Article

# Inverse problems for Schrödinger equations with Yang–Mills potentials in domains with obstacles and the Aharonov–Bohm effect

Journal of Physics Conference Series 04/2005; 12(1). DOI: 10.1088/1742-6596/12/1/003

Source: arXiv

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**ABSTRACT:**We study numerical methods of tomography in domains with a reflecting obstacle. It will be shown that tomography with sets containing both broken rays, i.e. rays reflecting at the obstacle, as well as unbroken rays, has a smaller error between the original and reconstructed image compared to classical tomography methods.07/2011; - [Show abstract] [Hide abstract]

**ABSTRACT:**This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with ubroken rays and for specular reflection. Our numerical method using Lambertian reflection improves the solution's accuracy by an order of magnitude compared to classical tomography with ubroken rays and for tomography in the presence of a specularly reflecting obstacle the numerical method improves the solution's accuracy approximately by a factor of three times. We present efficient new algorithms for the solution's software implementation and analyze the solution's performance and effectiveness.Journal of Physics Conference Series 02/2013; 410(1):2170-. - [Show abstract] [Hide abstract]

**ABSTRACT:**We present a new approach to the unique determination of the coefficients of the second order hyperbolic equations modulo diffeomorphisms and gauge transformations, assuming that the time-dependent Dirichlet-to-Neumann operator is given on a part of the boundary. We consider also the case of multi-connected domains with obstacles. The interest in this case is spurred by the Aharonov-Bohm effect.12/2007: pages 107-116;

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