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SUMMARY:Weakly nonlinear geometric optics for the Westervelt equation and 
 recovery of the nonlinearity - Plamen Stefanov (Purdue University)
DTSTART:20230518T103000Z
DTEND:20230518T113000Z
UID:TALK198127@talks.cam.ac.uk
DESCRIPTION:We study the Westervelt equation modeling nonlinear acoustic w
 ave propagation. In case there is no diffusion\, we show that the physical
  nonlinear effects\, predicted and observed\, appear in the so-called weak
 ly nonlinear regime: when the amplitude is of the same order as the wavele
 ngth. Then the leading transport/profile equation is of Burgers type and t
 he tilt of the wave recovers uniquely the X-ray transform of the nonlinear
 ity along the way\, hence the nonlinearity itself. In the diffusive case\,
  we suggest an asymptotic regime which is in line with what is expected an
 d known in acoustics. That part is work in progress.\nUltrasound imaging i
 s already in the nonlinear regime\, creating artifacts if the model is lin
 ear. On the other hard\, the nonlinearity creates higher order harmonics u
 sed by the engineers to increase the resolution and reduce strong backscat
 tering signals. The mathematical analysis of the implications for ultrasou
 nd imaging howver is left for future works.\nThe talk is based in a joint 
 work with Nikolas Eptaminitakis.
LOCATION:Seminar Room 1\, Newton Institute
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