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.

This thesis provides a thoroughly theoretical background in network theory and shows novel applications to real problems and data. In the first chapter a general introduction to network ensembles is given, and the relations with “standard” equilibrium statistical mechanics are described. Moreover, an entropy measure is considered to analyze statistical properties of the integrated PPI-signalling-mRNA expression networks in different cases. In the second chapter multilayer networks are introduced to evaluate and quantify the correlations between real interdependent networks. Multiplex networks describing citation-collaboration interactions and patterns in colorectal cancer are presented. The last chapter is completely dedicated to control theory and its relation with network theory. We characterise how the structural controllability of a network is affected by the fraction of low in-degree and low out-degree nodes. Finally, we present a novel approach to the controllability of multiplex networks

The work is divided into two parts. Theoretical part shows modern opinions of economics of sport events. Practical part is focused on concrete event- World Ski Championship, 2009 in Liberec

In this thesis we first review the theory of the normal state of the unitary Fermi gas at T = 0 and the main properties of the normal-to-superfluid transition. Then we study the trapped gas under adiabatic rotation, i.e., avoiding the formation of vortices. We show that for polarized systems the rotation enhances the Chandrasekhar-Clogston limit due to pair breaking at the border between the superfluid and the normal phase, while it leaves the global critical polarization Pc of the trapped system unaffected. In the case of an unpolarized unitary superfluid the rotation causes a phase separation between a superfluid core and an unpolarized normal shell, in which the densities of the spin-up and spin-down atom numbers is equal. For both the polarized and the unpolarized systems we calculate experimental observables such as the density profiles and the angular momenta. From the study of Bose-Einstein condensates it is well known that an adiabatic rotation induces a quadrupole deformation of the trapped atomic cloud when the rotation exceeds a certain angular velocity. In Fermi gases the situation is different due to the phase separation discussed above, and the quadrupole instabilities are found to set on at smaller angular velocity than in the BEC case. This phenomenon together with a more general discussion concerning not only the energetic but also the dynamic instabilities of the phase separated system is presented. We use the present knowledge of the equation of state of Fermi mixtures with unequal masses to give quantitative predictions for the phase separation between the normal and superfluid components. The analysis is based on the study of the zero temperature Î1⁄4-h phase diagram of the uniform two component gas. The phase diagram at unitarity is determined thanks to the knowledge of the equation of state available from diagrammatic techniques applied to highly polarized configurations and from Monte Carlo simulations. The phase diagram is then used, in the local density approximation, to calculate the density profiles of the two Fermi components in the presence of harmonic trapping. Eventually we investigate the polarization produced by the relative displacement of the potentials trapping two spin species of a unitary Fermi gas with population imbalance. We investigate the dipole polarizability of a polarized system both in the two-fluid and the three-fluid model at zero temperature and point out the major differences between the two treatments.

In un contesto generale i cui contorni risultano ancora non ben deï¬ niti e i cui principali problemi non hanno ancora trovato soluzioni certe o ricette “standard†, il lavoro descritto in questa tesi vuole presentarsi come il tentativo di testare ed esplorare approcci differenti e diversiï¬ cati — sia in relazione allo scopo dellâ€TManalisi, sia in relazione alle fondamenta teoriche cui fanno riferimento — per affrontare il fenomeno e il problema radon indoor: lâ€TMintenzione à ̈ stata quella di ricercare punti di vista alternativi e complementari dai quali poter osservare un problema comune secondo prospettive differenti.

Ultracold atoms are exceptional tools to explore the physics of quantum matter. In fact, the high degree of tunability of ultracold Bose and Fermi gases makes them ideal systems for quantum simulation and for investigating macroscopic manifestations of quantum effects, such as superfluidity. In ultracold gas research, a central role is played by collective oscillations. They can be used to study different dynamical regimes, such as superfluid, collisional, or collisionless limits or to test the equation of state of the system. In this thesis, we present a unified description of collective oscillations in low dimensions covering both Bose and Fermi statistics, different trap geometries and zero as well as finite temperature, based on the formalism of hydrodynamics and sum rules. We discuss the different behaviour exhibited by the second excited breathing mode in the collisional regime at low temperature and in the collisionless limit at high temperature in a 1D trapped Bose gas with repulsive contact interaction. We show how this mode exhibits a single-valued excitation spectrum in the collisional regime and two different frequencies in the collisionless limit. Our predictions could be important for future research related to the thermalization and damping phenomena in this low-dimensional system. We show that 1D uniform Bose gases exhibit a non-monotonic temperature dependence of the chemical potential characterized by an increasing-with-temperature behaviour at low temperature. This is due to the thermal excitation of phonons and reveals an interesting analogy with the behaviour of superfluids. Finally, we investigate a gas with a finite number N of atoms in a ring geometry at T = 0. We discuss explicitly the deviations of the thermodynamic behaviour in the ring from the one in the large N limit.

In this thesis I present results of my fully general relativistic magnetohydrodynamic (GRMHD) binary neutron star merger (BNS) simulations, conducted by using the numerical code "Whisky" under various conditions, such as, different Equation of State (EOS) for neutron matter (APR4, Ideal fluid and H4 EOSs), masses (with equal/unequal masses for two neutron stars), different magnetic field configurations (both fields of two neutron stars aligned with the inspiral axis, one aligned and one anti-aligned, and both anti-aligned) to investigate the effect of these parameters on the dynamics of the simulations and possibility of forming relativistic jets, which is thought to be one of the necessary conditions for the central engine of short gamma-ray bursts (SGRBs).

In the past century, two great discoveries revolutionized our understanding of the Universe. The first was the study of the NGC 3198 galaxy in the 80s. Looking at the rotation velocity of the galaxy objects with respect to its center, the so-called rotational curve of the galaxy, an anomaly was found. The rotational curve did not seem to obey the known laws of physics as the velocities of objects far away from the center of NCG 3198 were too big with respect to any theoretical prediction. The explanation for these anomalies involves the presence of an additional unknown matter in the galaxies, called dark matter. An interesting property of dark matter is its interaction nature. Since we have not yet observed this matter with telescopes but only looked at its effect on galaxies objects, we believe dark matter interacts with standard matter (baryons, leptons, ...), radiation and neutrinos only gravitationally and not through electromagnetic interactions. In fact, up to now, dark matter has not been directly observed with ground detection experiments. The second discovery came from the observation of type 1A supernovae emissions. Although we already knew that the Universe was expanding since the beginning of the 20th century, at the end of the millennium, two independent experiments discovered that this expansion was accelerating. Within the theory of General Relativity, the acceleration can not be explained with the known standard matter, radiation, neutrinos, or even with a different spatial curvature. This contradiction led to the resolutive hypothesis that a new kind of matter, which throughout the whole history of the Universe has a constant density achieved with negative pressure, should be considered. This matter is called dark energy. These two breakthroughs are the basis of the standard model of cosmology. However, even though this model has been proven astonishingly accurate in describing the history of the Universe, cosmologists still struggle with some fundamental questions about dark energy and dark matter. It is important to stress that both dark matter and dark energy are called "dark" to underline our ignorance about the fundamental nature of these additional matter types. We should think of them as a way to parametrize our ignorance about the actual nature of these two hypotheses rather than the solution of the two problems mentioned before. We know that there should be some matter with specific properties to explain the two aforementioned observational phenomena, and its inclusion in the theoretical model leads to satisfactory theory-observation accordance. However, we know nothing about the fundamental nature of dark matter and dark energy, nor any direct observation has proven their existence. Moreover, additional fundamental and mathematical questions arise when postulating dark matter and dark energy in the form proposed in the standard model. In the decades after these discoveries, we are witnessing two phenomena in theoretical and observational cosmology. On one hand, experiments are becoming more accurate and precise in detecting information from the Universe. One of the most recent examples is the Planck experiment, whose space telescope observed the photons coming from a moment in the Universe's history called recombination, which happened 13 billions of years ago. At that moment, photons and electrons decoupled, letting the firsts travel freely and unscattered. This radiation is called Cosmic Microwave Background (CMB). We can collect these photons with a detector to create a snapshot of the photon intensity distribution at that time. This distribution is tightly linked with dark matter and dark energy properties, helping physicists to shed some light on the two dark components. In general, the accuracy of new experiments puts very tight constraints on theoretical models. On the other hand, many theoretical models have been proposed as alternatives to the standard model to solve the problems mentioned above. These models modify the General Relativity equations of motion, the Einstein equations, either replacing the dark matter and dark energy matter contents with respect to the standard model or modifying the geometry of spacetime. They achieve this by including additional dynamical quantities or degrees of freedom, whose evolution can explain the accelerated expansion acceleration or dark matter effects (or both). For instance, a scalar field can be considered, but other models with more complex additional degrees of freedom have been proposed. All these models are usually called Modified Gravity theories. In the last few years, most of the modified gravity models have been under scrutiny due to increased observational data. For instance, the predictions of the CMB might change when we consider modified gravity models for dark energy or dark matter, putting constraints on the theory parameters or ruling the model out. The data are becoming accurate enough to put very tight constraints on the modified gravity models. Nevertheless, the analysis of the CMB power spectrum or similar observables is not an easy task. One of the main obstacles in checking the viability of the theoretical models against experimental data is the complexity of the theoretical study of these crucial observables. No analytical solution of the equations of motion valid at all times of the Universe's history can be found. Moreover, additional degrees of freedom can increase the complexity of the evaluations for modified gravity models. We should also consider that a single evaluation of the Universe's history is not enough to conclude anything about the viability of the model. When we compare a theoretical model with experiments, we should minimize the difference between the predictions and the data, varying the value of the theory parameters. This procedure usually needs an enormous number of evaluations that require significant computational power, even with the most efficient Monte Carlo algorithms. Moreover, especially in the modified gravity context, it is also essential to distinguish the theory predictivity given by the new proposals' real physical and mathematical power rather than the simple addition of new degrees of freedom. It is easier to fit three points with a parabola with respect to a straight line at the price of adding a new parameter to the theory. However, is it always necessary? In physics, like in other fields, Occam's razor principle tells us that the most straightforward theory should always be preferred. With the introduction of the Bayesian probability, we can perform comparisons between models to find the ones that fit the data with fewer parameters. But, again, this procedure is computationally expensive. Finally, we can ask ourselves if there is a way to parametrize the modified gravity models in a model-independent way. In other words, does it exist a way to write a general action or Lagrangian which can include all modified gravity models? The power of such a generalization would be undeniable: we would be able to compute the equations of motion from one single action and apply it for every modified gravity model. Such a theory, which we will call Effective Field Theory (EFT) of Gravity, has been developed, and it works for any theory with an additional degree of freedom with respect to General Relativity. The major drawback is that the general form of the EFT of Gravity does not provide an immediate physical interpretation of its Lagrangian terms, and therefore a mapping between a "standard" modified gravity theory and its EFT counterpart is always preferred.