Shielding material distributions and associated fractals.

The exponential growth of space exploration, and of nuclear energy applications, leads to optimize the material distribution in a shield to protect against hypervelocity impacts and radiation. In order to find the optimal distribution, we study multilayer and porous structures, regular and random, by simulating straight particle trajectories crossing a rectangle filled with a constant mass according to the different structures. These trajectories are analyzed theoretically in multilayer structures and following a Monte Carlo method in porous structures. In this second case, distribution and probability estimators are used to ensure results with almost sure convergence, which indicates that the amount of matter crossed by particles is independent of the underlying structure. However, in regular porous structures, there are singularities given by fractal sets of measure zero that allow a theoretical construction. These fractal sets reveal protection gaps in regular porous structures that make them extremely dangerous for shielding purposes. Furthermore, this result allows to explain X-ray fractal patterns of certain semi-crystalline materials. • Optimal distribution of mass is studied in shields • The degree of protection is independent of the structure: multilayer or porous • Regular porous structures show a protection singularity: a fractal set of measure zero • The fractal set involves a huge protection risk in spacecraft shields • X-ray diffraction patterns can be explained by the fractal set [ABSTRACT FROM AUTHOR]