Stratifying On-Shell Cluster Varieties: the Geometry of Non-Planar On-Shell Diagrams

The correspondence between on-shell diagrams in maximally supersymmetric Yang-Mills theory and cluster varieties in the Grassmannian remains largely unexplored beyond the planar limit. In this article, we describe a systematic program to survey such 'on-shell varieties', and use this to provide a complete classification in the case of $G(3,6)$. In particular, we find exactly 24 top-dimensional varieties and 10 co-dimension one varieties in $G(3,6)$---up to parity and relabeling of the external legs. We use this case to illustrate some of the novelties found for non-planar varieties relative to the case of positroids, and describe some of the features that we expect to hold more generally.Comment: 35 pages, 70 figures, and 1 table; also included is a file with explicit details for our classification. Signs corrected in two residue theorems, and a new interpretation (and formula) given for the las

Regional flow model of west Cape Cod and optimization analysis

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 1997.Includes bibliographical references (leaves 48-51).by Susanna Galloni.M.Eng

Optimization of an adaptive thermal lensing device for ground-based gravitational waves interferometers

The project of this thesis stems from a collaboration with the University of Florida lasting two months. The purpose is to design and test a new prototype of an adaptive thermal lensing device for ground-based gravitational waves interferometers, starting from the previously developed in the american university in 2015. Firstly, I will briefly introduce what gravitational waves are and how we have been able to detect them since September 2015, focusing the attention on the american LIGO interferometers, their current noise limits and how they will be upgraded in the next few years, exploiting squeezed light states to shape the quantum vacuum. Throughout the first chapter it will be clear that, in such a context, an adaptive thermal lensing device is an excellent way to allow the implementation of the squeezing. Then to create the theoretical base required to understand the work, it is necessary to introduce lasers, optical cavities, thermal lensing and the so-called mismatch problem. Moving to the actual work, I will describe the previous devices built at the University of Florida, analyzing their strengths, weaknesses and, starting from the latter, the reasons why a new prototype was needed and what improvement we tried to achieve with it. After portraying the new characteristics of my device, I will relate the data collected from some tests run on it and from an actual focal power change experiment. Finally, I will draw the conclusions on the efficiency and functionalities of my work based on the aforementioned data, trying to forecast its future.ope