An extensive sample (2%) of private vehicles in Italy are equipped with a GPS device that periodically measures their position and dynamical state for insurance purposes. Having access to this type of data allows to develop theoretical and practical applications of great interest: the real-time reconstruction of traffic state in a certain region, the development of accurate models of vehicle dynamics, the study of the cognitive dynamics of drivers. In order for these applications to be possible, we first need to develop the ability to reconstruct the paths taken by vehicles on the road network from the raw GPS data. In fact, these data are affected by positioning errors and they are often very distanced from each other (~2 Km). For these reasons, the task of path identification is not straightforward. This thesis describes the approach we followed to reliably identify vehicle paths from this kind of low-sampling data. The problem of matching data with roads is solved with a bayesian approach of maximum likelihood. While the identification of the path taken between two consecutive GPS measures is performed with a specifically developed optimal routing algorithm, based on A* algorithm. The procedure was applied on an off-line urban data sample and proved to be robust and accurate. Future developments will extend the procedure to real-time execution and nation-wide coverage.

The field of complex systems is a growing body of knowledge, It can be applied to countless different topics, from physics to computer science, biology, information theory and sociology. The main focus of this work is the use of microscopic models to study the behavior of urban mobility, which characteristics make it a paradigmatic example of complexity. In particular, simulations are used to investigate phase changes in a finite size open Manhattan-like urban road network under different traffic conditions, in search for the parameters to identify phase transitions, equilibrium and non-equilibrium conditions . It is shown how the flow-density macroscopic fundamental diagram of the simulation shows,like real traffic, hysteresis behavior in the transition from the congested phase to the free flow phase, and how the different regimes can be identified studying the statistics of road occupancy.

During the last few years, a great deal of interest has risen concerning the applications of stochastic methods to several biochemical and biological phenomena. Phenomena like gene expression, cellular memory, bet-hedging strategy in bacterial growth and many others, cannot be described by continuous stochastic models due to their intrinsic discreteness and randomness. In this thesis I have used the Chemical Master Equation (CME) technique to modelize some feedback cycles and analyzing their properties, including experimental data. In the first part of this work, the effect of stochastic stability is discussed on a toy model of the genetic switch that triggers the cellular division, which malfunctioning is known to be one of the hallmarks of cancer. The second system I have worked on is the so-called futile cycle, a closed cycle of two enzymatic reactions that adds and removes a chemical compound, called phosphate group, to a specific substrate. I have thus investigated how adding noise to the enzyme (that is usually in the order of few hundred molecules) modifies the probability of observing a specific number of phosphorylated substrate molecules, and confirmed theoretical predictions with numerical simulations. In the third part the results of the study of a chain of multiple phosphorylation-dephosphorylation cycles will be presented. We will discuss an approximation method for the exact solution in the bidimensional case and the relationship that this method has with the thermodynamic properties of the system, which is an open system far from equilibrium.In the last section the agreement between the theoretical prediction of the total protein quantity in a mouse cells population and the observed quantity will be shown, measured via fluorescence microscopy.

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

In this thesis, we extend some ideas of statistical physics to describe the properties of human mobility. By using a database containing GPS measures of individual paths (position, velocity and covered space at a spatial scale of 2 Km or a time scale of 30 sec), which includes the 2% of the private vehicles in Italy, we succeed in determining some statistical empirical laws pointing out "universal" characteristics of human mobility. Developing simple stochastic models suggesting possible explanations of the empirical observations, we are able to indicate what are the key quantities and cognitive features that are ruling individuals' mobility. To understand the features of individual dynamics, we have studied different aspects of urban mobility from a physical point of view. We discuss the implications of the Benford's law emerging from the distribution of times elapsed between successive trips. We observe how the daily travel-time budget is related with many aspects of the urban environment, and describe how the daily mobility budget is then spent. We link the scaling properties of individual mobility networks to the inhomogeneous average durations of the activities that are performed, and those of the networks describing people's common use of space with the fractional dimension of the urban territory. We study entropy measures of individual mobility patterns, showing that they carry almost the same information of the related mobility networks, but are also influenced by a hierarchy among the activities performed. We discover that Wardrop's principles are violated as drivers have only incomplete information on traffic state and therefore rely on knowledge on the average travel-times. We propose an assimilation model to solve the intrinsic scattering of GPS data on the street network, permitting the real-time reconstruction of traffic state at a urban scale.

Theories and numerical modeling are fundamental tools for understanding, optimizing and designing present and future laser-plasma accelerators (LPAs). Laser evolution and plasma wave excitation in a LPA driven by a weakly relativistically intense, short-pulse laser propagating in a preformed parabolic plasma channel, is studied analytically in 3D including the effects of pulse steepening and energy depletion. At higher laser intensities, the process of electron self-injection in the nonlinear bubble wake regime is studied by means of fully self-consistent Particle-in-Cell simulations. Considering a non-evolving laser driver propagating with a prescribed velocity, the geometrical properties of the non-evolving bubble wake are studied. For a range of parameters of interest for laser plasma acceleration, The dependence of the threshold for self-injection in the non-evolving wake on laser intensity and wake velocity is characterized. Due to the nonlinear and complex nature of the Physics involved, computationally challenging numerical simulations are required to model laser-plasma accelerators operating at relativistic laser intensities. The numerical and computational optimizations, that combined in the codes INF&RNO and INF&RNO/quasi-static give the possibility to accurately model multi-GeV laser wakefield acceleration stages with present supercomputing architectures, are discussed. The PIC code jasmine, capable of efficiently running laser-plasma simulations on Graphics Processing Units (GPUs) clusters, is presented. GPUs deliver exceptional performance to PIC codes, but the core algorithms had to be redesigned for satisfying the constraints imposed by the intrinsic parallelism of the architecture. The simulation campaigns, run with the code jasmine for modeling the recent LPA experiments with the INFN-FLAME and CNR-ILIL laser systems, are also presented.

Life Cycle Assessment (LCA) is a chain-oriented tool to evaluate the environment performance of products focussing on the entire life cycle of these products: from the extraction of resources, via manufacturing and use, to the final processing of the disposed products. Through all these stages consumption of resources and pollutant releases to air, water, soil are identified and quantified in Life Cycle Inventory (LCI) analysis. Subsequently to the LCI phase follows the Life Cycle Impact Assessment (LCIA) phase; that has the purpose to convert resource consumptions and pollutant releases in environmental impacts. The LCIA aims to model and to evaluate environmental issues, called impact categories. Several reports emphasises the importance of LCA in the field of ENMs. The ENMs offer enormous potential for the development of new products and application. There are however unanswered questions about the impacts of ENMs on human health and the environment. In the last decade the increasing production, use and consumption of nanoproducts, with a consequent release into the environment, has accentuated the obligation to ensure that potential risks are adequately understood to protect both human health and environment. Due to its holistic and comprehensive assessment, LCA is an essential tool evaluate, understand and manage the environmental and health effects of nanotechnology. The evaluation of health and environmental impacts of nanotechnologies, throughout the whole of their life-cycle by using LCA methodology. This is due to the lack of knowledge in relation to risk assessment. In fact, to date, the knowledge on human and environmental exposure to nanomaterials, such ENPs is limited. This bottleneck is reflected into LCA where characterisation models and consequently characterisation factors for ENPs are missed. The PhD project aims to assess limitations and challenges of the freshwater aquatic ecotoxicity potential evaluation in LCIA phase for ENPs and in particular nanoparticles as n-TiO2. / L’LCA è una metodologia standardizzata volta alla valutazione delle performance ambientali di un prodotto lungo il suo intero ciclo di vita. Il consumo di risorse e le emissioni di sostanze inquinanti in aria, acqua, suolo sono quantificate nella fase di inventario (LCI).La fase successiva di Life Cycle Impact Assessment ha lo scopo di convertire i consumi di risorse e le emissioni di inquinanti in impatti ambientali. classificate in categorie di impatto.Grazie all’ utilizzo di specifici fattori di caratterizzazione i risultati della fase d’inventario vengono convertiti in un unità comune ed espressi in termini di impact score per ogni categoria d’impatto. L’importanza di studi di LCA nel settore dei nanomateriali (ENM) è stata sottolineata da diversi studi. Nonostante le nanotecnologie, sembrano offrire enormi potenzialità per lo sviluppo di nuovi prodotti e applicazioni con migliori prestazioni energetiche o un ridotto uso di materiali ed energia, vi sono ancora forti incertezze legate ai loro possibili impatti ambientali e sanitari. Negli ultimi dieci anni l'aumento della produzione, l'uso e il consumo di nanoprodotti, ha accentuato l'obbligo di garantire che i rischi potenziali siano adeguatamente compresi per proteggere sia la salute umana e l'ambiente. Grazie al suo approccio olistico l’LCA è stato identificata come uno strumento essenziale per valutare, gli effetti sull'ambiente e sulla salute. Solo pochi studi di LCA sono stati condotti sui nanoprodotti e tra questi solo pochi considerando gli impatti ambientali di tipo tossicologico. La scarsa applicazione della metodologia LCA nel settore della nanotecnologia è principalmente dovuta alle frammentarie conoscenze scientifiche correlati alla valutazione del rischio ambientale.Ad oggi, nella metodologia LCA si risente della completa mancanza di opportuni modelli di caratterizzazione per gli impatto tossicologici. Il progetto di dottorato si propone di valutare i limiti e le sfide nella fase di LCIA per la valutazione degli impattiecotossicologi per nanoparticelle di n-TiO2.

One of the most important problems in inertial confinement fusion is how to find a way to mitigate the onset of the Rayleigh-Taylor instability which arises in the ablation front during the compression. In this thesis it is studied in detail the possibility of using for such a purpose the well-known mechanism of dynamic stabilization, already applied to other dynamical systems such as the inverted pendulum. In this context, a periodic acceleration superposed to the background gravity generates a vertical vibration of the ablation front itself. The effects of different driving modulations (Dirac deltas and square waves) are analyzed from a theoretical point of view, with a focus on stabilization of ion beam driven ablation fronts, and a comparison is made, in order to look for optimization.

The thesis work concerns X-ray spectrometry for both medical and space applications and is divided into two sections. The first section addresses an X-ray spectrometric system designed to study radiological beams and is devoted to the optimization of diagnostic procedures in medicine. A parametric semi-empirical model capable of efficiently reconstructing diagnostic X-ray spectra in 'middle power' computers was developed and tested. In addition, different silicon diode detectors were tested as real-time detectors in order to provide a real-time evaluation of the spectrum during diagnostic procedures. This project contributes to the field by presenting an improved simulation of a realistic X-ray beam emerging from a common X-ray tube with a complete and detailed spectrum that lends itself to further studies of added filtration, thus providing an optimized beam for different diagnostic applications in medicine. The second section describes the preliminary tests that have been carried out on the first version of an Application Specific Integrated Circuit (ASIC), integrated with large area position-sensitive Silicon Drift Detector (SDD) to be used on board future space missions. This technology has been developed for the ESA project: LOFT (Large Observatory for X-ray Timing), a new medium-class space mission that the European Space Agency has been assessing since February of 2011. The LOFT project was proposed as part of the Cosmic Vision Program (2015-2025).

It is well known that many realistic mathematical models of biological systems, such as cell growth, cellular development and differentiation, gene expression, gene regulatory networks, enzyme cascades, synaptic plasticity, aging and population growth need to include stochasticity. These systems are not isolated, but rather subject to intrinsic and extrinsic fluctuations, which leads to a quasi equilibrium state (homeostasis). The natural framework is provided by Markov processes and the Master equation (ME) describes the temporal evolution of the probability of each state, specified by the number of units of each species. The ME is a relevant tool for modeling realistic biological systems and allow also to explore the behavior of open systems. These systems may exhibit not only the classical thermodynamic equilibrium states but also the nonequilibrium steady states (NESS). This thesis deals with biological problems that can be treat with the Master equation and also with its thermodynamic consequences. It is organized into six chapters with four new scientific works, which are grouped in two parts: (1) Biological applications of the Master equation: deals with the stochastic properties of a toggle switch, involving a protein compound and a miRNA cluster, known to control the eukaryotic cell cycle and possibly involved in oncogenesis and with the propose of a one parameter family of master equations for the evolution of a population having the logistic equation as mean field limit. (2) Nonequilibrium thermodynamics in terms of the Master equation: where we study the dynamical role of chemical fluxes that characterize the NESS of a chemical network and we propose a one parameter parametrization of BCM learning, that was originally proposed to describe plasticity processes, to study the differences between systems in DB and NESS.