Abstract:

The connections between geometry and mechanics have been explored for centuries. How these connections shape computation is a question we are just beginning to explore. 

If computers can predict how materials move and deform, they can help us to understand, anticipate and manipulate the physical world. Our group develops models and algorithms that capture the characteristic behavior of a mechanical system. We focus on a geometric interpretation of the physics. Building a discrete geometric picture from the ground up, we mimic the axioms, structures, and symmetries of the smooth setting. The result is a readily computable model that preserves invariants and conservation laws. 

We develop models for elastic rods, thin shells, liquid threads, droplets, soap films, and granular media. As we explore applications ranging from flagellar propulsion and robotics to fashion design, we learn about the potential for impact on art, medicine, engineering and scientific research.