Fragmentation energy. (English) Zbl 1080.60080

Bertoin, Jean; Martínez, Servet

Adv. Appl. Probab. 37, No. 2, 553-570 (2005).

In mining the particles obtained by blasting are mechanically reduced in size by a combination of methods. Operating the machinery requires energy and that generates costs. The energy problem is investigated by modelling the fragmentation chain as a Crump-Mode-Jagers branching process in which time corresponds to the logarithm of the fragment size. Applying results of O. Nerman [Z. Wahrscheinlichkeitstheorie Verw. Geb. 57, 365–395 (1981; Zbl 0451.60078)] leads to limits for the distribution of sizes less than \(\eta\), say, and estimates for the energy \(E(\eta)\) required. In fact, \(E(\eta)\sim c\eta^{\beta-\alpha}\), where \(\alpha\) is the Malthusian parameter and \(\beta<\alpha\). The idea of modelling the fragmentation chain by a stochastic branching process dates back to A. N. Kolmogorov and B. A. Sevast’yanov [Dokl. Akad. Nauk SSSR, N. Ser. 56, 783–786 (1947; Zbl 0041.45502)].

Reviewer: Heinrich Hering (Rockenberg)

MSC:

60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60F15	Strong limit theorems

Keywords:

branching process

Citations:

Zbl 0451.60078; Zbl 0041.45502

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