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Andere Primärenergiequellen
(1974)
In most beers, producers strive to minimize haze to maximize visual appeal. To detect the formation of particulates, a measurement system for sub-micron particles is required. Beer haze is naturally occurring, composed of protein or polyphenol particles; in their early stage of growth their size is smaller than 2 µm. Microscopy analysis is time and resource intensive; alternatively, backscattering is an inexpensive option for detecting particle sizes of interest.
In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work.