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.     

A New Synthesis and the 13C-NMR OF β-Cyperone 1,3-Dibromo-2-Pentene,A New Ethyl Vinyl Ketone Equivalent

In connection with another study underway i n this lab we have been investigating the use of vinylogous thioester 1 as a synthon f o r sesquiterpene synthesis. We have found that 1 is useful for ring annelations and introduction of multiple substituents when pursuing carbocyclic synthesis. In recent studies with thioesters we have found that the lithium enolate of 1 (LDA/THF) will undergo 1,4-addition to Michael acceptors such as ethyl vinyl ketone (2, - EVK) in moderate yields (～60).     

A Convenient Procedure for the Hydrolysis of Hindered Esters

Although several procedures for the hydrolysis of hindered esters have been developed, most of them suffer from one or more disadvantages, either in lack of convenience or in stringent conditions which affect other functional groups. Among the presently available methods for effecting this conversion are lithium in ammonia, a strong reducing agent¹; boron trichloride, a Lewis acid²; and a variety of reagents which bring about alkyl-oxygen cleavage. Among the latter are lithium iodide in a variety of solvents, usually at elevated temperatures, or in the presence of an organic base³; 1,5-diazabicyclo [4, 3, 0] nonene-5, in boiling xylene⁴, a reaction which failed in this laboratory⁵; various mercaptides^6,7, which in addition to being experimentally offensive, also cleave aryl alkyl ethers.     

Platinum nanoclusters on graphite substrates: a molecular dynamics study

Molecular dynamics simulations are used to investigate the shape and structure evolution of single platinum clusters of cubic and spherical shape containing 256 and 260 atoms, respectively, deposited on a static graphite substrate. The evolution is monitored at variable temperature, and as a function of metal-substrate interactions at constant temperature. The Pt-Pt interactions are modelled with the many-body Sutton-Chen potential, whereas a Lennard-Jones potential is used to describe the Pt-C interactions. Heating and cooling curves calculated between 200 K and 1800 K are used to determine solid-solid and solid-liquid transitions. Structural changes are detected through analyses of density profiles and diffusion coefficients. A clear analogy is observed between temperature-induced wetting phenomena and those resulting from enhancement of the metal-substrate interactions.     

A prior1 bounds for a class of stationary diffusion systems

We establish a priori bounds for a class of semilinear elliptic systems which have semilinear boundary conditions. These bounds are obtained as a consequence of imposing a convex Lyapunov-like structure upon our systems.