Thesis--Columbia University, 1907. / Vita. Includes bibliographical references (p. 111-115).

Thesis (M.A.)--University of Wisconsin, 1961. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 136-139).

Variably dolomitized limestone samples from the Rundle Group in Western Alberta, Canada were deformed under a variety of confining pressures and at room temperature in a triaxial rock press. The aim of this research is to establish the mechanical behaviour and brittle constitutive laws of limestone and dolomite composites. This data can then be used to develop strength profiles of thrust faults in the Rocky Mountain Fold and Thrust Belt. For example, many of the thrust faults in the Canadian Foreland are composed of limestone–dolomite composites, yet the mechanical properties of these composites remain unknown. Sample protoliths were selected for their similar grain sizes and grain size distributions, low porosity and low silica content in order to best examine relationships between these parameters and the distribution of strain between the dolomite and calcite. This study shows that increasing dolomite content correlates to an increase in strength at low and medium confining pressures. At high confining pressures, distributed brittle deformation adds complexities that are attributed to textural controls. Microstructural analysis of deformed samples shows that at approximately thirty to forty-five weight percent dolomite is interconnected via a dolomite grain network that provides a load-bearing capacity to the dolomite. This load-bearing capacity correlates to dramatic jumps in the strength of dolomite–limestone composites observed with increasing confining pressures. Inherent weaknesses in calcite grains such as twin planes and cleavage intersections are exploited by fractures resulting in reduced peak strengths of calcite-rich composites. Calcite generally absorbs strain and distributes it into finer spaced fracture networks than in dolomite. In dolomitized rock that still contains calcite cleavage within dolomite is not exploited, rather transgranular cracks break dolomite down into irregular and angular particles. At near pure dolomite content and at high confining pressure dolomite will fracture and disaggregate along cleavage. Comminuted dolomite grains commonly show a larger distribution of sizes and have more irregular shapes than contiguous comminuted calcite grains. Comminuted calcite particles are commonly much smaller than comminuted dolomite grains and show more regular shapes and an even grain size distribution.

This thesis is divided into four chapters. In the first one, all the pre-requisite theory of semigroups and groupoids is introduced, as well as a few new results - such as a short study of ∨-ideals and quotients in distributive semigroups and a non-commutative Loomis-Sikorski Theorem. In the second chapter, we motivate and describe the sofic property for probability measure-preserving groupoids and prove several permanence properties for the class of sofic groupoids. This provides a common ground for similar results in the particular cases of groups and equivalence relations. In particular, we prove that soficity is preserved under finite index extensions of groupoids. We also prove that soficity can be determined in terms of the full group alone, answering a question by Conley, Kechris and Tucker-Drob. In the third chapter we turn to the classical problem of reconstructing a topological space from a suitable structure on the space of continuous functions. We prove that a locally compact Hausdorff space can be recovered from classes of functions with values on a Hausdorff space together with an appropriate notion of disjointness, as long as some natural regularity hypotheses are satisfied. This allows us to recover (and even generalize) classical theorem by Kaplansky, Milgram, Banach-Stone, among others, as well as recent results of the similar nature, and obtain new consequences as well. Furthermore, we extend the techniques used here to obtain structural theorems related to topological groupoids. In the fourth and final chapter, we study dynamical aspects of partial actions of inverse semigroups, and in particular how to construct groupoids of germs and (partial) crossed products and how do they relate to each other. This chapter is based on joint work with Viviane Beuter.