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Optimal foraging theory provides a suite of tools that model the best way that an animal will <br/>structure its searching and processing decisions in uncertain environments. It has been <br/>successful characterizing real patterns of animal decision making, thereby providing insights<br/>into why animals behave the way they do. However, it does not speak to how animals make<br/>decisions that tend to be adaptive. Using simulation studies, prior work has shown empirically<br/>that a simple decision-making heuristic tends to produce prey-choice behaviors that, on <br/>average, match the predicted behaviors of optimal foraging theory. That heuristic chooses<br/>to spend time processing an encountered prey item if that prey item's marginal rate of<br/>caloric gain (in calories per unit of processing time) is greater than the forager's<br/>current long-term rate of accumulated caloric gain (in calories per unit of total searching<br/>and processing time). Although this heuristic may seem intuitive, a rigorous mathematical<br/>argument for why it tends to produce the theorized optimal foraging theory behavior has<br/>not been developed. In this thesis, an analytical argument is given for why this<br/>simple decision-making heuristic is expected to realize the optimal performance<br/>predicted by optimal foraging theory. This theoretical guarantee not only provides support<br/>for why such a heuristic might be favored by natural selection, but it also provides<br/>support for why such a heuristic might a reliable tool for decision-making in autonomous<br/>engineered agents moving through theatres of uncertain rewards. Ultimately, this simple<br/>decision-making heuristic may provide a recipe for reinforcement learning in small robots<br/>with little computational capabilities.
The two general categories of structural health monitoring (SHM) systems include passive and active monitoring. Active SHM systems utilize an input of energy to monitor the health of a structure (such as sound waves in ultrasonics), while passive systems do not. As such, passive SHM tends to be more desirable. A system could be permanently fixed to a critical location, passively accepting signals until it records a damage event, then localize and characterize the damage. This is the goal of acoustic emissions testing.
When certain types of damage occur, such as matrix cracking or delamination in composites, the corresponding release of energy creates sound waves, or acoustic emissions, that propagate through the material. Audio sensors fixed to the surface can pick up data from both the time and frequency domains of the wave. With proper data analysis, a time of arrival (TOA) can be calculated for each sensor allowing for localization of the damage event. The frequency data can be used to characterize the damage.
In traditional acoustic emissions testing, the TOA combined with wave velocity and information about signal attenuation in the material is used to localize events. However, in instances of complex geometries or anisotropic materials (such as carbon fibre composites), velocity and attenuation can vary wildly based on the direction of interest. In these cases, localization can be based off of the time of arrival distances for each sensor pair. This technique is called Delta T mapping, and is the main focus of this study.
By means of optimized geometry analysis, pure Ge and Sn were found to adopt the alpha and beta structures, respectively, as observed experimentally. For all theoretical alloys, the corresponding αphase structure was found to have the lowest energy, for Sn percent compositions up to 90%. However at 50% Sn, the correspondingβ alloy energies are predicted to be only ~70 meV higher. The formation energy of α-phase alloys was found to be positive for all compositions, whereas only two beta formation energies were negative. Bond length distributions were analyzed and dependence on Sn incorporation was found, perhaps surprisingly, not to be directly correlated with cell volume. It is anticipated that the data collected in this project may help to elucidate observed complex vibrational properties in these systems.