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SUMMARY:Ray tracing approximations to the acoustic propagation in weakly n
 onlinear regime with applications in HIFU - Matt Foster (University Colleg
 e London)
DTSTART:20230330T110000Z
DTEND:20230330T113000Z
UID:TALK198265@talks.cam.ac.uk
DESCRIPTION:High Intensity Focused Ultrasound (HIFU) is a therapy that use
 s ultrasound waves to non-invasively destroy malignant cells inside the hu
 man body. The technique works by sending a high-energy beam of ultrasound 
 into the tissue using a focused transducer. Numerically modelling HIFU pre
 sents a problem due to nonlinear effects leading to the formation of harmo
 nics of the source frequency. Each harmonic requires a finer grid to resol
 ve\, rapidly increasing computational complexity.&nbsp\;\nI will present t
 he derivation and benefits of two ray tracing methods using weakly nonline
 ar ray theory formed by different asymptotic expansions of the governing a
 coustic equations. The first has the same ray equations as the linear case
  while the transport equation is a nonlinear transformation of the Burgers
 &rsquo\; equation. The final method has its Eikonal equation coupled with 
 the transport equation producing ray trajectories which depend on the ampl
 itude.\nThis is work done in collaboration with Marta Betcke (UCL)\, Ben C
 ox (UCL)\, Bradley Treeby (UCL)
LOCATION:Seminar Room 1\, Newton Institute
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