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.

SPACE-DEPLOYED, THIN-WALLED ENCLOSURE FOR A CRYOGENICALLY-COOLED HIGH TEMPERATURE SUPERCONDUCTING COIL

The interaction of magnetic fields generated by large superconducting coils has multiple applications in space, including actuation of spacecraft or spacecraft components, wireless power transfer, and shielding of spacecraft from radiation and high energy particles. These applications require coils with major diameters as large as 20 meters and a thermal management system to maintain the superconducting material of the coil below its critical temperature. Since a rigid thermal management system, such as a heat pipe, is unsuitable for compact stowage inside a 5 meter payload fairing, a thin-walled thermal enclosure is proposed. A 1.85 meter diameter test article consisting of a bladder layer for containing chilled nitrogen vapor, a restraint layer, and multilayer insulation was tested in a custom toroidal vacuum chamber. The material properties found during laboratory testing are used to predict the performance of the test article in low Earth orbit. Deployment motion of the same test article was measured using a motion capture system and the results are used to predict the deployment in space. A 20 meter major diameter and coil current of 6.7 MA is selected as a point design case. This design point represents a single coil in a high energy particle shielding system. Sizing of the thermal and structural components of the enclosure is completed. The thermal and deployment performance is predicted.