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Undular Bores in Nematic Liquid Crystals


por el

Dr. Noel Smyth


School of Mathematics, University of Edinburgh

Resumen:
The solitary wave, or soliton if the governing equation is integrable, is a well known generic solution of many nonlinear dispersive wave equations. Solitary waves occur in a vast range of physical applications, including surface and internal waves in fluids, oceanography, meteorology, optical fibres, nonlinear optics and mathematical biology. Another nonlinear wave form which is as readily observable as the solitary wave, but which has seen much less attention, is the undular bore, also termed a dispersive shock wave. Undular bores are the dispersive equivalent of a gas dynamics shock as they are a wave form which smooths out a discontinuity. In contrast to a gas dynamic shock (and solitary wave), however, they are unsteady and continuously expand. Examples of an undular bore are tidal bores, tsunamis and morning glory clouds. This talk will discuss undular bores in a nonlinear optical medium, a nematic liquid crystal. While the equations governing nonlinear optical beams in a nematic liquid crystal have some similarity to those for water waves, it is found that the undular bore for an optical beam in a nematic is distinctly different to those in water wave theory. A major feature of nematic bores is the generation of a resonant wavetrain which propagates ahead of the bore. A further feature is that the velocity of the bore is determined by the classical shock jump condition rather than conservation of Riemann invariants. The reasons for these differences, and others, are detailed.

MiƩrcoles 6 de abril, 2016
18:00 hrs.
Salón 203, Edificio Anexo, IIMAS

Informes: coloquiomym@gmail.com, o al 5622-3564.