Source: J. Appl. Probab. Volume 47, Number 2
(2010), 543-561.
Motivated by a problem arising in the mining industry, we present a first study
of the energy required to reduce a unit mass fragment by consecutively using
several devices. Two devices are considered, which we represent as different
stochastic fragmentation processes. Following the self-similar energy model
introduced in Bertoin and Martí nez (2005), we compute the average
energy required to attain a size η0 with this two-device
procedure. We then asymptotically compare, as η0 goes to 0 or
1, its energy requirement with that of individual fragmentation processes. In
particular, we show that, for a certain range of parameters of the
fragmentation processes and of their energy cost functions, the consecutive use
of two devices can be asymptotically more efficient than using each of them
separately, or vice versa.
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