Mathematical Models of Smart Obstacles
UNIVERSITA DI ROMA LA SAPIENZA ROMA (ITALY) DIPARTIMENTO DI MATEMATICA
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We propose mathematical models to describe the behaviour of smart obstacles. In the context of acoustic scattering a smart obstacle in an obstacle that when hit by an incoming acoustic wave reacts circulating on its boundary a pressure current to pursue a given goal. A pressure current is a quantity whose physical dimension is pressure divided by time. The goals considered are 1 to be undetectable, 2 to appear with a shape and an acoustic boundary impedance different from its actual ones, 3 to appear in a location in space different from its actual one eventually with a shape and an acoustic boundary impedance different from its actual ones. The mathematical models proposed for the smart obstacles are optimal control problem for the wave equation. These optimal control problems are studied analytically and solved quantitatively using ad hoc numerical methods.
- Operations Research