Regular homomorphisms of minimal sets

The classification of minimal sets is a central theme in abstract topological dynamics. Recently this work has been strengthened and extended by consideration of homomorphisms. Background material is presented in Chapter I. Given a flow on a compact Hausdorff space, the action extends naturally to the space of closed subsets, taken with the Hausdorff topology. These hyperspaces are discussed and used to give a new characterization of almost periodic homomorphisms. Regular minimal sets may be described as minimal subsets of enveloping semigroups. Regular homomorphisms are defined in Chapter II by extending this notion to homomorphisms with minimal range. Several characterizations are obtained. In Chapter III, some additional results on homomorphisms are obtained by relativizing enveloping semigroup notions. In Veech's paper on point distal flows, hyperspaces are used to associate an almost one-to-one homomorphism with a given homomorphism of metric minimal sets. In Chapter IV, a non-metric generalization of this construction is studied in detail using the new notion of a highly proximal homomorphism. An abstract characterization is obtained, involving only the abstract properties of homomorphisms. A strengthened version of the Veech Structure Theorem for point distal flows is proved. In Chapter V, the work in the earlier chapters is applied to the study of homomorphisms for which the almost periodic elements of the associated hyperspace are all finite. In the metric case, this is equivalent to having at least one fiber finite. Strong results are obtained by first assuming regularity, and then assuming that the relative proximal relation is closed as well.

A Thermal Management Solution for Compact Power Converters

Regulated Transformer Rectifier Units contain several power electronic boards to facilitate AC to DC power conversion. As these units become smaller, the number of devices on each board increases while their distance from each other decreases, making active cooling essential to maintaining reliable operation. Although it is widely accepted that liquid is a far superior heat transfer medium to air, the latter is still capable of yielding low device operating temperatures with proper heat sink and airflow design. The purpose of this study is to describe the models and methods used to design and build the thermal management system for one of the power electronic boards in a compact, high power regulated transformer rectifier unit. Maximum device temperature, available pressure drop and manufacturability were assessed when selecting the final design for testing. Once constructed, the thermal management system’s performance was experimentally verified at three different power levels.