[en] A systematic method for bandwidth parameter selection is desired for Thomson multitaper spectrum estimation. We give a method for determining the optimal bandwidth based on a mean squared error (MSE) criterion. When the true spectrum has a second-order Taylor series expansion, one can express quadratic local bias as a function of the curvature of the spectrum, which can be estimated by using a simple spline approximation. This is combined with a variance estimate, obtained by jackknifing over individual spectrum estimates, to produce an estimated MSE for the log spectrum estimate for each choice of time-bandwidth product. The bandwidth that minimizes the estimated MSE then gives the desired spectrum estimate. Additionally, the bandwidth obtained using our method is also optimal for cepstrum estimates. We give an example of a damped oscillatory (Lorentzian) process in which the approximate optimal bandwidth can be written as a function of the damping parameter. Furthermore, the true optimal bandwidth agrees well with that given by minimizing estimated the MSE in these examples.

[en] Grain size is an important factor in controlling the swelling behavior in irradiated U–Mo dispersion fuels. Increasing the grain size in U–Mo fuel particles by heat treatment is believed to delay the fuel swelling at high fission density. In this work, a multiscale simulation approach combining first-principles calculation and phase field modeling is used to investigate the grain growth behavior in U–7Mo alloy. The density functional theory based first-principles calculations were used to predict the material properties of U–7Mo alloy. The obtained grain boundary energies were then adopted as an input parameter for mesoscale phase field simulations. The effects of annealing temperature, annealing time and initial grain structures of fuel particles on the grain growth in U–7Mo alloy were examined. The predicted grain growth rate compares well with the empirical correlation derived from experiments.

[en] This paper presents a multiscale simulation of the microstructural evolution in the irradiated U-7Mo alloy fuel. Atomistic simulation methods, such as density functional theory and molecular dynamics simulations, are utilized to predict the material properties of U-7Mo alloys including the formation energies and diffusivities of defects, surface energies, and elastic constants. The obtained material properties are then incorporated into a mesoscale model to study the evolution of fission gas bubbles in the irradiated U-Mo. The predicted intragranular bubble size distribution is consistent with experimental measurement. The swelling of U-Mo due to the fission gas bubble is simulated and compared to experimental observations. Based on the dislocation density and critical recrystallization nucleation size and density predicted by the rate theory model, the fission-induced recrystallization in U-7Mo is studied using a multi-phase phase-field model. The predicted volume fraction of recrystallization agrees well with the experimental measurements. The effect of grain morphology in the initial grain structure is investigated. The grain size in the initial structure is found to have a great impact on the recrystallization kinetics. It is desirable to increase the grain size in the fuel in order to reduce the rate of recrystallization and therefore fuel swelling. We believe the current studies are useful for further improvement of the performance of U-Mo alloy fuels for future research reactors relying on low enriched uranium (LEU) fuels. (author)

[en] Sensitivity analysis is an important tool for describing power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this paper, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating sensitivities of larger systems and is consistent, within machine precision, with the function whose sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as dc exciters, by deriving and implementing the adjoint jump conditions that arise from state-dependent and time-dependent switchings. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach. In conclusion, this paper focuses primarily on the power system dynamics, but the approach is general and can be applied to hybrid dynamical systems in a broader range of fields.