Khinchin's theorem in Teichmüller dynamics

This thesis is concerned with two themes which are strictly linked with each other, and therefore will be developed in parallel. The first one is dynamics in Teichmueller space. The Teichmueller space of a (topological, closed and orientable) surface S is defined as the set of the complex structures one can endow S with, up to isotopies. Such a space can be given a structure of geodesic metric space. The description of this structure requires the notion of flat structures on the underlying surface, i.e. flat Riemannian metrics with conical singularities, such that a foliation in straight lines in each direction is defined. The space of all flat structures is a sort of tangent bundle to the Teichmueller space, and the geodesic flow, knows as Teichmueller flow, has a simple description in these terms. It becomes interesting from a dynamical viewpoint when projected onto the moduli space, namely the set of the complex structures up to diffeomorphisms. Invariant subspaces under the flow are called strata; we are concerned in particular with dynamics in the strata made up by translation structures, a subspecies of the flat structures. The second theme treated in this work are interval exchange maps (i.e.m.s)i.e. injective maps of an interval which are locally a translation except at finitely many singularities. They are completely determined by providing some combinatorial data as well as the length data of the sub-intervals. If one considers an adequate leftmost portion of the considered interval, the first return map of the i.e.m. on this portion is a new i.e.m.. This yields a dynamics on the parameter space for i.e.m.s, called Rauzy dynamics. The themes above are linked on two levels. First of all, if one fixes a translation surface, the first return map induced by the flow in vertical direction on a horizontal segment is an i.e.m.; and a `generic' i.e.m. can always be obtained this way. But a link at a higher level is possible, too: the Teichmueller flow admits a transverse section such that the return map can be interpreted as Rauzy dynamics. Chapter 0 of the thesis is an introduction: it includes the preliminary material from the theory of dynamical systems which will be used in this work, as well as a description of the simplest case of the theory, represented by flat tori and rotations of the circumference. In Chapter 1 Teichmueller dynamics is formally, but rapidly, introduced; whereas Chapter 2 is concerned with the formalism related to interval exchange maps and Rauzy dynamics. Moreover, it is explained how it is possible to switch from this setting to the one of translation structures, and conversely. The first half of Chapter 3 treats, still in an extremely concise manner, classical questions related to the themes above. In particular it deals with ergodicity of i.e.m.s and of the Teichmueller and Rauzy dynamics and briefly introduces the Kontsevich-Zorich cocycle. The chapter ends with a technical discussion needed for the results tackled in the following chapters: its protagonists will be the reduced triples for an i.e.m. T, namely triples (b,a;n) where b is a singular point for $T^{-1}$, a is a singular point for T, and n is a positive integer, such that no singularities for $T^{-1},...,T^-n$ appears between $T^n(b)$ and a. Chapter 4 thus deals with a first generalisation of a theorem of A.Ya. Khinchin, found by Luca Marchese (2010). The Khinchin theorem in its classical formulation states a condition for a Diophantine inequality to have finitely, or infinitely many, solutions. Its generalisation to i.e.m.s states: Let f(n) be a positive, decreasing sequence. We are concerned with the quantity of solutions (b,a;n) to the condition $|T^n(a)-b|<f(n)$ for a fixed i.e.m. T, where b is a singular point of $T^-1$, and a is a singular point for T. If the sequence f(n) has a finite sum, then solutions are finitely many for almost any T; if nf(n) is still a decreasing sequence, with infinite sum, then solutions are infinitely many for almost any T. This result will be partially proved. It is interesting not only as a property of singularities of an i.e.m., but also because it yields a weaker version of a theorem of Jon Chaika, which states a similar property for generic points. Chapter 5 is again about translation surfaces. The theorem above is restated as a property of lengths of connections, namely segments connecting two singular points on a translation surface. Hence it is possible to gain another result of Chaika, which gives a property of 'strong recurrence' of foliations. And, eventually, this restatement of the generalised Khinchin theorem yields a logarithm law for the Teichmueller flow: Let X be a translation surface, and let Sys(X) be the minimum length of a connection of X. Denote $g^t$ the Teichmueller flow. Then, for almost any X, it holds that $\limsup [-\log (Sys(g^t(X))]/(\log t)=1/2$

A direct elimination algorithm for quasi-static and dynamic contact problems

This paper deals with the computational modeling and numerical simulation of contact problems at Unite deformations using the Finite element method. Quasi-static and dynamic problems are considered and two particular frictional conditions, full stick friction and frictionless cases, are addressed. Lagrange multipliers and regularized formulations of the contact problem, such as penalty or augmented Lagrangian methods, are avoided and a new direct elimination method is proposed. Conserving algorithms are also introduced for the proposed formulation for dynamic contact problems. An assessment of he performance of the resulting formulation is shown in a number of selected benchmark tests and numerical examples, including both quasi-static and dynamic contact problems under full stick friction and frictionless contact conditions. Conservation of key discrete properties exhibited by the time stepping algorithm used for dynamic contact problems is also shown in an example. (C) 2014 Elsevier B.V. All rights reserved.Peer ReviewedPostprint (author’s final draft

Large mass dimuon detection in the LHCb experiment

The structure of this thesis consists of two main parts: in the first part (Detector studies), the work is focused on the performances of the Multiwire Proportional Chambers, adopted for the detection of muons in LHCb, while in the second part (Physics studies) it is focused on the study of the LHCb potentialities to improve the knowledges of the proton Parton Distribution Functions with the physical channel Z0 -> mu+ mu-. The work described in the first part is concentrated on the cosmic rays test station developed in Rome2 in order to carry out the study of the detectors performances. In particular, the cosmic rays stand allows to perform a detailed study of the detector tracking capabilities and to obtain precise measurements of the efficiency and gas gain uniformity of the produced chambers. In the second part of the thesis is reported a study of the process pp -> Z0 -> mu+ mu-. The aim of the study is to demonstrate that, in spite of the limited angular acceptance and the optimization for a different kind of physics, the number of Z0 detected at LHCb is sufficient to make profitable physics. Moreover, the foward design of the spectrometer allows to study the proton structure in a kinematic region not probed by the present experiments. A particular focus has been put on the effect of the LHCb geometrical acceptance on the cross section sensitivity to the various set of partons, simulating the process with two event generators, PYTHIA and MC@NLO

Towards global architecture. The project between technique and technology

Environment, ecosystem, greenhouse effect emissions, public health, energy, sustainable development. This is an incomplete list of elements that are part of our daily lives, which show today’s human footprint responsibility over the health of the planet. Although these issues have been for decades on all policy statements on development the situation is not improving. Indeed, constantly, we are called to change our lifestyle and our models of well-being that are causing an exaggerated and increasing waste of energy and resources, along with the increase of the overall impact of human species on natural systems. I do believe the environment is a resource that has been exploited and neglected for too long, however I am also convinced that excessive (ab)use of certain terms, such as the concept of sustainability, has weakened its driving force and innovation. There is no&nbsp;doubt that the thematic areas related to the monitoring of environmental quality and&nbsp;sustainable development dominate the cultural and socio-economic scenery for the&nbsp;articulation program design and governance of the territory, but the risk we are running today is to flatten themes of 'environment only for propaganda or even worse for the market. The report is a reasoning on innovation, technology and the complexity that now accompanies any work of transformation and that should lead to a "possible future”

The Research Laboratory of the Mediterranean University

The laboratory, called LAB RENEW MEL created to test new technologies for producing energy from renewable sources thanks to the decisions of the management committees of three projects funded under the National Operational Program for Research and Competitiveness 2007-2013:RENEW Project (2014-2016) Coordinator prof. Claudio De Capua (Note 5)MEL Project (2014-2016 Coordinator prof. Pasquale Fabio Filianoti (Note 6)GELMINCAL Project (2011-2014) Coordinator prof. Francesco Della Corte (Note 7)All three projects together have a budget of nearly thirty million Euros. These are substantial resources that can allow the Mediterranean to take on a role of excellence in research on renewables. The establishment of a research center aims to achieve this goal, involves three departments of the University of Reggio Calabria, two of Engineering area, the Department of Civil Engineering, Energy, Environment and Materials (DICEAM) and the Department of Information Engineering, Infrastructure and Sustainable Energy (DIIES) and one of Architecture area, the Department of Architecture and Territory (dArTe).The author of this article is also the designer together with professor Alessandro Villari and professor Angelo Di Chio, who have followed, from the initial stages, all aspects related to the relationship between the objectives of the research and those related to the implementation of the Laboratory

A Reflection on the Sustainable Architecture Project

Environment, ecosystem, harmful emissions, citizens’ health, energy consumption, sustainable development. It is a non-exhaustive list of terms that are part of our daily life and that show how much responsibility the human imprint has today on the state of health of the planet. Despite the fact that they have been deadlines for some decades, at the head of all the programmatic statements on development, issued by international bodies and governments, the situation does not seem to improve. We are, indeed, called to change our lifestyle and our well-being patterns which are causing an exaggerated and ever-increasing waste of energy and resources, just as the overall impact of the human species on natural systems continues to grow (De Capua, 2008). In recent years everything that has to do with architectural design, from the choices of materials to the technologies used, has had to deal with the term sustainability, whose meaning, despite trying to place it in a unique defining apparatus, always takes on nuances and different meanings. In spite of this it has universally generated, in the society of the last decades, the awareness that the lifestyle assumed will have a dramatic impact on the generations to come

Transverse vibration of a class of orthotropic plates

This study determines the eigenvalues, eigenvectors, and nodal patterns of a class of orthotropic plates whose geometry is governed by the equation (x/a)α + (y/b)β = 1, where the parameters a, b, a, and a permit the plate geometry to vary over a range which includes the rhombus, circle, ellipse, square, and rectangle. Variable thickness, inplane forces, and mixed or discontinuous boundary conditions are also considered. The following assumptions have been employed: i). plate is thin with respect to other dimensions, ii). deflections are small, iii). rotary inertia and shear are neglected. The method of analysis employed is the Rayleigh-Ritz energy technique using xy-polynomials as the approximated deflection. Eigenvalues and eigenvectors were computed by the method of reductions, and the evaluation of double integrals was achieved by the numerical procedure of Gauss-Legendre quadratures. The validity of the analysis was checked by comparison with known solutions for rectangular orthotropic plates, and isotropic plates with variable thickness, in-plane forces, and mixed or discontinuous boundary conditions. It was found that the calculated frequencies and nodal patterns were in good agreement with existing data

A search for Z' in muon neutrino associated charm production

In many extensions of the Standard Model the presence of an extra neutral boson, Z', is invoked. A precision study of weak neutral-current exchange processes involving only second generation fermions is still missing. We propose a search for Z' in muon neutrino associated charm production. This process only involves Z' couplings with fermions from the second generation. An experimental method is thoroughly described using an ideal detector. As an application, the accuracy reachable with present and future experiments has been estimated.Comment: 13 pages, 3 figures, late

Electronic phase separation near the superconductor-insulator transition of Nd1+xBa2−xCu3O7−δ thin films studied by an electric-field-induced doping effect

We report a detailed study of the transport properties of Nd(1+x)Ba(2-x)Cu(3)O(7-delta) thin films with doping changed by field effect. The data cover the whole superconducting to insulating transition and show remarkable Similarities with the effect of chemical doping in high critical temperature superconductors. The results suggest that the add-on of carriers is accompanied by an electronic phase separation, independent on the details of the doping mechanism