Technion - Israel Institute of Technology
 
          Department of Mathematics
 
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     PDE AND APPLIED MATHEMATICS SEMINAR
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DATE: Tuesday, April 17, 2012
 
SPEAKER: Sven Gnutzmann, The University of Nottingham, UK
 
TITLE: Topological resonances and nonlinear waves in metric graphs
 
PLACE: Room 814, Amado Mathematics Building, Technion
 
TIME: 14:30
 
ABSTRACT: We consider wave scattering from a complex system. Our
model is a metric graph with a nonlinear Schrodinger (NLS) operator
{a simple theoretical model either for a BEC in a quasi-1D trap with
non-trivial topology or for an optical fibre network. In the low
intensity limit the NLS operator becomes linear (a quantum graph).
For scattering with very low incoming intensities one may expect that
the nonlinearity is either irrelevant
or may be treated perturbatively. However, at resonances this
expectation often breaks down as the intensity inside the network may
be amplified by some orders of magnitude (constructive interference
on network cycles).
In certain networks narrow resonances with very high amplification
are far more frequent than in most other complex scattering models.
We identify the origin of these resonances which is of topological
nature and derive power
laws for the intensity amplification inside the network.
 
For further info: Yehuda Pinchover   <pincho@techunix.technion.ac.il> 
 
For past and future Applied Math/PDE seminars see:
 <http://www.math.technion.ac.il/pde/seminar.html>
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Yehuda Pinchover   <pincho@tx.technion.ac.il>