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SUMMARY:Parameter-Dependent Nonlinear Eigenvalue Problems: Examples from Q
 uasicrystals and Mechanical Systems - Mark Embree (Virginia Tech)
DTSTART:20260413T104500Z
DTEND:20260413T114500Z
UID:TALK243976@talks.cam.ac.uk
DESCRIPTION:Nonlinear eigenvalue problems often depend on a physical param
 eter\, about which one seeks to optimize or analyze. &nbsp\;We will descri
 be concrete examples from several collaborations\, showing how such proble
 ms can emerge from the exact reduction of infinite-dimensional linear prob
 lems to finite-dimensional nonlinear ones. &nbsp\;Our first case is motiva
 ted by a continuum Fibonacci quasicrystal model\, where the parameter scal
 es the potential in a Schroedinger equation. &nbsp\;As second class of exa
 mples comes from mechanical systems\, where the parameter can reflect a ma
 terial property\, such as a damping coefficient. &nbsp\;Contour integral m
 ethods approximate eigenvalues within some specified bounded domain. &nbsp
 \;To generalize such methods to parametric problems\, we describe a parame
 tric extension of Keldysh's theorem (work with Balicki and Gugercin). The 
 resulting algorithm reduces the dimension of nonlinear eigenvalue problems
  while allowing changes to eigenvalue multiplicity as the parameter evolve
 s.
LOCATION:Seminar Room 1\, Newton Institute
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