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Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

On Hidden Integrability in Nonlinear Continuum Mechanics

by
Professor Colin Rogers
Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems
and
School of Mathematics, University of New South Wales, Sydney, Australia

Date: February 23, 2005 (Wednesday)
Time: 4:30 pm to 5:30 pm
Venue: Room B6605 (Faculty Conference Room)
Blue Zone, Level 6
Academic Building
City University of Hong Kong

Abstract: The nonlinear equations that describe solitonic behaviour of physical systems have, to date, typically been derived by approximation or expansion methods. However, recently, hidden integrable structure, notably in spatial gasdynamics, the kinematics of fibre-reinforced fluids, and magnetohydrodynamics has been revealed via natural geometric constraints.

Here, we consider hidden integrable structure in an elastic shell model due to Kleman arising in liquid crystal theory. Thus, Friedel (1922) observed experimentally that certain types of liquid crystals (smectic A) can adopt geometric configurations composed of parallel layers of Dupin cyclides (G. Friedel, Les etats mesomorphes de la Matiere, Ann. de Phys 18, 273-474 (1921)). The geometric aspects of this work were elaborated upon by Lord Bragg (W. Bragg, Liquid crystals, Nature 133, 445-456 (1934)).

Here, it is established that, remarkably, the Kleman model admits exact layered Dupin cyclide solutions as observed experimentally by Friedel. The Dupin cyclides constitute soliton surfaces.

(Tea, coffee and cookies will be provided at the Faculty Common Room in B6501 before the colloquium from 4:00 to 4:30 pm. Please come and join us!)

** All interested are welcome **

For enquiry: 2788-9816

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