Analysis and validation of a run-of-mine ore grinding mill circuit model for process control

A simple and novel non-linear model of a run-of-mine ore grinding mill circuit, developed for process control and estimation purposes, is validated. The model makes use of the minimum number of states and parameters necessary to produce responses that are qualitatively accurate. It consists of separate feeder, mill, sump and hydrocyclone modules that can be connected to model different circuit configurations. The model uses five states: rocks, solids, fines, water and steel balls. Rocks are defined as too large to be discharged from the mill, whereas solids, defined as particles small enough to leave the mill, consist of out-of-specification coarse ore and in-specification fine ore fractions. The model incorporates a unique prediction of the rheology of the slurry within the mill. A new hydrocyclone model is also presented. The model parameters are fitted to an existing plant’s sampling campaign data and a step-wise procedure is given to fit the model to steady-state data. Simulation test results of the model are compared to sampling campaign data of the same plant at different steady-state conditions. The model shows promise in estimating important process variables such as mill power and product particle size and is deemed suitable for process control studies.http://www.elsevier.com/locate/minenghb2014ai201

Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces

Primordialists and Constructionists: a typology of theories of religion

This article adopts categories from nationalism theory to classify theories of religion. Primordialist explanations are grounded in evolutionary psychology and emphasize the innate human demand for religion. Primordialists predict that religion does not decline in the modern era but will endure in perpetuity. Constructionist theories argue that religious demand is a human construct. Modernity initially energizes religion, but subsequently undermines it. Unpacking these ideal types is necessary in order to describe actual theorists of religion. Three distinctions within primordialism and constructionism are relevant. Namely those distinguishing: a) materialist from symbolist forms of constructionism; b) theories of origins from those pertaining to the reproduction of religion; and c) within reproduction, between theories of religious persistence and secularization. This typology helps to make sense of theories of religion by classifying them on the basis of their causal mechanisms, chronology and effects. In so doing, it opens up new sightlines for theory and research

Reciprocity and conditional cooperation between great tit parents

When individuals invest in a common good, an efficient outcome is hard to achieve, because each can free ride on others’ efforts. This problem can lead parents that raise their young together to reduce their investment in care, with negative consequences for offspring. Here, we present a mathematical model to show that a strategy of conditional cooperation, in which parents take turns feeding their young, can resolve this problem. To test this idea, we studied the behaviour of great tit parents raising chicks together. We found that parents speed up their feeding rate after their partner has visited the chicks, but slow down again once they have visited in turn, promoting alternation. We conclude that conflict over parental investment in this species is partly ameliorated by a simple form of reciprocity