Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.

A new age of fuel performance code criteria studied through advanced atomistic simulation techniques

A fundamental step in understanding the effects of irradiation on metallic uranium and uranium dioxide ceramic fuels, or any material, must start with the nature of radiation damage on the atomic level. The atomic damage displacement results in a multitude of defects that influence the fuel performance. Nuclear reactions are coupled, in that changing one variable will alter others through feedback. In the field of fuel performance modeling, these difficulties are addressed through the use of empirical models rather than models based on first principles. Empirical models can be used as a predictive code through the careful manipulation of input variables for the limited circumstances that are closely tied to the data used to create the model. While empirical models are efficient and give acceptable results, these results are only applicable within the range of the existing data. This narrow window prevents modeling changes in operating conditions that would invalidate the model as the new operating conditions would not be within the calibration data set. This work is part of a larger effort to correct for this modeling deficiency. Uranium dioxide and metallic uranium fuels are analyzed through a kinetic Monte Carlo code (kMC) as part of an overall effort to generate a stochastic and predictive fuel code. The kMC investigations include sensitivity analysis of point defect concentrations, thermal gradients implemented through a temperature variation mesh-grid, and migration energy values. In this work, fission damage is primarily represented through defects on the oxygen anion sublattice. Results were also compared between the various models. Past studies of kMC point defect migration have not adequately addressed non-standard migration events such as clustering and dissociation of vacancies. As such, the General Utility Lattice Program (GULP) code was utilized to generate new migration energies so that additional non-migration events could be included into kMC code in the future for more comprehensive studies. Defect energies were calculated to generate barrier heights for single vacancy migration, clustering and dissociation of two vacancies, and vacancy migration while under the influence of both an additional oxygen and uranium vacancy.