In order to expose myself to more frontiers of  my research interest--inverse problem, I attended IPDE summer school in 2011. It was a  great opportunity  for me to look into both the theory of inverse problem arising from medical imaging and its application. The summer school offered  two mini-courses: Application of X-Ray Tomography and Transport Theory and  Application of Finite Volume Methods and the Clawpack Software. I personally focused on the first course, from which I learned a lot of powerful theory and numerical methods in solving inverse problem,such as Radon Transform, Inverse Radon Transform, Filtered Back-projection algorithm. I also attend the MATLAB sessions, which allowed me to reinforce my understanding of the theory and gain some valuable MATLAB programming experience on simulation and inversion of X-ray transforms and direct and inverse transport theory.
 
RadonTransform

Figure 1. Reconstruction of Micky mouse image using Back-projection

 

 It was the first time that I collaborated with graduate students outside of UD and worked on a interdisciplinary and practical industrial problem: Design of Fuel Tanks for High-Speed Vehicles. My main work of this project was to explore different shapes of fuel tanks and measure the remaining fuel in the tank of high-speed vehicles in a zero gravity atmosphere. I developed a Monte Carlo protocol to simulate the volume of remaining fuel in the tank and improved fuel tank efficiency for
rockets. This experience did help me to develop a similar Monte Carlo protocol to simulate the first passage time distribution in my current research.
fule

 Figure 2. Simulation of different levels of fluid in the spherical tank using Monte Carlo method