Minimal Fragmentation of Regular Polygonal Plates

Minimal fragmentation models intend to unveil the statistical properties of large ensembles of identical objects, each one segmented in {\it two} parts only. Contrary to what happens in the multifragmentation of a single body, minimally fragmented ensembles are often amenable to analytical treatments, while keeping key features of multifragmentation. In this work we present a study on the minimal fragmentation of regular polygonal plates with up to $100$ sides. We observe in our model the typical statistical behavior of a solid teared apart by a strong impact, for example. That is to say, a robust power law, valid for several decades, in the small mass limit. In the present case we were able to analytically determine the exponent of the accumulated mass distribution to be $\frac{1}{2}$. Less usual, but also reported in a number of experimental and numerical references on impact fragmentation, is the presence of a sharp crossover to a second power-law regime, whose exponent we found to be $\frac{1}{3}$ for an isotropic model and $\frac{2}{3}$ for a more realistic anisotropic model.