In inactive glasses used as models for French nuclear waste forms, Zr K-and L 2,3 -edge X-ray absorption spectroscopy spectra indicate that Zr is only 6-coordinated, with d(Zr-O) distances of 2.08 ± 0.01 Å and with a small radial disorder. Beyond, the first coordination shell, next-nearest Si neighbors occur at about 3.4 Å. These distances exclude the presence of [7] Zr and/or [8] Zr and suggest [6] Zr-O-Si angles close to 130°, indicating corner-shared ZrO 6 and SiO 4 polyhedra. This structural configuration is similar to those observed in some crystalline zirconosilicates and is in agreement with the stability of Zr in borosilicate melts and glasses.

The structural surrounding of Zn in inactive nuclear glasses was determined using extended x-ray absorption fine structure spectroscopy. Zn was found in tetrahedralcoordination ([4]Zn) with [4]Zn–O distances of 1.95 Å. ZnO4 tetrahedra shared corners with SiO4 tetrahedra [d(Zn–Si) around 3.20 Å]. The oxygens of the Zn–O–Si bonds were charge compensated by Na+ and, to a minor extent, by Cs+. The influence of [4]Zn on the formation of charge-compensating cations at the expense of network modifiers may explain the stabilizing effect of Zn in these glasses.

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The Stochastic Dual Dynamic Programming (SDDP) algorithm has become one of the main tools to address convex multistage stochastic optimal control problem. Recently a large amount of work has been devoted to improve the convergence speed of the algorithm through cut-selection and regularization, or to extend the field of applications to non-linear, integer or risk-averse problems. However one of the main downside of the algorithm remains the difficulty to give an upper bound of the optimal value, usually estimated through Monte Carlo methods and therefore difficult to use in the algorithm stopping criterion. In this paper we present a dual SDDP algorithm that yields a converging exact upper bound for the optimal value of the optimization problem. Incidently we show how to compute an alternative control policy based on an inner approximation of Bellman value functions instead of the outer approximation given by the standard SDDP algorithm. We illustrate the approach on an energy production problem involving zones of production and transportation links between the zones. The numerical experiments we carry out on this example show the effectiveness of the method.

R7T7 glass samples were tested to determine their sensitivity to variations in the chemical composition and in industrial scale operating parameters. Variations investigated included the composition of the feed solution and the glass frit, the frit/glass ratio and the glass melting temperature. The iniportant properties of the resulting glasses were measured. Permissible variation ranges defined on the basis of the results obtained ensure that the glass properties remain acceptable compared with the reference glass.