## Fragmentation energy.(English)Zbl 1080.60080

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)].

### MSC:

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

### Keywords:

branching process

### Citations:

Zbl 0451.60078; Zbl 0041.45502
Full Text:

### References:

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