• 대한수학회지
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• 제46권2호
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• pp.225-236
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• 2009

The equicontinuity and scattering properties of continuous semi-flows are studied on a compact metric space. The main results are obtained as follows: first, the complexity function defined by the spanning set is bounded if and only if the system is equicontinuous; secondly, if a continuous semi-flow is topologically weak mixing, then it is pointwise scattering; thirdly, several equivalent conditions for the time-one map of a continuous semi-flow to be scattering are presented; Finally, for a minimal continuous map it is shown that the "non-dense" requirement is unnecessary in the definition of scattering by using open covers.

• Nuclear Engineering and Technology
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• 제47권7호
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• pp.791-803
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• 2015

The effective cross sections (XSs) in the direct whole core calculation code nTRACER are evaluated by the equivalence theory-based resonance-integral-table method using the WIMS-based library as an alternative to the subgroup method. The background XSs, as well as the Dancoff correction factors, were evaluated by the enhanced neutron-current method. A method, with pointwise microscopic XSs on a union-lethargy grid, was used for the generation of resonance-interference factors (RIFs) for mixed resonant absorbers. This method was modified by the intermediate-resonance approximation by replacing the potential XSs for the non-absorbing moderator nuclides with the background XSs and neglecting the resonance-elastic scattering. The resonance-escape probability was implemented to incorporate the energy self-shielding effect in the spectrum. The XSs were improved using the proposed method as compared to the narrow resonance infinite massbased method. The RIFs were improved by 1% in $^{235}U$, 7% in $^{239}Pu$, and >2% in $^{240}Pu$. To account for thermal feedback, a new feature was incorporated with the interpolation of pre-generated RIFs at the multigroup level and the results compared with the conventional resonance-interference model. This method provided adequate results in terms of XSs and k-eff. The results were verified first by the comparison of RIFs with the exact RIFs, and then comparing the XSs with the McCARD calculations for the homogeneous configurations, with burned fuel containing a mixture of resonant nuclides at different burnups and temperatures. The RIFs and XSs for the mixture showed good agreement, which verified the accuracy of the RIF evaluation using the proposed method. The method was then verified by comparing the XSs for the virtual environment for reactor applicationbenchmark pin-cell problem, as well as the heterogeneous pin cell containing burned fuel with McCARD. The method works well for homogeneous, as well as heterogeneous configurations.

• Nuclear Engineering and Technology
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• 제50권3호
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• pp.340-355
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• 2018

The methods and performance of a fast reactor multigroup cross section (XS) generation code EXUS-F are described that is capable of directly processing Evaluated Nuclear Data File format nuclear data files. RECONR of NJOY is used to generate pointwise XS data, and Doppler broadening is incorporated by the Gauss-Hermite quadrature method. The self-shielding effect is incorporated in the ultrafine group XSs in the resolved and unresolved resonance ranges. Functions to generate scattering transfer matrices and fission spectrum matrices are realized. The extended transport approximation is used in zero-dimensional calculations, whereas the collision probability method and the method of characteristics are used for one-dimensional cylindrical geometry and two-dimensional hexagonal geometry problems, respectively. Verification calculations are performed first for various homogeneous mixtures and cylindrical problems. It is confirmed that the spectrum calculations and the corresponding multigroup XS generations are performed adequately in that the reactivity errors are less than 50 pcm with the McCARD Monte Carlo solutions. The nTRACER core calculations are performed with the EXUS-F-generated 47 group XSs for the two-dimensional Advanced Burner Reactor 1000 benchmark problem. The reactivity error of 160 pcm and the root mean square error of the pin powers of 0.7% indicate that EXUF-F generates properly the broad-group XSs.