Fast and accurate numerical solutions in some problems of particle and radiation transport: synthetic acceleration for the method of short characteristics, Doppler-broadened scattering kernel, remote sensing of the cryosphere

The aim of this work is to present various aspects of numerical simulation of particle and radiation transport for industrial and environmental protection applications, to enable the analysis of complex physical processes in a fast, reliable, and efficient way. In the first part we deal with speed-up of numerical simulation of neutron transport for nuclear reactor core analysis. The convergence properties of the source iteration scheme of the Method of Characteristics applied to be heterogeneous structured geometries has been enhanced by means of Boundary Projection Acceleration, enabling the study of 2D and 3D geometries with transport theory without spatial homogenization. The computational performances have been verified with the C5G7 2D and 3D benchmarks, showing a sensible reduction of iterations and CPU time. The second part is devoted to the study of temperature-dependent elastic scattering of neutrons for heavy isotopes near to the thermal zone. A numerical computation of the Doppler convolution of the elastic scattering kernel based on the gas model is presented, for a general energy dependent cross section and scattering law in the center of mass system. The range of integration has been optimized employing a numerical cutoff, allowing a faster numerical evaluation of the convolution integral. Legendre moments of the transfer kernel are subsequently obtained by direct quadrature and a numerical analysis of the convergence is presented. In the third part we focus our attention to remote sensing applications of radiative transfer employed to investigate the Earth's cryosphere. The photon transport equation is applied to simulate reflectivity of glaciers varying the age of the layer of snow or ice, its thickness, the presence or not other underlying layers, the degree of dust included in the snow, creating a framework able to decipher spectral signals collected by orbiting detectors.

Magnetohydrodynamic Effects On Mixed Convection Flows In Channels And Ducts

This work focuses on magnetohydrodynamic (MHD) mixed convection flow of electrically conducting fluids enclosed in simple 1D and 2D geometries in steady periodic regime. In particular, in Chapter one a short overview is given about the history of MHD, with reference to papers available in literature, and a listing of some of its most common technological applications, whereas Chapter two deals with the analytical formulation of the MHD problem, starting from the fluid dynamic and energy equations and adding the effects of an external imposed magnetic field using the Ohm's law and the definition of the Lorentz force. Moreover a description of the various kinds of boundary conditions is given, with particular emphasis given to their practical realization. Chapter three, four and five describe the solution procedure of mixed convective flows with MHD effects. In all cases a uniform parallel magnetic field is supposed to be present in the whole fluid domain transverse with respect to the velocity field. The steady-periodic regime will be analyzed, where the periodicity is induced by wall temperature boundary conditions, which vary in time with a sinusoidal law. Local balance equations of momentum, energy and charge will be solved analytically and numerically using as parameters either geometrical ratios or material properties. In particular, in Chapter three the solution method for the mixed convective flow in a 1D vertical parallel channel with MHD effects is illustrated. The influence of a transverse magnetic field will be studied in the steady periodic regime induced by an oscillating wall temperature. Analytical and numerical solutions will be provided in terms of velocity and temperature profiles, wall friction factors and average heat fluxes for several values of the governing parameters. In Chapter four the 2D problem of the mixed convective flow in a vertical round pipe with MHD effects is analyzed. Again, a transverse magnetic field influences the steady periodic regime induced by the oscillating wall temperature of the wall. A numerical solution is presented, obtained using a finite element approach, and as a result velocity and temperature profiles, wall friction factors and average heat fluxes are derived for several values of the Hartmann and Prandtl numbers. In Chapter five the 2D problem of the mixed convective flow in a vertical rectangular duct with MHD effects is discussed. As seen in the previous chapters, a transverse magnetic field influences the steady periodic regime induced by the oscillating wall temperature of the four walls. The numerical solution obtained using a finite element approach is presented, and a collection of results, including velocity and temperature profiles, wall friction factors and average heat fluxes, is provided for several values of, among other parameters, the duct aspect ratio. A comparison with analytical solutions is also provided, as a proof of the validity of the numerical method. Chapter six is the concluding chapter, where some reflections on the MHD effects on mixed convection flow will be made, in agreement with the experience and the results gathered in the analyses presented in the previous chapters. In the appendices special auxiliary functions and FORTRAN program listings are reported, to support the formulations used in the solution chapters.

Stability, viscous dissipation and local thermal non-equilibrium in fluid saturated porous media

In this thesis, the field of study related to the stability analysis of fluid saturated porous media is investigated. In particular the contribution of the viscous heating to the onset of convective instability in the flow through ducts is analysed. In order to evaluate the contribution of the viscous dissipation, different geometries, different models describing the balance equations and different boundary conditions are used. Moreover, the local thermal non-equilibrium model is used to study the evolution of the temperature differences between the fluid and the solid matrix in a thermal boundary layer problem. On studying the onset of instability, different techniques for eigenvalue problems has been used. Analytical solutions, asymptotic analyses and numerical solutions by means of original and commercial codes are carried out.

Active control of sound radiated by vibrating surfaces on a McLaren supercar

Sound radiators based on forced vibrations of plates are becoming widely employed, mainly for active sound enhancement and noise cancelling systems, both in music and automotive environment. Active sound enhancement solutions based on electromagnetic shakers hence find increasing interest. Mostly diffused applications deal with active noise control (ANC) and active vibration control systems for improving the acoustic experience inside or outside the vehicle. This requires investigating vibrational and, consequently, vibro-acoustic characteristics of vehicles. Therefore, simulation and processing methods capable of reducing the calculation time and providing high-accuracy results, are strongly demanded. In this work, an ideal case study on rectangular plates in fully clamped conditions preceded a real case analysis on vehicle panels. The sound radiation generated by a vibrating flat or shallow surface can be calculated by means of Rayleigh’s integral. The analytical solution of the problem is here calculated implementing the equations in MATLAB. Then, the results are compared with a numerical model developed in COMSOL Multiphysics, employing Finite Element Method (FEM). A very good matching between analytical and numerical solutions is shown, thus the cross validation of the two methods is achieved. The shift to the real case study, on a McLaren super car, led to the development of a mixed analytical-numerical method. Optimum results were obtained with mini shakers excitement, showing good matching of the recorded SPL with the calculated one over all the selected frequency band. In addition, a set of directivity measurements of the hood were realized, to start studying the spatiality of sound, which is fundamental to active noise control systems.

Implicazioni teoriche e sperimentali della sincronizzazione assoluta nella teoria della relatività speciale

Sono indagate le implicazioni teoriche e sperimentali derivanti dall'assunzione, nella teoria della relatività speciale, di un criterio di sincronizzazione (detta assoluta) diverso da quello standard. La scelta della sincronizzazione assoluta è giustificata da alcune considerazioni di carattere epistemologico sullo status di fenomeni quali la contrazione delle lunghezze e la dilatazione del tempo. Oltre che a fornire una diversa interpretazione, la sincronizzazione assoluta rappresenta una estensione del campo di applicazione della relatività speciale in quanto può essere attuata anche in sistemi di riferimento accelerati. Questa estensione consente di trattare in maniera unitaria i fenomeni sia in sistemi di riferimento inerziali che accelerati. L'introduzione della sincronizzazione assoluta implica una modifica delle trasformazioni di Lorentz. Una caratteristica di queste nuove trasformazioni (dette inerziali) è che la trasformazione del tempo è indipendente dalle coordinate spaziali. Le trasformazioni inerziali sono ottenute nel caso generale tra due sistemi di riferimento aventi velocità (assolute) u1 e u2 comunque orientate. Viene mostrato che le trasformazioni inerziali possono formare un gruppo pur di prendere in considerazione anche riferimenti non fisicamente realizzabili perché superluminali. È analizzato il moto rigido secondo Born di un corpo esteso considerando la sincronizzazione assoluta. Sulla base delle trasformazioni inerziali si derivano le trasformazioni per i campi elettromagnetici e le equazioni di questi campi (che sostituiscono le equazioni di Maxwell). Si mostra che queste equazioni contengono soluzioni in assenza di cariche che si propagano nello spazio come onde generalmente anisotrope in accordo con quanto previsto dalle trasformazioni inerziali. L'applicazione di questa teoria elettromagnetica a sistemi accelerati mostra l'esistenza di fenomeni mai osservati che, pur non essendo in contraddizione con la relatività standard, ne forzano l'interpretazione. Viene proposto e descritto un esperimento in cui uno di questi fenomeni è misurabile.

Two fluid numerical model for coastal applications

Wave breaking is an important coastal process, influencing hydro-morphodynamic processes such as turbulence generation and wave energy dissipation, run-up on the beach and overtopping of coastal defence structures. During breaking, waves are complex mixtures of air and water (“white water”) whose properties affect velocity and pressure fields in the vicinity of the free surface and, depending on the breaker characteristics, different mechanisms for air entrainment are usually observed. Several laboratory experiments have been performed to investigate the role of air bubbles in the wave breaking process (Chanson & Cummings, 1994, among others) and in wave loading on vertical wall (Oumeraci et al., 2001; Peregrine et al., 2006, among others), showing that the air phase is not negligible since the turbulent energy dissipation involves air-water mixture. The recent advancement of numerical models has given valuable insights in the knowledge of wave transformation and interaction with coastal structures. Among these models, some solve the RANS equations coupled with a free-surface tracking algorithm and describe velocity, pressure, turbulence and vorticity fields (Lara et al. 2006 a-b, Clementi et al., 2007). The single-phase numerical model, in which the constitutive equations are solved only for the liquid phase, neglects effects induced by air movement and trapped air bubbles in water. Numerical approximations at the free surface may induce errors in predicting breaking point and wave height and moreover, entrapped air bubbles and water splash in air are not properly represented. The aim of the present thesis is to develop a new two-phase model called COBRAS2 (stands for Cornell Breaking waves And Structures 2 phases), that is the enhancement of the single-phase code COBRAS0, originally developed at Cornell University (Lin & Liu, 1998). In the first part of the work, both fluids are considered as incompressible, while the second part will treat air compressibility modelling. The mathematical formulation and the numerical resolution of the governing equations of COBRAS2 are derived and some model-experiment comparisons are shown. In particular, validation tests are performed in order to prove model stability and accuracy. The simulation of the rising of a large air bubble in an otherwise quiescent water pool reveals the model capability to reproduce the process physics in a realistic way. Analytical solutions for stationary and internal waves are compared with corresponding numerical results, in order to test processes involving wide range of density difference. Waves induced by dam-break in different scenarios (on dry and wet beds, as well as on a ramp) are studied, focusing on the role of air as the medium in which the water wave propagates and on the numerical representation of bubble dynamics. Simulations of solitary and regular waves, characterized by both spilling and plunging breakers, are analyzed with comparisons with experimental data and other numerical model in order to investigate air influence on wave breaking mechanisms and underline model capability and accuracy. Finally, modelling of air compressibility is included in the new developed model and is validated, revealing an accurate reproduction of processes. Some preliminary tests on wave impact on vertical walls are performed: since air flow modelling allows to have a more realistic reproduction of breaking wave propagation, the dependence of wave breaker shapes and aeration characteristics on impact pressure values is studied and, on the basis of a qualitative comparison with experimental observations, the numerical simulations achieve good results.

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

Waste Heat Recovery Systems: Numerical and Experimental Analysis of organic Rankine Cycle Solutions

This thesis aims to present the ORC technology, its advantages and related problems. In particular, it provides an analysis of ORC waste heat recovery system in different and innovative scenarios, focusing on cases from the biggest to the lowest scale. Both industrial and residential ORC applications are considered. In both applications, the installation of a subcritical and recuperated ORC system is examined. Moreover, heat recovery is considered in absence of an intermediate heat transfer circuit. This solution allow to improve the recovery efficiency, but requiring safety precautions. Possible integrations of ORC systems with renewable sources are also presented and investigated to improve the non-programmable source exploitation. In particular, the offshore oil and gas sector has been selected as a promising industrial large-scale ORC application. From the design of ORC systems coupled with Gas Turbines (GTs) as topper systems, the dynamic behavior of the GT+ORC innovative combined cycles has been analyzed by developing a dynamic model of all the considered components. The dynamic behavior is caused by integration with a wind farm. The electric and thermal aspects have been examined to identify the advantages related to the waste heat recovery system installation. Moreover, an experimental test rig has been realized to test the performance of a micro-scale ORC prototype. The prototype recovers heat from a low temperature water stream, available for instance in industrial or residential waste heat. In the test bench, various sensors have been installed, an acquisitions system developed in Labview environment to completely analyze the ORC behavior. Data collected in real time and corresponding to the system dynamic behavior have been used to evaluate the system performance based on selected indexes. Moreover, various operational steady-state conditions are identified and operation maps are realized for a completely characterization of the system and to detect the optimal operating conditions.

Numerical simulations of magma chamber dynamics at Campi Flegrei, and associated seismicity, deformation and gravity changes

Understanding the complex relationships between quantities measured by volcanic monitoring network and shallow magma processes is a crucial headway for the comprehension of volcanic processes and a more realistic evaluation of the associated hazard. This question is very relevant at Campi Flegrei, a volcanic quiescent caldera immediately north-west of Napoli (Italy). The system activity shows a high fumarole release and periodic ground slow movement (bradyseism) with high seismicity. This activity, with the high people density and the presence of military and industrial buildings, makes Campi Flegrei one of the areas with higher volcanic hazard in the world. In such a context my thesis has been focused on magma dynamics due to the refilling of shallow magma chambers, and on the geophysical signals detectable by seismic, deformative and gravimetric monitoring networks that are associated with this phenomenologies. Indeed, the refilling of magma chambers is a process frequently occurring just before a volcanic eruption; therefore, the faculty of identifying this dynamics by means of recorded signal analysis is important to evaluate the short term volcanic hazard. The space-time evolution of dynamics due to injection of new magma in the magma chamber has been studied performing numerical simulations with, and implementing additional features in, the code GALES (Longo et al., 2006), recently developed and still on the upgrade at the Istituto Nazionale di Geofisica e Vulcanologia in Pisa (Italy). GALES is a finite element code based on a physico-mathematical two dimensional, transient model able to treat fluids as multiphase homogeneous mixtures, compressible to incompressible. The fundamental equations of mass, momentum and energy balance are discretised both in time and space using the Galerkin Least-Squares and discontinuity-capturing stabilisation technique. The physical properties of the mixture are computed as a function of local conditions of magma composition, pressure and temperature.The model features enable to study a broad range of phenomenologies characterizing pre and sin-eruptive magma dynamics in a wide domain from the volcanic crater to deep magma feeding zones. The study of displacement field associated with the simulated fluid dynamics has been carried out with a numerical code developed by the Geophysical group at the University College Dublin (O’Brien and Bean, 2004b), with whom we started a very profitable collaboration. In this code, the seismic wave propagation in heterogeneous media with free surface (e.g. the Earth’s surface) is simulated using a discrete elastic lattice where particle interactions are controlled by the Hooke’s law. This method allows to consider medium heterogeneities and complex topography. The initial and boundary conditions for the simulations have been defined within a coordinate project (INGV-DPC 2004-06 V3_2 “Research on active volcanoes, precursors, scenarios, hazard and risk - Campi Flegrei”), to which this thesis contributes, and many researchers experienced on Campi Flegrei in volcanological, seismic, petrological, geochemical fields, etc. collaborate. Numerical simulations of magma and rock dynamis have been coupled as described in the thesis. The first part of the thesis consists of a parametric study aimed at understanding the eect of the presence in magma of carbon dioxide in magma in the convection dynamics. Indeed, the presence of this volatile was relevant in many Campi Flegrei eruptions, including some eruptions commonly considered as reference for a future activity of this volcano. A set of simulations considering an elliptical magma chamber, compositionally uniform, refilled from below by a magma with volatile content equal or dierent from that of the resident magma has been performed. To do this, a multicomponent non-ideal magma saturation model (Papale et al., 2006) that considers the simultaneous presence of CO2 and H2O, has been implemented in GALES. Results show that the presence of CO2 in the incoming magma increases its buoyancy force promoting convection ad mixing. The simulated dynamics produce pressure transients with frequency and amplitude in the sensitivity range of modern geophysical monitoring networks such as the one installed at Campi Flegrei . In the second part, simulations more related with the Campi Flegrei volcanic system have been performed. The simulated system has been defined on the basis of conditions consistent with the bulk of knowledge of Campi Flegrei and in particular of the Agnano-Monte Spina eruption (4100 B.P.), commonly considered as reference for a future high intensity eruption in this area. The magmatic system has been modelled as a long dyke refilling a small shallow magma chamber; magmas with trachytic and phonolitic composition and variable volatile content of H2O and CO2 have been considered. The simulations have been carried out changing the condition of magma injection, the system configuration (magma chamber geometry, dyke size) and the resident and refilling magma composition and volatile content, in order to study the influence of these factors on the simulated dynamics. Simulation results allow to follow each step of the gas-rich magma ascent in the denser magma, highlighting the details of magma convection and mixing. In particular, the presence of more CO2 in the deep magma results in more ecient and faster dynamics. Through this simulations the variation of the gravimetric field has been determined. Afterward, the space-time distribution of stress resulting from numerical simulations have been used as boundary conditions for the simulations of the displacement field imposed by the magmatic dynamics on rocks. The properties of the simulated domain (rock density, P and S wave velocities) have been based on data from literature on active and passive tomographic experiments, obtained through a collaboration with A. Zollo at the Dept. of Physics of the Federici II Univeristy in Napoli. The elasto-dynamics simulations allow to determine the variations of the space-time distribution of deformation and the seismic signal associated with the studied magmatic dynamics. In particular, results show that these dynamics induce deformations similar to those measured at Campi Flegrei and seismic signals with energies concentrated on the typical frequency bands observed in volcanic areas. The present work shows that an approach based on the solution of equations describing the physics of processes within a magmatic fluid and the surrounding rock system is able to recognise and describe the relationships between geophysical signals detectable on the surface and deep magma dynamics. Therefore, the results suggest that the combined study of geophysical data and informations from numerical simulations can allow in a near future a more ecient evaluation of the short term volcanic hazard.

Numerical and analytical vibro-acoustic modelling of porous materials: the Cell Method for poroelasticity and the case of inclusions

Porous materials are widely used in many fields of industrial applications, to achieve the requirements of noise reduction, that nowadays derive from strict regulations. The modeling of porous materials is still a problematic issue. Numerical simulations are often problematic in case of real complex geometries, especially in terms of computational times and convergence. At the same time, analytical models, even if partly limited by restrictive simplificative hypotheses, represent a powerful instrument to capture quickly the physics of the problem and general trends. In this context, a recently developed numerical method, called the Cell Method, is described, is presented in the case of the Biot's theory and applied for representative cases. The peculiarity of the Cell Method is that it allows for a direct algebraic and geometrical discretization of the field equations, without any reduction to a weak integral form. Then, the second part of the thesis presents the case of interaction between two poroelastic materials under the context of double porosity. The idea of using periodically repeated inclusions of a second porous material into a layer composed by an original material is described. In particular, the problem is addressed considering the efficiency of the analytical method. A analytical procedure for the simulation of heterogeneous layers based is described and validated considering both conditions of absorption and transmission; a comparison with the available numerical methods is performed. ---------------- I materiali porosi sono ampiamente utilizzati per diverse applicazioni industriali, al fine di raggiungere gli obiettivi di riduzione del rumore, che sono resi impegnativi da norme al giorno d'oggi sempre più stringenti. La modellazione dei materiali porori per applicazioni vibro-acustiche rapprensenta un aspetto di una certa complessità. Le simulazioni numeriche sono spesso problematiche quando siano coinvolte geometrie di pezzi reali, in particolare riguardo i tempi computazionali e la convergenza. Allo stesso tempo, i modelli analitici, anche se parzialmente limitati a causa di ipotesi semplificative che ne restringono l'ambito di utilizzo, rappresentano uno strumento molto utile per comprendere rapidamente la fisica del problema e individuare tendenze generali. In questo contesto, un metodo numerico recentemente sviluppato, il Metodo delle Celle, viene descritto, implementato nel caso della teoria di Biot per la poroelasticità e applicato a casi rappresentativi. La peculiarità del Metodo delle Celle consiste nella discretizzazione diretta algebrica e geometrica delle equazioni di campo, senza alcuna riduzione a forme integrali deboli. Successivamente, nella seconda parte della tesi viene presentato il caso delle interazioni tra due materiali poroelastici a contatto, nel contesto dei materiali a doppia porosità. Viene descritta l'idea di utilizzare inclusioni periodicamente ripetute di un secondo materiale poroso all'interno di un layer a sua volta poroso. In particolare, il problema è studiando il metodo analitico e la sua efficienza. Una procedura analitica per il calcolo di strati eterogenei di materiale viene descritta e validata considerando sia condizioni di assorbimento, sia di trasmissione; viene effettuata una comparazione con i metodi numerici a disposizione.

Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.

Bistable elliptic equations with fractional diffusion

This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.

Numerical simulation of ion transport through ion channels and solid-state nanopores

Ion channels are pore-forming proteins that regulate the flow of ions across biological cell membranes. Ion channels are fundamental in generating and regulating the electrical activity of cells in the nervous system and the contraction of muscolar cells. Solid-state nanopores are nanometer-scale pores located in electrically insulating membranes. They can be adopted as detectors of specific molecules in electrolytic solutions. Permeation of ions from one electrolytic solution to another, through a protein channel or a synthetic pore is a process of considerable importance and realistic analysis of the main dependencies of ion current on the geometrical and compositional characteristics of these structures are highly required. The project described by this thesis is an effort to improve the understanding of ion channels by devising methods for computer simulation that can predict channel conductance from channel structure. This project describes theory, algorithms and implementation techniques used to develop a novel 3-D numerical simulator of ion channels and synthetic nanopores based on the Brownian Dynamics technique. This numerical simulator could represent a valid tool for the study of protein ion channel and synthetic nanopores, allowing to investigate at the atomic-level the complex electrostatic interactions that determine channel conductance and ion selectivity. Moreover it will provide insights on how parameters like temperature, applied voltage, and pore shape could influence ion translocation dynamics. Furthermore it will help making predictions of conductance of given channel structures and it will add information like electrostatic potential or ionic concentrations throughout the simulation domain helping the understanding of ion flow through membrane pores.

Advanced Numerical Simulation of Silicon-Based Solar Cells

Photovoltaic (PV) conversion is the direct production of electrical energy from sun without involving the emission of polluting substances. In order to be competitive with other energy sources, cost of the PV technology must be reduced ensuring adequate conversion efficiencies. These goals have motivated the interest of researchers in investigating advanced designs of crystalline silicon solar (c-Si) cells. Since lowering the cost of PV devices involves the reduction of the volume of semiconductor, an effective light trapping strategy aimed at increasing the photon absorption is required. Modeling of solar cells by electro-optical numerical simulation is helpful to predict the performance of future generations devices exhibiting advanced light-trapping schemes and to provide new and more specific guidelines to industry. The approaches to optical simulation commonly adopted for c-Si solar cells may lead to inaccurate results in case of thin film and nano-stuctured solar cells. On the other hand, rigorous solvers of Maxwell equations are really cpu- and memory-intensive. Recently, in optical simulation of solar cells, the RCWA method has gained relevance, providing a good trade-off between accuracy and computational resources requirement. This thesis is a contribution to the numerical simulation of advanced silicon solar cells by means of a state-of-the-art numerical 2-D/3-D device simulator, that has been successfully applied to the simulation of selective emitter and the rear point contact solar cells, for which the multi-dimensionality of the transport model is required in order to properly account for all physical competing mechanisms. In the second part of the thesis, the optical problems is discussed. Two novel and computationally efficient RCWA implementations for 2-D simulation domains as well as a third RCWA for 3-D structures based on an eigenvalues calculation approach have been presented. The proposed simulators have been validated in terms of accuracy, numerical convergence, computation time and correctness of results.

Experimental Analysis and Numerical Simulation of Quench in Superconducting HTS Tapes and Coils

The quench characteristics of second generation (2 G) YBCO Coated Conductor (CC) tapes are of fundamental importance for the design and safe operation of superconducting cables and magnets based on this material. Their ability to transport high current densities at high temperature, up to 77 K, and at very high fields, over 20 T, together with the increasing knowledge in their manufacturing, which is reducing their cost, are pushing the use of this innovative material in numerous system applications, from high field magnets for research to motors and generators as well as for cables. The aim of this Ph. D. thesis is the experimental analysis and numerical simulations of quench in superconducting HTS tapes and coils. A measurements facility for the characterization of superconducting tapes and coils was designed, assembled and tested. The facility consist of a cryostat, a cryocooler, a vacuum system, resistive and superconducting current leads and signal feedthrough. Moreover, the data acquisition system and the software for critical current and quench measurements were developed. A 2D model was developed using the finite element code COMSOL Multiphysics R . The problem of modeling the high aspect ratio of the tape is tackled by multiplying the tape thickness by a constant factor, compensating the heat and electrical balance equations by introducing a material anisotropy. The model was then validated both with the results of a 1D quench model based on a non-linear electric circuit coupled to a thermal model of the tape, to literature measurements and to critical current and quench measurements made in the cryogenic facility. Finally the model was extended to the study of coils and windings with the definition of the tape and stack homogenized properties. The procedure allows the definition of a multi-scale hierarchical model, able to simulate the windings with different degrees of detail.