Model reduction techniques in flexible multibody dynamics with application to engine cranktrain simulation

The development of a multibody model of a motorbike engine cranktrain is presented in this work, with an emphasis on flexible component model reduction. A modelling methodology based upon the adoption of non-ideal joints at interface locations, and the inclusion of component flexibility, is developed: both are necessary tasks if one wants to capture dynamic effects which arise in lightweight, high-speed applications. With regard to the first topic, both a ball bearing model and a journal bearing model are implemented, in order to properly capture the dynamic effects of the main connections in the system: angular contact ball bearings are modelled according to a five-DOF nonlinear scheme in order to grasp the crankshaft main bearings behaviour, while an impedance-based hydrodynamic bearing model is implemented providing an enhanced operation prediction at the conrod big end locations. Concerning the second matter, flexible models of the crankshaft and the connecting rod are produced. The well-established Craig-Bampton reduction technique is adopted as a general framework to obtain reduced model representations which are suitable for the subsequent multibody analyses. A particular component mode selection procedure is implemented, based on the concept of Effective Interface Mass, allowing an assessment of the accuracy of the reduced models prior to the nonlinear simulation phase. In addition, a procedure to alleviate the effects of modal truncation, based on the Modal Truncation Augmentation approach, is developed. In order to assess the performances of the proposed modal reduction schemes, numerical tests are performed onto the crankshaft and the conrod models in both frequency and modal domains. A multibody model of the cranktrain is eventually assembled and simulated using a commercial software. Numerical results are presented, demonstrating the effectiveness of the implemented flexible model reduction techniques. The advantages over the conventional frequency-based truncation approach are discussed.

Shaping transverse beam distributions by means of adiabatic crossing of resonances

Non-linear effects are responsible for peculiar phenomena in charged particles dynamics in circular accelerators. Recently, they have been used to propose novel beam manipulations where one can modify the transverse beam distribution in a controlled way, to fulfil the constraints posed by new applications. One example is the resonant beam splitting used at CERN for the Multi-Turn Extraction (MTE), to transfer proton beams from PS to SPS. The theoretical description of these effects relies on the formulation of the particle's dynamics in terms of Hamiltonian systems and symplectic maps, and on the theory of adiabatic invariance and resonant separatrix crossing. Close to resonance, new stable regions and new separatrices appear in the phase space. As non-linear effects do not preserve the Courant-Snyder invariant, it is possible for a particle to cross a separatrix, changing the value of its adiabatic invariant. This process opens the path to new beam manipulations. This thesis deals with various possible effects that can be used to shape the transverse beam dynamics, using 2D and 4D models of particles' motion. We show the possibility of splitting a beam using a resonant external exciter, or combining its action with MTE-like tune modulation close to resonance. Non-linear effects can also be used to cool a beam acting on its transverse beam distribution. We discuss the case of an annular beam distribution, showing that emittance can be reduced modulating amplitude and frequency of a resonant oscillating dipole. We then consider 4D models where, close to resonance, motion in the two transverse planes is coupled. This is exploited to operate on the transverse emittances with a 2D resonance crossing. Depending on the resonance, the result is an emittance exchange between the two planes, or an emittance sharing. These phenomena are described and understood in terms of adiabatic invariance theory.

Simulation of photoinduced processes in organic chromophores: mapping photochemically relevant states for accurate dynamics

The simulation of ultrafast photoinduced processes is a fundamental step towards the understanding of the underlying molecular mechanism and interpretation/prediction of experimental data. Performing a computer simulation of a complex photoinduced process is only possible introducing some approximations but, in order to obtain reliable results, the need to reduce the complexity must balance with the accuracy of the model, which should include all the relevant degrees of freedom and a quantitatively correct description of the electronic states involved in the process. This work presents new computational protocols and strategies for the parameterisation of accurate models for photochemical/photophysical processes based on state-of-the-art multiconfigurational wavefunction-based methods. The required ingredients for a dynamics simulation include potential energy surfaces (PESs) as well as electronic state couplings, which must be mapped across the wide range of geometries visited during the wavepacket/trajectory propagation. The developed procedures allow to obtain solid and extended databases reducing as much as possible the computational cost, thanks to, e.g., specific tuning of the level of theory for different PES regions and/or direct calculation of only the needed components of vectorial quantities (like gradients or nonadiabatic couplings). The presented approaches were applied to three case studies (azobenzene, pyrene, visual rhodopsin), all requiring an accurate parameterisation but for different reasons. The resulting models and simulations allowed to elucidate the mechanism and time scale of the internal conversion, reproducing or even predicting new transient experiments. The general applicability of the developed protocols to systems with different peculiarities and the possibility to parameterise different types of dynamics on an equal footing (classical vs purely quantum) prove that the developed procedures are flexible enough to be tailored for each specific system, and pave the way for exact quantum dynamics with multiple degrees of freedom.

Diffusive models and chaos indicators for non-linear betatron motion in circular hadron accelerators

Understanding the complex dynamics of beam-halo formation and evolution in circular particle accelerators is crucial for the design of current and future rings, particularly those utilizing superconducting magnets such as the CERN Large Hadron Collider (LHC), its luminosity upgrade HL-LHC, and the proposed Future Circular Hadron Collider (FCC-hh). A recent diffusive framework, which describes the evolution of the beam distribution by means of a Fokker-Planck equation, with diffusion coefficient derived from the Nekhoroshev theorem, has been proposed to describe the long-term behaviour of beam dynamics and particle losses. In this thesis, we discuss the theoretical foundations of this framework, and propose the implementation of an original measurement protocol based on collimator scans in view of measuring the Nekhoroshev-like diffusive coefficient by means of beam loss data. The available LHC collimator scan data, unfortunately collected without the proposed measurement protocol, have been successfully analysed using the proposed framework. This approach is also applied to datasets from detailed measurements of the impact on the beam losses of so-called long-range beam-beam compensators also at the LHC. Furthermore, dynamic indicators have been studied as a tool for exploring the phase-space properties of realistic accelerator lattices in single-particle tracking simulations. By first examining the classification performance of known and new indicators in detecting the chaotic character of initial conditions for a modulated Hénon map and then applying this knowledge to study the properties of realistic accelerator lattices, we tried to identify a connection between the presence of chaotic regions in the phase space and Nekhoroshev-like diffusive behaviour, providing new tools to the accelerator physics community.

An experimental and theoretical approach to correct for the scattered radiation in an X-ray computer tomography system for industrial applications

The main problem connected to cone beam computed tomography (CT) systems for industrial applications employing 450 kV X-ray tubes is the high amount of scattered radiation which is added to the primary radiation (signal). This stray radiation leads to a significant degradation of the image quality. A better understanding of the scattering and methods to reduce its effects are therefore necessary to improve the image quality. Several studies have been carried out in the medical field at lower energies, whereas studies in industrial CT, especially for energies up to 450 kV, are lacking. Moreover, the studies reported in literature do not consider the scattered radiation generated by the CT system structure and the walls of the X-ray room (environmental scatter). In order to investigate the scattering on CT projections a GEANT4-based Monte Carlo (MC) model was developed. The model, which has been validated against experimental data, has enabled the calculation of the scattering including the environmental scatter, the optimization of an anti-scatter grid suitable for the CT system, and the optimization of the hardware components of the CT system. The investigation of multiple scattering in the CT projections showed that its contribution is 2.3 times the one of primary radiation for certain objects. The results of the environmental scatter showed that it is the major component of the scattering for aluminum box objects of front size 70 x 70 mm2 and that it strongly depends on the thickness of the object and therefore on the projection. For that reason, its correction is one of the key factors for achieving high quality images. The anti-scatter grid optimized by means of the developed MC model was found to reduce the scatter-toprimary ratio in the reconstructed images by 20 %. The object and environmental scatter calculated by means of the simulation were used to improve the scatter correction algorithm which could be patented by Empa. The results showed that the cupping effect in the corrected image is strongly reduced. The developed CT simulation is a powerful tool to optimize the design of the CT system and to evaluate the contribution of the scattered radiation to the image. Besides, it has offered a basis for a new scatter correction approach by which it has been possible to achieve images with the same spatial resolution as state-of-the-art well collimated fan-beam CT with a gain in the reconstruction time of a factor 10. This result has a high economic impact in non-destructive testing and evaluation, and reverse engineering.

Applications of High Speed Configurable Logic Devices in Modern Particle Physics Experiments

Several activities were conducted during my PhD activity. For the NEMO experiment a collaboration between the INFN/University groups of Catania and Bologna led to the development and production of a mixed signal acquisition board for the Nemo Km3 telescope. The research concerned the feasibility study for a different acquisition technique quite far from that adopted in the NEMO Phase 1 telescope. The DAQ board that we realized exploits the LIRA06 front-end chip for the analog acquisition of anodic an dynodic sources of a PMT (Photo-Multiplier Tube). The low-power analog acquisition allows to sample contemporaneously multiple channels of the PMT at different gain factors in order to increase the signal response linearity over a wider dynamic range. Also the auto triggering and self-event-classification features help to improve the acquisition performance and the knowledge on the neutrino event. A fully functional interface towards the first level data concentrator, the Floor Control Module, has been integrated as well on the board, and a specific firmware has been realized to comply with the present communication protocols. This stage of the project foresees the use of an FPGA, a high speed configurable device, to provide the board with a flexible digital logic control core. After the validation of the whole front-end architecture this feature would be probably integrated in a common mixed-signal ASIC (Application Specific Integrated Circuit). The volatile nature of the configuration memory of the FPGA implied the integration of a flash ISP (In System Programming) memory and a smart architecture for a safe remote reconfiguration of it. All the integrated features of the board have been tested. At the Catania laboratory the behavior of the LIRA chip has been investigated in the digital environment of the DAQ board and we succeeded in driving the acquisition with the FPGA. The PMT pulses generated with an arbitrary waveform generator were correctly triggered and acquired by the analog chip, and successively they were digitized by the on board ADC under the supervision of the FPGA. For the communication towards the data concentrator a test bench has been realized in Bologna where, thanks to a lending of the Roma University and INFN, a full readout chain equivalent to that present in the NEMO phase-1 was installed. These tests showed a good behavior of the digital electronic that was able to receive and to execute command imparted by the PC console and to answer back with a reply. The remotely configurable logic behaved well too and demonstrated, at least in principle, the validity of this technique. A new prototype board is now under development at the Catania laboratory as an evolution of the one described above. This board is going to be deployed within the NEMO Phase-2 tower in one of its floors dedicated to new front-end proposals. This board will integrate a new analog acquisition chip called SAS (Smart Auto-triggering Sampler) introducing thus a new analog front-end but inheriting most of the digital logic present in the current DAQ board discussed in this thesis. For what concern the activity on high-resolution vertex detectors, I worked within the SLIM5 collaboration for the characterization of a MAPS (Monolithic Active Pixel Sensor) device called APSEL-4D. The mentioned chip is a matrix of 4096 active pixel sensors with deep N-well implantations meant for charge collection and to shield the analog electronics from digital noise. The chip integrates the full-custom sensors matrix and the sparsifification/readout logic realized with standard-cells in STM CMOS technology 130 nm. For the chip characterization a test-beam has been set up on the 12 GeV PS (Proton Synchrotron) line facility at CERN of Geneva (CH). The collaboration prepared a silicon strip telescope and a DAQ system (hardware and software) for data acquisition and control of the telescope that allowed to store about 90 million events in 7 equivalent days of live-time of the beam. My activities concerned basically the realization of a firmware interface towards and from the MAPS chip in order to integrate it on the general DAQ system. Thereafter I worked on the DAQ software to implement on it a proper Slow Control interface of the APSEL4D. Several APSEL4D chips with different thinning have been tested during the test beam. Those with 100 and 300 um presented an overall efficiency of about 90% imparting a threshold of 450 electrons. The test-beam allowed to estimate also the resolution of the pixel sensor providing good results consistent with the pitch/sqrt(12) formula. The MAPS intrinsic resolution has been extracted from the width of the residual plot taking into account the multiple scattering effect.

Biologia di Tuta absoluta (Lepidoptera: Gelechiidae), interazioni con l’ambiente e valutazione di tecniche di contenimento ecocompatibili

Tuta absoluta (Meyrick) è un lepidottero originario dell’America meridionale, infeudato a pomodoro e ad altre solanacee coltivate e spontanee. Con l’attività trofica le larve causano mine fogliari e gallerie nei frutti, con conseguenti ingenti danni alle colture. T. absoluta è stato segnalato per la prima volta in Italia nel 2008 e in Piemonte nel 2009. Pertanto le ricerche sono state condotte per rilevarne la distribuzione in Piemonte, studiarne l’andamento di popolazione in condizioni naturali e controllate, e valutare l’efficacia di differenti mezzi di lotta al fine di definire le strategie di difesa. Il monitoraggio, condotto nel 2010, ha evidenziato come T. absoluta sia ormai largamente diffuso sul territorio regionale già pochi mesi dopo la segnalazione. L’insetto ha mostrato di prediligere condizioni climatiche più miti; infatti è stato ritrovato con maggiore frequenza nelle aree più calde. Il fitofago ha raggiunto densità di popolazione elevate a partire dalla seconda metà dell’estate, a ulteriore dimostrazione che, in una regione a clima temperato come il Piemonte, T. absoluta dà origine a infestazioni economicamente rilevanti solo dopo il culmine della stagione estiva. Per definire le strategie di lotta, sono state condotte prove in laboratorio, semi-campo e campo volte a valutare la tossicità nei confronti del lepidottero di preparati a base di emamectina benzoato, rynaxypyr, spinosad e Bacillus thuringiensis Berliner. In campo è stata verificata anche l’efficacia del miride dicifino Macrolophus pygmaeus (Rambur), reperibile in commercio. In tutte le prove, è stata riscontrata una maggiore efficacia di rynaxypyr ed emamectina benzoato. In campo M. pygmaeus ha mostrato difficoltà d’insediamento ed è stato in grado di contenere efficacemente il fitofago soltanto con bassi livelli d’infestazione. Per contro è stata costantemente osservata la presenza naturale di un altro miride dicifino Dicyphus errans (Wolff), che in laboratorio ha mostrato di non essere particolarmente disturbato dalle sostanze saggiate.

Modelli semplificati per valutazione di vulnerabilità sismica di strutture in muratura

L'obiettivo della tesi è stato quello di indagare il complesso problema della vulnerabilità sismica dei ponte in muratura ad arco utilizzando modelli semplificati. Dopo una descrizione dei materiali da costruzione impiegati nella realizzazione e dei principali elementi dei un ponti in muratura, si è indirizzato lo studio di un ponte ad arco situato nel comune di San Marcello Pistoiese. Viene mostrato un modello numerico che permette di descrivere il comportamento strutturale del ponte sotto azione sismica e di valutare la capacità di carico del ponte sottoposto ad una azione trasversale. In un secondo momento viene descritta la realizzazione di un modello in scala del ponte, che è stato sottoposto a prove distruttive effettuate per valutare la capacità di carico del ponte rispetto ad un ipotetica azione orizzontale. Si è cercato poi di inquadrare il problema in un modello teorico che faccia riferimento all'analisi limite. Esso descrive un cinematismo di collasso a telaio che prende spunto dal quadro fessurativo del modello in muratura. Infine sono stati presentati modelli FEM numerici in ordine di complessità crescente, cercando di inquadrare il comportamento meccanico del prototipo del ponte. Tre tipi di modelli sono rappresentati: un telaio incernierato alle estremità costituito da elementi beam con resistenza alla flessione . Il secondo tipo è costituito da una reticolare equivalente che mima lo schema del ponte ed è formato solo da bielle. Infine, il terzo tipo cerca di descrivere l'intero modello con elementi tridimensionali.

Paleosol-based stratigraphy of late Quaternary deposits from the Po basin, between Bologna and the Po river (Northern Italy)

Stratigraphic studies carried out over the last decades in Italy and elsewhere testify a growing interest in Quaternary deposits and in the influence of climate change on their architecture. The subsurface of the Po Plain, in its topmost portion, is made up of alluvial deposits organized in depositional cycles at different scales. This PhD thesis provides millennial-scale stratigraphic reconstruction of the Late Pleistocene-Holocene deposits beneath the southern Po Plain, based on basin-scale correlation of laterally-extensive buried soil horizons. Far from the aim of characterizing palaeosols from a mineralogical and geochemical point of view, we focused on the physical and stratigraphic significance of these horizons. In the Bologna urban area, which hosts an abundance of stratigraphic data, the correlation between seventeen continuously-cored boreholes led to the identification of five vertically-stacked palaeosol-bounded sequences within the 14C time window. In a wide portion of the alluvial plain north of Bologna, far away from the Apenninic margin and from the Po River, where subsurface stratigraphic architecture is dominated by markedly lenticular sediment bodies, palaeosols revealed to be the only stratigraphic marker of remarkable lateral continuity. These horizons are characterized by peculiar resistance values, which make them easily identifiable via pocket penetration tests. Palaeosols reveal specific geometric relationships with the associated alluvial facies associations, allowing reliable estimates of soil development as a function of alluvial dynamics. With the aid of sixty new radiocarbon dates, a reliable age attribution and likely time intervals of exposure were assigned to each palaeosol. Vertically-stacked palaeosols delimitate short-term depositional cycles, likely related to the major episodes of climatic change of the last 40 ky. Through integration of stratigraphic data with 750 archaeological reports from the Bologna area, the impact of human settlements on depositional and pedogenic processes during the late Holocene was investigated.

Neural states in parietal areas during arm reaching

Since the first subdivisions of the brain into macro regions, it has always been thought a priori that, given the heterogeneity of neurons, different areas host specific functions and process unique information in order to generate a behaviour. Moreover, the various sensory inputs coming from different sources (eye, skin, proprioception) flow from one macro area to another, being constantly computed and updated. Therefore, especially for non-contiguous cortical areas, it is not expected to find the same information. From this point of view, it would be inconceivable that the motor and the parietal cortices, diversified by the information encoded and by the anatomical position in the brain, could show very similar neural dynamics. With the present thesis, by analyzing the population activity of parietal areas V6A and PEc with machine learning methods, we argue that a simplified view of the brain organization do not reflect the actual neural processes. We reliably detected a number of neural states that were tightly linked to distinct periods of the task sequence, i.e. the planning and execution of movement and the holding of target as already observed in motor cortices. The states before and after the movement could be further segmented into two states related to different stages of movement planning and arm posture processing. Rather unexpectedly, we found that activity during the movement could be parsed into two states of equal duration temporally linked to the acceleration and deceleration phases of the arm. Our findings suggest that, at least during arm reaching in 3D space, the posterior parietal cortex (PPC) shows low-level population neural dynamics remarkably similar to those found in the motor cortices. In addition, the present findings suggest that computational processes in PPC could be better understood if studied using a dynamical system approach rather than studying a mosaic of single units.

Vibro-acoustic analysis and design optimization to improve comfort and sustainability of future passenger aircraft

Due to the interest of general public and the industrial stakeholders, new challenges and demands are rising in aircraft design. The sustainability is taking its place amongst more traditional design factors, such as safety, performances and costs. Sustainability is both environmental and economic, and among the factors contributing to economic sustainability, there is also passengers' comfort. In order to win these two challenges, they must be considered in the early stages of aircraft design. In this work, the focus is on emissions generation and acoustic comfort, aiming at reducing pollution and internal noise in the preliminary design phases. These results can be achieved with both unconventional aircraft configurations and advanced materials, which also require new numerical formulations to be assessed. In this research, on one hand, the windowless configuration for a commercial aircraft is studied with traditional preliminary design methods in order to achieve a weight reduction and consequently a return in terms of emissions and costs. On the other hand, a new class of insulating materials, the acoustic metamaterials, is applied on the passenger cabin lining panels. The complex kinematic behaviour of these advanced materials is studied through the Carrera's Unified Formulation, that enhances a wide class of powerful refined shell and beam theories with a unique formulation.

Neutrino velocity measurement with the OPERA experiment in the CNGS beam

In the thesis is presented the measurement of the neutrino velocity with the OPERA experiment in the CNGS beam, a muon neutrino beam produced at CERN. The OPERA detector observes muon neutrinos 730 km away from the source. Previous measurements of the neutrino velocity have been performed by other experiments. Since the OPERA experiment aims the direct observation of muon neutrinos oscillations into tau neutrinos, a higher energy beam is employed. This characteristic together with the higher number of interactions in the detector allows for a measurement with a much smaller statistical uncertainty. Moreover, a much more sophisticated timing system (composed by cesium clocks and GPS receivers operating in “common view mode”), and a Fast Waveform Digitizer (installed at CERN and able to measure the internal time structure of the proton pulses used for the CNGS beam), allows for a new measurement with a smaller systematic error. Theoretical models on Lorentz violating effects can be investigated by neutrino velocity measurements with terrestrial beams. The analysis has been carried out with blind method in order to guarantee the internal consistency and the goodness of each calibration measurement. The performed measurement is the most precise one done with a terrestrial neutrino beam, the statistical accuracy achieved by the OPERA measurement is about 10 ns and the systematic error is about 20 ns.

Fiber beam-columns models with flexure-shear interaction for nonlinear analysis of reinforced concrete structures

The aim of this study was to develop a model capable to capture the different contributions which characterize the nonlinear behaviour of reinforced concrete structures. In particular, especially for non slender structures, the contribution to the nonlinear deformation due to bending may be not sufficient to determine the structural response. Two different models characterized by a fibre beam-column element are here proposed. These models can reproduce the flexure-shear interaction in the nonlinear range, with the purpose to improve the analysis in shear-critical structures. The first element discussed is based on flexibility formulation which is associated with the Modified Compression Field Theory as material constitutive law. The other model described in this thesis is based on a three-field variational formulation which is associated with a 3D generalized plastic-damage model as constitutive relationship. The first model proposed in this thesis was developed trying to combine a fibre beamcolumn element based on the flexibility formulation with the MCFT theory as constitutive relationship. The flexibility formulation, in fact, seems to be particularly effective for analysis in the nonlinear field. Just the coupling between the fibre element to model the structure and the shear panel to model the individual fibres allows to describe the nonlinear response associated to flexure and shear, and especially their interaction in the nonlinear field. The model was implemented in an original matlab® computer code, for describing the response of generic structures. The simulations carried out allowed to verify the field of working of the model. Comparisons with available experimental results related to reinforced concrete shears wall were performed in order to validate the model. These results are characterized by the peculiarity of distinguishing the different contributions due to flexure and shear separately. The presented simulations were carried out, in particular, for monotonic loading. The model was tested also through numerical comparisons with other computer programs. Finally it was applied for performing a numerical study on the influence of the nonlinear shear response for non slender reinforced concrete (RC) members. Another approach to the problem has been studied during a period of research at the University of California Berkeley. The beam formulation follows the assumptions of the Timoshenko shear beam theory for the displacement field, and uses a three-field variational formulation in the derivation of the element response. A generalized plasticity model is implemented for structural steel and a 3D plastic-damage model is used for the simulation of concrete. The transverse normal stress is used to satisfy the transverse equilibrium equations of at each control section, this criterion is also used for the condensation of degrees of freedom from the 3D constitutive material to a beam element. In this thesis is presented the beam formulation and the constitutive relationships, different analysis and comparisons are still carrying out between the two model presented.

Transposable elements dynamics in taxa with different reproductive strategies or speciation rate

In recent years the advances in genomics allowed to understand the importance of Transposable Elements (TE) in the evolution of eukaryotic genomes. In this thesis I face two aspects of the TE impact on the in the animal kingdom. The first part is a comparison of the dynamics of the TE dynamics in three species of stick-insects of the Genus Bacillus. I produced three random genomic libraries of 200 Kbps for the three parental species of the taxon: a gonochoric population of Bacillus rossius (facultative parthenogenetic), Bacillus grandii (gonochoric) and Bacillus atticus (obligate parthenogenetic). The unisexual taxon Bacillus atticus does not shows dramatic differences in TE total content and activity with respect to Bacillus grandii and Bacillus rossius. This datum does not confirm the trend observed in other animal models in which unisexual taxa tend to repress the activity of TE to escape the extinction by accumulation of harmful mutations. In the second part I tried to add a contribute to the debate initiated in recent years about the possibility that a high TE content is linked to a high rate of speciation. I designed an evolutionary framework to establish the different rate of speciation among two or more taxa, then I compared TE dynamics considering the different rates of speciation. The species dataset comprises: 29 mammals, four birds, two fish and two insects. On the whole the majority of comparisons confirms the expected trend. In particular the amount of species analyzed in Mammalia allowed me to get a statistical support (p<0,05) of the fact that the TE activity of recently mobilized elements is positively related with the rate of speciation.

Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.