Research

Current research

My primary research interests are mathematical modeling, fluids dynamics, geophysical fluids and uncertainty quantification. I am currently working with Dr. Shankar Venkataramani on modeling the oil spilling on the ocean.

The actual process of oil spilling on the sea is complicated. It consists of many different physical processes schematically (see the above figure) The spread of an oil slick on the sea is affected by many factors. These include transport driven by winds and currents, and the tendency of the oil to spread even in calm water. On the other hand, crude oil is a mixture of a very large number of components, each with its own properties. During the spreading process, the properties of oil such as density and viscosity vary with time and also in space. Such variation is caused by evaporation of the lighter components into the air, dissolution of the soluble components into sea water and the different rates of spreading for different components. Thus, it is difficult to model such a spilling process with consideration of all the aspects.

Our goal is to develop a comprehensive model that includes multiple physical processes, and a statistical framework that blends model outcomes with observational data to better predict the transport of oil spreading on the sea.

Talks

1. U2 can UQ Showcasing Uncertainty Quantification Research, University of Arizona, March 2018.

Filtering for a Dimension Reduced System with Slow Relaxation

2. Modeling and Computation Seminar, University of Arizona, Program in Applied Mathematics, May 2017.

The dynamics of an oil slick spreading on water surface

3. Student Brown Bag Seminar, University of Arizona, Program in Applied Mathematics, April 2017.

Oil spreading on the sea

Other projects

Introduction to geophysical fluids and numerical simulation, advised by Dr. Shankar Venkataramani, 2014-2015 (RTG project)

Packing probelems and PDEs, advised by Dr. Shankar Venkataramani, 2014 spring (term project)

Oscillation of spectra of viscous water droplet, worked with Andrew Hofstrand and Adam Martinez, 2013 fall (term project)

The analysis of patterns for iodine dissolving in starch solution, advised by Dr. Patrick Shipman and Dr. Stephen Thompson, 2012-2013 (undergraduate research)

The analysis of PDEs for coupled pattern forming systems, advised by Dr. Patrick Shipman, 2012 (undergraduate research)