Mesoscopic computer simulations of polymers and colloids have provided an important bridge between atomistic and continuum models. These models have been used as alternatives to constitutive equations or to develop constitutive equations. They also allow for calculations of microstructure and how flow influences that microstructure. One example of these models is bead-spring chain models of polymers. They have been used extensively to understand the behavior of polymers, in particular the dynamics of DNA in microfluidic devices. My thesis work under Patrick Doyle at MIT focused on developing and analyzing the response of new bead-spring chain models. As microfluidic devices get increasingly small and approach the regime of nanofluidics, the previously used bead-spring chain models are no longer accurate coarse-grained representations, while more detailed micromechanical models are too computationally expensive. Using statistical mechanics and Brownian dynamics simulations, we developed new models which bridge the gap between the micromechanical and coarse-grained models. These intermediate level models capture the necessary physics, are computationally tractable, and are needed when analyzing new devices for DNA separations and gene mapping.

My postdoctoral work under Michael Graham at the University of Wisconsin-Madison has focused on simulating suspensions of self-propelled particles. Recently large collections of swimming microorganisms have been observed producing collective motions on a scale much larger than the scale of a single organism. The study of swimming microorganisms has a long history in the fluid mechanics literature. The linearity of the hydrodynamic equations at small Reynolds number require that microorganisms swim differently than macroscopic organisms. This has been studied previously by looking at the swimming of a \emph{single} organism. In contrast, large collections of swimming organisms have been analyzed using continuum theories written as differential equations for field variables.

We have approached the problem by directly simulating a large collection of coarse-grained representations of the swimming organisms. Inspired by the coarse-grained models of polymers and colloids, we model them as a series of beads connected by rods. The model is coarse enough that we can directly follow the dynamics of large populations while still including the far-field multi-body hydrodynamics. The model also natural extends to include other interactions between organisms.