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Development of teaching-learning sequences on quantum physics for the Italian secondary school
Get PDFIn the past 15 years, quantum mechanics has been included in most secondary school
standards, including the Italian ones, but still in a rather marginal way. The conceptual complexity
of quantum mechanics is often a hurdle for students as well as for teachers; as a consequence, most
teachers and textbooks opt for narrative/historical approaches which, however, are not sufficient to
grasp the deepest conceptual aspects of quantum physics, nor to deal with its technological
applications. Teaching quantum physics in secondary school is therefore a challenge that calls for a
close collaboration between physics teachers and physics education researchers. The goal of this
work is to develop and test research-based teaching-learning sequences (TLS) based on the study of
relevant literature in physics education research and on a survey to be conducted with secondary
school teachers. More specifically, the thesis work will include the following phases. A review of
the literature on the teaching and learning of quantum mechanics, with particular reference to the
proposals developed in the Italian context. A survey with a sample of secondary school physics
teachers aimed at understanding the needs and difficulties of teaching quantum mechanics. On the
basis of the literature and of the results of the survey, development of a teaching-learning sequence
(TLS) on quantum mechanics for the fifth year of the Italian “liceo scientifico”. Testing and
evaluation of the TLS in a real classroom context
Del Pezzo surfaces and points in the plane
Get PDFThis thesis will focus on the study of the relationship that exists between Del Pezzo surfaces, a kind of surface defined as "a smooth birationally trivial surface V on which the anticanonical sheaf is ample" and counting points in the projective plane P2(k) built over a finite field k. The result allowing us to to link the two concepts says that a Del Pezzo surface of degree d bigger that 1 is isomorphic to the blowup up of 9-d points in P2(k). Once we have settled the relationship between the two concepts the results will revolve around counting n-tuples of points in P2(k) both from a theoretical and computational point of view. In particular the case of 8-tuples, corresponding to Del Pezzo surfaces of degree 1, will be the one around which most of the work will revolve, culminating with the statement of a degree 8 monic polynomial expressing the number of -tuples of points in general position as a function of the dimension of the base field. The work concludes by considering further instances of counting points in a projective plane, in particular in the case of points on which the Frobenius morphism acts in a specific way
Un metodo non supervisionato di machine learning per la classificazione morfologica di galassie lontane
No full textNella tesi si verifica se un metodo di machine learning non supervisionato (in particolare il K-means) è indicato per classificare in maniera automatica la morfologia delle galassie. Nella tesi vengono descritte le diverse classi morfologiche delle galassie, i metodi parametrici e non parametrici per lo studio della morfologia, l'utilizzo dell'intelligenza artificiale e come viene applicato il K-means al data set preso in esame
Control of drop motion by means of optical patterns imprinted on Fe:LiNbO3 crystals.
Get PDFControlling and predicting the mobility of sessile droplets in contact with a solid surface has fundamental implications and technological applications. In the last decade, the use of liquid impregnated surfaces has become the best way to improve the wettability of a substrate and promote the motion of sessile droplets. In this thesis we will couple the realization of a liquid impregnated surface with the photovoltaic effect exhibited by Lithium Niobate crystals to control in an active way the motion of sessile droplets. The resulting method is simple and versatile, enabling the successful manipulation of many consecutive drops having typical volumes of micro-liters, without the need for electrodes or power supplies. In particular, the pattern of illumination arriving on the Lithium Niobate is generated by a spatial light modulator which permits to write any shape to control the droplet. After a preliminary exploration of the dynamics of the system, the main goal of this thesis work consists in finding the best parameters to realize and control the motion of a train of droplets in a reproducible way
The use of persistent homology in data science for topological data analysis
Get PDFTopological data analysis (TDA) is a young field that has been rapidly
growing over the last years and which blends algebraic topology, statistics
and computer science. It arises motivated by the fact that the topology of
a space gives useful information about it. In particular, when working with
scientific data, information about their internal structure may provide
important properties about the phenomena that it represents or its
behaviour. The goal of topological data analysis is to provide well-founded
mathematical, statistical and algorithmic methods to infer the topological
structure underlying the data. The aims of this thesis are two. On the one hand, to introduce this field and its mathematical tools, focusing on persistent homology and its representation by persistence diagrams. On the other hand, the study of the latter using techniques from optimal transport, proposing a vectorization based on transport maps
Il grafo aleatorio di Erdos-Renyi: transizione di fase e proprietà di struttura
No full textLo scopo di questa tesi è quello di presentare alcune proprietà di
connettività e di struttura del grafo di Erdős-Rényi. In primo luogo,
analizziamo la transizione di fase, che permette di capire sotto quali
ipotesi il grafo di Erdős-Rényi possiede una grande componente connessa,
dove si trova la maggior parte dei vertici. In seguito, mostriamo la
distribuzione dei vertici in base al loro grado, la probabilità di trovare
un determinato sottografo e la struttura locale. Infine, confrontiamo il
modello matematico fornito dal grafo di Erdős-Rényi con le reti complesse
reali, andando a testare sul grafo le proprietà tipiche delle reti reali
An introduction to Grothendieck's Galois theory
No full textGrothendieck's Galois Theory is a reformulation of the classical Galois
Theory on a more abstract level. It was developed by Alexander Grothendieck around 1960 and his main purpose was that of studying Galois Theory in terms of categories. The objective of this thesis is to enunciate and prove the Fundamental Theorem of the Grothendieck's Galois Theory, starting from the introduction of the involved algebraic structures and assuming the classical Galois Theory for finite extensions as known. This thesis could be considered as a fascinating journey in Algebra and Galois Theory, which starts from some crucial prerequisites and leds to the Fundamental Theorem. It is divided into four chapters: "Basics in Category Theory", "Algebras and Tensor Product", "Galois Theory for infinite extensions" and "Grothendieck's Galois Theory"
