Quantum solitons in the XXZ model with staggered external magnetic field

The 1-D 1/2-spin XXZ model with staggered external magnetic field, when restricting to low field, can be mapped into the quantum sine-Gordon model through bosonization: this assures the presence of soliton, antisoliton and breather excitations in it. In particular, the action of the staggered field opens a gap so that these physical objects are stable against energetic fluctuations. In the present work, this model is studied both analytically and numerically. On the one hand, analytical calculations are made to solve exactly the model through Bethe ansatz: the solution for the XX + h staggered model is found first by means of Jordan-Wigner transformation and then through Bethe ansatz; after this stage, efforts are made to extend the latter approach to the XXZ + h staggered model (without finding its exact solution). On the other hand, the energies of the elementary soliton excitations are pinpointed through static DMRG (Density Matrix Renormalization Group) for different values of the parameters in the hamiltonian. Breathers are found to be in the antiferromagnetic region only, while solitons and antisolitons are present both in the ferromagnetic and antiferromagnetic region. Their single-site z-magnetization expectation values are also computed to see how they appear in real space, and time-dependent DMRG is employed to realize quenches on the hamiltonian parameters to monitor their time-evolution. The results obtained reveal the quantum nature of these objects and provide some information about their features. Further studies and a better understanding of their properties could bring to the realization of a two-level state through a soliton-antisoliton pair, in order to implement a qubit.

Tolerance optimization with statistical approach in the CAT environment

Nowadays, product development in all its phases plays a fundamental role in the industrial chain. The need for a company to compete at high levels, the need to be quick in responding to market demands and therefore to be able to engineer the product quickly and with a high level of quality, has led to the need to get involved in new more advanced methods/ processes. In recent years, we are moving away from the concept of 2D-based design and production and approaching the concept of Model Based Definition. By using this approach, increasingly complex systems turn out to be easier to deal with but above all cheaper in obtaining them. Thanks to the Model Based Definition it is possible to share data in a lean and simple way to the entire engineering and production chain of the product. The great advantage of this approach is precisely the uniqueness of the information. In this specific thesis work, this approach has been exploited in the context of tolerances with the aid of CAD / CAT software. Tolerance analysis or dimensional variation analysis is a way to understand how sources of variation in part size and assembly constraints propagate between parts and assemblies and how that range affects the ability of a project to meet its requirements. It is critically important to note how tolerance directly affects the cost and performance of products. Worst Case Analysis (WCA) and Statistical analysis (RSS) are the two principal methods in DVA. The thesis aims to show the advantages of using statistical dimensional analysis by creating and examining various case studies, using PTC CREO software for CAD modeling and CETOL 6σ for tolerance analysis. Moreover, it will be provided a comparison between manual and 3D analysis, focusing the attention to the information lost in the 1D case. The results obtained allow us to highlight the need to use this approach from the early stages of the product design cycle.

Dosimetric optimization of CT protocols for the preoperative planning of hip arthroplasty

Radiation dose in x-ray computed tomography (CT) has become a topic of great interest due to the increasing number of CT examinations performed worldwide. In fact, CT scans are responsible of significant doses delivered to the patients, much larger than the doses due to the most common radiographic procedures. This thesis work, carried out at the Laboratory of Medical Technology (LTM) of the Rizzoli Orthopaedic Institute (IOR, Bologna), focuses on two primary objectives: the dosimetric characterization of the tomograph present at the IOR and the optimization of the clinical protocol for hip arthroplasty. In particular, after having verified the reliability of the dose estimates provided by the system, we compared the estimates of the doses delivered to 10 patients undergoing CT examination for the pre-operative planning of hip replacement with the Diagnostic Reference Level (DRL) for an osseous pelvis examination. Out of 10 patients considered, only for 3 of them the doses were lower than the DRL. Therefore, the necessity to optimize the clinical protocol emerged. This optimization was investigated using a human femur from a cadaver. Quantitative analysis and comparison of 3D reconstructions were made, after having performed manual segmentation of the femur from different CT acquisitions. Dosimetric simulations of the CT acquisitions on the femur were also made and associated to the accuracy of the 3D reconstructions, to analyse the optimal combination of CT acquisition parameters. The study showed that protocol optimization both in terms of Hausdorff distance and in terms of effective dose (ED) to the patient may be realized simply by modifying the value of the pitch in the protocol, by choosing between 0.98 and 1.37.