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UID:3c50cfb9b8e1be6eb259b9ba5f9c1e57
CATEGORIES:Applied and Computational Math Seminar
CREATED:20251104T234039
SUMMARY:Scattering of waves.
LOCATION:Hill 525
DESCRIPTION:We study the scattering of waves from a planar inclusion with constant refr
 active index, governed by the Helmholtz equation. It is well understood tha
 t singular inclusions—those whose boundary has a singular point—generically
  scatter every incident wave. Far less is known about the scattering behavi
 or of regular inclusions. We consider a large class of regular inclusions a
 nd show that they generically scatter any (complex-analytic) incident wave.
  Focusing on incident plane waves, we prove that they always scatter from a
 ny regular inclusion whose refractive index is less than one. For inclusion
 s with refractive index greater than one, under an additional convexity ass
 umption, we obtain explicit wavenumber intervals in which scattering occurs
 . These intervals drift to infinity and expand, and are given by explicit f
 ormulas in terms of the geometry (directional widths) of the inclusion. If 
 the inclusion is elongated (its maximal width is at least twice its minimal
  width), the union of these intervals covers the entire spectrum, and hence
  such inclusions scatter every incident plane wave. Our approach makes use 
 of a connection between this scattering problem and the Schiffer/Pompeiu pr
 oblem. This is based on a joint work with Michael Vogelius.
X-ALT-DESC;FMTTYPE=text/html:<div data-olk-copy-source="MailCompose" style="text-align: left; text-inden
 t: 0px; line-height: 1.1; background-color: white; margin: 0px; font-family
 : Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-
 serif; font-size: 12pt; color: #242424;">We study the scattering of waves f
 rom a planar inclusion with constant refractive index, governed by the Helm
 holtz equation. It is well understood that singular inclusions—those whose 
 boundary has a singular point—generically scatter every incident wave. Far 
 less is known about the scattering behavior of regular inclusions. We consi
 der a large class of regular inclusions and show that they generically scat
 ter any (complex-analytic) incident wave. Focusing on incident plane waves,
  we prove that they always scatter from any regular inclusion whose refract
 ive index is less than one. For inclusions with refractive index greater th
 an one, under an additional convexity assumption, we obtain explicit wavenu
 mber intervals in which scattering occurs. These intervals drift to infinit
 y and expand, and are given by explicit formulas in terms of the geometry (
 directional widths) of the inclusion. If the inclusion is elongated (its ma
 ximal width is at least twice its minimal width), the union of these interv
 als covers the entire spectrum, and hence such inclusions scatter every inc
 ident plane wave. Our approach makes use of a connection between this scatt
 ering problem and the Schiffer/Pompeiu problem.</div><div style="text-align
 : left; text-indent: 0px; line-height: 1.1; background-color: white; margin
 : 0px; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri
 , Helvetica, sans-serif; font-size: 12pt; color: #242424;">&nbsp;</div><div
  style="text-align: left; text-indent: 0px; line-height: 1.1; background-co
 lor: white; margin: 0px; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFo
 ntService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: #242424;
 ">This is based on a joint work with Michael Vogelius.</div>
CONTACT:Narek Hovsepyan (Rutgers)
DTSTAMP:20260827T204607
DTSTART;TZID=America/New_York:20251111T110000
DTEND;TZID=America/New_York:20251111T120000
SEQUENCE:0
TRANSP:OPAQUE
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