in existing truss structures, using static loads and strain measurements. In the cases of missing data and of damages that interest only a small portion of the bar, Genetic Algorithm have proved to be an effective tool to solve the problem.

Quantum Integrability in Non-Linear Sigma Models related to Gauge/String Correspondences

The Thermodynamic Bethe Ansatz analysis is carried out for the extended-CP^N class of integrable 2-dimensional Non-Linear Sigma Models related to the low energy limit of the AdS_4xCP^3 type IIA superstring theory. The principal aim of this program is to obtain further non-perturbative consistency check to the S-matrix proposed to describe the scattering processes between the fundamental excitations of the theory by analyzing the structure of the Renormalization Group flow. As a noteworthy byproduct we eventually obtain a novel class of TBA models which fits in the known classification but with several important differences. The TBA framework allows the evaluation of some exact quantities related to the conformal UV limit of the model: effective central charge, conformal dimension of the perturbing operator and field content of the underlying CFT. The knowledge of this physical quantities has led to the possibility of conjecturing a perturbed CFT realization of the integrable models in terms of coset Kac-Moody CFT. The set of numerical tools and programs developed ad hoc to solve the problem at hand is also discussed in some detail with references to the code.

Galaxy evolution in the VIMOS public extragalactic redshift survey (VIPERS)

In this work I present the first measurements of the galaxy stellar mass function (GSMF) from the first public release of the VIPERS catalogue, containing ∼55,000 objects. First, I present the survey design, its scientific goal, the redshift measurements and validation. Then, I provide details about the estimate of galaxy stellar masses, star formation rates, and other physical quantities. I derive the GSMF of different galaxy types (e.g. active and passive galaxies) and as a function of the environment (defined through the local galaxy density contrast). These estimates represent new observational evidence useful to characterise the mechanism of galaxy evolution.

Rigorous results in Spin Glasses and Monomer-Dimer systems

In this work I reported recent results in the field of Statistical Mechanics of Equilibrium, and in particular in Spin Glass models and Monomer Dimer models . We start giving the mathematical background and the general formalism for Spin (Disordered) Models with some of their applications to physical and mathematical problems. Next we move on general aspects of the theory of spin glasses, in particular to the Sherrington-Kirkpatrick model which is of fundamental interest for the work. In Chapter 3, we introduce the Multi-species Sherrington-Kirkpatrick model (MSK), we prove the existence of the thermodynamical limit and the Guerra's Bound for the quenched pressure together with a detailed analysis of the annealed and the replica symmetric regime. The result is a multidimensional generalization of the Parisi's theory. Finally we brie y illustrate the strategy of the Panchenko's proof of the lower bound. In Chapter 4 we discuss the Aizenmann-Contucci and the Ghirlanda-Guerra identities for a wide class of Spin Glass models. As an example of application, we discuss the role of these identities in the proof of the lower bound. In Chapter 5 we introduce the basic mathematical formalism of Monomer Dimer models. We introduce a Gaussian representation of the partition function that will be fundamental in the rest of the work. In Chapter 6, we introduce an interacting Monomer-Dimer model. Its exact solution is derived and a detailed study of its analytical properties and related physical quantities is performed. In Chapter 7, we introduce a quenched randomness in the Monomer Dimer model and show that, under suitable conditions the pressure is a self averaging quantity. The main result is that, if we consider randomness only in the monomer activity, the model is exactly solvable.

Aging of nuclear power plant cables: in search of non-destructive diagnostic quantities

The safety systems of nuclear power plants rely on low-voltage power, instrumentation and control cables. Inside the containment area, cables operate in harsh environments, characterized by relatively high temperature and gamma-irradiation. As these cables are related to fundamental safety systems, they must be able to withstand unexpected accident conditions and, therefore, their condition assessment is of utmost importance as plants age and lifetime extensions are required. Nowadays, the integrity and functionality of these cables are monitored mainly through destructive test which requires specific laboratory. The investigation of electrical aging markers which can provide information about the state of the cable by non-destructive testing methods would improve significantly the present diagnostic techniques. This work has been made within the framework of the ADVANCE (Aging Diagnostic and Prognostics of Low-Voltage I\&C Cables) project, a FP7 European program. This Ph.D. thesis aims at studying the impact of aging on cable electrical parameters, in order to understand the evolution of the electrical properties associated with cable degradation. The identification of suitable aging markers requires the comparison of the electrical property variation with the physical/chemical degradation mechanisms of polymers for different insulating materials and compositions. The feasibility of non-destructive electrical condition monitoring techniques as potential substitutes for destructive methods will be finally discussed studying the correlation between electrical and mechanical properties. In this work, the electrical properties of cable insulators are monitored and characterized mainly by dielectric spectroscopy, polarization/depolarization current analysis and space charge distribution. Among these techniques, dielectric spectroscopy showed the most promising results; by means of dielectric spectroscopy it is possible to identify the frequency range where the properties are more sensitive to aging. In particular, the imaginary part of permittivity at high frequency, which is related to oxidation, has been identified as the most suitable aging marker based on electrical quantities.