Il problema di Dirichlet per equazioni lineari ellittiche in forma di divergenza

The purpose of this dissertation is to prove that the Dirichlet problem in a bounded domain is uniquely solvable for elliptic equations in divergence form. The proof can be achieved by Hilbert space methods based on generalized or weak solutions. Existence and uniqueness of a generalized solution for the Dirichlet problem follow from the Fredholm alternative and weak maximum principle.

Prediction and measurement of forced response of a composite blade undergoing nonlinear vibration

The main objective of this project is to experimentally demonstrate geometrical nonlinear phenomena due to large displacements during resonant vibration of composite materials and to explain the problem associated with fatigue prediction at resonant conditions. Three different composite blades to be tested were designed and manufactured, being their difference in the composite layup (i.e. unidirectional, cross-ply, and angle-ply layups). Manual envelope bagging technique is explained as applied to the actual manufacturing of the components; problems encountered and their solutions are detailed. Forced response tests of the first flexural, first torsional, and second flexural modes were performed by means of a uniquely contactless excitation system which induced vibration by using a pulsed airflow. Vibration intensity was acquired by means of Polytec LDV system. The first flexural mode is found to be completely linear irrespective of the vibration amplitude. The first torsional mode exhibits a general nonlinear softening behaviour which is interestingly coupled with a hardening behaviour for the unidirectional layup. The second flexural mode has a hardening nonlinear behaviour for either the unidirectional and angle-ply blade, whereas it is slightly softening for the cross-ply layup. By using the same equipment as that used for forced response analyses, free decay tests were performed at different airflow intensities. Discrete Fourier Trasform over the entire decay and Sliding DFT were computed so as to visualise the presence of nonlinear superharmonics in the decay signal and when they were damped out from the vibration over the decay time. Linear modes exhibit an exponential decay, while nonlinearities are associated with a dry-friction damping phenomenon which tends to increase with increasing amplitude. Damping ratio is derived from logarithmic decrement for the exponential branch of the decay.

Processi markoviani nascosti

We introduce the notation of Markov chains and their properties, and give the definition of ergodic, irreducible and aperiodic chains with correspective examples. Then, the definition of hidden Markov models is given and their characteristics are examined. We formulate three basic problems regarding the hidden Markov models and discuss the solution of two of them - the Viterbi algorithm and the forward-backward algorithm.

Laying the path to consumer-level immersive simulation environment

Since the end of the long winter of virtual reality (VR) at the beginning of the 2010 decade, many improvements have been made in terms of hardware technologies and software platforms performances and costs. Many expect such trend will continue, pushing the penetration rate of virtual reality headsets to skyrocket at some point in the future, just as mobile platforms did before. In the meantime, virtual reality is slowly transitioning from a specialized laboratory-only technology, to a consumer electronics appliance, opening interesting opportunities and challenges. In this transition, two interesting research questions amount to how 2D-based content and applications may benefit (or be hurt) by the adoption of 3D-based immersive environments and to how to proficiently support such integration. Acknowledging the relevance of the former, we here consider the latter question, focusing our attention on the diversified family of PC-based simulation tools and platforms. VR-based visualization is, in fact, widely understood and appreciated in the simulation arena, but mainly confined to high performance computing laboratories. Our contribution here aims at characterizing the simulation tools which could benefit from immersive interfaces, along with a general framework and a preliminary implementation which may be put to good use to support their transition from uniquely 2D to blended 2D/3D environments.