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Stoyan, D., Zhang, ZX. A stochastic model leading to various particle mass distributions including the RRSB distribution. Granular Matter 25, 67 (2023).

A stochastic model leading to various particle mass distributions including the RRSB distribution

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Author: Stoyan, Dietrich1; Zhang, Zong‑Xian2
Organizations: 1Institute for Stochastics, TU Bergakademie Freiberg, 09596 Freiberg, Germany
2Oulu Mining School, University of Oulu, 90570 Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 4 MB)
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Language: English
Published: Springer Nature, 2023
Publish Date: 2023-10-18


Modern particle size statistics uses many different statistical distributions, but these distributions are empirical approximations for theoretically unknown relationships. This also holds true for the famous RRSB (Rosin-Rammler-Sperling-Bennett) distribution. Based on the compound Poisson process, this paper introduces a simple stochastic model that leads to a general product form of particle mass distributions. The beauty of this product form is that its two factors characterize separately the two main components of samples of particles, namely, individual particle masses and total particle number. The RRSB distribution belongs to the class of distributions following the new model. Its simple product form can be a starting point for developing new particle mass distributions. The model is applied to the statistical analysis of samples of blast-produced fragments measured by hand, which enables a precise investigation of the mass-size relationship. This model-based analysis leads to plausible estimates of the mass and size factors and helps to understand the influence of blasting conditions on fragment-mass distributions.

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Series: Granular matter
ISSN: 1434-5021
ISSN-E: 1434-7636
ISSN-L: 1434-5021
Volume: 25
Issue: 4
Article number: 67
DOI: 10.1007/s10035-023-01359-2
Type of Publication: A1 Journal article – refereed
Field of Science: 216 Materials engineering
1171 Geosciences
Funding: Open Access funding provided by University of Oulu including Oulu University Hospital.
Copyright information: © The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit