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.

Enhanced Mixed Integer Programming Techniques and Routing Problems

Mixed integer programming is up today one of the most widely used techniques for dealing with hard optimization problems. On the one side, many practical optimization problems arising from real-world applications (such as, e.g., scheduling, project planning, transportation, telecommunications, economics and finance, timetabling, etc) can be easily and effectively formulated as Mixed Integer linear Programs (MIPs). On the other hand, 50 and more years of intensive research has dramatically improved on the capability of the current generation of MIP solvers to tackle hard problems in practice. However, many questions are still open and not fully understood, and the mixed integer programming community is still more than active in trying to answer some of these questions. As a consequence, a huge number of papers are continuously developed and new intriguing questions arise every year. When dealing with MIPs, we have to distinguish between two different scenarios. The first one happens when we are asked to handle a general MIP and we cannot assume any special structure for the given problem. In this case, a Linear Programming (LP) relaxation and some integrality requirements are all we have for tackling the problem, and we are ``forced" to use some general purpose techniques. The second one happens when mixed integer programming is used to address a somehow structured problem. In this context, polyhedral analysis and other theoretical and practical considerations are typically exploited to devise some special purpose techniques. This thesis tries to give some insights in both the above mentioned situations. The first part of the work is focused on general purpose cutting planes, which are probably the key ingredient behind the success of the current generation of MIP solvers. Chapter 1 presents a quick overview of the main ingredients of a branch-and-cut algorithm, while Chapter 2 recalls some results from the literature in the context of disjunctive cuts and their connections with Gomory mixed integer cuts. Chapter 3 presents a theoretical and computational investigation of disjunctive cuts. In particular, we analyze the connections between different normalization conditions (i.e., conditions to truncate the cone associated with disjunctive cutting planes) and other crucial aspects as cut rank, cut density and cut strength. We give a theoretical characterization of weak rays of the disjunctive cone that lead to dominated cuts, and propose a practical method to possibly strengthen those cuts arising from such weak extremal solution. Further, we point out how redundant constraints can affect the quality of the generated disjunctive cuts, and discuss possible ways to cope with them. Finally, Chapter 4 presents some preliminary ideas in the context of multiple-row cuts. Very recently, a series of papers have brought the attention to the possibility of generating cuts using more than one row of the simplex tableau at a time. Several interesting theoretical results have been presented in this direction, often revisiting and recalling other important results discovered more than 40 years ago. However, is not clear at all how these results can be exploited in practice. As stated, the chapter is a still work-in-progress and simply presents a possible way for generating two-row cuts from the simplex tableau arising from lattice-free triangles and some preliminary computational results. The second part of the thesis is instead focused on the heuristic and exact exploitation of integer programming techniques for hard combinatorial optimization problems in the context of routing applications. Chapters 5 and 6 present an integer linear programming local search algorithm for Vehicle Routing Problems (VRPs). The overall procedure follows a general destroy-and-repair paradigm (i.e., the current solution is first randomly destroyed and then repaired in the attempt of finding a new improved solution) where a class of exponential neighborhoods are iteratively explored by heuristically solving an integer programming formulation through a general purpose MIP solver. Chapters 7 and 8 deal with exact branch-and-cut methods. Chapter 7 presents an extended formulation for the Traveling Salesman Problem with Time Windows (TSPTW), a generalization of the well known TSP where each node must be visited within a given time window. The polyhedral approaches proposed for this problem in the literature typically follow the one which has been proven to be extremely effective in the classical TSP context. Here we present an overall (quite) general idea which is based on a relaxed discretization of time windows. Such an idea leads to a stronger formulation and to stronger valid inequalities which are then separated within the classical branch-and-cut framework. Finally, Chapter 8 addresses the branch-and-cut in the context of Generalized Minimum Spanning Tree Problems (GMSTPs) (i.e., a class of NP-hard generalizations of the classical minimum spanning tree problem). In this chapter, we show how some basic ideas (and, in particular, the usage of general purpose cutting planes) can be useful to improve on branch-and-cut methods proposed in the literature.

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.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Development discourse in Romania: from Socialism to EU Membership

With their accession to the European Union, twelve new countries - Romania among them - (re)entered the international community of international donors. In the history of development aid this can be seen as a unique event: it is for the first time in history that such a large number of countries become international donors, with such short notice and in such a particular context that sees some scholars announcing the ‘death’ of development. But in spite of what might be claimed regarding the ‘end’ of the development era, development discourse seems to be rather vigorous and in good health: it is able to extert an undeniable force of attraction over the twelve countries that, in a matter of years, have already convinced themselves of its validity and adhered to its main tenets. This thesis collects evidence for improving our understanding of this process that sees the co-optation of twelve new countries to the dominant theory and practice of development cooperation. The evidence collected seems to show that one of the tools employed by the promoters of this co-optation process is that of constructing the ‘new’ Member States as ‘new’, inexpert donors that need to learn from the ‘old’ ones. By taking a case-study approach, this thesis gathers data that suggests that conceiving of the ‘twelve’ as ‘new’ donors is both historically inaccurate and value-ladden. On one hand, Romania’s case-study illustrates how in the (socialist) past at least one in the group of the twelve was particularly conversant in the discourse of international development. On the other hand, the process of co-optation, while being presented as a knowledgeproducing process, can also be seen as an ignorance-producing procedure: Romania, along with its fellow new Member States, takes the opportunity of ‘building its capacity’ and ‘raising its awareness’ of development cooperation along the line drawn by the European Union, but at the same time it seems to un-learn and ‘lower’ its awareness of development experience in the (socialist) past. This is one possible reading of this thesis. At a different level, this thesis can also be seen as an attempt to account of almost five decades of international development discourse in one specific country – Romania – in three different socio-political contexts: the socialist years (up to the year 1989), the ‘transition years’ (from 1989 to the pre-accession years) and the membership to the European Union. In this second reading, the thesis seeks to illustrate how – contrary to widespread beliefs – before 1989 Romania’s international development discourse was particularly vivid: in the most varied national and international settings President Ceausescu unfolded an extensive discursive activity on issues pertaining to international development; generous media coverage of affairs concerning the developing countries and their fight for development was the rule rather than the exception; the political leadership wanted the Romanians not only to be familiarized with (or ‘aware of’ to use current terminology) matters of underdevelopment, but also to prove a sense of solidarity with these countries, as well as a sense of pride for the relations of ‘mutual help’ that were being built with them; finally, international development was object of academic attention and the Romanian scholars were able not only to reflect on major developments, but could also formulate critical positions towards the practices of development aid. Very little remains of all this during the transition years, while in the present those who are engaged in matters pertaining to international development do so with a view of building Romania as an EU-compliant donor.

Regulating State Aid: Inter-jurisdictional competition, public choice, and corporate governance

Depending on the regulatory regime they are subject to, governments may or may not be allowed to hand out state aid to private firms. The economic justification for state aid can address several issues present in the competition for capital and the competition for transfers from the state. First, there are principal-agent problems involved at several stages. Self-interested politicians might enter state aid deals that are the result of extensive rent-seeking activities of organized interest groups. Thus the institutional design of political systems will have an effect on the propensity of a jurisdiction to award state aid. Secondly, fierce competition for firm locations can lead to over-spending. This effect is stronger if the politicians do not take into account the entirety of the costs created by their participation in the firm location race. Thirdly, state aid deals can be incomplete and not in the interest of the citizens. This applies if there are no sanctions if firms do not meet their obligations from receiving aid, such as creating a certain number of jobs or not relocating again for a certain amount of time. The separation of ownership and control in modern corporations leads to principal-agent problems on the side of the aid recipient as well. Managers might receive personal benefits from subsidies, the use of which is sometimes less monitored than private finance. This can eventually be to the detriment of the shareholders. Overall, it can be concluded that state aid control should also serve the purpose of regulating the contracting between governments and firms. An extended mandate for supervision by the European Commission could include requirements to disincentive the misuse of state aid. The Commission should also focus on the corporate governance regime in place in the jurisdiction that awards the aid as well as in the recipient firm.

Studio delle risposte comportamentali, produttive e sanitarie di bovine in lattazione esposte a diversi regimi dietetici

L'unifeed a secco è il più diffuso nell'areale del Parmigiano Reggiano. In questa situazione, la peNDF deve essere ridotta per evitare selezione. Di conseguenza spesso presenta valori sotto la soglia minima. In più, spesso i fieni utilizzati sono di scarso valore nutritivo e si rendono necessari elevati livelli di concentrati nella razione. Tutto questo può portare alla diminuzione del tempo di ruminazione e produzione di saliva, aumentando il rischio di SARA. Dopo queste brevi premesse, due prove sono state effettuate presso la stalla sperimentale dell'università di Bologna. La prima con lo scopo di studiare il comportamento alimentare di vacche in lattazione sottoposte a regimi ad libitum/razionato con assenza/presenza di fieno lungo. La seconda si svolse con un improvviso cambio di stabulazione, dalla libera alla fissa, e quota di concentrati nell'unifeed. Da queste prove un grande mole di dati è stata registrata, grazie ai collari della ruminazione, boli reticolari e mangiatoie automatiche. I risultati ottenuti ci hanno permesso di confermare le interconnessioni tra comportamento alimentare, ruminazione e pH. Abbiamo anche verificato l'importanza di costanza di preparazione dell'unifeed e la grande capacità di adattamento delle bovine. Infatti la variabilità nelle gestione della mandria può provocare importanti sanitari. Quindi suggeriamo la supplementazione di fieno lungo in mangiatoia e lo sviluppo di tecnologia NIR in linea sul carro miscelatore. Infine sono state registrate importanti differenze individuali nel far fronte agli stati di stress alimentare. Uno studio più approfondito di questi aspetti sicuramente avrebbe risvolti positivi nella gestione della mandria e aprile la possibilità all'introduzione di nuovi indici di selezione.

Evaluation of a 2D multileader training system for improving sustainability and precision orchard management applications in italian apple orchards

The presented study aimed to evaluate the productive and physiological behavior of a 2D multileader apple training systems in the Italian environment both investigating the possibility to increase yield and precision crop load management resolution. Another objective was to find valuable thinning thresholds guaranteeing high yields and matching fruit market requirements. The thesis consists in three studies carried out in a Pink Lady®- Rosy Glow apple orchard trained as a planar multileader training system (double guyot). Fruiting leaders (uprights) dimension, crop load, fruit quality, flower and physiological (leaf gas exchanges and fruit growth rate) data were collected and analysed. The obtained results found that uprights present dependence among each other and as well as a mutual support during fruit development. However, individual upright fruit load and upright’s fruit load distribution on the tree (~ plant crop load) seems to define both upright independence from the other, and single upright crop load effects on the final fruit quality production. Correlations between fruit load and harvest fruit size were found and thanks to that valuable thinning thresholds, based on different vegetative parameters, were obtained. Moreover, it comes out that an upright’s fruit load random distribution presents a widening of those thinning thresholds, keeping un-altered fruit quality. For this reason, uprights resulted a partially physiologically-dependent plant unit. Therefore, if considered and managed as independent, then no major problems on final fruit quality and production occurred. This partly confirmed the possibility to shift crop load management to single upright. The finding of the presented studies together with the benefits coming from multileader planar training systems suggest a high potentiality of the 2D multileader training systems to increase apple production sustainability and profitability for Italian apple orchard, while easing the advent of automation in fruit production.

Automorphisms of irreducible holomorphic symplectic manifolds and related problems

We study automorphisms and the mapping class group of irreducible holomorphic symplectic (IHS) manifolds. We produce two examples of manifolds of K3[2] type with a symplectic action of the alternating group A7. Our examples are realized as double EPW-sextics, the large cardinality of the group allows us to prove the irrationality of the associated families of Gushel-Mukai threefolds. We describe the group of automorphisms of double EPW-cubes. We give an answer to the Nielsen realization problem for IHS manifolds in analogy to the case of K3 surfaces, determining when a finite group of mapping classes fixes an Einstein (or Kähler-Einstein) metric. We describe, for some deformation classes, the mapping class group and its representation in second cohomology. We classify non-symplectic involutions of manifolds of OG10 type determining the possible invariant and coinvariant lattices. We study non-symplectic involutions on LSV manifolds that are geometrically induced from non-symplectic involutions on cubic fourfolds.