Nick Derr

Math, computing, biology, physics

My research centers on interactions between fluid and solid aspects of systems, often in porous, deforming systems arising in biological contexts. Here are a few of my past and present projects.

Erosion dynamics

Branching patterns can be seen in nature in a wide variety of contexts, from small biological systems (venation systems) to large geophysical settings (river systems.) A simple mechanical model for erosion is capable of producing branching patterns such as these. (PRL, arXiv)

Branching patterns

Reference map methods

The reference map technique is a fully Eulerian technique for the coupled simulation of immersed soft solid bodies in fluid. In three dimensions, the technique is well-suited for the simulation of many interacting bodies, such as the setting spheres shown here, or active solids. (PNAS, arXiv).

Settling soft spheres

Reciprocal swimmers

In extremely viscous flow, inertia is unimportant. Purcell’s scallop theorem states that swimmers in such settings with time-reversible (“reciprocal”) strokes don’t move over time. An asymmetric dimer with oscillating length is a simple example of such a swimmer. A general model for the steady flow field generated by small-amplitude actuation unifies several previous results, including motion of a dense dimer in Stokes flow and a dimer in inertial flow. The latter, shown below, displays interesting dynamics where the direction of motion flips from towards the small sphere (left) to the large sphere (right) as the flow’s degree of inertia increases. (arXiv).

Steady flow fields

Cytoskeletal gels

Our cells’ interiors consist of a complex network of polymer filaments. This porous medium is subject to active stresses imparted by mechanical motor proteins. Experimental results show actin networks actuated by myosin proteins display a wide range of behaviors. Our model of the system, coupling active tension to motor binding dynamics, show behavior that may be reminiscent of thermodynamic phase separation (bottom right) or novel (top left) depending on system parameters.

Gel patterns