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Monte Carlo Geometry Modeling for Particle Transport Using Conformal Geometric Algebra


The Monte Carlo (MC) simulations are considered the gold-standard method for calculating the transport and interaction of radiation with the matter. A fundamental component of any MC simulation is the geometrical modeling. Current implementations of the geometrical modeling are based only on the Euclidean representations. However, Euclidean representations may not be the best option for speed up the geometric debugging-modeling computations of radiation transport, due to the number of operations involved in the estimation of position and direction of particles within each geometry shape. In this work, it is proposed for the first time, the use of Conformal Geometric Algebra (CGA), for geometric modeling in MC simulation for radiation transport. In this context, we present some elemental CGA equations for the microscopic modeling of positions and rotations of a radiation particle and the macroscopic modeling of geometrical shapes. It is shown that it is possible to take advantage of the expression power of CGA to create and debug geometry modeling with a triboelectric X-ray application. Additionally, some advantages of the CGA for the microscopic geometric computations are explored.

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This research has been supported by the CONACYT SNI Grant.

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Correspondence to E. Ulises Moya-Sánchez.

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We gratefully acknowledge the help provided by Prof. Sebatià Xambó and the constructive comments of the anonymous referees

This article is part of the Topical Collection on Proceedings ICCA 11, Ghent, 2017, edited by Hennie De Schepper, Fred Brackx, Joris van der Jeugt, Frank Sommen, and Hendrik De Bie.

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Moya-Sánchez, E.U., Maciel-Hernández, A.M., Niebla, A.S. et al. Monte Carlo Geometry Modeling for Particle Transport Using Conformal Geometric Algebra. Adv. Appl. Clifford Algebras 29, 26 (2019).

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  • Monte Carlo geometry
  • Ray tracing
  • Conformal Geometry Algebra