Decoupled UMDO formulation for interdisciplinary coupling satisfaction under uncertainty

International audienceAt early design phases, taking into account uncertainty for the optimization of a multidisciplinary system is essential to establish the optimal system characteristics and performances. Uncertainty Multidisciplinary Design Optimization (UMDO) formulations have to eciently organize the dierent disciplinary analyses, the uncertainty propagation, the optimization, but also the handling of interdisciplinary couplings under uncertainty. A decoupled UMDO formulation (Individual Discipline Feasible - Polynomial Chaos Expansion) ensuring the coupling satisfaction for all the instantiations of the uncertain variables is presented in this paper. Ensuring coupling satisfaction in instantiations is essential to ensure the equivalence between the coupled and decoupled UMDO problem formulations. The proposed approach relies on the iterative construction of surrogate models based on Polynomial Chaos Expansion in order to represent at the convergence of the optimization problem, the coupling functional relations as a coupled approach under uncertainty does. The performances of the proposed formulation is assessed on an analytic test case and on the design of a new Vega launch vehicle upper stage

An Interior-Point Approach to Trajectory Optimization

This paper presents an interior-point approach for solving optimal control problems. Combining a flexible refinement scheme with dedicated linear algebra solvers, we obtain an efficient algorithm. Numerical results are displayed for various problems, among them several variants of atmospheric reentry

Animated molecular dynamics simulations of hydrated caesium-smectite interlayers

Computer animation of center of mass coordinates obtained from 800 ps molecular dynamics simulations of Cs-smectite hydrates (1/3 and 2/3 water monolayers) provided information concerning the structure and dynamics of the interlayer region that could not be obtained through traditional simulation analysis methods. Cs(+ )formed inner sphere complexes with the mineral surface, and could be seen to jump from one attracting location near a layer charge site to the next, while water molecules were observed to migrate from the hydration shell of one ion to that of another. Neighboring ions maintained a partial hydration shell by sharing water molecules, such that a single water molecule hydrated two ions simultaneously for hundreds of picoseconds. Cs-montmorillonite hydrates featured the largest extent of this sharing interaction, because interlayer ions were able to inhabit positions near surface cavities as well as at their edges, close to oxygen triads. The greater positional freedom of Cs(+ )within the montmorillonite interlayer, a result of structural hydroxyl orientation and low tetrahedral charge, promoted the optimization of distances between cations and water molecules required for water sharing. Preference of Cs(+ )for locations near oxygen triads was observed within interlayer beidellite and hectorite. Water molecules also could be seen to interact directly with the mineral surface, entering its surface cavities to approach attracting charge sites and structural hydroxyls. With increasing water content, water molecules exhibited increased frequency and duration of both cavity habitation and water sharing interactions. Competition between Cs(+ )and water molecules for surface sites was evident. These important cooperative and competitive features of interlayer molecular behavior were uniquely revealed by animation of an otherwise highly complex simulation output

Acidities of confined water in interlayer space of clay minerals

The acid chemistry of confined waters in smectite interlayers have been investigated with first principles molecular dynamics (FPMD) simulations. Aiming at a systematic picture, we establish the model systems to take account of the three possible controlling factors: layer charge densities (0 e, 0.5 e and 1.0 e per cell), layer charge locations (tetrahedral and octahedral) and interlayer counterions (Na+ and Mg2+). For all models, the interlayer structures are characterized in detail. Na+ and Mg2+ show significantly different hydration characteristics: Mg2+ forms a rigid octahedral hydration shell and resides around the midplane, whereas Na+ binds to a basal oxygen atom and forms a very flexible hydration shell, which consists of five waters on average and shows very fast water exchanges. The method of constraint is employed to enforce the water dissociation reactions and the thermodynamic integration approach is used to derive the free-energy values and the acidity constants. Based on the simulations, the following points have been gained. (1) The layer charge is found to be the direct origin of water acidity enhancement in smectites because the neutral pore almost does not have influences on water dissociations but all charged pores do. (2) With a moderate charge density of 0.5 e per cell, the interlayer water shows a pKa value around 11.5. While increasing layer charge density to 1.0 e, no obvious difference is found for the free water molecules. Since 1.0 e is at the upper limit of smectites’ layer charge, it is proposed that the calculated acidity of free water in octahedrally substituted Mg2+-smectite, 11.3, can be taken as the lower limit of acidities of free waters. (3) In octahedrally and tetrahedrally substituted models, the bound waters of Mg2+ show very low pKa values: 10.1 vs 10.4. This evidences that smectites can also promote the dissociations of the coordinated waters of metal cations. The comparison between the two Mg2+-smectites reveals that different layer charge locations do not lead to obvious differences for bound and free water acidities.<br/

Rhodes, encore

Abstract. - Ashton availes himself of the unique emission of tetradrachms carrying a round incuse to revise the arrangement of the earliest coinage of Rhodes. The author examines the new order which would imply the succession of Rhodian weight, then heavy and then again Rhodian weight tetradrachms in the light of the evolution of the types and hoard evidence.Bérend Denyse. Rhodes, encore. In: Revue numismatique, 6e série - Tome 150, année 1995 pp. 251-255

Carmen Arnold-Biucchi, The Randazzo hoard 1980 and Sicilian Chronology in the early fifth century b.c.

Bérend Denyse. Carmen Arnold-Biucchi, The Randazzo hoard 1980 and Sicilian Chronology in the early fifth century b.c.. In: Revue numismatique, 6e série - Tome 34, année 1992 pp. 251-254

Carmen Arnold-Biucchi, The Randazzo hoard 1980 and Sicilian Chronology in the early fifth century b.c.

Bérend Denyse. Carmen Arnold-Biucchi, The Randazzo hoard 1980 and Sicilian Chronology in the early fifth century b.c.. In: Revue numismatique, 6e série - Tome 34, année 1992 pp. 251-254