Kevin A. O’Neil
My research has concentrated on a fascinating but (until recently) neglected area in fluid mechanics called “vortex statics,” and on a certain type of problem that can arise in the area of robotic control.
Vorticity is a fundamental concept in fluid motion, and the important features of many practical and idealized fluid flows can be explained in terms of it. The study of how the vorticity field influences itself is called vortex dynamics, and leads to a number of interesting (and unsolved) mathematical problems. The equations of vortex statics yield time-invariant vorticity fields, sometimes called "vortex crystals," and the techniques used to solve them have application to many seemingly unrelated areas. Recent research has uncovered connections to algebraic geometry, to the theory of orthogonal polynomials, and to functions that satisfy certain singular integral equations. Under my supervision, several research groups of TU undergraduates have done theoretical and numerical work towards characterizing the number and nature of vortex crystals on the plane and sphere.
My other research has been in the area of robotic control, the art and science of getting a robotic mechanism to do what you want it to do. Some control schemes work quite well almost all the time, but contain hidden singularities that cause them to behave in unexpected and undesirable ways. An analogous situation is the way a baseball infielder can field most balls smoothly, but can be “handcuffed” by a ball that forces him into an awkward posture. My co-workers and I explored ways of using mathematical tools to predict, understand and subdue these singularities.
Education and Degrees Earned
A.B. 1978, Princeton University
Ph.D. 1985, University of Illinois at Urbana-Champaign
Areas of Research Focus
Vortex dynamics and vortex statics
Singularities of robotic control