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.

Flow Field–Flow Fractionation for size analysis and characterization of nanoparticles for applications in Life Sciences

Nanotechnologies are rapidly expanding because of the opportunities that the new materials offer in many areas such as the manufacturing industry, food production, processing and preservation, and in the pharmaceutical and cosmetic industry. Size distribution of the nanoparticles determines their properties and is a fundamental parameter that needs to be monitored from the small-scale synthesis up to the bulk production and quality control of nanotech products on the market. A consequence of the increasing number of applications of nanomaterial is that the EU regulatory authorities are introducing the obligation for companies that make use of nanomaterials to acquire analytical platforms for the assessment of the size parameters of the nanomaterials. In this work, Asymmetrical Flow Field-Flow Fractionation (AF4) and Hollow Fiber F4 (HF5), hyphenated with Multiangle Light Scattering (MALS) are presented as tools for a deep functional characterization of nanoparticles. In particular, it is demonstrated the applicability of AF4-MALS for the characterization of liposomes in a wide series of mediums. Afterwards the technique is used to explore the functional features of a liposomal drug vector in terms of its biological and physical interaction with blood serum components: a comprehensive approach to understand the behavior of lipid vesicles in terms of drug release and fusion/interaction with other biological species is described, together with weaknesses and strength of the method. Afterwards the size characterization, size stability, and conjugation of azidothymidine drug molecules with a new generation of metastable drug vectors, the Metal Organic Frameworks, is discussed. Lastly, it is shown the applicability of HF5-ICP-MS for the rapid screening of samples of relevant nanorisk: rather than a deep and comprehensive characterization it this time shown a quick and smart methodology that within few steps provides qualitative information on the content of metallic nanoparticles in tattoo ink samples.