# Ponytail physics

## 28 Oct 2015

Robin Ball talks about a theoretical model of fibers in which their elasticity and curliness produce the characteristic shape of a ponytail.

How do you describe the behaviour of hair? Leonardo da Vinci thought it flowed like water, but modeling realistic hair in computer animated films is challenging. Hair fibers are elastic filaments with random intrinsic curvature, like cotton and fiberglass. A bundle of fibers is subject to the combined effects of bending elasticity, gravity and orientational disorder. Despite the ubiquity of fiber bundles in the natural and man-made world, a mathematical description of how a bundle behaves has remained elusive.

In this talk Robin Ball develops a mathematical model of the behaviour of a bundle of fibers and applies this formalism to the iconic problem of the ponytail. The elasticity, gravity, and disorder are recast as a differential equation for the envelope of the ponytail bundle, in which the compressibility enters through an equation of state. From this, it is possible to identify the balance of forces in various regions of the ponytail, extract a remarkably simple equation of state from laboratory measurements of real ponytails, and relate the pressure to the random curvatures of individual fibers.

### London Institute Seminars

London Institute Seminars are given by invited speakers to members of the Institute and nearby universities. They start at the end of the day with drinks and after the talk informal discussion continues into the evening. The goal of the talk is to inspire as much as to inform.