## Research

I am an applied mathematician and I am interested in mathematical modeling and scientific computation, particularly for multi-disciplinary research. Across science and engineering, mathematical ideas enter into almost every area of study, and this creates many exciting opportunities for mathematicians to collaborate. Most of my work has been done in collaboration with researchers in other fields, where I have been able to provide mathematical and computational expertise to a research team. The web pages linked to below provide more detailed information about the areas on which I am currently working.

### Simulation of complex elasto-plastic materials

Many materials of scientific and technological importance are challenging to model. I developed new simulation techniques to simulate elasto-plastic materials, and used them to study of metallic glasses, a promising new class of metallic alloy. With Ken Kamrin at MIT, I developed a “reference map” simulation technique for large strain elasticity and fluid–structure interaction.

### Material porosity and permeability

I wrote a software library, Voro++, for computing the Voronoi diagram. In collaboration with LBL's Scientific Computing Group, I used the library to develop high-throughput analysis tools for crystalline porous materials, which were subsequently employed to identify materials for carbon capture applications. I have also worked on a continuum mathematical model of permeability in shales.

### Modeling of cellular mechanics

Since 2010, I have been part of the Bay Area Physical Sciences in Oncology Center, which is an initiative to encourage interaction between the physical sciences and cancer research. I am working on several collaborative projects with experimentalists at Berkeley and UCSF, and I am developing new numerical techniques to model mechanical interactions between cells and their environment.

### Modeling of dense granular materials

Granular materials are common in everyday experience and are used in many industrial processes, but accurately modeling them remains challenging. I have worked on the modeling of granular mixing and rheology, and I have carried out several collaborative projects, most recently with the PSI Laboratory for Thermal-Hydraulics to examine graphite wear in a pebble-bed nuclear reactor.

### Multigrid and optimization algorithms

The multigrid algorithm is a method of solving large linear systems of equations that occur in many computational studies. I have developed multigrid algorithms in relation to the study of adaptive octree grids, and searching for time-periodic three-dimensional water waves.

## Brief articles about previous work

Several brief articles are available about the research I carried out during my PhD on granular materials. I also have several articles highlighting some specific results and movies from my collaborations.