Semiclassical analysis of systems of Schrödinger equations

The scalar Schrödinger equation models the probability density distribution for a particle to be found in a point x given a certain potential V(x) forming a well with respect to a fixed energy level E_0. Formally two real inversion points a,b exist such that V(a)=V(b)=E_0, V(x)<0 in (a,b) and V(x)>0 for xb. Following the work made by D.Yafaev and performing a WKB approximation we obtain solutions defined on specific intervals. The aim of the first part of the thesis is to find a condition on E, which belongs to a neighbourhood of E_0, such that it is an eigenvalue of the Schrödinger operator, obtaining in this way global and linear dependent solutions in L2. In quantum mechanics this condition is known as Bohr-Sommerfeld quantization. In the second part we define a Schrödinger operator referred to two potential wells and we study the quantization conditions on E in order to have a global solution in L2xL2 with respect to the mutual position of the potentials. In particular their wells can be disjoint,can have an intersection, can be included one into the other and can have a single point intersection. For these cases we refer to the works of A.Martinez, S. Fujiié, T. Watanabe, S. Ashida.

Elementary properties of Modular curves and Modular forms

Lo scopo di questa tesi è introdurre in breve le prime proprietà delle curve modulari e delle forme modulari, per poi mostrarne alcune applicazioni archetipiche. Per farlo, dopo aver richiamato alcune nozioni utili nel primo capitolo, sviluppiamo, nel secondo capitolo, la teoria di base delle curve modulari compatte come superfici di Riemann, calcolandone il genere nel caso dei sottogruppi principali di congruenza. Dunque, nel terzo capitolo, dopo un estesa trattazione dell'esempio delle forme modulari rispetto al gruppo modulare, viene calcolata la dimensione degli spazi delle forme intere e delle forme cuspidali rispetto a un sottogruppo di indice finito del gruppo modulare. Questo capitolo si conclude con tre esempi di applicazione della teoria esposta, tra i quali spiccano la dimostrazione del Grande Teorema di Picard e del Teorema dei quattro quadrati di Jacobi.

Probabilistic Envelope Curves for Extreme Rainfall Events - Curve Inviluppo Probabilistiche per Precipitazioni Estreme

A regional envelope curve (REC) of flood flows summarises the current bound on our experience of extreme floods in a region. RECs are available for most regions of the world. Recent scientific papers introduced a probabilistic interpretation of these curves and formulated an empirical estimator of the recurrence interval T associated with a REC, which, in principle, enables us to use RECs for design purposes in ungauged basins. The main aim of this work is twofold. First, it extends the REC concept to extreme rainstorm events by introducing the Depth-Duration Envelope Curves (DDEC), which are defined as the regional upper bound on all the record rainfall depths at present for various rainfall duration. Second, it adapts the probabilistic interpretation proposed for RECs to DDECs and it assesses the suitability of these curves for estimating the T-year rainfall event associated with a given duration and large T values. Probabilistic DDECs are complementary to regional frequency analysis of rainstorms and their utilization in combination with a suitable rainfall-runoff model can provide useful indications on the magnitude of extreme floods for gauged and ungauged basins. The study focuses on two different national datasets, the peak over threshold (POT) series of rainfall depths with duration 30 min., 1, 3, 9 and 24 hrs. obtained for 700 Austrian raingauges and the Annual Maximum Series (AMS) of rainfall depths with duration spanning from 5 min. to 24 hrs. collected at 220 raingauges located in northern-central Italy. The estimation of the recurrence interval of DDEC requires the quantification of the equivalent number of independent data which, in turn, is a function of the cross-correlation among sequences. While the quantification and modelling of intersite dependence is a straightforward task for AMS series, it may be cumbersome for POT series. This paper proposes a possible approach to address this problem.

Fatigue Design Challenges of Transition Pieces from Decommissioned Platforms for Offshore Wind Energy

All structures are subjected to various loading conditions and combinations. For offshore structures, these loads include permanent loads, hydrostatic pressure, wave, current, and wind loads. Typically, sea environments in different geographical regions are characterized by the 100-year wave height, surface currents, and velocity speeds. The main problems associated with the commonly used, deterministic method is the fact that not all waves have the same period, and that the actual stochastic nature of the marine environment is not taken into account. Offshore steel structure fatigue design is done using the DNVGL-RP-0005:2016 standard which takes precedence over the DNV-RP-C203 standard (2012). Fatigue analysis is necessary for oil and gas producing offshore steel structures which were first constructed in the Gulf of Mexico North Sea (the 1930s) and later in the North Sea (1960s). Fatigue strength is commonly described by S-N curves which have been obtained by laboratory experiments. The rapid development of the Offshore wind industry has caused the exploration into deeper ocean areas and the adoption of new support structural concepts such as full lattice tower systems amongst others. The optimal design of offshore wind support structures including foundation, turbine towers, and transition piece components putting into consideration, economy, safety, and even the environment is a critical challenge. In this study, fatigue design challenges of transition pieces from decommissioned platforms for offshore wind energy are proposed to be discussed. The fatigue resistance of the material and structural components under uniaxial and multiaxial loading is introduced with the new fatigue design rules whilst considering the combination of global and local modeling using finite element analysis software programs.

Robotic grasping: State of the art and modular real-world implementation

Robotic Grasping is an important research topic in robotics since for robots to attain more general-purpose utility, grasping is a necessary skill, but very challenging to master. In general the robots may use their perception abilities like an image from a camera to identify grasps for a given object usually unknown. A grasp describes how a robotic end-effector need to be positioned to securely grab an object and successfully lift it without lost it, at the moment state of the arts solutions are still far behind humans. In the last 5–10 years, deep learning methods take the scene to overcome classical problem like the arduous and time-consuming approach to form a task-specific algorithm analytically. In this thesis are present the progress and the approaches in the robotic grasping field and the potential of the deep learning methods in robotic grasping. Based on that, an implementation of a Convolutional Neural Network (CNN) as a starting point for generation of a grasp pose from camera view has been implemented inside a ROS environment. The developed technologies have been integrated into a pick-and-place application for a Panda robot from Franka Emika. The application includes various features related to object detection and selection. Additionally, the features have been kept as generic as possible to allow for easy replacement or removal if needed, without losing time for improvement or new testing.