• Nuclear Engineering and Technology
• /
• v.54 no.1
• /
• pp.1-10
• /
• 2022

This study discusses the effect of using ²³²Th instead of ²³⁸U on the neutronic characteristics and the main operating parameters of the pressurized water reactor (PWR). MCNPX version 2.7 was used to compare the neutronic characteristics of UO₂ with (Th, ²³⁵U)O₂ and (Th, ²³³U) O₂. Firstly, the infinity multiplication factor (K_inf), thermal neutron flux, and power distribution have been studied for the investigated fuel types. Secondly, the effect of Gd₂O₃ and Er₂O₃ on the K_inf and on the radial thermal neutron flux and thermal power has been investigated to distinguish which of them is more suitable than the other in reactivity management. Thirdly, to illustrate the effectiveness of ²³²Th in decreasing the inventory of both the actinides and non-actinides, the concentration of plutonium (Pu) isotopes and minor actinides (MAs) has been simulated with the fuel burnup. Besides, due to their large thermal neutron absorption cross-section, the concentrations of ¹³⁵Xe, ¹⁴⁹Sm, and ¹⁵¹Sm with the fuel burnup have been investigated. Finally, the main safety parameters such as the reactivity worth of the control rods (ρ_CR), the effective delayed neutron fraction β_eff, and the Doppler reactivity coefficient (DRC) were calculated to determine to which extent these fuel types achieve the acceptable limits.

• Journal of Educational Research in Mathematics
• /
• v.22 no.1
• /
• pp.53-68
• /
• 2012

This paper investigated the conceptual schemes four children constructed as they related division number sentences to various types of fraction: Proper fractions, improper fractions, and mixed numbers in both contextual and abstract symbolic forms. Methods followed those of the constructivist teaching experiment. Four fifth-grade students from an inner city school in the southwest United States were interviewed eight times: Pre-test clinical interview, six teaching / semi-structured interviews, and a final post-test clinical interview. Results showed that for equal sharing situations, children conceptualized division in two ways: For mixed numbers, division generated a whole number portion of quotient and a fractional portion of quotient. This provided the conceptual basis to see improper fractions as quotients. For proper fractions, they tended to see the quotient as an instance of the multiplicative structure: $a{\times}b=c$ ; $a{\div}c=\frac{1}{b}$ ; $b{\div}c=\frac{1}{a}$. Results suggest that first, facility in recall of multiplication and division fact families and understanding the multiplicative structure must be emphasized before learning fraction division. Second, to facilitate understanding of the multiplicative structure children must be fluent in representing division in the form of number sentences for equal sharing word problems. If not, their reliance on long division hampers their use of syntax and their understanding of divisor and dividend and their relation to the concepts of numerator and denominator.