Abstract— Direct and inverse acoustic scattering problems involving smart obstacles are proposed and some ideas to study them are suggested. A smart obstacle is an obstacle that when hit by an incoming acoustic wave reacts circulating on its boundary a pressure current, that is a quantity dimensionally given by a pressure divided by a time, in order to generate a scattered wave that pursues a preassigned goal. In our models (see [6–10,12]) the smart obstacle pursues one of the following goals: i) to be undetectable, ii) to appear with a shape and/or acoustic boundary impedance diﬀerent from its actual ones, iii) to appear with a shape and/or acoustic boundary impedance and in a location in space diﬀerent from its actual ones. That is, in the ﬁrst case the smart obstacle tries to be furtive, in the second case it tries to be masked that is it tries to appear as another obstacle that we call the mask and ﬁnally in the third case it tries to appear as another obstacle in a location in space diﬀerent from its actual one. We refer to this last apparent obstacle as the ghost. The direct scattering problem considered is the following: given the incoming acoustic ﬁeld, the obstacle, its acoustic impedance and its goal formulate an adequate mathematical model for the problems previously considered and ﬁnd the optimal strategy to pursue the assigned goal within the proposed model. The inverse scattering problem considered is the following: given the knowledge of several far ﬁelds generated by the smart obstacle when hit by known incident acoustic ﬁelds it reacts with the optimal strategy and the knowledge of the goal pursued by the obstacle ﬁnd the obstacle (i. e. ﬁnd the shape, acoustic impedance and spatial location of the obstacle). For simplicity in this paper we limit our attention to the case of the obstacle that tries to be masked when the incoming acoustic ﬁeld is time harmonic. Moreover in the inverse problem we assume that the acoustic boundary impedance of the obstacle and of the mask are known. In this case the direct scattering problem is translated in a constrained optimization problem and its solution is characterized as the solution of a set of auxiliary equations. The inverse scattering problem is translated in a two steps optimization procedure. Finally in a test case the inverse problem is solved numerically.

Titolo: | DIRECT AND INVERSE ACOUSTIC SCATTERING PROBLEMS INVOLVING SMART OBSTACLES , IN JOURNAL OF INVERSE AND ILL-POSED PROBLEMS |

Autori: | |

Data di pubblicazione: | 2005 |

Rivista: | |

Abstract: | Abstract— Direct and inverse acoustic scattering problems involving smart obstacles are proposed and some ideas to study them are suggested. A smart obstacle is an obstacle that when hit by an incoming acoustic wave reacts circulating on its boundary a pressure current, that is a quantity dimensionally given by a pressure divided by a time, in order to generate a scattered wave that pursues a preassigned goal. In our models (see [6–10,12]) the smart obstacle pursues one of the following goals: i) to be undetectable, ii) to appear with a shape and/or acoustic boundary impedance diﬀerent from its actual ones, iii) to appear with a shape and/or acoustic boundary impedance and in a location in space diﬀerent from its actual ones. That is, in the ﬁrst case the smart obstacle tries to be furtive, in the second case it tries to be masked that is it tries to appear as another obstacle that we call the mask and ﬁnally in the third case it tries to appear as another obstacle in a location in space diﬀerent from its actual one. We refer to this last apparent obstacle as the ghost. The direct scattering problem considered is the following: given the incoming acoustic ﬁeld, the obstacle, its acoustic impedance and its goal formulate an adequate mathematical model for the problems previously considered and ﬁnd the optimal strategy to pursue the assigned goal within the proposed model. The inverse scattering problem considered is the following: given the knowledge of several far ﬁelds generated by the smart obstacle when hit by known incident acoustic ﬁelds it reacts with the optimal strategy and the knowledge of the goal pursued by the obstacle ﬁnd the obstacle (i. e. ﬁnd the shape, acoustic impedance and spatial location of the obstacle). For simplicity in this paper we limit our attention to the case of the obstacle that tries to be masked when the incoming acoustic ﬁeld is time harmonic. Moreover in the inverse problem we assume that the acoustic boundary impedance of the obstacle and of the mask are known. In this case the direct scattering problem is translated in a constrained optimization problem and its solution is characterized as the solution of a set of auxiliary equations. The inverse scattering problem is translated in a two steps optimization procedure. Finally in a test case the inverse problem is solved numerically. |

Handle: | http://hdl.handle.net/11566/30486 |

Appare nelle tipologie: | 1.1 Articolo in rivista |