General Transmission Problems in the Theory of Elastic Oscillations of Anisotropic Bodies (Basic Interface Problems)

Here we discuss three-dimensional so-called basic and mixed boundary value problems (BVP) for steady state oscillations of piecewise homogeneous anisotropic bodies imbedded into an infinite elastic continuum. Uniqueness is shown with the help of generalized Sommerfeld–Kupradze radiation conditions, while existence follows for arbitrary values of the oscillation parameter by the reduction of the original interface transmission BVPs to equivalent uniquely solvable boundary integral or pseudodifferential equations on the interfaces. For the basic BVPs, we show classical regularity and, in addition for the mixed BVPs that the solutions are Hölder continuous with exponent α ∈ (0, 1/2) in the neighbourhood of the curves of discontinuity of the boundary and transmission conditions.     

Characterization of Particulate Mixtures by In-Line Measurments

The quality of particulate mixtures influences strongly the efficiency of downstream process steps. The design or optimization of mixing processes requires fast and accurate methods for determining mixture quality. This paper describes an optical method for the in-line concentration measurement of the key (tracer) component in particulate mixtures with fiber optical probes. Small fluctuations of tracer concentration equivalent to a low concentration variance represent a high degree of mixing. Monochromatic light penetrates via fiber optical probes into a powder sample. A photometer measures the intensity of the diffuse reflected light. If the tracer differs in colour from the other components of the mixture its concentration can be determined. Three types of fiber optical probes were tested. For calibration two series of mixed samples covering a broad concentration range were prepared, one consisting of white Al(OH)₃ and dark SiC and the other of Al(OH)₃ and a much finer green pigment. The calibration graphs are described by the Kubelka-Munk theory. The influence of changes in particle size on the signals is reduced by choosing a probe with an angled arrangement of the fibers. The sample mass of the probes is estimated to ca. 0.01 g, based on comparison with random mixtures at different tracer concentrations. In-line measurements provide extensive data sets which allow advanced statistical intepretations of mixing processes.