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The evolution of spherically symmetric configurations in the Schrödinger equation approach to cosmic structure formation
Get PDFThe evolution of spherically symmetric cold dark matter overdensities in an expanding Universe is
studied using Schrödinger-Newton (SN) equations, which model self-gravitating collisionless matter.
For doing so, the density profiles of the perturbations are ideally divided into shells, for which an explicit SN
solution for a Λ=0 background can be found. Then, supposing absence of shell crossing during the whole
evolution of the overdensity, the free-particle approximation is applied to each shell. This approximation,
under appropriate limits, which are separately discussed, reduces either to the Zel'dovich approximation or
to the adhesion one.
Then the evolution of the overdensity is treated with SN equations in Zel'dovich approximation as a whole,
without dividing the system into shells, obtaining results that perfectly overlap with the ones held by the
shell by shell study in the Zel'dovich limit.
Eventually, for a specific density profile, time dependent perturbation theory is used to refine the evolution
of its shells computed in the free-particle approximation.
Then it is studied the evolution of a density profile coherent with the initial conditions of the Universe
which are described in literature. For this system, it is explicitly found the shell by shell exact SN solution,
the SN solution in Zel'dovich approximation, and it is discussed the evolution of a mini halo placed inside it.
Independently on the specific density profile considered, the exact solution prescribes that the shells of the
overdensity initially expand at a slower rate than the background, then they turn around and collapse.
The free-particle approximation similarly predicts that regions of the overdensity for which the density is
below a critical value initially expand, then turn around and collapse; but differently, if they exist, regions
whose density exceeds, at the initial time, the critical density, directly contract.
In both treatments, eventually the density diverges: in the centre of symmetry of the perturbation if it is
spherically symmetric, or possibly elsewhere if a test halo is added to the system.
Finally, the effect on the system of a non-null cosmological constant is studied, by deriving its effect on the
solution which describes a shell. For low enough cosmological constants, the evolution quantitatively
resembles the one computed for the Λ=0 case
Il processo di inviluppo comune nell'evoluzione di una binaria di stelle massicce.
Get PDFLo scopo di questa tesi è comprendere quali siano i principali processi che portano
all’evoluzione in inviluppo comune nei sistemi binari formati da stelle massicce, e come questa
fase possa influire sul destino del sistema.
The aim if this thesis is to comprehend which are the main processes that lead to a common
envelope evolution in a binary systems formed by massive stars, and how this phase can influence
the outcome of the systems’ evolution
Corporate liquidity needs during Covid-19 crisis: a preliminary analysis of the response to the adoption of the Guarantee Fund for SMEs
Get PDFKernel-based methods for persistent homology and their applications to Alzheimer's Disease
Get PDFKernel-based methods are powerful tools that are widely applied in many applications and fields of research. In recent years, methods from computational topology have emerged for characterizing the intrinsic geometry of data. Persistence homology is a central tool in topological data analysis, which allows to capture the evolution of topological features of the data. Persistence diagrams represent a natural way to summarize these features, but they can not be directly used in machine learning algorithms. To deal with them, we first analyse various kernel-based methods of recent development, then we propose and apply Variable Scaled Kernels (VSKs) to the persistence diagrams framework. We therefore discuss the application of these kernels in medical imaging in the context of Alzheimer’s Disease classification. Taking into account the
cortical thickness measures on the cortical surface, we build the
persistence diagrams upon different MRI subjects and we perform some classification tests using the support vector machines classifier
Logarithmic construction of the moduli space of admissible covers
Get PDFFor the thesis project, we are interested in learning about the
Harris-Mumford modular compactification of the classical Hurwitz stack using log admissible covers. The Hurwitz stack parametrizes d-sheeted, simple branched coverings of {P}^{1} with b branched points. In this thesis, we present a complete proof of the fact that the stack of log admissible covers is a proper Deligne-Mumford logarithmic stack
On the Mazur-Tate-Teitelbaum conjecture
Get PDFThis thesis is intended to explain the result proved by Greenberg and Stevens on the Mazur-Tate-Teitelbaum conjecture. Specially, the objective of the thesis is to develop all the necessary theory in order to understand Greenberg and Stevens' paper in detail
Percolazione sui grafi aleatori Booleani
No full textCon la presente tesi vogliamo studiare e caratterizzare la transizione di
fase di percolazione per la famiglia dei grafi aleatori booleani. Abbiamo
definito e costruito un grafo aleatorio booleano dipendente da parametro
per poi illustrarne le principali caratteristiche. In particolare, partendo
da modelli aleatori più semplici, abbiamo dimostrato che esiste un valore
soglia sopra il quale il grafo avrà sicuramente una componente connessa con
numero infinito di vertici, e sotto il quale tutte le componenti connesse
rimangono finite