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Wednesday, July 10 • 10:30 - 10:50
GAUGE INVARIANCE APPROACH TO NONLINEAR ACOUSTICS IN CURVILINEAR SPACETIME

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Curvilinear spacetime is a more accurate treatment of nonlinear acoustics as the high intensity acoustic fields has a curved path. A wellknown illustration is that the general theory of relativity is developed based on curvilinear spacetime. This is because of the curved path of the gravitational force field and Albert Einstein used this approach to obtain a more accurate calculation of the gravitational force. Some popular topics of nonlinear acoustics are acoustic radiation force, multiple scattering, interaction, and acoustic levitation. The curvilinear spacetime treatment will include gravitational force. As an illustration one will choose the relativistic Euler equation which was derived in a previous paper. This is an extension of my previous paper using the gauge invariance approach to nonlinear acoustics on curvilinear spacetime. The purpose is to obtain the solution of the relativistic Euler equation using the gauge invariance approach. The first step is to replace the time derivative in the Euler equation by the covariant derivative to take account of the local gauge invariance. An alternative approach is to use the Lagrangian approach and the variational formulation as what was done by T Kambe. Here one extends his treatment to the curvilinear spacetime. The Galilean translational symmetry of the local gauge invariance has to be replaced by the covariance. A new covariant derivative has to be used.

Moderators
GP

Giorgio Palma

Ing., Università Roma Tre

Authors

Wednesday July 10, 2019 10:30 - 10:50 EDT
Westmount 1

Attendees (7)