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On the Information Content of Coarse Data with Respect to the Particle Size Distribution of Complex Granular Media: Rationale Approach and Testing

1
Department of Applied Mathematics, Universidad Politécnica de Madrid, 28040 Madrid, Spain
2
USDA-ARS Environmental Microbial and Food Safety Laboratory, Beltsville, MD 20705, USA
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(6), 601; https://doi.org/10.3390/e21060601
Received: 3 June 2019 / Revised: 15 June 2019 / Accepted: 17 June 2019 / Published: 17 June 2019
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Abstract

The particle size distribution (PSD) of complex granular media is seen as a mathematical measure supported in the interval of grain sizes. A physical property characterizing granular products used in the Andreasen and Andersen model of 1930 is re-interpreted in Information Entropy terms leading to a differential information equation as a conceptual approach for the PSD. Under this approach, measured data which give a coarse description of the distribution may be seen as initial conditions for the proposed equation. A solution of the equation agrees with a selfsimilar measure directly postulated as a PSD model by Martín and Taguas almost 80 years later, thus both models appear to be linked. A variant of this last model, together with detailed soil PSD data of 70 soils are used to study the information content of limited experimental data formed by triplets and its ability in the PSD reconstruction. Results indicate that the information contained in certain soil triplets is sufficient to rebuild the whole PSD: for each soil sample tested there is always at least a triplet that contains enough information to simulate the whole distribution. View Full-Text
Keywords: information entropy; particle size distribution; selfsimilar measure; simulation information entropy; particle size distribution; selfsimilar measure; simulation
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García-Gutiérrez, C.; Martín, M.Á.; Pachepsky, Y. On the Information Content of Coarse Data with Respect to the Particle Size Distribution of Complex Granular Media: Rationale Approach and Testing. Entropy 2019, 21, 601.

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