Edge states and zero modes in quadratic fermionic models on a 1-D lattice

In una formulazione rigorosa della teoria quantistica, la definizione della varietà Riemanniana spaziale su cui il sistema è vincolato gioca un ruolo fondamentale. La presenza di un bordo sottolinea l'aspetto quantistico del sistema: l'imposizione di condizioni al contorno determina la discretizzazione degli autovalori del Laplaciano, come accade con condizioni note quali quelle periodiche, di Neumann o di Dirichlet. Tuttavia, non sono le uniche possibili. Qualsiasi condizione al bordo che garantisca l'autoaggiunzione dell' operatore Hamiltoniano è ammissibile. Tutte le possibili boundary conditions possono essere catalogate a partire dalla richiesta di conservazione del flusso al bordo della varietà. Alcune possibili condizioni al contorno, permettono l'esistenza di stati legati al bordo, cioè autostati dell' Hamiltoniana con autovalori negativi, detti edge states. Lo scopo di questa tesi è quello di investigare gli effetti di bordo in sistemi unidimensionali implementati su un reticolo discreto, nella prospettiva di capire come simulare proprietà di edge in un reticolo ottico. Il primo caso considerato è un sistema di elettroni liberi. La presenza di edge states è completamente determinata dai parametri di bordo del Laplaciano discreto. Al massimo due edge states emergono, e possono essere legati all' estremità destra o sinistra della catena a seconda delle condizioni al contorno. Anche il modo in cui decadono dal bordo al bulk e completamente determinato dalla scelta delle condizioni. Ammettendo un' interazione quadratica tra siti primi vicini, un secondo tipo di stati emerge in relazione sia alle condizioni al contorno che ai parametri del bulk. Questi stati sono chiamati zero modes, in quanto esiste la possibilità che siano degeneri con lo stato fondamentale. Per implementare le più generali condizioni al contorno, specialmente nel caso interagente, è necessario utilizzare un metodo generale per la diagonalizzazione, che estende la tecnica di Lieb-Shultz-Mattis per Hamiltoniane quadratiche a matrici complesse.

Pushover analysis of an existing reinforced concrete bridge:Jamboree Road Overcrossing in Irvine, California

The work for the present thesis started in California, during my semester as an exchange student overseas. California is known worldwide for its seismicity and its effort in the earthquake engineering research field. For this reason, I immediately found interesting the Structural Dynamics Professor, Maria Q. Feng's proposal, to work on a pushover analysis of the existing Jamboree Road Overcrossing bridge. Concrete is a popular building material in California, and for the most part, it serves its functions well. However, concrete is inherently brittle and performs poorly during earthquakes if not reinforced properly. The San Fernando Earthquake of 1971 dramatically demonstrated this characteristic. Shortly thereafter, code writers revised the design provisions for new concrete buildings so to provide adequate ductility to resist strong ground shaking. There remain, nonetheless, millions of square feet of non-ductile concrete buildings in California. The purpose of this work is to perform a Pushover Analysis and compare the results with those of a Nonlinear Time-History Analysis of an existing bridge, located in Southern California. The analyses have been executed through the software OpenSees, the Open System for Earthquake Engineering Simulation. The bridge Jamboree Road Overcrossing is classified as a Standard Ordinary Bridge. In fact, the JRO is a typical three-span continuous cast-in-place prestressed post-tension box-girder. The total length of the bridge is 366 ft., and the height of the two bents are respectively 26,41 ft. and 28,41 ft.. Both the Pushover Analysis and the Nonlinear Time-History Analysis require the use of a model that takes into account for the nonlinearities of the system. In fact, in order to execute nonlinear analyses of highway bridges it is essential to incorporate an accurate model of the material behavior. It has been observed that, after the occurrence of destructive earthquakes, one of the most damaged elements on highway bridges is a column. To evaluate the performance of bridge columns during seismic events an adequate model of the column must be incorporated. Part of the work of the present thesis is, in fact, dedicated to the modeling of bents. Different types of nonlinear element have been studied and modeled, with emphasis on the plasticity zone length determination and location. Furthermore, different models for concrete and steel materials have been considered, and the selection of the parameters that define the constitutive laws of the different materials have been accurate. The work is structured into four chapters, to follow a brief overview of the content. The first chapter introduces the concepts related to capacity design, as the actual philosophy of seismic design. Furthermore, nonlinear analyses both static, pushover, and dynamic, time-history, are presented. The final paragraph concludes with a short description on how to determine the seismic demand at a specific site, according to the latest design criteria in California. The second chapter deals with the formulation of force-based finite elements and the issues regarding the objectivity of the response in nonlinear field. Both concentrated and distributed plasticity elements are discussed into detail. The third chapter presents the existing structure, the software used OpenSees, and the modeling assumptions and issues. The creation of the nonlinear model represents a central part in this work. Nonlinear material constitutive laws, for concrete and reinforcing steel, are discussed into detail; as well as the different scenarios employed in the columns modeling. Finally, the results of the pushover analysis are presented in chapter four. Capacity curves are examined for the different model scenarios used, and failure modes of concrete and steel are discussed. Capacity curve is converted into capacity spectrum and intersected with the design spectrum. In the last paragraph, the results of nonlinear time-history analyses are compared to those of pushover analysis.

Wind analysis of the Messina Strait Bridge design project proposal with stabilizing cables

A new study on suspension bridges has been prompted by the big disaster of the Tacoma Narrow Bridge at half its design speed. The aerodynamic instability of long-span bridges has been studied using wind tunnel tests. As a result of improved aerodynamic performance from the geometrical configuration of the bridge deck, the aerodynamic criteria for suspension and cable-stayed bridges have become well established in recent years, thereby allowing longer bridge spans to be developed. Although the Messina Strait Bridge has yet to be constructed, we are looking forward to evaluating the impact of different deck cross-sections on both aerodynamic stability and cost reduction. To further improve the aerodynamic characteristics of long-span suspension bridges, an optimized multi-box bridge deck model with two side decks for traffic lanes, two middle railway decks, and three gaps separating them has been proposed aerodynamic performance has been experimentally verified. 1:80 scale wind tunnel tests have been conducted. According to the current MIDAS Model, the first torsional and the first vertical frequency ratios are 1.27787 and 1.36[1] respectively. It is the torsional/vertical frequency ratio, combined with the deck aerodynamic properties, that determines the wind response properties of the bridge for the most dangerous possible form of aeroelastic instability. The classic flutter is caused by the coupling of torsional and vertical modes. Stabilizing cables to the deck could be a solution to this classic flutter by reducing lateral displacement of the deck and increasing frequency ratios. Stabilizing cables will be installed on the deck in three different orientations: vertical, inclined, and horizontal, with diameters of 80 cm, 60 cm, and 40 cm in each orientation respectively. An overview of the research undertaken on this topic will be presented, as well as the most important findings.

Multi-mode communications in near field exploiting OAM properties

This dissertation analyzes the exploitation of the orbital angular momentum (OAM) of the electromagnetic waves with large intelligent surfaces in the near-field region and line-of-sight conditions, in light of the holographic MIMO communication concept. Firstly, a characterization of the OAM-based communication problem is presented, and the relationship between OAM-carrying waves and communication modes is discussed. Then, practicable strategies for OAM detection using large intelligent surfaces and optimization methods based on beam focusing are proposed. Numerical results characterize the effectiveness of OAM with respect to other strategies, also including the proposed detection and optimization methods. It is shown that OAM waves constitute a particular choice of communication modes, i.e., an alternative basis set, which is sub-optimum with respect to optimal basis functions that can be derived by solving eigenfunction problems. Moreover, even the joint utilization of OAM waves with focusing strategies led to the conclusion that no channel capacity achievements can be obtained with these transmission techniques.

Characterization of ENSO changes under idealised radiative forcing in an intermediate complexity general circulation model

Intermediate-complexity general circulation models are a fundamental tool to investigate the role of internal and external variability within the general circulation of the atmosphere and ocean. The model used in this thesis is an intermediate complexity atmospheric general circulation model (SPEEDY) coupled to a state-of-the-art modelling framework for the ocean (NEMO). We assess to which extent the model allows a realistic simulation of the most prominent natural mode of variability at interannual time scales: El-Niño Southern Oscillation (ENSO). To a good approximation, the model represents the ENSO-induced Sea Surface Temperature (SST) pattern in the equatorial Pacific, despite a cold tongue-like bias. The model underestimates (overestimates) the typical ENSO spatial variability during the winter (summer) seasons. The mid-latitude response to ENSO reveals that the typical poleward stationary Rossby wave train is reasonably well represented. The spectral decomposition of ENSO features a spectrum that lacks periodicity at high frequencies and is overly periodic at interannual timescales. We then implemented an idealised transient mean state change in the SPEEDY model. A warmer climate is simulated by an alteration of the parametrized radiative fluxes that corresponds to doubled carbon dioxide absorptivity. Results indicate that the globally averaged surface air temperature increases of 0.76 K. Regionally, the induced signal on the SST field features a significant warming over the central-western Pacific and an El-Niño-like warming in the subtropics. In general, the model features a weakening of the tropical Walker circulation and a poleward expansion of the local Hadley cell. This response is also detected in a poleward rearrangement of the tropical convective rainfall pattern. The model setting that has been here implemented provides a valid theoretical support for future studies on climate sensitivity and forced modes of variability under mean state changes.

String inflationary models with non-monotonic slow-roll and detectable tensor modes

The first chapter of this work has the aim to provide a brief overview of the history of our Universe, in the context of string theory and considering inflation as its possible application to cosmological problems. We then discuss type IIB string compactifications, introducing the study of the inflaton, a scalar field candidated to describe the inflation theory. The Large Volume Scenario (LVS) is studied in the second chapter paying particular attention to the stabilisation of the Kähler moduli which are four-dimensional gravitationally coupled scalar fields which parameterise the size of the extra dimensions. Moduli stabilisation is the process through which these particles acquire a mass and can become promising inflaton candidates. The third chapter is devoted to the study of Fibre Inflation which is an interesting inflationary model derived within the context of LVS compactifications. The fourth chapter tries to extend the zone of slow-roll of the scalar potential by taking larger values of the field φ. Everything is done with the purpose of studying in detail deviations of the cosmological observables, which can better reproduce current experimental data. Finally, we present a slight modification of Fibre Inflation based on a different compactification manifold. This new model produces larger tensor modes with a spectral index in good agreement with the date released in February 2015 by the Planck satellite.