Substructuring approache in state space models for dynamic system parameters identification

In the recent decade, the request for structural health monitoring expertise increased exponentially in the United States. The aging issues that most of the transportation structures are experiencing can put in serious jeopardy the economic system of a region as well as of a country. At the same time, the monitoring of structures is a central topic of discussion in Europe, where the preservation of historical buildings has been addressed over the last four centuries. More recently, various concerns arose about security performance of civil structures after tragic events such the 9/11 or the 2011 Japan earthquake: engineers looks for a design able to resist exceptional loadings due to earthquakes, hurricanes and terrorist attacks. After events of such a kind, the assessment of the remaining life of the structure is at least as important as the initial performance design. Consequently, it appears very clear that the introduction of reliable and accessible damage assessment techniques is crucial for the localization of issues and for a correct and immediate rehabilitation. The System Identification is a branch of the more general Control Theory. In Civil Engineering, this field addresses the techniques needed to find mechanical characteristics as the stiffness or the mass starting from the signals captured by sensors. The objective of the Dynamic Structural Identification (DSI) is to define, starting from experimental measurements, the modal fundamental parameters of a generic structure in order to characterize, via a mathematical model, the dynamic behavior. The knowledge of these parameters is helpful in the Model Updating procedure, that permits to define corrected theoretical models through experimental validation. The main aim of this technique is to minimize the differences between the theoretical model results and in situ measurements of dynamic data. Therefore, the new model becomes a very effective control practice when it comes to rehabilitation of structures or damage assessment. The instrumentation of a whole structure is an unfeasible procedure sometimes because of the high cost involved or, sometimes, because it’s not possible to physically reach each point of the structure. Therefore, numerous scholars have been trying to address this problem. In general two are the main involved methods. Since the limited number of sensors, in a first case, it’s possible to gather time histories only for some locations, then to move the instruments to another location and replay the procedure. Otherwise, if the number of sensors is enough and the structure does not present a complicate geometry, it’s usually sufficient to detect only the principal first modes. This two problems are well presented in the works of Balsamo [1] for the application to a simple system and Jun [2] for the analysis of system with a limited number of sensors. Once the system identification has been carried, it is possible to access the actual system characteristics. A frequent practice is to create an updated FEM model and assess whether the structure fulfills or not the requested functions. Once again the objective of this work is to present a general methodology to analyze big structure using a limited number of instrumentation and at the same time, obtaining the most information about an identified structure without recalling methodologies of difficult interpretation. A general framework of the state space identification procedure via OKID/ERA algorithm is developed and implemented in Matlab. Then, some simple examples are proposed to highlight the principal characteristics and advantage of this methodology. A new algebraic manipulation for a prolific use of substructuring results is developed and implemented.

Numerical and semi-analytical models of sliding masses: application to the 1783 Scilla tsunamigenic landslide

The Scilla rock avalanche occurred on 6 February 1783 along the coast of the Calabria region (southern Italy), close to the Messina Strait. It was triggered by a mainshock of the Terremoto delle Calabrie seismic sequence, and it induced a tsunami wave responsible for more than 1500 casualties along the neighboring Marina Grande beach. The main goal of this work is the application of semi-analtycal and numerical models to simulate this event. The first one is a MATLAB code expressly created for this work that solves the equations of motion for sliding particles on a two-dimensional surface through a fourth-order Runge-Kutta method. The second one is a code developed by the Tsunami Research Team of the Department of Physics and Astronomy (DIFA) of the Bologna University that describes a slide as a chain of blocks able to interact while sliding down over a slope and adopts a Lagrangian point of view. A wide description of landslide phenomena and in particular of landslides induced by earthquakes and with tsunamigenic potential is proposed in the first part of the work. Subsequently, the physical and mathematical background is presented; in particular, a detailed study on derivatives discratization is provided. Later on, a description of the dynamics of a point-mass sliding on a surface is proposed together with several applications of numerical and analytical models over ideal topographies. In the last part, the dynamics of points sliding on a surface and interacting with each other is proposed. Similarly, different application on an ideal topography are shown. Finally, the applications on the 1783 Scilla event are shown and discussed.

String inflationary models with non-monotonic slow-roll and detectable tensor modes

The first chapter of this work has the aim to provide a brief overview of the history of our Universe, in the context of string theory and considering inflation as its possible application to cosmological problems. We then discuss type IIB string compactifications, introducing the study of the inflaton, a scalar field candidated to describe the inflation theory. The Large Volume Scenario (LVS) is studied in the second chapter paying particular attention to the stabilisation of the Kähler moduli which are four-dimensional gravitationally coupled scalar fields which parameterise the size of the extra dimensions. Moduli stabilisation is the process through which these particles acquire a mass and can become promising inflaton candidates. The third chapter is devoted to the study of Fibre Inflation which is an interesting inflationary model derived within the context of LVS compactifications. The fourth chapter tries to extend the zone of slow-roll of the scalar potential by taking larger values of the field φ. Everything is done with the purpose of studying in detail deviations of the cosmological observables, which can better reproduce current experimental data. Finally, we present a slight modification of Fibre Inflation based on a different compactification manifold. This new model produces larger tensor modes with a spectral index in good agreement with the date released in February 2015 by the Planck satellite.

Modelling the Halo mass number counts in modified gravity cosmological scenarios

In this Thesis work we investigate some of different cosmological background scenarios using one of the main probes used in cosmology: the halo mass function. The observed abundance of galaxy clusters (or similarly DM haloes) can indeed be compared to its theoretical predictions to derive fundamental constrains on the cosmological scenario assumed. Given the importance of exploring and constraining models degenerate with the ΛCDM one, we test the applicability of some notable halo mass function models to these scenarios. To this purpose, we made use of the DUSTGRAIN-pathfinder N-body simulations, which assume cosmological scenarios that include modified gravity in the form of f(R) models and massive neutrinos. We carried on the analysis of 3 simulation snapshots at different redshifts, z = 0, 0.5, 1, building multiple samples of dark matter haloes by applying different overdensity thresholds during the procedure of halo identification. We started our analysis by considering the halo mass function model introduced by Despali et al. (2016), who proposed a parametrization that encapsulates the effect of the different halo mass definitions and the relative evolution with the redshift. We calibrated the main parameters of this relation by using the ΛCDM halo catalogues extracted from the DUSTGRAIN-pathfinder simulations, fitting the measured halo abundances at all redshifts and density thresholds. Afterwards we tested the same model parametrization with halo catalogues extracted from the simulations implementing both modified gravity and massive neutrinos. We repeated therefore the calibration procedure on these data to search for discrepancies with respect to the ΛCDM model. Finally we focused the analysis on the cosmological models implementing modified gravity only. We took our ΛCDM calibrated halo mass function and we modified it with the additional f (R) gravity form proposed by Gupta et al. (2022).

Analytic models of self-gravitating rotating gaseous tori with central black hole

In this thesis project, I present stationary models of rotating fluids with toroidal distributions that can be used to represent the active galactic nuclei (AGN) central obscurers, i.e. molecular tori (Combes et al., 2019), as well as geometrically thick accretion discs, like ADAF discs (Narayan and Yi, 1995) or Polish doughnuts (Abramowicz, 2005). In particular, I study stationary rotating systems with a more general baroclinic distribution (with a vertical gradient of the angular velocity), which are often more realistic and less studied, due to their complexity, than the barotropic ones (with cylindrical rotation), which are easier to construct. In the thesis, I compute analytically the main intrinsic and projected properties of the power-law tori based on the potential-density pairs of Ciotti and Bertin (2005). I study the density distribution and the resulting gravitational potential for different values of α, in the range 2 < α < 5. For the same models, I compute the surface density of the systems when seen face-on and edge-on. I then apply the stationary Euler equations to obtain rotational velocity and temperature distributions of the self-gravitating models in the absence of an external gravitational potential. In the thesis I also consider the power-law tori with the presence of a central black hole in addition to the gas self-gravity, and solving analytically the stationary Euler equations, I compute how the properties of the system are modified by the black hole and how they vary as a function of the black hole mass. Finally, applying the Solberg-Høiland criterion, I show that these baroclinic stationary models are linearly stable in the absence of the black hole. In the presence of the black hole I derive the analytical condition for stability, which depends on α and on the black hole mass. I also study the stability of the tori in the hypothesis that they are weakly magnetized, finding that they are always unstable to this instability.

Stellar mass loss from the Fornax dwarf spheroidal galaxy

Dwarf galaxies often experience gravitational interactions from more massive companions. These interactions can deform galaxies, turn star formation on or off, or give rise to mass loss phenomena. In this thesis work we propose to study, through N-body simulations, the stellar mass loss suffered by the dwarf spheroid galaxy (dSph) Fornax orbiting in the Milky Way gravitational potential. Which is a key phenomenon to explain the mass budget problem: the Fornax globular clusters together have a stellar mass comparable to that of Fornax itself. If we look at the stellar populations which they are made of and we apply the scenarios of stellar population formation we find that, originally, they must have been >= 5 times more massive. For this reason, they must have lost or ejected stars through dynamic interactions. However, as presented in Larsen et al (2012), field stars alone are not sufficient to explain this scenario. We may assume that some of those stars fell into Fornax, and later were stripped by Milky Way. In order to study this solution we built several illustrative single component simulations, with a tabulated density model using the P07ecc orbit studied from Battaglia et al (2015). To divide the single component into stellar and dark matter components we have defined a posterior the probability function P(E), where E is the initial energy distribution of the particles. By associating each particle with a fraction of stellar mass and dark matter. In this way we built stellar density profiles without repeating simulations. We applied the method to Fornax using the profile density tables obtained in Pascale et al (2018) as observational constraints and to build the model. The results confirm the results previously obtained with less flexible models by Battaglia et al (2015). They show a stellar mass loss < 4% within 1.6 kpc and negligible within 3 kpc, too small to solve the mass budget problem.