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SUMMARY:Eulerian dispersive shock waves and instabilities - Mark Hoefer (N
 orth Carolina State)
DTSTART:20121012T150000Z
DTEND:20121012T160000Z
UID:TALK39730@talks.cam.ac.uk
CONTACT:Dr Ed Brambley
DESCRIPTION:Recent experimental and theoretical research in Bose-Einstein 
 condensation and nonlinear optics have demonstrated novel supersonic\, flu
 id-like phenomena.  Shock waves in these and other systems are modeled by 
 a dispersive regularization of Euler's equations\, implemented by use of t
 he Whitham averaging technique.  Normal and oblique dispersive shock waves
  (DSWs) connecting two constant states are constructed.  Numerical computa
 tions of supersonic\, dispersive flow over a corner in the special case of
  systems modeled by the Nonlinear Schrodinger equation (NLS) exhibit stabl
 e pattern formation (oblique DSWs) or instability (turbulent-like behavior
 ) depending on the flow parameters.  A combination of analytical and compu
 tational approaches are used to demonstrate that this change in behavior c
 an be identified with the transition from convective to absolute instabili
 ty of dark solitons.  The linearized NLS behavior about the dark soliton D
 SW trailing edge is studied in detail to identify the separatrix between c
 onvective and absolute instabilities.
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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