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SUMMARY:Snakes and Ladders: localized states in the Swift-Hohenberg equati
 on - John Burke (Boston)
DTSTART:20080704T150000Z
DTEND:20080704T160000Z
UID:TALK12752@talks.cam.ac.uk
CONTACT:Dr Jonathan Dawes
DESCRIPTION:Stable spatially localized structures occur in many systems of
  physical interest.  Examples can be found in the fields of optics\, chemi
 stry\, fluid mechanics\, and neuroscience to name a few.  The models used 
 to describe\nthese systems have much in common.  They are typically of at 
 least fourth order in spatial derivatives\, invariant under spatial transl
 ations and reflections\, and exhibit bistability between two spatially ext
 ended solutions.\n\nIn this talk I will focus on one particular model\, th
 e Swift-Hohenberg equation\, which arises in many of the applications list
 ed above.  This equation contains a remarkable wealth of localized states\
 , organized in a 'snakes-and-ladders' structure\; a large number of these 
 localized states are simultaneously stable.  The talk will include an over
 view of the results for this model in both one and two spatial dimensions.
   The goal is to present a physical understanding of the mathematical and 
 numerical results.\n\nDespite the simple model used in this analysis there
  is evidence that the localized states observed in some experiments are or
 ganized in similar structures. Results will be presented for the example o
 f natural doubly diffusive convection.
LOCATION:MR2\, Centre for Mathematical Sciences
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