Cepheid variable stars have been used as “standard candles” to find distances to other stars. The fluctuation of brightness in variable stars can help identify their distance by comparing the observed (apparent) luminosity (or brightness) to the true (absolute) luminosity as determined by a relationship between the period of the fluctuation and the absolute luminosity of the star (called the period-luminosity relationship). Stars that have shorter periods with a lower luminosity than Cepheid variables, can be classified as RR Lyrae stars. We observed the brightness of an RR Lyrae star over time using the robotic telescopes of Las Cumbres Observatory to determine its period and apparent luminosity. We used that information and theoretical period-luminosity relationships for RR Lyrae stars to determine the distance We will compare the distance to that found by the GAIA; satellite using stellar parallax; if the distances are not the same within experimental error, then the theoretical RR Lyrae period-luminosity relationships may be inaccurate.

Interferometry is a well-established technique in the field of plasma diagnostics for obtaining measurements of plasma density. However, the most prevalent equipment available to implement such approaches is highly specialized and costly. This project intends to demonstrate that comparatively basic and economical radar equipment can be equipped to perform interferometry on plasma for diagnostic purposes. The main resources are a radar emitting/receiving board, a data capture card, and their associated software. Methodologically, this research entails the manipulation of the radar and data parameters to accurately measure the phase shift induced by the plasma in question; subsequent processing and analysis of that information will yield the relevant density measurements. The main sources directing this work are the existing theoretical precedents for interferometry, as they will guide the experimental work of employing new hardware methods. This project is in progress, and its future steps are concerned with mastering the operation of the hardware and software and applying the configuration to actual plasma. Developing a methodology using this specific equipment will establish a salient precedent for less specialized hardware applications of plasma interferometry that can be implemented in a variety of similarly basic equipment. As such, this research has important implications for the accessibility of diagnostic methods across the field of plasma physics, an important discipline for future prospects in nuclear power.

Optimal Transport Theory is a branch of mathematics that seeks the most efficient way of transporting one distribution of mass to another location. A question originally posed in the 1700s as a means of optimally allocating resources, Optimal Transport has regained traction for its ability to compare images by quantifying both texture and shape information, proving useful in the settings of economics, data science, and particle physics. A downside to Optimal Transport, however, is that it requires all pairwise 2-Wasserstein distances between images to be computed, which is computationally costly, and for large scale image processing, cannot be done on a personal computer. Wang et al. (2013) proposed a new approximation scheme called Linear Optimal Transport (LOT) that uses a linearized approximation of the 2-Wasserstein distance that is computationally faster than standard Optimal Transport without sacrificing its classification capabilities. What remains unknown is if there are any similarities or differences between the LOT and the 2-Wasserstein distances. In this talk, I will present new results that gives a comparison of the two distances that may justify some of the properties of the LOT approximation scheme.