Hedgehog-antihedgehog annihilation to a static solution

Saturday, November 6, 2004 - 2:00pm - 2:45pm
EE/CS 3-180
Patricia Cladis (Advanced Liquid Crystal Technologies, Inc.)
Nematic liquid crystals are liquids with orientational order in a preferred direction denoted by n, a unit pseudo-vector i.e. with neither head nor tail. We call one of its point defects a hedgehog (H) because, in that case, n radiates from a point so is reminiscent of a hedgehog's quills when in a defensive posture. The other point defect is then, by default, an antihedgehog (.H), because it annihilates with a hedgehog to leave behind a static soliton [1].

Hedgehogs and antihedghogs are a direct consequence of the intrinsic nonlinear elastic properties of nematics in a cylindrical geometry to break spontaneously the symmetry imposed by the boundary condition. This was first pointed out by me and Maurice Kléman in 1972 [2] then subsequently dubbed escape into the third dimension [3]. While the statics of nematic point defects is relatively well understood (or so we thought), their surprising dynamics is of general interest in fields extending beyond liquid crystals.

As Jerry asked (based on preliminary observations Mayola Walters and I found at Bell Labs in the late '70's using my first computer controlled imaging system}[4]: Why is H.H annihilation dynamics so nonlinear? Indeed, why do point defects move at all when their range of interactions is limited by the cylinder radius, R, so that they should be asymptotically free when separated by many times R?

Most recently, using observations from my latest imaging system at ALCT, Helmut Brand and I found a new, unprecedented result: during annihilation, the hedgehog always moved faster than the antihedgehog. This gave us an idea that, after many referee battles, we finally published [5]. This talk is a tribute to Jerry's long standing affection and profound appreciation for all hedgehogs big and small.


[1] C. E. Williams, P. Pieranski and P. E. Cladis, Phys. Rev. Lett. 29, 90 (1972).

[2] P. E. Cladis and M. Kléman, J. de Phys. (Paris), 33, 591 (1972).

[3] P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, Clarendon Press, Oxford (1993).

[4] J.L. Ericksen in Nonlinear Effects in Fluids and Solids, M.M. Carroll and M.A. Hayes (eds), Plenum, New York (1996).

[5] P.E. Cladis and H. R. Brand, Hedgehog-antihedgehog pair annihilation to a static soliton, Physica A326, 322 (2003).