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Applied Mathematics Seminar
    
  
 
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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.