Limiting theorems in statistical mechanics. The mean-field case.

The Curie-Weiss model is defined by ah Hamiltonian according to spins interact. For some particular values of the parameters, the sum of the spins normalized with square-root normalization converges or not toward Gaussian distribution. In the thesis we investigate some correlations between the behaviour of the sum and the central limit for interacting random variables.

Microwave breast imaging reconstruction

In this thesis I analyzed the microwave tomography method to recognize breast can- cer. I study how identify the dielectric permittivity, the Helmoltz equation parameter used to model the real physic problem. Through a non linear least squares method I solve a problem of parameters identification; I show the theoric approach and the devel- opment to reach the results. I use the Levenberg-Marquardt algorithm, applied on COMSOL software to multiphysic models; so I do numerical proofs on semplified test problems compared to the specific real problem to solve.

Statistical mechanics of polymer models: rigorous results and applications

Monomer-dimer models are amongst the models in statistical mechanics which found application in many areas of science, ranging from biology to social sciences. This model describes a many-body system in which monoatomic and diatomic particles subject to hard-core interactions get deposited on a graph. In our work we provide an extension of this model to higher-order particles. The aim of our work is threefold: first we study the thermodynamic properties of the newly introduced model. We solve analytically some regular cases and find that, differently from the original, our extension admits phase transitions. Then we tackle the inverse problem, both from an analytical and numerical perspective. Finally we propose an application to aggregation phenomena in virtual messaging services.

Tomographic 3D reconstruction through linear inversion for breast microwave imaging

In the present thesis we address the problem of detecting and localizing a small spherical target with characteristic electrical properties inside a volume of cylindrical shape, representing female breast, with MWI. One of the main works of this project is to properly extend the existing linear inversion algorithm from planar slice to volume reconstruction; results obtained, under the same conditions and experimental setup are reported for the two different approaches. Preliminar comparison and performance analysis of the reconstruction algorithms is performed via numerical simulations in a software-created environment: a single dipole antenna is used for illuminating the virtual breast phantom from different positions and, for each position, the corresponding scattered field value is registered. Collected data are then exploited in order to reconstruct the investigation domain, along with the scatterer position, in the form of image called pseudospectrum. During this process the tumor is modeled as a dielectric sphere of small radius and, for electromagnetic scattering purposes, it's treated as a point-like source. To improve the performance of reconstruction technique, we repeat the acquisition for a number of frequencies in a given range: the different pseudospectra, reconstructed from single frequency data, are incoherently combined with MUltiple SIgnal Classification (MUSIC) method which returns an overall enhanced image. We exploit multi-frequency approach to test the performance of 3D linear inversion reconstruction algorithm while varying the source position inside the phantom and the height of antenna plane. Analysis results and reconstructed images are then reported. Finally, we perform 3D reconstruction from experimental data gathered with the acquisition system in the microwave laboratory at DIFA, University of Bologna for a recently developed breast-phantom prototype; obtained pseudospectrum and performance analysis for the real model are reported.

Experimental set up and characterization of a prototype for breast microwave imaging

Nella presente tesi è stato sviluppato un sistema di acquisizione automatico finalizzato allo studio del breast microwave imaging. Le misure sono state eseguite in configurazione monostatica, in cui viene acquisito un segnale da diverse posizioni lungo il perimetro dell’area di indagine. A questo scopo, è stato installato un motore ad alta precisione che permette la rotazione del fantoccio e l’esecuzione automatica delle misure da un numero di posizioni fissato. Per automatizzare il processo di acquisizione, è stato inoltre sviluppato appositamente un software in ambiente LabView. Successivamente, è stata eseguita una intensa sessione di misure finalizzate alla caratterizzazione del sistema sviluppato al variare delle condizioni di misura. Abbiamo quindi utilizzato dei fantocci di tumore di diverse dimensioni e permittività elettrica per studiare la sensibilità della strumentazione in condizione di mezzo omogeneo. Dall’analisi delle ricostruzioni multifrequenza effettuate tramite diversi algoritmi di tipo TR-MUSIC sul range di frequenze selezionato, abbiamo notato che il tumore è ricostruito correttamente in tutti gli scenari testati. Inoltre, abbiamo creato un ulteriore fantoccio per simulare la presenza di una disomogeneità nel dominio di imaging. In questo caso, abbiamo studiato le performances del sistema di acquisizione al variare della posizione del tumore, le cui caratteristiche sono state fissate, e della permittività associata al fantoccio. Dall’analisi dei risultati appare che le performances di ricostruzione sono condizionate dalla presenza della disomogeneità, in modo particolare se il tumore è posizionato all’interno di essa. Infine, abbiamo studiato delle performance di due algoritmi di ricostruzione 3D: uno di essi è basato sulla sovrappo- sizione tomografica e sfrutta metodi di interpolazione, l’altro si basa sull’utilizzo di un propagatore 3D per il dipolo Hertziano in approssimazione scalare.

Structure and thermodynamics of H3O+(H2O)8 clusters: A combined molecular dynamics and quantum mechanics approach

We have studied the structure and stability of (H3O+)(H2O)8 clusters using a combination of molecular dynamics sampling and high-level ab initio calculations. 20 distinct oxygen frameworks are found within 2 kcal/mol of the electronic or standard Gibbs free energy minimum. The impact of quantum zero-point vibrational corrections on the relative stability of these isomers is quite significant. The box-like isomers are favored in terms of electronic energy, but with the inclusion of zero-point vibrational corrections and entropic effects tree-like isomers are favored at higher temperatures. Under conditions from 0 to 298.15 K, the global minimum is predicted to be a tree-like structure with one dangling singly coordinated water molecule. Above 298.15 K, higher entropy tree-like isomers with two or more singly coordinated water molecules are favored. These assignments are generally consistent with experimental IR spectra of (H3O+)(H2O)8 obtained at 150 K.

Observations of middle atmospheric H2O and O3 during the 2010 major sudden stratospheric warming by a network of microwave radiometers

In this study, we present middle atmospheric water vapor (H2O) and ozone (O3) measurements obtained by ground-based microwave radiometers at three European locations in Bern (47° N), Onsala (57° N) and Sodankylä (67° N) during Northern winter 2009/2010. In January 2010, a major sudden stratospheric warming (SSW) occurred in the Northern Hemisphere whose signatures are evident in the ground-based observations of H2O and O3. The observed anomalies in H2O and O3 are mostly explained by the relative location of the polar vortex with respect to the measurement locations. The SSW started on 26 January 2010 and was most pronounced by the end of January. The zonal mean temperature in the middle stratosphere (10 hPa) increased by approximately 25 Kelvin within a few days. The stratospheric vortex weakened during the SSW and shifted towards Europe. In the mesosphere, the vortex broke down, which lead to large scale mixing of polar and midlatitudinal air. After the warming, the polar vortex in the stratosphere split into two weaker vortices and in the mesosphere, a new, pole-centered vortex formed with maximum wind speed of 70 m s−1 at approximately 40° N. The shift of the stratospheric vortex towards Europe was observed in Bern as an increase in stratospheric H2O and a decrease in O3. The breakdown of the mesospheric vortex during the SSW was observed at Onsala and Sodankylä as a sudden increase in mesospheric H2O. The following large-scale descent inside the newly formed mesospheric vortex was well captured by the H2O observations in Sodankylä. In order to combine the H2O observations from the three different locations, we applied the trajectory mapping technique on our H2O observations to derive synoptic scale maps of the H2O distribution. Based on our observations and the 3-D wind field, this method allows determining the approximate development of the stratospheric and mesospheric polar vortex and demonstrates the potential of a network of ground-based instruments.