Abstract

In this study, a nonlocal approach to neutron diffusion equation with a memory is constructed in terms of moments of the displacement kernel with a modified geometric buckling. This approach leads to a family of partial differential equations which belong to the class of Fisher-Kolmogorov and Swift-Hohenberg equations. The stability of the problem depends on the signs of the second and fourth moments. The energy is a conserved quantity along orbits and a constant of integration is obtained. It was observed that the buckling is affected by the types of the kernel moment and for an explicit symmetric kernel, the ratio between the maximum and the average flux for a slab reactor is less than the ratio obtained using the conventional local diffusion equation, a result which is motivating technically in nuclear reactor engineering.

摘要

在这项研究中，根据位移核的矩和修正的几何屈曲，构造了具有记忆的中子扩散方程的非局部方法。这种方法导致了一系列偏微分方程，它们属于Fisher-Kolmogorov和Swift-Hohenberg方程的类别。问题的稳定性取决于第二和第四时刻的信号。能量是沿着轨道的守恒量，并且获得了积分常数。观察到屈曲受核矩类型的影响，对于显式对称核，平板反应器的最大通量和平均通量之比小于使用常规局部扩散方程获得的比值，结果这从技术上激励了核反应堆工程。