PHYSICAL MATHEMATICS SEMINAR
TOPIC: SUPERLATTICE PATTERN SELECTION IN FARADAY WAVES
SPEAKER: CHAD MICHAEL TOPAZ
Northwestern University
Abstract:
Standing wave patterns are excited on the free surface of a fluid layer
when it is subjected to a periodic vertical acceleration of sufficient
strength. This is the well-known Faraday instability. When Faraday wave
patterns are forced with rationally-related frequency components m*omega
and n*omega, the resulting waves may be either harmonic or subharmonic
with respect to the overall forcing period. Exotic SL-I superlattice
patterns (Kudrolli, Pier and Gollub) have been observed near a
codimension-two point in parameter space at which both instabilities onset
simultaneously.
In this talk, I discuss the role that resonant triad interactions play in
the nonlinear pattern selection process. Using symmetry considerations and
an amplitude equation framework, I predict which resonant modes will be
most important for pattern selection. The resonance effects predicted by
symmetry are borne out in explicit perturbative and numerical calculations
on Faraday wave equations of Zhang and Vinals which apply to
small-amplitude waves on weakly inviscid, semi-infinite fluid layers. A
bifurcation analysis reveals that in practice, the "difference frequency"
mode oscillating with dominant frequency |n-m|*omega may contribute to the
stabilization of the SL-I pattern. Based on the understanding of this
mechanism, I suggest a four-frequency forcing function which is engineered
to produce a particular SL-I pattern.
This is work done under the supervision of my advisor, Professor Mary
Silber, at Northwestern University.
DATE: TUESDAY, DECEMBER 11, 2001
TIME: 2:30 PM
LOCATION: Building 2, Room 338
Refreshments will be served at 3:30 PM in Room 2-349
Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA 0213