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Shielding material distributions and associated fractals

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  • Rodríguez-Cuadrado, Javier
  • San Martín, Jesús

Abstract

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.

Suggested Citation

  • Rodríguez-Cuadrado, Javier & San Martín, Jesús, 2022. "Shielding material distributions and associated fractals," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002181
    DOI: 10.1016/j.chaos.2022.112008
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    References listed on IDEAS

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    1. Gordillo-Cruz, E. & Alvarez-Ramirez, J. & González, F. & de los Reyes, J.A, 2018. "Fractal analysis of X-ray diffraction patterns of zirconia–alumina mixed oxides," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 635-643.
    2. Al-Hadeethi, Y. & Sayyed, M.I., 2020. "X-ray attenuation features of some tellurite glasses evaluated at medical diagnostic energies," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    3. Ortiz-Cruz, A. & Santolalla, C. & Moreno, E. & de los Reyes-Heredia, J.A. & Alvarez-Ramirez, J., 2012. "Fractal analysis of powder X-ray diffraction patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1642-1651.
    4. Lafaye de Micheaux, Pierre & Liquet, Benoit, 2009. "Understanding Convergence Concepts: A Visual-Minded and Graphical Simulation-Based Approach," The American Statistician, American Statistical Association, vol. 63(2), pages 173-178.
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