Energy efficiency of consecutive fragmentation processes

Abstract

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 Martínez (2005), we compute the average energy required to attain a size η 0 with this two-device procedure. We then asymptotically compare, as η 0 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.

Asymptotic properties of the process counted with a random characteristic in the context of fragmentation processes

“…As a motivation for the main result of this paper let us now discuss two special random characteristics for which Theorem 1 is applicable. In the spirit of [BM05] this section is concerned with the energy that is needed to crush block in the mining industry, a theme that was taken up also in [FKM10]. Moreover, we derive some asymptotic properties of the empirical mean associated with the stopped fragmentation process that we defined in Section 2.…”

Limit theorems for fragmentation processes with immigration

“…Convergence results for the process counted with this particular characteristic were obtained in [BM05] as well as [Kno12]. In this regard we also refer to [FKM10].…”