Optimal designs for model discrimination and fitting for the flow of particles

During the discharge of a two-dimensional silo, the flow of grains through an opening is arrested if the size of the outlet is not large enough. In the outpouring of grains, jamming occurs due to the formation of an arch at the outlet. After breaking the arch, the grains fall until a new arch is formed. Several models have been proposed to explain this process. The goal of this work is twofold. First, we developed a comparative study of the models proposed by Janda et al. (Europhys Lett 84(4):44002-1–44002-6, 2008) and To (Phys Rev E 71(6):060301-1–060301-4, 2005). We have computed D-optimal and c-optimal designs for the most important parameter of the models. Secondly, using the criterion of KL-optimality developed by López-Fidalgo et al. (J R Stat Soc Ser B 69(2):231–242, 2007), optimal designs for discriminating between these models have been computed.