On the application of random searching for the hard particles packing problem for composite solid propellant structure modeling

The paper presents a problem statement for random hard particles packing as minimization of an objective function that is the measure of overlapping of $\mathbb R^3$ subdomains representing particles and forbidden zones, with desired pack characteristics being accounted for by an additional summand in the objective function. A new algorithm based on the random search approach is proposed; it assesses a new particles configuration after each movement, and particles grow from an initial to full size as overlaps being removed. This algorithm is matched with the viscous suspension algorithm for the case of packing equal-sized spheres in a periodic cube. For packing fractions $\varphi<0,55$ the random search algorithm yields packs with fewer and smaller particle clusters than the viscous suspension one, in denser packs differences are insignificant. An example of creating a pack with the feature that particles are shifted closely to the solid boundary is shown as well.