Efficient computation of operator‐type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

This work honors the 75th birthday of Professor Ionel Michael Navon by presenting original results highlighting the computational efficiency of the adjoint sensitivity analysis methodology for function‐valued operator responses by means of an illustrative paradigm dissolver model. The dissolver model analyzed in this work has been selected because of its applicability to material separations and its potential role in diversion activities associated with proliferation and international safeguards. This dissolver model comprises eight active compartments in which the 16 time‐dependent nonlinear differential equations modeling the physical and chemical processes comprise 619 scalar and time‐dependent model parameters, related to the model's equation of state and inflow conditions. The most important response for the dissolver model is the time‐dependent nitric acid in the compartment furthest away from the inlet, where measurements are available at 307 time instances over the transient's duration of 10.5 h. The sensitivities to all model parameters of the acid concentrations at each of these instances in time are computed efficiently by applying the adjoint sensitivity analysis methodology for operator‐valued responses. The uncertainties in the model parameters are propagated using the above‐mentioned sensitivities to compute the uncertainties in the computed responses. A predictive modeling formalism is subsequently used to combine the computational results with the experimental information measured in the compartment furthest from the inlet and then predict optimal values and uncertainties throughout the dissolver. This predictive modeling methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution for the a priori known mean values and uncertainties characterizing the model parameters and the computed and experimentally measured model responses. This approximate a priori distribution is subsequently combined using Bayes' theorem with the “likelihood” provided by the multi‐physics computational models. Finally, the posterior distribution is evaluated using the saddle‐point method to obtain analytical expressions for the optimally predicted values for the parameters and responses of both multi‐physics models, along with corresponding reduced uncertainties. This work shows that even though the experimental data pertains solely to the compartment furthest from the inlet (where the data were measured), the predictive modeling procedure used herein actually improves the predictions and reduces the predicted uncertainties for the entire dissolver, including the compartment furthest from the measurements, because this predictive modeling methodology combines and transmits information simultaneously over the entire phase‐space, comprising all time steps and spatial locations. Copyright © 2016 John Wiley & Sons, Ltd.     

Gibbs ensemble simulation of nematic-isotropic coexistence in a liquid crystal mixture

The results are presented of Gibbs ensemble Monte Carlo (GEMC) simulations examining the nematic–isotropic (N–I) coexistence envelope of a liquid crystal mixture. The system studied is a 50:50 mixture of 1000 generalized Gay–Berne particles with axial ratios 2.0:1 and 2.5:1. For this system, stable N–I coexistence is observed over run lengths in excess of 5 x 10⁵ GEMC sweeps. There is unambiguous evidence of fractionation, the mole fractions of long particles in the coexisting phases typically differing by 11%. The measured coexistence envelope does not conform to the lens shape predicted by Onsager theory; qualitative finite size arguments are given in explanation of this distortion.     

Compressive advection and multi‐component methods for interface‐capturing

This paper develops methods for interface‐capturing in multiphase flows. The main novelties of these methods are as follows: (a) multi‐component modelling that embeds interface structures into the continuity equation; (b) a new family of triangle/tetrahedron finite elements, in particular, the P₁DG‐P₂(linear discontinuous between elements velocity and quadratic continuous pressure); (c) an interface‐capturing scheme based on compressive control volume advection methods and high‐order finite element interpolation methods; (d) a time stepping method that allows use of relatively large time step sizes; and (e) application of anisotropic mesh adaptivity to focus the numerical resolution around the interfaces and other areas of important dynamics. This modelling approach is applied to a series of pure advection problems with interfaces as well as to the simulation of the standard computational fluid dynamics benchmark test cases of a collapsing water column under gravitational forces (in two and three dimensions) and sloshing water in a tank. Two more test cases are undertaken in order to demonstrate the many‐material and compressibility modelling capabilities of the approach. Numerical simulations are performed on coarse unstructured meshes to demonstrate the potential of the methods described here to capture complex dynamics in multiphase flows. Copyright © 2015 John Wiley & Sons, Ltd.     

Molecular QTAIM Topology Is Sensitive to Relativistic Corrections

The topology of the molecular electron density of benzene dithiol gold cluster complex Au₄−S−C₆H₄−S′−Au′₄ changed when relativistic corrections were made and the structure was close to a minimum of the Born–Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization.     

Preparation,characterization and evaluation of a series of heterogeneous platinum catalysts immobilized on magnetic silica with different acid ligands

Transition Metal Chemistry - Platinum was immobilized on magnetic silica gel by means of boronic, nitric, carboxylic or sulfuric acid ligands to give four heterogeneous Pt nano-catalysts,...     

Advances in positron and electron scattering*

The topical issue on Advances in Positron and Electron Scattering” combines contributionsfrom POSMOL 2015 together with others devoted to celebrate the unprecedented scientificcareers of our loyal colleagues and trusted friends Steve Buckman (Australian NationalUniversity, Australia) and Michael Allan (University of Fribourg, Switzerland) on theoccasion of their retirements. POSMOL 2015, the XVIII International Workshop on Low-EnergyPositron and Positronium Physics and the XIX International Symposium on Electron-MoleculeCollisions and Swarms, was held at Universidade NOVA de Lisboa, Lisboa, Portugal, from17–20 July 2015. The international workshop and symposium allowed to achieve a veryprivileged forum of sharing and developing our scientific expertise on current aspects ofpositron, positronium and antiproton interactions with electrons, atoms, molecules andsolid surfaces, and related topics, as well as electron interactions with molecules inboth gaseous and condensed phases. Particular topics include studies of electroninteractions with biomolecules, electron induced surface chemistry and the study of plasmaprocesses. Recent developments in the study of swarms are also fully addressed.