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Lorenz Kramer
Theoretische Physik II, University of Bayreuth, Germany
Pattern formation and selection in systems with broken reflection symmetry
Wednesday 9th, March 14:05-14:55pm,
Carslaw Building Room 373.
We start from traditional pattern-forming systems that describe the
creation of stationary periodic patterns. Such systems always exhibit
reflection symmetry. We consider perturbations that break this
symmetry. This can be done in the bulk by applying a spatially
periodic forcing that moves with some velocity ("traveling wave
forcing"). Whereas at low velocity the pattern is dragged along the
forcing and at high velocity the system averages over the forcing,
interesting bifurcation scenarios occur inbetween. In two dimensions
one may have transitions to various types of hexagons (including
chaotic ones). Such effects were observed experimentally and can be
understood on the basis of universal amplitude equations. We will also
discuss briefly the situation where a step in the control parameter
from undercritical to overcritical moves with a certain (slow)
velocity. In one dimension the wavelength of the resulting pattern
depends sensitively on the velocity, and this has consequences in two
dimensions. The limit of very slow velocities turns out to be
particularly intriguing.
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