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BEGIN:VEVENT
UID:c46f7b6297d00fdc0c1ddde9c227b26f
CATEGORIES:Colloquia
CREATED:20240227T091514
SUMMARY:Some unconventional PDE problems from photonics
LOCATION:Hill 705
DESCRIPTION:<p><span style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (Wes
 t European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helve
 tica Neue', sans-serif; font-size: 14.6667px; font-style: normal; font-weig
 ht: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent:
  0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: norm
 al; background-color: #ffffff; float: none;">Speaker: Robert Kohn (Courant 
 Institute)</span><br aria-hidden="true" style="color: #242424; font-family:
  'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, Bli
 nkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6667px
 ; font-style: normal; font-weight: 400; letter-spacing: normal; orphans: 2;
  text-align: left; text-indent: 0px; text-transform: none; widows: 2; word-
 spacing: 0px; white-space: normal; background-color: #ffffff;"><br aria-hid
 den="true" style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (W
 est European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Hel
 vetica Neue', sans-serif; font-size: 14.6667px; font-style: normal; font-we
 ight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-inden
 t: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: no
 rmal; background-color: #ffffff;"><span style="color: #242424; font-family:
  'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, Bli
 nkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6667px
 ; font-style: normal; font-weight: 400; letter-spacing: normal; orphans: 2;
  text-align: left; text-indent: 0px; text-transform: none; widows: 2; word-
 spacing: 0px; white-space: normal; background-color: #ffffff; float: none;"
 >Title: Some unconventional PDE problems from photonics</span><br aria-hidd
 en="true" style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (We
 st European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helv
 etica Neue', sans-serif; font-size: 14.6667px; font-style: normal; font-wei
 ght: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent
 : 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: nor
 mal; background-color: #ffffff;"><br aria-hidden="true" style="color: #2424
 24; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -a
 pple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font
 -size: 14.6667px; font-style: normal; font-weight: 400; letter-spacing: nor
 mal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; 
 widows: 2; word-spacing: 0px; white-space: normal; background-color: #fffff
 f;"><span style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (We
 st European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helv
 etica Neue', sans-serif; font-size: 14.6667px; font-style: normal; font-wei
 ght: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent
 : 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: nor
 mal; background-color: #ffffff; float: none;">Abstract: Electromagnetic wav
 es are described by Maxwell's equations.&nbsp;</span><span style="color: #2
 42424; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI',
  -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; f
 ont-size: 14.6667px; font-style: normal; font-weight: 400; letter-spacing: 
 normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: non
 e; widows: 2; word-spacing: 0px; white-space: normal; background-color: #ff
 ffff; float: none;">For transverse-magnetic waves in a time-harmonic settin
 g, the Maxwell&nbsp;</span><span style="color: #242424; font-family: 'Segoe
  UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSy
 stemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6667px; font-
 style: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-a
 lign: left; text-indent: 0px; text-transform: none; widows: 2; word-spacing
 : 0px; white-space: normal; background-color: #ffffff; float: none;">system
  reduces to a simple-looking divergence-form Helmholtz equation:&nbsp;</spa
 n><span style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West
  European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvet
 ica Neue', sans-serif; font-size: 14.6667px; font-style: normal; font-weigh
 t: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 
 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: norma
 l; background-color: #ffffff; float: none;">div( a(x,omega) grad u) + omega
 ^2 m(x, omega) u = 0. Here u is scalar&nbsp;</span><span style="color: #242
 424; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -
 apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; fon
 t-size: 14.6667px; font-style: normal; font-weight: 400; letter-spacing: no
 rmal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none;
  widows: 2; word-spacing: 0px; white-space: normal; background-color: #ffff
 ff; float: none;">valued, omega is the frequency, and the coefficients a(x,
 omega) and&nbsp;</span><span style="color: #242424; font-family: 'Segoe UI'
 , 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSystem
 Font, Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6667px; font-styl
 e: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align
 : left; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0p
 x; white-space: normal; background-color: #ffffff; float: none;">m(x,omega)
  represent the material properties of the medium --&nbsp;</span><span style
 ="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 
 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sa
 ns-serif; font-size: 14.6667px; font-style: normal; font-weight: 400; lette
 r-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-tra
 nsform: none; widows: 2; word-spacing: 0px; white-space: normal; background
 -color: #ffffff; float: none;">specifically, a(x,omega) is 1/(dielectric pe
 rmittivity) and m(x,omega)&nbsp;</span><span style="color: #242424; font-fa
 mily: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system
 , BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6
 667px; font-style: normal; font-weight: 400; letter-spacing: normal; orphan
 s: 2; text-align: left; text-indent: 0px; text-transform: none; widows: 2; 
 word-spacing: 0px; white-space: normal; background-color: #ffffff; float: n
 one;">is the magnetic permeability. One might think that we have, by now, a
 &nbsp;</span><span style="color: #242424; font-family: 'Segoe UI', 'Segoe U
 I Web (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Robo
 to, 'Helvetica Neue', sans-serif; font-size: 14.6667px; font-style: normal;
  font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; te
 xt-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-s
 pace: normal; background-color: #ffffff; float: none;">full understanding o
 f the mathematical issues raised by this equation --&nbsp;</span><span styl
 e="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West European)',
  'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', s
 ans-serif; font-size: 14.6667px; font-style: normal; font-weight: 400; lett
 er-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-tr
 ansform: none; widows: 2; word-spacing: 0px; white-space: normal; backgroun
 d-color: #ffffff; float: none;">but in fact it isn't so. Indeed, due to the
  frequency-dependence of the&nbsp;</span><span style="color: #242424; font-
 family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-syst
 em, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 14
 .6667px; font-style: normal; font-weight: 400; letter-spacing: normal; orph
 ans: 2; text-align: left; text-indent: 0px; text-transform: none; widows: 2
 ; word-spacing: 0px; white-space: normal; background-color: #ffffff; float:
  none;">permittivity, there are materials for which the dielectric permitti
 vity&nbsp;</span><span style="color: #242424; font-family: 'Segoe UI', 'Seg
 oe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, 
 Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6667px; font-style: nor
 mal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left
 ; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; whi
 te-space: normal; background-color: #ffffff; float: none;">is near zero or 
 even negative at frequencies of practical interest. The&nbsp;</span><span s
 tyle="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West European
 )', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue'
 , sans-serif; font-size: 14.6667px; font-style: normal; font-weight: 400; l
 etter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text
 -transform: none; widows: 2; word-spacing: 0px; white-space: normal; backgr
 ound-color: #ffffff; float: none;">analysis of devices made by combining su
 ch materials with ``ordinary''&nbsp;</span><span style="color: #242424; fon
 t-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-sy
 stem, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 
 14.6667px; font-style: normal; font-weight: 400; letter-spacing: normal; or
 phans: 2; text-align: left; text-indent: 0px; text-transform: none; widows:
  2; word-spacing: 0px; white-space: normal; background-color: #ffffff; floa
 t: none;">dielectrics (for which the permittivity is positive) raises numer
 ous PDE&nbsp;</span><span style="color: #242424; font-family: 'Segoe UI', '
 Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFon
 t, Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6667px; font-style: 
 normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: l
 eft; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; 
 white-space: normal; background-color: #ffffff; float: none;">issues that a
 re still not well understood.</span></p>
CONTACT:Robert Kohn (Courant Institute)
DTSTAMP:20260828T122121
DTSTART;TZID=America/New_York:20240306T153000
DTEND;TZID=America/New_York:20240306T163000
SEQUENCE:0
TRANSP:OPAQUE
END:VEVENT
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