Energy efficiency of consecutive fragmentation processes

Joaquin Fontbona (1) , Nathalie Krell (2) , Servet Martinez (1)

1 Departamento de Ingenieria Matematica, Centro Modelamiento Matematico
2 IRMAR - Institut de Recherche Mathématique de Rennes

We present a first study on the energy required to reduce a unit mass fragment by consecutively using several devices, as it happens in the mining industry. Two devices are considered, which we represent as different stochastic fragmentation processes. Following the self-similar energy model introduced by Bertoin and Martinez, we compute the average energy required to attain a size x with this two-device procedure. We then asymptotically compare, as x goes to 0 or 1, its energy requirement with that of individual fragmentation processes. In particular, we show that for 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 conversely.

Mots clés: Laplace exponents; fragmentation process; fragmentation energy; subordinators; Laplace exponents.

Domaines: Probabilités [math.PR]

Joaquin Fontbona, Nathalie Krell, Servet Martinez. Energy efficiency of consecutive fragmentation processes. Journal of Applied Probability, 2010, 47 (2), pp.543-561. ⟨hal-00457647⟩