Mathematical models for cellular aggregation: the chemotactic instability and clustering formation

In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).

Nonlinear modelling of non-structural masonry walls under a low-intensity earthquake motion: calibration through a parametric study

This thesis aims to understand the behavior of a low-rise unreinforced masonry building (URM), the typical residential house in the Netherlands, when subjected to low-intensity earthquakes. In fact, in the last decades, the Groningen region was hit by several shallow earthquakes caused by the extraction of natural gas. In particular, the focus is addressed to the internal non-structural walls and to their interaction with the structural parts of the building. A simple and cost-efficient 2D FEM model is developed, focused on the interfaces representing mortar layers that are present between the non-structural walls and the rest of the structure. As a reference for geometries and materials, it has been taken into consideration a prototype that was built in full-scale at the EUCENTRE laboratory of Pavia (Italy). Firstly, a quasi-static analysis is performed by gradually applying a prescribed displacement on the roof floor of the structure. Sensitivity analyses are conducted on some key parameters characterizing mortar. This analysis allows for the calibration of their values and the evaluation of the reliability of the model. Successively, a transient analysis is performed to effectively subject the model to a seismic action and hence also evaluate the mechanical response of the building over time. Moreover, it was possible to compare the results of this analysis with the displacements recorded in the experimental tests by creating a model representing the entire considered structure. As a result, some conditions for the model calibration are defined. The reliability of the model is then confirmed by both the reasonable results obtained from the sensitivity analysis and the compatibility of the values obtained for the top displacement of the roof floor of the experimental test, and the same value acquired from the structural model.

From point cloud to HBIM: an integrated workflow for 3D reconstruction of heritage building with model accuracy evaluation

Modern society is now facing significant difficulties in attempting to preserve its architectural heritage. Numerous challenges arise consequently when it comes to documentation, preservation and restoration. Fortunately, new perspectives on architectural heritage are emerging owing to the rapid development of digitalization. Therefore, this presents new challenges for architects, restorers and specialists. Additionally, this has changed the way they approach the study of existing heritage, changing from conventional 2D drawings in response to the increasing requirement for 3D representations. Recently, Building Information Modelling for historic buildings (HBIM) has escalated as an emerging trend to interconnect geometrical and informational data. Currently, the latest 3D geomatics techniques based on 3D laser scanners with enhanced photogrammetry along with the continuous improvement in the BIM industry allow for an enhanced 3D digital reconstruction of historical and existing buildings. This research study aimed to develop an integrated workflow for the 3D digital reconstruction of heritage buildings starting from a point cloud. The Pieve of San Michele in Acerboli’s Church in Santarcangelo Di Romagna (6th century) served as the test bed. The point cloud was utilized as an essential referential to model the BIM geometry using Autodesk Revit® 2022. To validate the accuracy of the model, Deviation Analysis Method was employed using CloudCompare software to determine the degree of deviation between the HBIM model and the point cloud. The acquired findings showed a very promising outcome in the average distance between the HBIM model and the point cloud. The conducted approach in this study demonstrated the viability of producing a precise BIM geometry from point clouds.