Centrifuge Modeling of Sandy Slopes

Slope failure occurs in many areas throughout the world and it becomes an important problem when it interferes with human activity, in which disasters provoke loss of life and property damage. In this research we investigate the slope failure through the centrifuge modeling, where a reduced-scale model, N times smaller than the full-scale (prototype), is used whereas the acceleration is increased by N times (compared with the gravity acceleration) to preserve the stress and the strain behavior. The aims of this research “Centrifuge modeling of sandy slopes” are in extreme synthesis: 1) test the reliability of the centrifuge modeling as a tool to investigate the behavior of a sandy slope failure; 2) understand how the failure mechanism is affected by changing the slope angle and obtain useful information for the design. In order to achieve this scope we arranged the work as follows: Chapter one: centrifuge modeling of slope failure. In this chapter we provide a general view about the context in which we are working on. Basically we explain what is a slope failure, how it happens and which are the tools available to investigate this phenomenon. Afterwards we introduce the technology used to study this topic, that is the geotechnical centrifuge. Chapter two: testing apparatus. In the first section of this chapter we describe all the procedures and facilities used to perform a test in the centrifuge. Then we explain the characteristics of the soil (Nevada sand), like the dry unit weight, water content, relative density, and its strength parameters (c,φ), which have been calculated in laboratory through the triaxial test. Chapter three: centrifuge tests. In this part of the document are presented all the results from the tests done in centrifuge. When we talk about results we refer to the acceleration at failure for each model tested and its failure surface. In our case study we tested models with the same soil and geometric characteristics but different angles. The angles tested in this research were: 60°, 75° and 90°. Chapter four: slope stability analysis. We introduce the features and the concept of the software: ReSSA (2.0). This software allows us to calculate the theoretical failure surfaces of the prototypes. Then we show in this section the comparisons between the experimental failure surfaces of the prototype, traced in the laboratory, and the one calculated by the software. Chapter five: conclusion. The conclusion of the research presents the results obtained in relation to the two main aims, mentioned above.

Data sanitization in a clearing system for public transport operators

In this work we will discuss about a project started by the Emilia-Romagna Regional Government regarding the manage of the public transport. In particular we will perform a data mining analysis on the data-set of this project. After introducing the Weka software used to make our analysis, we will discover the most useful data mining techniques and algorithms; and we will show how these results can be used to violate the privacy of the same public transport operators. At the end, despite is off topic of this work, we will spend also a few words about how it's possible to prevent this kind of attack.

Analysis of the Kohn Laplacian on the Heisenberg Group and on Cauchy-Riemann Manifolds

The purpose of this study is to analyse the regularity of a differential operator, the Kohn Laplacian, in two settings: the Heisenberg group and the strongly pseudoconvex CR manifolds. The Heisenberg group is defined as a space of dimension 2n+1 with a product. It can be seen in two different ways: as a Lie group and as the boundary of the Siegel UpperHalf Space. On the Heisenberg group there exists the tangential CR complex. From this we define its adjoint and the Kohn-Laplacian. Then we obtain estimates for the Kohn-Laplacian and find its solvability and hypoellipticity. For stating L^p and Holder estimates, we talk about homogeneous distributions. In the second part we start working with a manifold M of real dimension 2n+1. We say that M is a CR manifold if some properties are satisfied. More, we say that a CR manifold M is strongly pseudoconvex if the Levi form defined on M is positive defined. Since we will show that the Heisenberg group is a model for the strongly pseudo-convex CR manifolds, we look for an osculating Heisenberg structure in a neighborhood of a point in M, and we want this structure to change smoothly from a point to another. For that, we define Normal Coordinates and we study their properties. We also examinate different Normal Coordinates in the case of a real hypersurface with an induced CR structure. Finally, we define again the CR complex, its adjoint and the Laplacian operator on M. We study these new operators showing subelliptic estimates. For that, we don't need M to be pseudo-complex but we ask less, that is, the Z(q) and the Y(q) conditions. This provides local regularity theorems for Laplacian and show its hypoellipticity on M.

The Feynman-Kac formula and applications to PDEs

The thesis presents a probabilistic approach to the theory of semigroups of operators, with particular attention to the Markov and Feller semigroups. The first goal of this work is the proof of the fundamental Feynman-Kac formula, which gives the solution of certain parabolic Cauchy problems, in terms of the expected value of the initial condition computed at the associated stochastic diffusion processes. The second target is the characterization of the principal eigenvalue of the generator of a semigroup with Markov transition probability function and of second order elliptic operators with real coefficients not necessarily self-adjoint. The thesis is divided into three chapters. In the first chapter we study the Brownian motion and some of its main properties, the stochastic processes, the stochastic integral and the Itô formula in order to finally arrive, in the last section, at the proof of the Feynman-Kac formula. The second chapter is devoted to the probabilistic approach to the semigroups theory and it is here that we introduce Markov and Feller semigroups. Special emphasis is given to the Feller semigroup associated with the Brownian motion. The third and last chapter is divided into two sections. In the first one we present the abstract characterization of the principal eigenvalue of the infinitesimal generator of a semigroup of operators acting on continuous functions over a compact metric space. In the second section this approach is used to study the principal eigenvalue of elliptic partial differential operators with real coefficients. At the end, in the appendix, we gather some of the technical results used in the thesis in more details. Appendix A is devoted to the Sion minimax theorem, while in appendix B we prove the Chernoff product formula for not necessarily self-adjoint operators.

Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

Modelling, simulation and optimization of maintenance considerations on condition based maintenance

Globalization has increased the pressure on organizations and companies to operate in the most efficient and economic way. This tendency promotes that companies concentrate more and more on their core businesses, outsource less profitable departments and services to reduce costs. By contrast to earlier times, companies are highly specialized and have a low real net output ratio. For being able to provide the consumers with the right products, those companies have to collaborate with other suppliers and form large supply chains. An effect of large supply chains is the deficiency of high stocks and stockholding costs. This fact has lead to the rapid spread of Just-in-Time logistic concepts aimed minimizing stock by simultaneous high availability of products. Those concurring goals, minimizing stock by simultaneous high product availability, claim for high availability of the production systems in the way that an incoming order can immediately processed. Besides of design aspects and the quality of the production system, maintenance has a strong impact on production system availability. In the last decades, there has been many attempts to create maintenance models for availability optimization. Most of them concentrated on the availability aspect only without incorporating further aspects as logistics and profitability of the overall system. However, production system operator’s main intention is to optimize the profitability of the production system and not the availability of the production system. Thus, classic models, limited to represent and optimize maintenance strategies under the light of availability, fail. A novel approach, incorporating all financial impacting processes of and around a production system, is needed. The proposed model is subdivided into three parts, maintenance module, production module and connection module. This subdivision provides easy maintainability and simple extendability. Within those modules, all aspect of production process are modeled. Main part of the work lies in the extended maintenance and failure module that offers a representation of different maintenance strategies but also incorporates the effect of over-maintaining and failed maintenance (maintenance induced failures). Order release and seizing of the production system are modeled in the production part. Due to computational power limitation, it was not possible to run the simulation and the optimization with the fully developed production model. Thus, the production model was reduced to a black-box without higher degree of details.