IIMAS - FENOMEC
UNAM
Undular Bores in Nematic Liquid Crystals
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.
Informes: coloquiomym@gmail.com, o al 5622-3564.