The last decade has seen an increasing interest in bio-mathematical modelling and scientific computing, resulting in new applications to relevant physiological phenomena and to a better understanding of the origin of various diseases. A topic of great interest to several degenerative diseases is filtration across microvessel walls. The role of the microvessel wall is to let oxygen and nutrients contained in the blood stream to reach the interstitium, and ultimately the surrounding cells, while blocking macromolecules. An understanding of these processes is important in preventing and curing neuro-degenerative diseases, as well as for exploring possible mechanisms to make drug delivery more efficient. This work presents a one-dimensional, time dependent mathematical model describing transport of blood plasma and macromolecules across blood vessel walls. The model takes into account the heterogeneous microvessel wall composition, in order to accurately describe trans-vascular flow. This results in a multi-layered domain, accounting for variable physical properties across the layers forming the micro-vascular wall. In particular, the glycocalyx and endothelium, accounted for in many biological studies, are represented in our model. This micro-structural, yet simplified description of the vascular wall, allows us to simulate the effect of glycocalyx damage and of other pathologies, such as hypertension, hemorrhage and hypovolemia, both in steady and time-dependent states. Due to the simplicity, and thus efficiency of the proposed model, simulations are fast and provide results which are in line with published experimental studies. Furthermore, the simulation tool may be useful for practical applications in physiological and medical studies, by evaluating the possible consequences of pathological conditions.

This thesis is about the development and testing of a novel two-dimensional numerical model (the GIAMT2D model) able to address the hydro-morphodynamic evolution of gravel-bed rivers. The model solves the two-dimensional hyperbolic system of partial differential equations (PDEs) arising from the shallow water-Exner model, describing free surface shallow flows over erodible bed, with suitable closure relations for bedload transport. A coupled formulation of the mathematical problem, which is needed in order to correctly handle sediment transport in Froude trans-critical flow conditions, is implemented, resulting in a non-conservative hyperbolic problem, which requires the adoption of a path-conservative scheme. A drawback of the fully-coupled shallow water-Exner model is that in general the solution of the Riemann problem is not easily available, at least if complex empirical sediment transport formulae are applied, which makes the upwind approach inadequate for designing numerical approximations to the solutions. Adoption of the more general, Riemann solver-free centred approach is thus required, the drawback being that centred schemes are significantly less accurate than upwind schemes in some specific cases, namely for intermediate waves and computations at low CFL number. In GIAMT2D an original centred upwind-biased scheme (UPRICE2-C delta) is applied, recovering accuracy typical of upwind methods, still being able to include any bedload transport formula. The proposed scheme results from original studies in applied mathematics, presented in the first part of the thesis, concerning the development of upwind-biased variations of the centred FORCE scheme for the solution of hyperbolic systems of PDEs, in conservative and non-conservative form. The performance of these schemes is thoroughly assessed in a suite of tests for the shallow water equations. The GIAMT2D model embeds the UPRICE2-Cd scheme extended to second-order accuracy in the ADER framework, inserted in a robust second-order preserving splitting technique for the treatment of frictional source terms, and includes an original wetting-and-drying procedure. The model performance is checked in well-established classical test cases with fixed and movable bed. These applications highlight the capability of the model in correctly and accurately solving the equations in various cases, e.g. in computations at low local CFL number, in the solution of wet-dry fronts with fixed and movable bed and in the prediction of sediment transport in Froude trans-critical conditions. The concept of "morphodynamic benchmark" is introduced for the purpose of assessing the model performance in reproducing basic river morphodynamic processes for which established theoretical and experimental knowledge is available. Unit processes with utmost importance for gravel-bed river morphodynamics, like free and forced bar instability and the stability of channel bifurcations, are chosen for this aim. In this novel approach for assessing the model capabilities, the numerical solutions satisfactorily compare with approximate analytical morphodynamic solution and laboratory data. Having proved that the model is able to reproduce the salient features of these classical morphodynamic solutions, an original morphodynamic study is finally carried out, concerning the non-linear interaction of free and forced bars in straight channels, for which a mature analytical theory is not available at present. The numerical runs of GIAMT2D are used to validate the research hypotheses developed on the basis of existing analytical theories and satisfactorily compare with field observations.

In this thesis we investigate variational problems involving 1-dimensional sets (e.g., curves, networks) and variational inequalities related to obstacle-type dynamics from a twofold prospective. On one side, we provide variational approximations and convex relaxations of the relevant energies and dynamics, moving mainly within the framework of Gamma-convergence and of convex analysis. On the other side, we thoroughly investigate the numerical optimization of the corresponding approximating energies, both to recover optimal 1-dimensional structures and to accurately simulate the actual dynamics.

As recently shown in laboratory bench scale experiments, chemotaxis, i.e.the movement of microorganisms toward or away from the concentration gradient of a chemical species, could have a fundamental role in the transport of bacteria through saturated porous media. Chemotactic bacteria could enhance bioremediation by directing their own motions to residual contaminants in less conductive zones in aquifers. The aim of the present work is to develop a proper numerical scheme to define and to quantify the magnitude and the role of chemotaxis in the complex groundwater system framework. We present a new class of meshless Lagrangian particle methods based on the Smooth Particle Hydrodinamics (SPH) formulation of Vila & Ben Moussa, combined with a new Weighted Essentially Non-Oscillatory (WENO) reconstruction technique on moving point clouds in multiple space dimensions. The purpose of this new scheme is to fully exploit the advantages of SPH among traditional meshbased and meshfree schemes and to overcome its inapplicability for modeling chemotaxis in porous media. The key idea is to produce for each particle first a set of high order accurate Moving Least Squares (MLS) reconstructions on a set of different reconstruction stencils. Then, these reconstructions are combined with each other using a nonlinear WENO technique in order to capture at the same time discontinuities and to maintain accuracy and low numerical dissipation in smooth regions. The numerical fluxes between interacting particles are subsequently evaluated using this MLS-WENO reconstruction at the midpoint between two particles, in combination with a Riemann solver that provides the necessary stabilization of the scheme based on the underlying physics of the governing equations. We propose the use of two different Riemann solvers: the Rusanov flux and an Osher-type flux. The use of monotone fluxes together with a WENO reconstruction ensures accuracy, stability, robustness and an essentially non oscillatory solution without the artificial viscosity term usually employed in conventional SPH schemes. To our knowledge, this is the first time that the WENO method, which has originally been developed for mesh-based schemes in the Eulerian framework on fixed grids, is extended to meshfree Lagrangian particle methods like SPH in multiple space dimensions. In the first part, we test the new algorithm on two dimensional blast wave problems and on the classical one-dimensional Sod shock tube problem for the Euler equations of compressible gas dynamics. We obtain a good agreement with the exact or numerical reference solution in all cases and an improved accuracy and robustness compared to existing standard SPH schemes. In the second part, the new SPH scheme is applied to advection-diffusion equation in heterogeneous porous media with anisotropic diffusion tensor. Several numerical test case shows that the new scheme is accurate. Unlike standard SPH, it reduces the occurrence of negative concentration. In the third part, we show the applicability of the new scheme for modeling chemotaxis in porous media. We test the new scheme against analytical reference solutions. Under the assumption of complete mixing at the Darcy scale, we perform different two-dimensional conservative solute transport simulations under steady-state conditions with instant injection showing that chemotaxis significantly affect the quantification of field-scale mixing processes.

From industrial revolution to the present day, fossil fuels are the main sources for ensuring energy supply. Fossil fuel usages have negative effects on environment that are highlighted by several local or international policy initiatives at support of the big energy transition. The effects urge energy planners to integrate renewable energies into the corresponding energy systems. However, large-scale incorporation of renewable energies into the systems is difficult because of intermittent behaviors, limited availability and economic barriers. It requires intricate balancing among different energy producing resources and the syringes among all the major energy sectors. Although it is possible to evaluate a given energy scenario (complete set of parameters describing a system) by using a simulation model, however, identifying optimal energy scenarios with respect to multiple objectives is a very difficult to accomplished. In addition, no generalized optimization framework is available that can handle all major sectors of an energy system. In this regards, we propose a complete generalized framework for identifying scenarios with respect to multiple objectives. The framework is developed by coupling a multi-objective evolutionary algorithm and EnergyPLAN. The results show that the tool has the capability to handle multiple energy sectors together; moreover, a number of optimized trade-off scenarios are identified. Furthermore, several improvements are proposed to the framework for finding better-optimized scenarios in a computationally efficient way. The framework is applied on two different real-world energy system optimization problems. The results show that the framework is capable to identify optimized scenarios both by considering recent demands and by considering projected demands. The proposed framework and the corresponding improvements make it possible to provide a complete tool for policy makers for designing optimized energy scenarios. The tool can be able to handle all major energy sectors and can be applied in short and long-term energy planning.

This Ph.D. thesis presents a threefold revisitation and reformulation of the linear sampling method (LSM) for the qualitative solution of inverse scattering problems (in the resonance region and in time-harmonic regime): 1) from the viewpoint of its implementation (in a 3D setting), the LSM is recast in appropriate Hilbert spaces, whereby the set of algebraic systems arising from an angular discretization of the far-field equation (written for each sampling point of the numerical grid covering the investigation domain and for each sampling polarization) is replaced by a single functional equation. As a consequence, this 'no-sampling' LSM requires a single regularization procedure, thus resulting in an extremely fast algorithm: complex 3D objects are visualized in around one minute without loss of quality if compared to the traditional implementation; 2) from the viewpoint of its application (in a 2D setting), the LSM is coupled with the reciprocity gap functional in such a way that the influence of scatterers outside the array of receiving antennas is excluded and an inhomogeneous background inside them can be allowed for: then, the resulting 'no-sampling' algorithm proves able to detect tumoural masses inside numerical (but rather realistic) phantoms of the female breast by inverting the data of an appropriate microwave scattering experiment; 3) from the viewpoint of its theoretical foundation, the LSM is physically interpreted as a consequence of the principle of energy conservation (in a lossless background). More precisely, it is shown that the far-field equation at the basis of the LSM (which does not follow from physical laws) can be regarded as a constraint on the power flux of the scattered wave in the far-field region: if the flow lines of the Poynting vector carrying this flux verify some regularity properties (as suggested by numerical simulations), the information contained in the far-field constraint is back-propagated to each point of the background up to the near-field region, and the (approximate) fulfilment of such constraint forces the L^2-norm of any (approximate) solution of the far-field equation to behave as a good indicator function for the unknown scatterer, i.e., to be 'small' inside the scatterer itself and 'large' outside.

The AEgIS experiment pursues the ambitious goal of measuring for the first time the gravitational pull on neutral antimatter. The envisioned method consists in producing a beam of cold anti-hydrogen and measuring the deflection of its free fall by means of a Moiré deflectometer. To do so the pulsed production of abundant cold anti-hydrogen is paramount, therefore the charge exchange production mechanism has been elected as the most promising candidate production method. Performing the charge exchange anti-hydrogen production requires access to an abundant source of cold positronium which can be achieved by the employment of oxide-coated nanochanneled silica plates (NCPs). We spend chapter 1 formulating a classical model of positronium production and thermalisation in NCPs and validating it by testing it against the available experimental data. In chapter 2 we describe the measurement of the energy spectrum of positronium produced by nanochanneled plates using the beam produced by the SURF machine. We then compare the measured energy spectra with the model proposed in chapter 1 showing, in the comparison, the indication of a transition during thermalisation process to a regime where quantum phenomena become significant. We describe in detail in chapter 3 several positronium spectroscopy measurements that we performed during the course of the last three years by employing the positron beam line of the experiment AEgIS. We will the proceed to illustrate an improved version of the detrending technique commonly employed in signal analysis which, applied to the analysis of SSPALS spectra, improves the achievable precision on the experimental results. In chapter 4 we describe an innovative approach that we are currently pursuing to employ the detector FACT, part of the AEgIS apparatus, to confirm the successful production of anti-hydrogen.

Gravel-bed braided rivers are distinctive natural environments that provid a wide range of key environmental, economic and recreational services. There is, however,a growing concern that over the twentieth century, an increasing number of braided rivers have metamorphosed into wandering or single thread channels, representing a loss of key habitats, geodiversity and amenity. While in some situations, shifts in channel pattern may be unambiguously linked to abrupt changes in flow or sediment supply, the lack of a theoretical basis underpinning the development and maintenance of braiding makes identification of the cause and effect of channel metamorphosis hazardous. A growing body of research has suggested that the transition between channelpatterns may depend on the poorly understood interaction between the flow regime,sediment supply and vegetation colonisation. Such interactions are governed by critical thresholds, due to changes in flow resistance and bank strength associated with the distribution, form and intensity of vegetation colonisation. Subtle changes in flow or sediment supply that promote vegetation growth or indeed remove itthrough inundation or attrition. This can lead to complex non-linear shifts in the balance of forces that govern sediment transport and bedform morphodynamics, ultimately resulting in one-way changes in channel morphology. There is, therefore, a critical need to develop a quantitative understanding of these feedbacks in orderto design sustainable river management programmes that seek to optimize the ecological and socio-economic benefits these rivers offer. In summary, this thesis aims to advance our understanding of the morphodynamics of braided rivers and the role numerical models may have in helping to interrogate their behavior and governing controls.

This thesis gives an overview of the process that led to the development of a novel semi-implicit fluid-structure interaction model. The thesis is dedicated to the creation of a new numerical model that allows to study ship generated waves and ship manoeuvers in waterways for various vessel characteristics and speeds in different external current situations. A model like this requires a coupling between the fluid and the solid to generate the waves and the hydrodynamic forces on the hull. Since the horizontal dimensions are significantly larger than the vertical dimension, we started by employing the shallow water equations, which are based on the assumption of hydrostatic pressure. The discretization was carried out taking only the nonlinear advective terms explicitly while the pressure terms are discretized implicitly, which makes the CFL condition milder. The price to pay for this semi-implicit discretization is an increase in the algorithm complexity compared to a fully-explicit method, but it is still much simpler than a fully-implicit discretization of the governing equations. Indeed, the mass and momentum equations couple, and finding the unknowns involves solving a system of equations with dimensions equal to the number of cells. The grid supporting the discretization is staggered, overlapping and Cartesian. Since the aimed application domain is inland waterways, it is paramount to allow wetting and drying of the cells. This was achieved by acting on the depth function, the relationship between the free-surface elevation and the water depth in the cell. The main novelty of this research project is the two-way coupling of the PDE system for the water flow with the ODE system for the rigid body motion of the ship. The hull defines the ship region, and its shape can range from a simple box to an STL file of a real 3D ship geometry. Where the hull is in contact with the water, the cells are pressurized. This pressurized group of cells generates waves as it moves, and its motion is influenced by incoming external waves. This result is obtained by imposing an upper bound to the depth function, so that the water depth does not increase when it reaches the hull elevation, while the pressure is allowed to increase. This upper bound increases the nonlinearity of the system, which may have dry cells, wet free-surface cells and pressurized cells. The solution of this system is found by a single nested-Newton iterative solver of Casulli and Zanolli [36], in which with two separate linearizations the system is written in a sparse, symmetric, positive semi-definite form. This particular form allows us to employ a matrix-free conjugate gradient method, and efficiently get the unknown pressure. The integral of the pressure over the hull is applied for the hydrodynamic force and torque acting on the ship. After adding the skin friction and other external forces from the propeller or the rudder, the total force is inserted in the equation of motion of the rigid body. The ODE system is discretized with a second-order Taylor method, and it is solved for the six degrees of freedom (3 coordinates for the position vector of the barycenter and 3 rotation angles), providing the next position and orientation of the ship. The vertical translation of the rigid body is governed by the gravitational force and the restoring force from Archimedes' principle. As the ship oscillates up and down, the gravitational potential energy is partially transferred to the radiated free-surface water waves, damping and eventually stopping the motion. Also, the ship pushes and pulls the water around it, inducing the added mass force. All these elements constitute the ODE that was used for the verification of the vertical degree of freedom. The numerical simulation gave the expected results for the vertical motion. The horizontal translation, important for the manoeuvers, presented a numerical instability unseen in our previous test cases, which is connected to the relative motion between the ship and the grid. In each time step in which the ship enters a new cell, the pressure sharply increases and decreases at the ship bow. An oscillation can build up in time and create an unphysical void below the vessel. We implemented a few ideas to attenuate the oscillations. At the heart of all the following techniques is the reduction of the time derivative of the water depth, especially for those cells transitioning to a pressurized state. All these modifications were effective at controlling the oscillations, each with a different intensity, and simulations with a horizontal motion are much more stable than without these techniques. With the collaboration of the BAW research institute, we worked on the model validation. We used data from two separate experiments to compare the measurements with the numerical results. Specifically, we focused on the ship-generated wave height and the hydrodynamic forces on the hull. The comparison is satisfactory for the wave height. The force and torque prediction is plausible but underestimated compared to the measurements. The model seems to displace the water volume correctly during the ship passage, while the force and torque response might need additional work to be trusted in applications. Even though the hydrostatic assumption is mostly correct in our range of applications, the presence and the motion of a ship could generate strong vertical accelerations of the flow, which may not be negligible. For this reason, we implemented an algorithm that corrects the velocity field, introducing also dispersive effects due to a non-hydrostatic pressure. The correction consists of a higher-order Bousinnesq-type term in the momentum equation and the solution of the resulting system. The non-hydrostatic update has a small influence on the wave generation, while it alters significantly the reaction forces. The subgrid method implementation allowed to benefit from high-resolution bottom descriptions while keeping the grid size coarse. The same subgrid can also be used for a refined definition of the hull, which makes the volume computations more accurate. Furthermore, the subgrid introduces new possible states for the cells, as they can be partially dry or partially pressurized. These intermediate states translate into smoother transitions from one state to the other when the free-surface is close to the bathymetry or to the hull. Concerning the software implementation of the developed scheme, in order to improve the execution performance of the prototype script formulated initially in Matlab, the numerical method was rewritten as a Fortran program. Also, thanks to the domain decomposition technique and the MPI standard, each simulation can run in parallel on multiple CPUs, leveraging the computational power of supercomputers. The coupling of the PDE and ODE system, together with an appropriate redefinition of the depth function, proved to be a valuable method for studying fluid-structure interaction problems. The combination of efficient numerical techniques led to the development of a tool with a potential to be applied in the practice for the simulation of floating objects in wide domains.

The theory of partial differential equations constitutes today one of the most important topics of scientific understanding. A standard approach for solving a time-dependent partial differential equation consists in discretizing the spatial variables by finite differences or finite elements. This results in a huge system of (stiff) ordinary differential equations that has to be integrated in time. Exponential integrators constitute an interesting class of numerical methods for the time integration of stiff systems of differential equations. Their efficient implementation heavily relies on the fast computation of the action of certain matrix functions; among those, the matrix exponential is the most prominent one. In this manuscript, we go through the steps that led to the development of backward error accurate routines for computing the action of the matrix exponential.