Analysis of Lead-Acid batteries with a third-order dynamical model

Electrical energy storage is a really important issue nowadays. As electricity is not easy to be directly stored, it can be stored in other forms and converted back to electricity when needed. As a consequence, storage technologies for electricity can be classified by the form of storage, and in particular we focus on electrochemical energy storage systems, better known as electrochemical batteries. Largely the more widespread batteries are the Lead-Acid ones, in the two main types known as flooded and valve-regulated. Batteries need to be present in many important applications such as in renewable energy systems and in motor vehicles. Consequently, in order to simulate these complex electrical systems, reliable battery models are needed. Although there exist some models developed by experts of chemistry, they are too complex and not expressed in terms of electrical networks. Thus, they are not convenient for a practical use by electrical engineers, who need to interface these models with other electrical systems models, usually described by means of electrical circuits. There are many techniques available in literature by which a battery can be modeled. Starting from the Thevenin based electrical model, it can be adapted to be more reliable for Lead-Acid battery type, with the addition of a parasitic reaction branch and a parallel network. The third-order formulation of this model can be chosen, being a trustworthy general-purpose model, characterized by a good ratio between accuracy and complexity. Considering the equivalent circuit network, all the useful equations describing the battery model are discussed, and then implemented one by one in Matlab/Simulink. The model has been finally validated, and then used to simulate the battery behaviour in different typical conditions.

Variational Quantum Splines: Moving Beyond Linearity for Quantum Activation Functions

Activation functions within neural networks play a crucial role in Deep Learning since they allow to learn complex and non-trivial patterns in the data. However, the ability to approximate non-linear functions is a significant limitation when implementing neural networks in a quantum computer to solve typical machine learning tasks. The main burden lies in the unitarity constraint of quantum operators, which forbids non-linearity and poses a considerable obstacle to developing such non-linear functions in a quantum setting. Nevertheless, several attempts have been made to tackle the realization of the quantum activation function in the literature. Recently, the idea of the QSplines has been proposed to approximate a non-linear activation function by implementing the quantum version of the spline functions. Yet, QSplines suffers from various drawbacks. Firstly, the final function estimation requires a post-processing step; thus, the value of the activation function is not available directly as a quantum state. Secondly, QSplines need many error-corrected qubits and a very long quantum circuits to be executed. These constraints do not allow the adoption of the QSplines on near-term quantum devices and limit their generalization capabilities. This thesis aims to overcome these limitations by leveraging hybrid quantum-classical computation. In particular, a few different methods for Variational Quantum Splines are proposed and implemented, to pave the way for the development of complete quantum activation functions and unlock the full potential of quantum neural networks in the field of quantum machine learning.

Hybrid foundations for offshore wind turbines

Nowadays offshore wind turbines represents a valid answer for energy production but with an increasing in costs mainly due to foundation technology required. Hybrid foundations composed by suction caissons over which is welded a tower supporting the nacelle and the blades allows a strong costs reduction. Here a monopod configuration is studied in a sandy soil in a 10 m water depth. Bearing capacity, sliding resistance and pull-out resistance are evaluated. In a second part the installation process occurring in four steps is analysed. considering also the effect of stress enhancement due to frictional forces opposing to penetration growing at skirt sides both inside and outside. In a three dimensional finite element model using Straus7 the soil non-linearity is considered in an approximate way through an iterative procedure using the Yokota empirical decay curves.

Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.

Black holes as quantum bound states

We present a new quantum description for the Oppenheimer-Snyder model of gravitational collapse of a ball of dust. Starting from the geodesic equation for dust in spherical symmetry, we introduce a time-independent Schrödinger equation for the radius of the ball. The resulting spectrum is similar to that of the Hydrogen atom and Newtonian gravity. However, the non-linearity of General Relativity implies that the ground state is characterised by a principal quantum number proportional to the square of the ADM mass of the dust. For a ball with ADM mass much larger than the Planck scale, the collapse is therefore expected to end in a macroscopically large core and the singularity predicted by General Relativity is avoided. Mathematical properties of the spectrum are investigated and the ground state is found to have support essentially inside the gravitational radius, which makes it a quantum model for the matter core of Black Holes. In fact, the scaling of the ADM mass with the principal quantum number agrees with the Bekenstein area law and the corpuscular model of Black Holes. Finally, the uncertainty on the size of the ground state is interpreted within the framework of an Uncertainty Principle.

Design for uncertainty of aerospace structures

The aim of this work is to present a general overview of state-of-the-art related to design for uncertainty with a focus on aerospace structures. In particular, a simulation on a FCCZ lattice cell and on the profile shape of a nozzle will be performed. Optimization under uncertainty is characterized by the need to make decisions without complete knowledge of the problem data. When dealing with a complex problem, non-linearity, or optimization, two main issues are raised: the uncertainty of the feasibility of the solution and the uncertainty of the objective value of the function. In the first part, the Design Of Experiments (DOE) methodologies, Uncertainty Quantification (UQ), and then Uncertainty optimization will be deepened. The second part will show an application of the previous theories on through a commercial software. Nowadays multiobjective optimization on high non-linear problem can be a powerful tool to approach new concept solutions or to develop cutting-edge design. In this thesis an effective improvement have been reached on a rocket nozzle. Future work could include the introduction of multi scale modelling, multiphysics approach and every strategy useful to simulate as much possible real operative condition of the studied design.

Lipschitz regularity for weak solutions of parabolic p-Laplacian type equations in certain subriemannian structures

The main aim of the thesis is to prove the local Lipschitz regularity of the weak solutions to a class of parabolic PDEs modeled on the parabolic p-Laplacian. This result is well known in the Euclidean case and recently has been extended in the Heisenberg group, while higher regularity results are not known in subriemannian parabolic setting. In this thesis we will consider vector fields more general than those in the Heisenberg setting, introducing some technical difficulties. To obtain our main result we will use a Moser-like iteration. Due to the non linearity of the equation, we replace the usual parabolic cylinders with new ones, whose dimension also depends on the L^p norm of the solution. In addition, we deeply simplify the iterative procedure, using the standard Sobolev inequality, instead of the parabolic one.