We consider the thermal relaxation of a particle in a piecewise constant potential landscape subject to thermal fluctuations in the overdamped limit. We study the connection between the occurrence of the Mpemba effect, the presence of metastable states, and phase transitions as a function of the potential. We find that the Mpemba effect exists even in cases without metastable states. The borders of the areas where the effect happens correspond to eigenvalue crossings, eigenvector changes of direction, or phase transitions. Finally, we discuss the topological aspects of the strong Mpemba effect and propose using topology to search for the Mpemba effect in a physical system.

Assessment of Unmanned Aerial Systems and lidar for the Utility Vegetation Management of Electrical Distribution Rights-of-WaysMatthew R. Walker Utility Vegetation Management (UVM) is often the largest maintenance expense for many utilities. However, with advances in Unmanned Aerial Systems (UAS; or more commonly, "drones") and lidar technologies, vegetation managers may be able to more rapidly and accurately identify vegetation threats to critical infrastructures. The goal of this study was to assess the utility of Geodetics' UAS-lidar system for vegetation threat assessment for 1.6 km of a distribution electric circuit. We investigated factors which contribute to accurate tree crown detection and segmentation of trees from within an UAS-lidar derived point cloud, and the factors which contribute to accurate tree risk assessment. The study adapted the International Society of Arboriculture's (ISA) tree risk assessment methodology to the application of remotely sensed tree inventory. We utilized the lidar detected and segmented tree crowns for tree risk analysis based upon each tree's height, elevation, and location in relation to the electrical infrastructure. The individual tree detection and segmentation results show that our canopy type parameter and the routine used for field-and lidar-derived tree matching to have the largest effect on the classification agreement of field and lidar derived datasets. The Threat Detection classification also demonstrated a significant effect due to our canopy modeling parameter, where single canopy models possessed higher average Kappa agreement statistic and divided canopy models detected a larger number of threats on average. Ultimately, our best model was capable of the correct detection, segmentation, matching, and classification of half of the field trees which were determined to be vegetation threats.