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Stochastic particle transport in disordered media : beyond the Boltzmann equation

Abstract : Heterogeneous and disordered media emerges in several applications in nuclear science and engineering, especially in relation to neutron and photon propagation. Examples are widespread and concern for instance the double-heterogeneity of the fuel elements in pebble-bed reactors, or the assessment of re-criticality probability due to the random arrangement of fuel resulting from severe accidents. In this Thesis, we will investigate linear particle transport in random media. In the first part, we will focus on some mathematical models that can be used for the description of random media. Special emphasis will be given to stochastic tessellations, where a domain is partitioned into convex polyhedra by sampling random hyperplanes according to a given probability. Stochastic inclusions of spheres into a matrix will be also briefly introduced. A computer code will be developed in order to explicitly construct such geometries by Monte Carlo methods. In the second part, we will then assess the general features of particle transport within random media. For this purpose, we will consider some benchmark problems that are simple enough so as to allow for a thorough understanding of the effects of the random geometries on particle trajectories and yet retain the key properties of linear transport. Transport calculations will be realized by using the Monte Carlo particle transport code Tripoli4, developed at SERMA. The cases of quenched and annealed disorder models will be separately considered. In the former, an ensemble of geometries will be generated by using our computer code, and the transport problem will be solved for each configuration: ensemble averages will then be taken for the observables of interest. In the latter, effective transport model capable of reproducing the effects of disorder in a single realization will be investigated. The approximations of the annealed disorder models will be elucidated, and significant ameliorations will be proposed.
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Submitted on : Monday, November 5, 2018 - 4:53:06 PM
Last modification on : Friday, May 29, 2020 - 3:47:48 AM
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  • HAL Id : tel-01912811, version 1


Coline Larmier. Stochastic particle transport in disordered media : beyond the Boltzmann equation. Computational Physics [physics.comp-ph]. Université Paris-Saclay, 2018. English. ⟨NNT : 2018SACLS388⟩. ⟨tel-01912811⟩



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