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.

Mitochondrial respiratory supercomplex association limits production of reactive oxygen species from Complex I

Evidence accumulated in the last ten years has demonstrated that a large proportion of the mitochondrial respiratory chain complexes in a variety of organisms is arranged in supramolecular assemblies called supercomplexes or respirasomes. Besides conferring a kinetic advantage (substrate channeling) and being required for the assembly and stability of Complex I, indirect considerations support the view that supercomplexes may also prevent excessive formation of reactive oxygen species (ROS) from the respiratory chain. Following this line of thought we have decided to directly investigate ROS production by Complex I under conditions in which the complex is arranged as a component of the supercomplex I1III2 or it is dissociated as an individual enzyme. The study has been addressed both in bovine heart mitochondrial membranes and in reconstituted proteoliposomes composed of complexes I and III in which the supramolecular organization of the respiratory assemblies is impaired by: (i) treatment either of bovine heart mitochondria or liposome-reconstituted supercomplex I-III with dodecyl maltoside; (ii) reconstitution of Complexes I and III at high phospholipids to protein ratio. The results of this investigation provide experimental evidence that the production of ROS is strongly increased in either model; supporting the view that disruption or prevention of the association between Complex I and Complex III by different means enhances the generation of superoxide from Complex I . This is the first demonstration that dissociation of the supercomplex I1III2 in the mitochondrial membrane is a cause of oxidative stress from Complex I. Previous work in our laboratory demonstrated that lipid peroxidation can dissociate the supramolecular assemblies; thus, here we confirm that preliminary conclusion that primary causes of oxidative stress may perpetuate reactive oxygen species (ROS) generation by a vicious circle involving supercomplex dissociation as a major determinant.

Displacement Analysis of Under-Constrained Cable-Driven Parallel Robots

This dissertation studies the geometric static problem of under-constrained cable-driven parallel robots (CDPRs) supported by n cables, with n ≤ 6. The task consists of determining the overall robot configuration when a set of n variables is assigned. When variables relating to the platform posture are assigned, an inverse geometric static problem (IGP) must be solved; whereas, when cable lengths are given, a direct geometric static problem (DGP) must be considered. Both problems are challenging, as the robot continues to preserve some degrees of freedom even after n variables are assigned, with the final configuration determined by the applied forces. Hence, kinematics and statics are coupled and must be resolved simultaneously. In this dissertation, a general methodology is presented for modelling the aforementioned scenario with a set of algebraic equations. An elimination procedure is provided, aimed at solving the governing equations analytically and obtaining a least-degree univariate polynomial in the corresponding ideal for any value of n. Although an analytical procedure based on elimination is important from a mathematical point of view, providing an upper bound on the number of solutions in the complex field, it is not practical to compute these solutions as it would be very time-consuming. Thus, for the efficient computation of the solution set, a numerical procedure based on homotopy continuation is implemented. A continuation algorithm is also applied to find a set of robot parameters with the maximum number of real assembly modes for a given DGP. Finally, the end-effector pose depends on the applied load and may change due to external disturbances. An investigation into equilibrium stability is therefore performed.