Derivative-free algorithms are frequently required for the optimization of nonsmooth scalar functions in n dimensions resulting, for example, from physical experiments or from the statistical averaging of numerical simulations of chaotic systems such as turbulent flows. The core idea of all...

High resistance concrete or hard ceramics needs extremely dense granular packings which can only be realised when the size distribution of grains follows a powerlaw. We discuss the perfectly dense limit, namely Apollonian packings in three dimensions and show in particular the existence of space...

Bead packs of up to 150,000 mono-sized spheres with packing densities ranging from 0.58 to 0.64 have been studied by means of X-ray computed tomography. These studies represent the largest and the most accurate description of the structure of disordered packings at the grain-scale ever...

We employ the Monte Carlo method to study a constrained optimization problem, that is packing spheres with unequal radii into a 3-D bounded region. Selection of the best fit solution is based on using the Boltzmann factor, e−ΔE/T to determine the transition probability, which allows us to...