Multi-scalar critical theories: first steps for a non perturbative functional renormalization group analysis

In this work the fundamental ideas to study properties of QFTs with the functional Renormalization Group are presented and some examples illustrated. First the Wetterich equation for the effective average action and its flow in the local potential approximation (LPA) for a single scalar field is derived. This case is considered to illustrate some techniques used to solve the RG fixed point equation and study the properties of the critical theories in D dimensions. In particular the shooting methods for the ODE equation for the fixed point potential as well as the approach which studies a polynomial truncation with a finite number of couplings, which is convenient to study the critical exponents. We then study novel cases related to multi field scalar theories, deriving the flow equations for the LPA truncation, both without assuming any global symmetry and also specialising to cases with a given symmetry, using truncations based on polynomials of the symmetry invariants. This is used to study possible non perturbative solutions of critical theories which are extensions of known perturbative results, obtained in the epsilon expansion below the upper critical dimension.

Analysis, Design, and Hardware-in-the-Loop Validation of Multi-Active Bridge Converters

This master's thesis investigates different aspects of Dual-Active-Bridge (DAB) Converter and extends aspects further to Multi-Active-Bridges (MAB). The thesis starts with an overview of the applications of the DAB and MAB and their importance. The analytical part of the thesis includes the derivation of the peak and RMS currents, which is required for finding the losses present in the system. The power converters, considered in this thesis are DAB, Triple-Active Bridge (TAB) and Quad-Active Bridge (QAB). All the theoretical calculations are compared with the simulation results from PLECS software for identifying the correctness of the reviewed and developed theory. The Hardware-in-the-Loop (HIL) simulation is conducted for checking the control operation in real-time with the help of the RT box from the Plexim. Additionally, as in real systems digital signal processor (DSP), system-on-chip or field programmable gate array is employed for the control of the power electronic systems, and the execution of the control in the real-time simulation (RTS) conducted is performed by DSP.