Shape of a Ponytail and the Statistical Physics of Hair Fiber Bundles

Raymond E. Goldstein, Patrick B. Warren, Robin C. Ball
2012 Physical Review Letters  
A general continuum theory for the distribution of hairs in a bundle is developed, treating individual fibers as elastic filaments with random intrinsic curvatures. Applying this formalism to the iconic problem of the ponytail, the combined effects of bending elasticity, gravity, and orientational disorder are recast as a differential equation for the envelope of the bundle, in which the compressibility enters through an 'equation of state'. From this, we identify the balance of forces in
more » ... of forces in various regions of the ponytail, extract a remarkably simple equation of state from laboratory measurements of human ponytails, and relate the pressure to the measured random curvatures of individual hairs.
doi:10.1103/physrevlett.108.078101 pmid:22401258 fatcat:6d4bzt5qhjehdbdbvgdcdgen34