Doing the math that reveals the physics all around us

May 6, 2019

Particle physics, cosmology and genetics are fascinating subjects that fire up the imagination. But my passion lies in the physics of the mundane.

I’m an applied mathematician specializing in fluid dynamics, which deals with gases such as air and liquids such as water, but also with more esoteric fluids such as blood, shampoo and toothpaste.

These fluids obey mathematical equations with complex nonlinear solutions.

I develop methods for finding these solutions. Exact solutions are almost always impossible, but every problem has a chink in its armor – usually in the form of a small parameter that can be exploited with the right tools.

For example, recently I studied hagfish slime. The hagfish uses a peculiar defense mechanism: when attacked by a predator, it secretes a mucus that explodes into slime, choking the assailant.

The slime is created by entanglement of fibers, and the mechanism for their rapid deployment is still poorly understood.

My co-authors and I devised a model where small cells in the mucus are unraveled rapidly into long fibers by fluid turbulence. In this case, the small parameter comes from the long length of the fibers.

The model helps explain how hagfish slime can be created so quickly. Perhaps we can use this to design similar wondrous materials with unforeseen applications, such as firefighting.

Some of my research also involves optimization. For example, what is the best way to heat or cool a medium? This is important for heat exchangers used in heating buildings, but also for cooling large arrays of microprocessors.

The mathematical approach can also be applied to cooking: my students and I are determining how many times a steak on a grill should be turned, for optimal tastiness. Mathematical models allow us to try a much wider range of scenarios than is possible with time-consuming real-world experiments.