Microwave resonator for non-invasive evaluationofdegradation processes in liquid composites

Optimization approach for the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions from limited observations

“…We reformulate our inverse problem as an optimization problem, where we seek for two functions, the permittivity ε(x) and permeability µ(x), which result in a solution of equations (14) with best fit to time and space domain observations Ẽ, measured at a finite number of observation points on ∂ 1 Ω. Our goal is to minimize the Tikhonov functional…”

“…We consider the following test cases for the generation of the backscattering data: To generate backscattering data at the observation points at S T in each cases i)-iv), we solve the forward problem (14), with function f (t) given by (27) in the time interval t = [0, 1.2] with the exact values of the parameters ε(x) = 12.0, µ(x) = 2 inside scatterers of figure 2, and ε(x) = µ(x) = 1.0 everywhere else in Ω. We avoid the variational crime in our tests since the data were generated on a locally refined mesh where inclusions were presented.…”

“…The isosurfaces of the simulated exact solution of the initialized component E 2 (x, t) of the electrical field E(x, t) in the forward problem (14) with ω = 30 at different times are presented in figure 3. Using this figure we observe the backscattering wave field of the component E 2 (x, t).…”

“…Potential applications of our algorithm are in reconstructing the electromagnetic parameters in nanocomposites or artificial materials [45,47,48], imaging of defects and their sizes in a non-destructive testing of materials and in photonic crystals [15], measurement of the moisture content [14] and drying processes [38], for example.…”

Determination of the permittivity and permeability for waveguides partially loaded with isotropic samples

“…The determination of the values of the complex relative permittivity (ε r = ε r − jε r ) and complex relative permeability (µ r = µ r − jµ r ) of a material at microwave frequencies is a problem that has important applications in the industrial and scientific world, such as measurement of the moisture content [1], measurement of the dielectric and magnetic properties of the absorbing materials [2] and drying processes [3].…”