Subdivision schemes are used to generate smooth curves or surfaces by iteratively refining an initial control polygon or mesh. We focus on univariate, linear, binary subdivision schemes, where the vertices of the refined polygon are computed as linear combinations of the current neighbouring vertices. In the classical stationary setting, there are just two such subdivision rules, which are used throughout all subdivision steps to construct the new vertices with even and odd indices, respectively. These schemes are well understood and many tools have been developed for deriving their properties, including the smoothness of the limit curves. For non-stationary schemes, the subdivision rules are not fixed and can be different in each subdivision step. Non-uniform schemes are even more general, as they allow the subdivision rules to be different for every new vertex that is generated by the scheme. The properties of non-stationary and non-uniform schemes are usually derived by relating the scheme to a corresponding stationary scheme and then exploiting the fact that the properties of the stationary scheme carry over under certain proximity conditions. In particular, this approach can be used to show that the limit curves of a non-stationary or non-uniform scheme are as smooth as those of a corresponding stationary scheme. In this paper we show that non-uniform subdivision schemes have the potential to generate limit curves that are smoother than those of stationary schemes with the same support size of the subdivision rule. For that, we derive interpolatory 2-point and 4-point schemes that generate C 1 and C 2 limit curves, respectively. These values of smoothness exceed the smoothness of classical interpolating schemes with the same support size by one.
Analysis of the steady-state and reactivity insertion accident is very important for the safety of reactor operations. In this study, steady-state and reactivity insertion accident analysis when the low enriched uranium foil target is irradiated in the reactor core has been carried out. The analysis is carried out by the best estimate method by using a coupled neutronic, kinetic, and thermal-hydraulic code, MTR-DYN. The MTR-DYN code is based on the 3-D multigroup neutron diffusion method. The cell calculations for the target are carried out by the WIMSD/5 and MTR-DYN code. After reactivity insertion, the coolant, fuel, and clad temperature are observed. The calculation results for the initial power of 1 W showed that the maximum temperature of the coolant, clad, and fuel are 49.76?C, 65.01?C, and 65.26?C, respectively. Meanwhile, when the reactivity insertion at the initial power of 1 MW, the maximum temperature of the coolant, clad, and fuel are 72.23?C, 140.79?C, and 141.97?C, respectively. Based on those calculation results during irradiation low enriched uranium foil target, the temperature in the steady-state and reactivity insertion accident does not exceed the allowable safety limit.
This paper documents the foreign asset ownership and investment theory of the dynamic GTAP model (GTAP-Dyn). The new investment theory offers a disequilibrium approach to modeling endogenously international capital mobility. It permits a recursive solution procedure, a feature that allows easy implementation of dynamics into any static AGE model without imposing limitations on the model's size. The method involves treating time as a variable, not as an index. Having time as a variable allows the construction of dynamic GTAP with minimum modifications to the existing structure of GTAP, by separating the theory of static GTAP from the length of run.