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.

Effect of multiple sources of disturbance on rocky benthic assemblages in some localities of Salento, Apulia

The first part of my work consisted in samplings conduced in nine different localities of the salento peninsula and Apulia (Italy): Costa Merlata (BR), Punta Penne (BR), Santa Cesarea terme (LE), Santa Caterina (LE), Torre Inserraglio (LE), Torre Guaceto (BR), Porto Cesareo (LE), Otranto (LE), Isole Tremiti (FG). I collected data of species percentage covering from the infralittoral rocky zone, using squares of 50x50 cm. We considered 3 sites for location and 10 replicates for each site, which has been taken randomly. Then I took other data about the same places, collected in some years, and I combined them together, to do a spatial analysis. So I started from a data set of 1896 samples but I decided not to consider time as a factor because I have reason to think that in this period of time anthropogenic stressors and their effects (if present), didn’t change considerably. The response variable I’ve analysed is the covering percentage of an amount of 243 species (subsequently merged into 32 functional groups), including seaweeds, invertebrates, sediment and rock. 2 After the sampling, I have been spent a period of two months at the Hopkins Marine Station of Stanford University, in Monterey (California,USA), at Fiorenza Micheli's laboratory. I've been carried out statistical analysis on my data set, using the software PRIMER 6. My explorative analysis starts with a nMDS in PRIMER 6, considering the original data matrix without, for the moment, the effect of stressors. What comes out is a good separation between localities and it confirms the result of ANOSIM analysis conduced on the original data matrix. What is possible to ensure is that there is not a separation led by a geographic pattern, but there should be something else that leads the differences. Is clear the presence of at least three groups: one composed by Porto cesareo, Torre Guaceto and Isole tremiti (the only marine protected areas considered in this work); another one by Otranto, and the last one by the rest of little, impacted localities. Inside the localities that include MPA(Marine Protected Areas), is also possible to observe a sort of grouping between protected and controlled areas. What comes out from SIMPER analysis is that the most of the species involved in leading differences between populations are not rare species, like: Cystoseira spp., Mytilus sp. and ECR. Moreover I assigned discrete values (0,1,2) of each stressor to all the sites I considered, in relation to the intensity with which the anthropogenic factor affect the localities. 3 Then I tried to estabilish if there were some significant interactions between stressors: by using Spearman rank correlation and Spearman tables of significance, and taking into account 17 grades of freedom, the outcome shows some significant stressors interactions. Then I built a nMDS considering the stressors as response variable. The result was positive: localities are well separeted by stressors. Consequently I related the matrix with 'localities and species' with the 'localities and stressors' one. Stressors combination explains with a good significance level the variability inside my populations. I tried with all the possible data transformations (none, square root, fourth root, log (X+1), P/A), but the fourth root seemed to be the best one, with the highest level of significativity, meaning that also rare species can influence the result. The challenge will be to characterize better which kind of stressors (including also natural ones), act on the ecosystem; and give them a quantitative and more accurate values, trying to understand how they interact (in an additive or non-additive way).

Root cause analysis applied to a finite element model's refinement of a negative stiffness structure

Negative Stiffness Structures are mechanical systems that require a decrease in the applied force to generate an increase in displacement. They are structures that possess special characteristics such as snap-through and bi-stability. All of these features make them particularly suitable for different applications, such as shock-absorption, vibration isolation and damping. From this point of view, they have risen awareness of their characteristics and, in order to match them to the application needed, a numerical simulation is of great interest. In this regard, this thesis is a continuation of previous studies in a circular negative stiffness structure and aims at refine the numerical model by presenting a new solution. To that end, an investigation procedure is needed. Amongst all of the methods available, root cause analysis was the chosen one to perform the investigation since it provides a clear view of the problem under analysis and a categorization of all the causes behind it. As a result of the cause-effect analysis, the main causes that have influence on the numerical results were obtained. Once all of the causes were listed, solutions to them were proposed and it led to a new numerical model. The numerical model proposed was of nonlinear type of analysis with hexagonal elements and a hyperelastic material model. The results were analyzed through force-displacement curves, allowing for the visualization of the structure’s energy recovery. When compared to the results obtained from the experimental part, it is evident that the trend is similar and the negative stiffness behaviour is present.

Hardware-in-the-loop implementation of single- and dual-phase shift control for dual active bridge converters in EV applications

Isolated DC-DC converters play a significant role in fast charging and maintaining the variable output voltage for EV applications. This study aims to investigate the different Isolated DC-DC converters for onboard and offboard chargers, then, once the topology is selected, study the control techniques and, finally, achieve a real-time converter model to accomplish Hardware-In-The-Loop (HIL) results. Among the different isolated DC-DC topologies, the Dual Active Bridge (DAB) converter has the advantage of allowing bidirectional power flow, which enables operating in both Grid to Vehicle (G2V) and Vehicle to Grid (V2G) modalities. Recently, DAB has been used in the offboard chargers for high voltage applications due to SiC and GaN MOSFETs; this new technology also allows the utilization of higher switching frequencies. By empowering soft switching techniques to reduce switching losses, higher switching frequency operation is possible in DAB. There are four phase shift control techniques for the DAB converter. They are Single Phase shift, Extended Phase shift, Dual Phase shift, Triple Phase shift controls. This thesis considers two control strategies; Single-Phase, and Dual-Phase shifts, to understand the circulating currents, power losses, and output capacitor size reduction in the DAB. Hardware-In-The-Loop (HIL) experiments are carried out on both controls with high switching frequencies using the PLECS software tool and the RT box supporting the PLECS. Root Mean Square Error is also calculated for steady-state values of output voltage with different sampling frequencies in both the controls to identify the achievable sampling frequency in real-time. DSP implementation is also executed to emulate the optimized DAB converter design, and final real-time simulation results are discussed for both the Single-Phase and Dual-Phase shift controls.