Motivic Decomposition of Projective Pseudo-Homogeneous Varieties

Let G be a semi-simple algebraic group over a field k. Projective G-homogeneous varieties are projective varieties over which G acts transitively. The stabilizer or the isotropy subgroup at a point on such a variety is a parabolic subgroup which is always smooth when the characteristic of k is zero. However, when k has positive characteristic, we encounter projective varieties with transitive G-action where the isotropy subgroup need not be smooth. We call these varieties projective pseudo-homogeneous varieties. To every such variety, we can associate a corresponding projective homogeneous variety. In this thesis, we extensively study the Chow motives (with coefficients from a finite connected ring) of projective pseudo-homogeneous varieties for G inner type over k and compare them to the Chow motives of the corresponding projective homogeneous varieties. This is done by proving a generic criterion for the motive of a variety to be isomorphic to the motive of a projective homogeneous variety which works for any characteristic of k. As a corollary, we give some applications and examples of Chow motives that exhibit an interesting phenomenon. We also show that the motives of projective pseudo-homogeneous varieties satisfy properties such as Rost Nilpotence and Krull-Schmidt.

Evaluation of Information Entropy from Acoustic Emission Waveforms as a Fatigue Damage Metric for Al7075-T6

Information entropy measured from acoustic emission (AE) waveforms is shown to be an indicator of fatigue damage in a high-strength aluminum alloy. Several tension-tension fatigue experiments were performed with dogbone samples of aluminum alloy, Al7075-T6, a commonly used material in aerospace structures. Unlike previous studies in which fatigue damage is simply measured based on visible crack growth, this work investigated fatigue damage prior to crack initiation through the use of instantaneous elastic modulus degradation. Three methods of measuring the AE information entropy, regarded as a direct measure of microstructural disorder, are proposed and compared with traditional damage-related AE features. Results show that one of the three entropy measurement methods appears to better assess damage than the traditional AE features, while the other two entropies have unique trends that can differentiate between small and large cracks.