The project is in computational and algorithmic aspects of arithmetic dynamicals. Arithmetic dynamics, a relatively new branch of mathematics, is a combination of number theory and dynamical systems. At its most fundamental, it is the search for rational solutions to equations that arise from iteration. There are two main aspects to this project: (1) Implementation in the mathematical software Sage of functionality and algorithms for working with dynamical systems. (2) Resolution of open computational problems in arithmetic dynamics and subsequent implementation in Sage.
(1) Design and develop a database for scientific research data. We will work with the Lawrence Berkeley National Lab (US Department of Energy) on this project. Our data will come from nuclear molecular imaging research for cardiac disease. (2) Understand and analyze different types of motions associated with cardiac imaging, e.g., patient motion, respiratory motion, cardiac motion, and kinetics of tracer molecules. We will try to detect such motion, correct for them, and extract diagnostic information from such dynamic data.
Each summer from 2014 to 2016, 9 undergraduate students will participate in an 8 week summer REU Site designed to involve undergraduate students in innovative research in nonlinear partial differential equations, optimal control and inverse problems, and dynamical systems and chaos theory, while utilizing modern tools of mathematical and numerical analysis. The REU aims to train a new generation of well-rounded mathematicians to shed light on the mathematical problems which arise by modeling complex real life problems, and attacking them with the tools of modern analysis.
The primary focus of the project is to examine the performance of the National Hurricane Center (NHC) Wind Speed Probability Forecast product. The 45th Weather Squadron makes extensive use of the NHC product for advising operational customers in preparations associated with mitigating the risks from tropical cyclones at Cape Canaveral Air Force Station/Kennedy Space Center/Patrick Air Force Base (CCAFS/KSC/PAFB). Specifically, this work is intended to help customers make educated evacuation decisions, including timing for setting the various hurricane conditions for CCAFS/KSC/PAFB.