Analysis of Proportional Scopes on Probability Density Functions of Random Chords of Spherical Particles
DOI:
https://doi.org/10.24425/afe.2021.138680Abstract
The paper presents an experimental confirmation of the fact that if a three-dimensional volume does not contain spherical particles with particular size, the Probability Density Function (PDF1) of half-chord lengths has proportional ranges. This fact has been deduced in work [1] during the derivation process of the Probability Density Function (PDF3) that maps the particle radii on the basis of data (PDF1) collected from flat cross-sections. The experiment has been executed virtually by using a simple computer program written in the C++11 language. The computer generation of particles allowed imposing various kinds of known PDF3 and the ranges in which the particles could not be created. Next, the virtual nodules have been used to produce sets of chords that served as input data to create histograms that approximated the continuous PDF1. Having such histograms, it was possible to reveal proportional scopes of the PDF1. The proportional dependencies occurred in the same ranges where the nodules had not been generated.References
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