Non-Linear Pricing in Imperfectly Competitive Markets

This thesis is dedicated to the analysis of non-linear pricing in oligopoly. Non-linear pricing is a fairly predominant practice in most real markets, mostly characterized by some amount of competition. The sophistication of pricing practices has increased in the latest decades due to the technological advances that have allowed companies to gather more and more data on consumers preferences. The first essay of the thesis highlights the main characteristics of oligopolistic non-linear pricing. Non-linear pricing is a special case of price discrimination. The theory of price discrimination has to be modified in presence of oligopoly: in particular, a crucial role is played by the competitive externality that implies that product differentiation is closely related to the possibility of discriminating. The essay reviews the theory of competitive non-linear pricing by starting from its foundations, mechanism design under common agency. The different approaches to model non-linear pricing are then reviewed. In particular, the difference between price and quantity competition is highlighted. Finally, the close link between non-linear pricing and the recent developments in the theory of vertical differentiation is explored. The second essay shows how the effects of non-linear pricing are determined by the relationship between the demand and the technological structure of the market. The chapter focuses on a model in which firms supply a homogeneous product in two different sizes. Information about consumers' reservation prices is incomplete and the production technology is characterized by size economies. The model provides insights on the size of the products that one finds in the market. Four equilibrium regions are identified depending on the relative intensity of size economies with respect to consumers' evaluation of the good. Regions for which the product is supplied in a single unit or in several different sizes or in only a very large one. Both the private and social desirability of non-linear pricing varies across different equilibrium regions. The third essay considers the broadband internet market. Non discriminatory issues seem the core of the recent debate on the opportunity or not of regulating the internet. One of the main questions posed is whether the telecom companies, owning the networks constituting the internet, should be allowed to offer quality-contingent contracts to content providers. The aim of this essay is to analyze the issue through a stylized two-sided market model of the web that highlights the effects of such a discrimination over quality, prices and participation to the internet of providers and final users. An overall welfare comparison is proposed, concluding that the final effects of regulation crucially depend on both the technology and preferences of agents.

Application-oriented Mixed Integer Non-Linear Programming

In the most recent years there is a renovate interest for Mixed Integer Non-Linear Programming (MINLP) problems. This can be explained for different reasons: (i) the performance of solvers handling non-linear constraints was largely improved; (ii) the awareness that most of the applications from the real-world can be modeled as an MINLP problem; (iii) the challenging nature of this very general class of problems. It is well-known that MINLP problems are NP-hard because they are the generalization of MILP problems, which are NP-hard themselves. However, MINLPs are, in general, also hard to solve in practice. We address to non-convex MINLPs, i.e. having non-convex continuous relaxations: the presence of non-convexities in the model makes these problems usually even harder to solve. The aim of this Ph.D. thesis is to give a flavor of different possible approaches that one can study to attack MINLP problems with non-convexities, with a special attention to real-world problems. In Part 1 of the thesis we introduce the problem and present three special cases of general MINLPs and the most common methods used to solve them. These techniques play a fundamental role in the resolution of general MINLP problems. Then we describe algorithms addressing general MINLPs. Parts 2 and 3 contain the main contributions of the Ph.D. thesis. In particular, in Part 2 four different methods aimed at solving different classes of MINLP problems are presented. Part 3 of the thesis is devoted to real-world applications: two different problems and approaches to MINLPs are presented, namely Scheduling and Unit Commitment for Hydro-Plants and Water Network Design problems. The results show that each of these different methods has advantages and disadvantages. Thus, typically the method to be adopted to solve a real-world problem should be tailored on the characteristics, structure and size of the problem. Part 4 of the thesis consists of a brief review on tools commonly used for general MINLP problems, constituted an integral part of the development of this Ph.D. thesis (especially the use and development of open-source software). We present the main characteristics of solvers for each special case of MINLP.

Non-Linear Analysis and Design of Synchronous Bearingless Multiphase Permanent Magnet Machines and Drives

A two-dimensional model to analyze the distribution of magnetic fields in the airgap of a PM electrical machines is studied. A numerical algorithm for non-linear magnetic analysis of multiphase surface-mounted PM machines with semi-closed slots is developed, based on the equivalent magnetic circuit method. By using a modular structure geometry, whose the basic element can be duplicated, it allows to design whatever typology of windings distribution. In comparison to a FEA, permits a reduction in computing time and to directly changing the values of the parameters in a user interface, without re-designing the model. Output torque and radial forces acting on the moving part of the machine can be calculated. In addition, an analytical model for radial forces calculation in multiphase bearingless Surface-Mounted Permanent Magnet Synchronous Motors (SPMSM) is presented. It allows to predict amplitude and direction of the force, depending on the values of torque current, of levitation current and of rotor position. It is based on the space vectors method, letting the analysis of the machine also during transients. The calculations are conducted by developing the analytical functions in Fourier series, taking all the possible interactions between stator and rotor mmf harmonic components into account and allowing to analyze the effects of electrical and geometrical quantities of the machine, being parametrized. The model is implemented in the design of a control system for bearingless machines, as an accurate electromagnetic model integrated in a three-dimensional mechanical model, where one end of the motor shaft is constrained to simulate the presence of a mechanical bearing, while the other is free, only supported by the radial forces developed in the interactions between magnetic fields, to realize a bearingless system with three degrees of freedom. The complete model represents the design of the experimental system to be realized in the laboratory.

Quantum Integrability in Non-Linear Sigma Models related to Gauge/String Correspondences

The Thermodynamic Bethe Ansatz analysis is carried out for the extended-CP^N class of integrable 2-dimensional Non-Linear Sigma Models related to the low energy limit of the AdS_4xCP^3 type IIA superstring theory. The principal aim of this program is to obtain further non-perturbative consistency check to the S-matrix proposed to describe the scattering processes between the fundamental excitations of the theory by analyzing the structure of the Renormalization Group flow. As a noteworthy byproduct we eventually obtain a novel class of TBA models which fits in the known classification but with several important differences. The TBA framework allows the evaluation of some exact quantities related to the conformal UV limit of the model: effective central charge, conformal dimension of the perturbing operator and field content of the underlying CFT. The knowledge of this physical quantities has led to the possibility of conjecturing a perturbed CFT realization of the integrable models in terms of coset Kac-Moody CFT. The set of numerical tools and programs developed ad hoc to solve the problem at hand is also discussed in some detail with references to the code.

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.

Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.

A Unitary Approach to Information and Estimation Theory in Digital Communication Systems

This thesis presents the outcomes of a Ph.D. course in telecommunications engineering. It is focused on the optimization of the physical layer of digital communication systems and it provides innovations for both multi- and single-carrier systems. For the former type we have first addressed the problem of the capacity in presence of several nuisances. Moreover, we have extended the concept of Single Frequency Network to the satellite scenario, and then we have introduced a novel concept in subcarrier data mapping, resulting in a very low PAPR of the OFDM signal. For single carrier systems we have proposed a method to optimize constellation design in presence of a strong distortion, such as the non linear distortion provided by satellites' on board high power amplifier, then we developed a method to calculate the bit/symbol error rate related to a given constellation, achieving an improved accuracy with respect to the traditional Union Bound with no additional complexity. Finally we have designed a low complexity SNR estimator, which saves one-half of multiplication with respect to the ML estimator, and it has similar estimation accuracy.

Heterogeneous multicore systems for signal processing

This thesis explores the capabilities of heterogeneous multi-core systems, based on multiple Graphics Processing Units (GPUs) in a standard desktop framework. Multi-GPU accelerated desk side computers are an appealing alternative to other high performance computing (HPC) systems: being composed of commodity hardware components fabricated in large quantities, their price-performance ratio is unparalleled in the world of high performance computing. Essentially bringing “supercomputing to the masses”, this opens up new possibilities for application fields where investing in HPC resources had been considered unfeasible before. One of these is the field of bioelectrical imaging, a class of medical imaging technologies that occupy a low-cost niche next to million-dollar systems like functional Magnetic Resonance Imaging (fMRI). In the scope of this work, several computational challenges encountered in bioelectrical imaging are tackled with this new kind of computing resource, striving to help these methods approach their true potential. Specifically, the following main contributions were made: Firstly, a novel dual-GPU implementation of parallel triangular matrix inversion (TMI) is presented, addressing an crucial kernel in computation of multi-mesh head models of encephalographic (EEG) source localization. This includes not only a highly efficient implementation of the routine itself achieving excellent speedups versus an optimized CPU implementation, but also a novel GPU-friendly compressed storage scheme for triangular matrices. Secondly, a scalable multi-GPU solver for non-hermitian linear systems was implemented. It is integrated into a simulation environment for electrical impedance tomography (EIT) that requires frequent solution of complex systems with millions of unknowns, a task that this solution can perform within seconds. In terms of computational throughput, it outperforms not only an highly optimized multi-CPU reference, but related GPU-based work as well. Finally, a GPU-accelerated graphical EEG real-time source localization software was implemented. Thanks to acceleration, it can meet real-time requirements in unpreceeded anatomical detail running more complex localization algorithms. Additionally, a novel implementation to extract anatomical priors from static Magnetic Resonance (MR) scansions has been included.

Advanced signal and receiver design for next generation OFDM systems

This thesis deal with the design of advanced OFDM systems. Both waveform and receiver design have been treated. The main scope of the Thesis is to study, create, and propose, ideas and novel design solutions able to cope with the weaknesses and crucial aspects of modern OFDM systems. Starting from the the transmitter side, the problem represented by low resilience to non-linear distortion has been assessed. A novel technique that considerably reduces the Peak-to-Average Power Ratio (PAPR) yielding a quasi constant signal envelope in the time domain (PAPR close to 1 dB) has been proposed.The proposed technique, named Rotation Invariant Subcarrier Mapping (RISM),is a novel scheme for subcarriers data mapping,where the symbols belonging to the modulation alphabet are not anchored, but maintain some degrees of freedom. In other words, a bit tuple is not mapped on a single point, rather it is mapped onto a geometrical locus, which is totally or partially rotation invariant. The final positions of the transmitted complex symbols are chosen by an iterative optimization process in order to minimize the PAPR of the resulting OFDM symbol. Numerical results confirm that RISM makes OFDM usable even in severe non-linear channels. Another well known problem which has been tackled is the vulnerability to synchronization errors. Indeed in OFDM system an accurate recovery of carrier frequency and symbol timing is crucial for the proper demodulation of the received packets. In general, timing and frequency synchronization is performed in two separate phases called PRE-FFT and POST-FFT synchronization. Regarding the PRE-FFT phase, a novel joint symbol timing and carrier frequency synchronization algorithm has been presented. The proposed algorithm is characterized by a very low hardware complexity, and, at the same time, it guarantees very good performance in in both AWGN and multipath channels. Regarding the POST-FFT phase, a novel approach for both pilot structure and receiver design has been presented. In particular, a novel pilot pattern has been introduced in order to minimize the occurrence of overlaps between two pattern shifted replicas. This allows to replace conventional pilots with nulls in the frequency domain, introducing the so called Silent Pilots. As a result, the optimal receiver turns out to be very robust against severe Rayleigh fading multipath and characterized by low complexity. Performance of this approach has been analytically and numerically evaluated. Comparing the proposed approach with state of the art alternatives, in both AWGN and multipath fading channels, considerable performance improvements have been obtained. The crucial problem of channel estimation has been thoroughly investigated, with particular emphasis on the decimation of the Channel Impulse Response (CIR) through the selection of the Most Significant Samples (MSSs). In this contest our contribution is twofold, from the theoretical side, we derived lower bounds on the estimation mean-square error (MSE) performance for any MSS selection strategy,from the receiver design we proposed novel MSS selection strategies which have been shown to approach these MSE lower bounds, and outperformed the state-of-the-art alternatives. Finally, the possibility of using of Single Carrier Frequency Division Multiple Access (SC-FDMA) in the Broadband Satellite Return Channel has been assessed. Notably, SC-FDMA is able to improve the physical layer spectral efficiency with respect to single carrier systems, which have been used so far in the Return Channel Satellite (RCS) standards. However, it requires a strict synchronization and it is also sensitive to phase noise of local radio frequency oscillators. For this reason, an effective pilot tone arrangement within the SC-FDMA frame, and a novel Joint Multi-User (JMU) estimation method for the SC-FDMA, has been proposed. As shown by numerical results, the proposed scheme manages to satisfy strict synchronization requirements and to guarantee a proper demodulation of the received signal.

Quantum Correlations in Field Theory and Integrable Systems

In this thesis we will investigate some properties of one-dimensional quantum systems. From a theoretical point of view quantum models in one dimension are particularly interesting because they are strongly interacting, since particles cannot avoid each other in their motion, and you we can never ignore collisions. Yet, integrable models often generate new and non-trivial solutions, which could not be found perturbatively. In this dissertation we shall focus on two important aspects of integrable one- dimensional models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will be therefore devoted to the study of the entanglement entropy in one- dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting model. We will derive its Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap will be analysed. In the second part of the thesis we will instead study the dynamics of correlators after a quantum quench , which represent a powerful tool to measure how perturbations and signals propagate through a quantum chain. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, which will be both studied by means of a semi-classical approach. Moreover in the last chapter we will demonstrate a general result about the dynamics of correlation functions of local observables after a quantum quench in integrable systems. In particular we will show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations).

Tools and methods for the quality assurance of force platforms in human movement analysis

The human movement analysis (HMA) aims to measure the abilities of a subject to stand or to walk. In the field of HMA, tests are daily performed in research laboratories, hospitals and clinics, aiming to diagnose a disease, distinguish between disease entities, monitor the progress of a treatment and predict the outcome of an intervention [Brand and Crowninshield, 1981; Brand, 1987; Baker, 2006]. To achieve these purposes, clinicians and researchers use measurement devices, like force platforms, stereophotogrammetric systems, accelerometers, baropodometric insoles, etc. This thesis focus on the force platform (FP) and in particular on the quality assessment of the FP data. The principal objective of our work was the design and the experimental validation of a portable system for the in situ calibration of FPs. The thesis is structured as follows: Chapter 1. Description of the physical principles used for the functioning of a FP: how these principles are used to create force transducers, such as strain gauges and piezoelectrics transducers. Then, description of the two category of FPs, three- and six-component, the signals acquisition (hardware structure), and the signals calibration. Finally, a brief description of the use of FPs in HMA, for balance or gait analysis. Chapter 2. Description of the inverse dynamics, the most common method used in the field of HMA. This method uses the signals measured by a FP to estimate kinetic quantities, such as joint forces and moments. The measures of these variables can not be taken directly, unless very invasive techniques; consequently these variables can only be estimated using indirect techniques, as the inverse dynamics. Finally, a brief description of the sources of error, present in the gait analysis. Chapter 3. State of the art in the FP calibration. The selected literature is divided in sections, each section describes: systems for the periodic control of the FP accuracy; systems for the error reduction in the FP signals; systems and procedures for the construction of a FP. In particular is detailed described a calibration system designed by our group, based on the theoretical method proposed by ?. This system was the “starting point” for the new system presented in this thesis. Chapter 4. Description of the new system, divided in its parts: 1) the algorithm; 2) the device; and 3) the calibration procedure, for the correct performing of the calibration process. The algorithm characteristics were optimized by a simulation approach, the results are here presented. In addiction, the different versions of the device are described. Chapter 5. Experimental validation of the new system, achieved by testing it on 4 commercial FPs. The effectiveness of the calibration was verified by measuring, before and after calibration, the accuracy of the FPs in measuring the center of pressure of an applied force. The new system can estimate local and global calibration matrices; by local and global calibration matrices, the non–linearity of the FPs was quantified and locally compensated. Further, a non–linear calibration is proposed. This calibration compensates the non– linear effect in the FP functioning, due to the bending of its upper plate. The experimental results are presented. Chapter 6. Influence of the FP calibration on the estimation of kinetic quantities, with the inverse dynamics approach. Chapter 7. The conclusions of this thesis are presented: need of a calibration of FPs and consequential enhancement in the kinetic data quality. Appendix: Calibration of the LC used in the presented system. Different calibration set–up of a 3D force transducer are presented, and is proposed the optimal set–up, with particular attention to the compensation of non–linearities. The optimal set–up is verified by experimental results.

Ingegneria di sistemi auto‐organizzanti con il paradigma multiagente

Self-organisation is increasingly being regarded as an effective approach to tackle modern systems complexity. The self-organisation approach allows the development of systems exhibiting complex dynamics and adapting to environmental perturbations without requiring a complete knowledge of the future surrounding conditions. However, the development of self-organising systems (SOS) is driven by different principles with respect to traditional software engineering. For instance, engineers typically design systems combining smaller elements where the composition rules depend on the reference paradigm, but typically produce predictable results. Conversely, SOS display non-linear dynamics, which can hardly be captured by deterministic models, and, although robust with respect to external perturbations, are quite sensitive to changes on inner working parameters. In this thesis, we describe methodological aspects concerning the early-design stage of SOS built relying on the Multiagent paradigm: in particular, we refer to the A&A metamodel, where MAS are composed by agents and artefacts, i.e. environmental resources. Then, we describe an architectural pattern that has been extracted from a recurrent solution in designing self-organising systems: this pattern is based on a MAS environment formed by artefacts, modelling non-proactive resources, and environmental agents acting on artefacts so as to enable self-organising mechanisms. In this context, we propose a scientific approach for the early design stage of the engineering of self-organising systems: the process is an iterative one and each cycle is articulated in four stages, modelling, simulation, formal verification, and tuning. During the modelling phase we mainly rely on the existence of a self-organising strategy observed in Nature and, hopefully encoded as a design pattern. Simulations of an abstract system model are used to drive design choices until the required quality properties are obtained, thus providing guarantees that the subsequent design steps would lead to a correct implementation. However, system analysis exclusively based on simulation results does not provide sound guarantees for the engineering of complex systems: to this purpose, we envision the application of formal verification techniques, specifically model checking, in order to exactly characterise the system behaviours. During the tuning stage parameters are tweaked in order to meet the target global dynamics and feasibility constraints. In order to evaluate the methodology, we analysed several systems: in this thesis, we only describe three of them, i.e. the most representative ones for each of the three years of PhD course. We analyse each case study using the presented method, and describe the exploited formal tools and techniques.

Sulla progettazione in zona sismica di strutture dotate di dissipatori fluido-viscosi: proposta di una metodologia

CHAPTER 1:FLUID-VISCOUS DAMPERS In this chapter the fluid-viscous dampers are introduced. The first section is focused on the technical characteristics of these devices, their mechanical behavior and the latest evolution of the technology whose they are equipped. In the second section we report the definitions and the guide lines about the design of these devices included in some international codes. In the third section the results of some experimental tests carried out by some authors on the response of these devices to external forces are discussed. On this purpose we report some technical schedules that are usually enclosed to the devices now available on the international market. In the third section we show also some analytic models proposed by various authors, which are able to describe efficiently the physical behavior of the fluid-viscous dampers. In the last section we propose some cases of application of these devices on existing structures and on new-construction structures. We show also some cases in which these devices have been revealed good for aims that lies outside the reduction of seismic actions on the structures. CHAPTER 2:DESIGN METHODS PROPOSED IN LITERATURE In this chapter the more widespread design methods proposed in literature for structures equipped by fluid-viscous dampers are introduced. In the first part the response of sdf systems in the case of harmonic external force is studied, in the last part the response in the case of random external force is discussed. In the first section the equations of motion in the case of an elastic-linear sdf system equipped with a non-linear fluid-viscous damper undergoing a harmonic force are introduced. This differential problem is analytically quite complex and it’s not possible to be solved in a closed form. Therefore some authors have proposed approximate solution methods. The more widespread methods are based on equivalence principles between a non-linear device and an equivalent linear one. Operating in this way it is possible to define an equivalent damping ratio and the problem becomes linear; the solution of the equivalent problem is well-known. In the following section two techniques of linearization, proposed by some authors in literature, are described: the first technique is based on the equivalence of the energy dissipated by the two devices and the second one is based on the equivalence of power consumption. After that we compare these two techniques by studying the response of a sdf system undergoing a harmonic force. By introducing the equivalent damping ratio we can write the equation of motion of the non-linear differential problem in an implicit form, by dividing, as usual, for the mass of the system. In this way, we get a reduction of the number of variables, by introducing the natural frequency of the system. The equation of motion written in this form has two important properties: the response is linear dependent on the amplitude of the external force and the response is dependent on the ratio of the frequency of the external harmonic force and the natural frequency of the system only, and not on their single values. All these considerations, in the last section, are extended to the case of a random external force. CHAPTER 3: DESIGN METHOD PROPOSED In this chapter the theoretical basis of the design method proposed are introduced. The need to propose a new design method for structures equipped with fluid-viscous dampers arises from the observation that the methods reported in literature are always iterative, because the response affects some parameters included in the equation of motion (such as the equivalent damping ratio). In the first section the dimensionless parameterε is introduced. This parameter has been obtained from the definition of equivalent damping ratio. The implicit form of the equation of motion is written by introducing the parameter ε, instead of the equivalent damping ratio. This new implicit equation of motions has not any terms affected by the response, so that once ε is known the response can be evaluated directly. In the second section it is discussed how the parameter ε affects some characteristics of the response: drift, velocity and base shear. All the results described till this point have been obtained by keeping the non-linearity of the behavior of the dampers. In order to get a linear formulation of the problem, that is possible to solve by using the well-known methods of the dynamics of structures, as we did before for the iterative methods by introducing the equivalent damping ratio, it is shown how the equivalent damping ratio can be evaluated from knowing the value of ε. Operating in this way, once the parameter ε is known, it is quite easy to estimate the equivalent damping ratio and to proceed with a classic linear analysis. In the last section it is shown how the parameter ε could be taken as reference for the evaluation of the convenience of using non-linear dampers instead of linear ones on the basis of the type of external force and the characteristics of the system. CHAPTER 4: MULTI-DEGREE OF FREEDOM SYSTEMS In this chapter the design methods of a elastic-linear mdf system equipped with non-linear fluidviscous dampers are introduced. It has already been shown that, in the sdf systems, the response of the structure can be evaluated through the estimation of the equivalent damping ratio (ξsd) assuming the behavior of the structure elastic-linear. We would to mention that some adjusting coefficients, to be applied to the equivalent damping ratio in order to consider the actual behavior of the structure (that is non-linear), have already been proposed in literature; such coefficients are usually expressed in terms of ductility, but their treatment is over the aims of this thesis and we does not go into further. The method usually proposed in literature is based on energy equivalence: even though this procedure has solid theoretical basis, it must necessary include some iterative process, because the expression of the equivalent damping ratio contains a term of the response. This procedure has been introduced primarily by Ramirez, Constantinou et al. in 2000. This procedure is reported in the first section and it is defined “Iterative Method”. Following the guide lines about sdf systems reported in the previous chapters, it is introduced a procedure for the assessment of the parameter ε in the case of mdf systems. Operating in this way the evaluation of the equivalent damping ratio (ξsd) can be done directly without implementing iterative processes. This procedure is defined “Direct Method” and it is reported in the second section. In the third section the two methods are analyzed by studying 4 cases of two moment-resisting steel frames undergoing real accelerogramms: the response of the system calculated by using the two methods is compared with the numerical response obtained from the software called SAP2000-NL, CSI product. In the last section a procedure to create spectra of the equivalent damping ratio, affected by the parameter ε and the natural period of the system for a fixed value of exponent α, starting from the elasticresponse spectra provided by any international code, is introduced.

Modelli non lineari statici e dinamici su dati microeconomici: analisi delle condizioni finanziarie delle famiglie italiane

The thesis studies the economic and financial conditions of Italian households, by using microeconomic data of the Survey on Household Income and Wealth (SHIW) over the period 1998-2006. It develops along two lines of enquiry. First it studies the determinants of households holdings of assets and liabilities and estimates their correlation degree. After a review of the literature, it estimates two non-linear multivariate models on the interactions between assets and liabilities with repeated cross-sections. Second, it analyses households financial difficulties. It defines a quantitative measure of financial distress and tests, by means of non-linear dynamic probit models, whether the probability of experiencing financial difficulties is persistent over time. Chapter 1 provides a critical review of the theoretical and empirical literature on the estimation of assets and liabilities holdings, on their interactions and on households net wealth. The review stresses the fact that a large part of the literature explain households debt holdings as a function, among others, of net wealth, an assumption that runs into possible endogeneity problems. Chapter 2 defines two non-linear multivariate models to study the interactions between assets and liabilities held by Italian households. Estimation refers to a pooling of cross-sections of SHIW. The first model is a bivariate tobit that estimates factors affecting assets and liabilities and their degree of correlation with results coherent with theoretical expectations. To tackle the presence of non normality and heteroskedasticity in the error term, generating non consistent tobit estimators, semi-parametric estimates are provided that confirm the results of the tobit model. The second model is a quadrivariate probit on three different assets (safe, risky and real) and total liabilities; the results show the expected patterns of interdependence suggested by theoretical considerations. Chapter 3 reviews the methodologies for estimating non-linear dynamic panel data models, drawing attention to the problems to be dealt with to obtain consistent estimators. Specific attention is given to the initial condition problem raised by the inclusion of the lagged dependent variable in the set of explanatory variables. The advantage of using dynamic panel data models lies in the fact that they allow to simultaneously account for true state dependence, via the lagged variable, and unobserved heterogeneity via individual effects specification. Chapter 4 applies the models reviewed in Chapter 3 to analyse financial difficulties of Italian households, by using information on net wealth as provided in the panel component of the SHIW. The aim is to test whether households persistently experience financial difficulties over time. A thorough discussion is provided of the alternative approaches proposed by the literature (subjective/qualitative indicators versus quantitative indexes) to identify households in financial distress. Households in financial difficulties are identified as those holding amounts of net wealth lower than the value corresponding to the first quartile of net wealth distribution. Estimation is conducted via four different methods: the pooled probit model, the random effects probit model with exogenous initial conditions, the Heckman model and the recently developed Wooldridge model. Results obtained from all estimators accept the null hypothesis of true state dependence and show that, according with the literature, less sophisticated models, namely the pooled and exogenous models, over-estimate such persistence.

Modeling hydrothermal system: deriving observables and hydrothermal instability in volcanic and non-volcanic setting

Hydrothermal fluids are a fundamental resource for understanding and monitoring volcanic and non-volcanic systems. This thesis is focused on the study of hydrothermal system through numerical modeling with the geothermal simulator TOUGH2. Several simulations are presented, and geophysical and geochemical observables, arising from fluids circulation, are analyzed in detail throughout the thesis. In a volcanic setting, fluids feeding fumaroles and hot spring may play a key role in the hazard evaluation. The evolution of the fluids circulation is caused by a strong interaction between magmatic and hydrothermal systems. A simultaneous analysis of different geophysical and geochemical observables is a sound approach for interpreting monitored data and to infer a consistent conceptual model. Analyzed observables are ground displacement, gravity changes, electrical conductivity, amount, composition and temperature of the emitted gases at surface, and extent of degassing area. Results highlight the different temporal response of the considered observables, as well as the different radial pattern of variation. However, magnitude, temporal response and radial pattern of these signals depend not only on the evolution of fluid circulation, but a main role is played by the considered rock properties. Numerical simulations highlight differences that arise from the assumption of different permeabilities, for both homogeneous and heterogeneous systems. Rock properties affect hydrothermal fluid circulation, controlling both the range of variation and the temporal evolution of the observable signals. Low temperature fumaroles and low discharge rate may be affected by atmospheric conditions. Detailed parametric simulations were performed, aimed to understand the effects of system properties, such as permeability and gas reservoir overpressure, on diffuse degassing when air temperature and barometric pressure changes are applied to the ground surface. Hydrothermal circulation, however, is not only a characteristic of volcanic system. Hot fluids may be involved in several mankind problems, such as studies on geothermal engineering, nuclear waste propagation in porous medium, and Geological Carbon Sequestration (GCS). The current concept for large-scale GCS is the direct injection of supercritical carbon dioxide into deep geological formations which typically contain brine. Upward displacement of such brine from deep reservoirs driven by pressure increases resulting from carbon dioxide injection may occur through abandoned wells, permeable faults or permeable channels. Brine intrusion into aquifers may degrade groundwater resources. Numerical results show that pressure rise drives dense water up to the conduits, and does not necessarily result in continuous flow. Rather, overpressure leads to new hydrostatic equilibrium if fluids are initially density stratified. If warm and salty fluid does not cool passing through the conduit, an oscillatory solution is then possible. Parameter studies delineate steady-state (static) and oscillatory solutions.