A robust and parsimonious model for caesium sorption on clay minerals and natural clay materials. Applied Geochemistry, Elsevier, 2017, 87, pp.ABSTRACT 12 Caesium (Cs) is one of the most studied radionuclides in the fields of nuclear waste disposal 13 and environmental sciences. The overall objective of this work is to improve the tools designed to 14 describe and predict migration, retention, and bioaccumulation processes in the geosphere and the 15 biosphere, particularly in the soil / solution soil / plant roots systems. Cs sorption on clay minerals 16 has been extensively measured and modelled because these minerals control Cs mobility and 17 (bio)availability in the environment. 18A critical analysis of published experimental data on Cs sorption by clay minerals and 19 natural clay materials along with the different models was performed in an attempt to elaborate and 20 evaluate a generic model for Cs sorption. This work enabled us to propose a robust and 21 parsimonious model for Cs sorption, which combines the surface complexation and cation 22 exchange approaches invoking only two types of surface sites: frayed edge and exchange sites. Our 23 model, referred to as the "1-pK DL/IE model", takes into account the competition between Cs and 24 *Revised manuscript with no changes marked 1999) and the principal source of radioactivity of nuclear waste in the timeframe of the first one 48 hundred years. Moreover, radiocaesium always exists as the monovalent cation Cs + , with chemical 49

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The first aim of this paper is to illustrate numerically that the Dirichlet-to-Neumann semigroup represented by P. Lax acts as a magnifying glass. In this perspective, we used the finite element method for the discretization of the correspondent boundary dynamical system using the implicit and explicit Euler schemes. We prove by using the Chernoff's Theorem that the implicit and explicit Euler methods converge to the exact solution and we use the (P1)-finite elements to illustrate this convergence through a FreeFem++ implementation which provides a movie available online. In the Dirichlet-to-Neumann semigroup represented by P. Lax the conductivity γ is the identity matrix I n , but for an other conductivity γ, the authors of [3] supplied an estimation of the operator norm of the difference between the Dirichlet-to-Neumann operator Λ γ and Λ 1 , when γ = βI n and β = 1 near the boundary ∂Ω (see Lemma 2.1). We will use this result to estimate the accuracy between the correspondent Dirichlet-to-Neumann semigroup and the Lax semigroup, for f ∈ H 1/2 (∂Ω).

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