Research

In our research group, we work on problems related to materials (mostly polymers), algorithms, and uncertainty quantification. 

1. Inverse Problems in Polymer Characterization

A lot of effort has gone into building mathematical and computational models that accept the architecture and composition of a polymer mixture as input, and predict properties such as conformations and rheology. We hope to "invert" this operating paradigm to enable the model-based characterization of polymer mixtures from experimental data. That is, we seek to determine the structure, given the SEC and rheological data of an unknown polymeric sample.

In the busy schematic shown above the bold "m"s represent mathematical models that take in a structure "x" of a sample and make predictions that can be tested against experimental measurements.

We cast the inverse problem into a Bayesian framework, which transforms it into a sampling problem that can be investigated using Markov Chain Monte Carlo.

2. Modeling Structure and Dynamics of Materials

We leverage theory and coarse-grained simulation methods across a range of length- and time-scales to understand the structure and dynamics of materials such as polymer melts, filled-polymer systems, nanocrystals etc. 

The picture below depicts the damage profile following a projectile smashing into a brittle disc. We used a mesh based on centroidal Voronoi tessellation, and modeled the dynamics using peridynamics.

3. Other Research Interests

Some of our interests such as characterizing uncertainty, developing new algorithms, or improving existing ones, don't neatly fall into the two buckets above.