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Entropy 2010, 12(1), 1-13; doi:10.3390/e12010001

Lorenz Curves, Size Classification, and Dimensions of Bubble Size Distributions

Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 12, D-14195 Berlin, Germany
Received: 13 October 2009 / Accepted: 11 December 2009 / Published: 25 December 2009
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Abstract

Lorenz curves of bubble size distributions and their Gini coefficients characterize demixing processes. Through a systematic size classification, bubble size histograms are generated and investigated concerning their statistical entropy. It turns out that the temporal development of the entropy is preserved although characteristics of the histograms like number of size classes and modality are remarkably reduced. Examinations by Rényi dimensions show that the bubble size distributions are multifractal and provide information about the underlying structures like self-similarity.
Keywords: Lorenz curve; Gini coefficient; bin width selection; Rényi dimensions; bubble size distributions Lorenz curve; Gini coefficient; bin width selection; Rényi dimensions; bubble size distributions
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Sauerbrei, S. Lorenz Curves, Size Classification, and Dimensions of Bubble Size Distributions. Entropy 2010, 12, 1-13.

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