2008/05/07 by Filippo Visco Comandini, Mazyar Mirrahimi, Comandini, Filippo Visco +3
Engineering · Physics and Astronomy · #15A29 #47A40 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Microwave Imaging and Scattering Analysis #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.0805.0936
openalex publication_date 2008/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The study of the scattering data for a star-shape network of LC-transmission lines is transformed into the scattering analysis of a Schrödinger operator on the same graph. The boundary conditions coming from the Kirchhoff rules ensure the existence of a unique self-adjoint extension of the mentioned Schrödinger operator. While the graph consists of a number of infinite branches and a number finite ones, all joining at a central node, we provide a construction of the scattering solutions. Under non-degenerate circumstances (different wave travelling times for finite branches), we show that the study of the reflection coefficient in the high-frequency regime must provide us with the number of the infinite branches as well as the the wave travelling times for finite ones.