Ore crushing in the high-pressure roller-press as a modelling object under stochastic properties of feed materials

The results of improving ore crushing in a high-pressure roller-press are presented. Application of a roller-press enables higher crushing efficiency due to both power saving and reduction of sizes of ore crush products to release mineral aggregates. Ore disintegration by compressive strain prevails among currently applied crushing methods. Disintegration occurs not only due to the compressive, but also to the shear strain. Considering smaller power consumption of the shear strain than that of the compressive strain, it is concluded that roller-press application is quite efficient. Simulation of crushing by using the Bond law frequently applied in practice is under consideration. It is essential to consider the stochasticity of the ore flow to be crushed. Presentation of this flow as a random figure by transforming it by the Bond crushing law results in a probabilistic characteristic of the crushing result. This characteristic enables finding properties of the crush product and probabilistic formulation of the problem of improving the crushing process by setting a relevant functional. To apply the results obtained to practical uses, the crushing process is simulated. The theoretical results are confirmed by setting the stochastic properties of the input ore flow by means of Rosen-Rammler’s law followed by statistical substantiation of the conducted calculations in Mathcad. After stimulation and considering stochastic properties of the feed ore flow, the solution of the optimal stabilization problem reveals that stabilization is achieved, while dispersion in relation to the stabilization goal reduces sharply almost five-fold

Stopping sets: Gamma-type results and hitting properties

Recently in the paper by Møller and Zuyev (1996), the following Gamma-type result was established. Given n points of a homogeneous Poisson process defining a random figure, its volume is Γ(n,λ) distributed, where λ is the intensity of the process. In this paper we give an alternative description of the class of random sets for which the Gamma-type results hold. We show that it corresponds to the class of stopping sets with respect to the natural filtration of the point process with certain scaling properties. The proof uses the martingale technique for directed processes, in particular, an analogue of Doob's optional sampling theorem proved in Kurtz (1980). As well as being compact, this approach provides a new insight into the nature of geometrical objects constructed with respect to a Poisson point process. We show, in particular, that in this framework the probability that a point is covered by a stopping set does not depend on whether it is a point of the process or not.

Stopping sets: Gamma-type results and hitting properties

Recently in the paper by Møller and Zuyev (1996), the following Gamma-type result was established. Given n points of a homogeneous Poisson process defining a random figure, its volume is Γ(n,λ) distributed, where λ is the intensity of the process. In this paper we give an alternative description of the class of random sets for which the Gamma-type results hold. We show that it corresponds to the class of stopping sets with respect to the natural filtration of the point process with certain scaling properties. The proof uses the martingale technique for directed processes, in particular, an analogue of Doob's optional sampling theorem proved in Kurtz (1980). As well as being compact, this approach provides a new insight into the nature of geometrical objects constructed with respect to a Poisson point process. We show, in particular, that in this framework the probability that a point is covered by a stopping set does not depend on whether it is a point of the process or not.