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This paper presents a review and analysis of the research that has been carried out on dynamic calibration for optical-fiber solids concentration probes. An introduction to the optical-fiber solids concentration probe was given. Different calibration methods of optical-fiber solids concentration probes reported in the literature were reviewed. In addition, a reflection-type optical-fiber solids concentration probe was uniquely calibrated at nearly full range of the solids concentration from 0 to packed bed concentration. The effects of particle properties (particle size, sphericity and color) on the calibration results were comprehensively investigated. The results show that the output voltage has a tendency to increase with the decreasing particle size, and the effect of particle color on calibration result is more predominant than that of sphericity.

We revisit the superadditivity conjecture for skew information which has recently been disproved by Hansen (2007 J. Stat. Phys. 126 643). We establish two weak forms of superadditivity which are conjectured to be optimal. Our results show that in a certain sense the superadditivity is true with ‘50% off’.