Research projects

Diffusion-limited Dissolution and Aggregation


I took this photo on a hike along the Devil’s garden trail in Arches National Park. In that part of the US, fantastic patterns are abundant and breathtaking. They range from the entire canyon of hoodoos in Bryce National Park, to the world famous arches, to smooth cavities of all sizes and shapes in the rocks. The patterns are formed, among others, by slow diffusive and erosive processes that happen over a long time scale. But sometimes, a sudden structure failure can cause rapid changes, for example, the rock falls at the Landscape arch in the 1960s.

In one of my research projects, I look at a simplified computational model of this type of dissolution processes in 2D. In particular, I focus on a type of process called the diffusion-limited dissolution. The matter to be dissolved is modeled as a cluster of uniformed particles on a regular lattice, and the diffusion of a dissolving particle is modeled as a random walk. The conformal mapping technique is used to accurately calculate the probability of contact between a diffusing particle and a particle in the matter cluster. Using this model, we can explore the statistical properties of dissolving interfaces, and the dynamics at the end of the dissolution event, i.e. when a clump of matter is about to be completely dissolved away. I presented a poster on this project at the 2017 DOE CSGF program review, the poster can be found be found here.

More simulation movies can be found in this post.

The reference map technique for fluid-structure interaction problems

Fluid-structure interactions (FSI) are ubiquitous in nature, laboratory, and industrial setting. For example, animal locomotion, fluid flowing through porous media, or cheese being stirred and pumped through a cheese making machine. However, FSI problems are challenging to solve analytically or simulate numerically, due to their nonlinear, multi-physics nature.

In particular, it is difficult to reconcile the dilemma of choosing a discretization framework. Solid simulations are typically computed in a Lagrangian framework. whereas fluid dynamics are more conveniently done from the Eulerian perspective.  Methods such as Arbitrary Lagrangian-Eulerian and Immersed Boundary methods are proposed to address this challenge, but they require extra computations to bridge the discretization from different perspectives.

My group mate Nick Derr and I have been working with our advisor, Chris, on developing a fully Eulerian method, the reference map technique (Rycroft 2018) along with a 3D implementation of it.

Snapshots from a simulation movie, where an incompressible neo-Hookian solid is stretch in the x direction at T=0, then let relax to equilibrium.

The reference map technique is rooted in large deformation solid mechanics, so the method is particularly suitable for simulating immersed soft, very deformable solids. The idea of the reference map is simple and elegant, and the essence of it is to find a way to calculate the deformation in the material in the current physical space, rather than the undeformed reference space. Being on a fixed regular grid comes with computational time advantages, giving the method a performance edge in many-body interaction problems.

The 3D code is developed with distributed memory parallelism, specialized data structures and methods to ensure efficiency. For instance, a new least squares-regression based extrapolation algorithm is developed to address challenges of field extrapolation in 3D.

I did a poster presentation on the progress of the project at DOE CSGF program review in 2018, see here for the poster.

Some spheres sedimenting on a permeable incline in fluid.
Two spinners rotating in opposite directions, stirring a box of fluid.
An immersed beam being twisted at both ends.

A numerical model of Vibrio fischeri growth and intraspecific competition

E. scolopes is a species of small squids living off the coast of Hawaii. Early in its life cycle, it forms a life-long symbiosis with V. fischeri bacteria. The squids need the bioluminescent bacteria for counter-illumination, a form of camouflage that help the squid blend in with the moonlit ocean surface at night. Scientist also find that the bacteria is crucial in squid’s development – without the bacterial infection, squids do not develop mature light organs (McFall-Ngai, M., Annu. Rev. Microbiol. 2014 68(), 177-94).

What we are interested in is the microbial component of the symbiosis. V. fischeri is very abundant in the ocean, and some strains of it have evolved what’s called Type VI Secretion System (T6SS). When I first heard of this, my mind was blown — what T6SS does is it allows a bacterium to put together a spear, and shoot it at another cell and kill it. I knew bacteria can swim and swarm, but the ability to shoot and kill adds a whole new level of complexity. What’s also fascinating is that these spears, commonly called sheaths, are very similar to that of bacteria phages’. One theory is that at one point in the evolution of bacteria, some species co-opted bacteria phages’ DNA to build T6SS molecular machine – we may have on our hand a classic example of what doesn’t kill you makes you stronger!

Chris and I were instantly drawn to the quest of understanding T6SS-dependent interactions using computational model. We visited Prof. Eva Kanso when she was on her sabbatical at Flatiron Institute and had a brainstorm about what could be explored, and a collaboration was born. Later, Eva introduced us to Prof. Alecia Septer and her graduate student, Stephanie Smith, at UNC Chapel Hill. They have been collaborating with Eva, doing experiments on Vibrio assays. Eva and Alecia have long been a part of a growing consortium of researchers who work on the myriad questions in the squid-Vibrio system.

At this year’s CSGF program, I’d be presenting a poster with preliminary results. In the meanwhile, we are still hard at work to explore more type of numerical and physical experiments.

I hope E. scolopes and V. fischeri make it to the cast of Sponge Bob Square Pants one day. I think they’ll really shine.
Two species of bacteria, both equipped with T6SS and ready to kill, grow from random initial condition without spatial limit.
Two species of bacteria, both equipped with T6SS and ready to kill, grow from random initial condition within limited space (periodic boundary condition).