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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Weakly nonlinear geometric optics for the Westerve
lt equation and recovery of the nonlinearity - Pla
men Stefanov (Purdue University)
DTSTART;TZID=Europe/London:20230518T113000
DTEND;TZID=Europe/London:20230518T123000
UID:TALK198127AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198127
DESCRIPTION:We study the Westervelt equation modeling nonlinea
r acoustic wave propagation. In case there is no d
iffusion\, we show that the physical nonlinear eff
ects\, predicted and observed\, appear in the so-c
alled weakly nonlinear regime: when the amplitude
is of the same order as the wavelength. Then the l
eading transport/profile equation is of Burgers ty
pe and the tilt of the wave recovers uniquely the
X-ray transform of the nonlinearity along the way\
, hence the nonlinearity itself. In the diffusive
case\, we suggest an asymptotic regime which is in
line with what is expected and known in acoustics
. That part is work in progress.\nUltrasound imagi
ng is already in the nonlinear regime\, creating a
rtifacts if the model is linear. On the other hard
\, the nonlinearity creates higher order harmonics
used by the engineers to increase the resolution
and reduce strong backscattering signals. The math
ematical analysis of the implications for ultrasou
nd imaging howver is left for future works.\nThe t
alk is based in a joint work with Nikolas Eptamini
takis.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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