17 августа 2010 г. (вторник), 16:00, ауд. 307.
Е.Лакштанов, Б.Р.Вайнберг,
High Frequency Scattering by a Classically Invisible Body
We consider a polyhedron with zero classical resistance, i.e., a polyhedron invisible for an observer which rely only on geometrical optical rays. The corresponding wave problem (scattering of the plane wave by the polyhedron) is studied. The quasiclassic approximation is obtained and justified in the case of impedance boundary conditions with a non zero absorbing part. We show that the total momentum transmitted to the obstacle vanishes when the frequency goes to infinity, and that the total cross section oscillates at high frequencies. When impedance $lambda$ is real (there is no absorption), it is shown that there exists an increasing sequence of frequencies ${k_n}$ such that the average of the total cross section over interval $(lambda-varepsilon_n, lambda+varepsilon_n),~varepsilon_n ightarrow0,$ goes to zero.
| 14.08.2010 | Петров Леонид Александрович |