多标度性、渗透阈值和核反应堆的临界点
Multifractality, percolation threshold and critical point of a nuclear reactor
AI总结：
本文通过多标度模型分析核反应堆中子行为，揭示临界点与渗透阈值的关系，探讨链式反应的临界特性及应用。
摘要：
本文利用多标度模型分析反应堆中中子的演化过程。对于链式反应，确定了多标度中子行为的各种特性。这些包括多标度载体的维度、信息维度和相关维度、 fractal 集合的熵、最大和最小维度值以及多标度谱函数。多标度的几何特征允许描述由分层从属的统计集合组成的随机系统，这些集合由 Cayley 树特征化。在层次上建立了一个平稳分布，其遵循 Tsallis 幂律。本文还指出了一些分形图案在核反应堆理论中的潜在应用。渗透概率，即在 Bethe 晶格中存在至少一条连续路径通过邻近导电节点贯穿整个结构的状态，类似于自维持裂变链式反应发生的可能性。当此概率达到临界点时，会形成一个（条件性）无限的中子集群。渗透概率受反应堆运行时间及其大小的影响，并与反应堆的临界性相关。我们研究了中子乘数因子随时间的变化。特别关注自维持核裂变链式反应的早期阶段。我们还强调了识别临界区域边界的途径。
英文摘要：
A multifractal model is used to analyze neutron evolution within a reactor. For chain reactions, various characteristics of multifractal neutron behavior have been determined. These include the dimension of the multifractal carrier, information and correlation dimensions, the entropy of the fractal set, maximum and minimum dimension values, and the multifractal spectrum function. The geometric features of a multifractal allow for the description of a stochastic system consisting of hierarchically subordinate statistical ensembles, which are characterized by Cayley trees. A stationary distribution over hierarchical levels is established, which follows the Tsallis power law. The text also points out some potential applications of fractal patterns in nuclear reactor theory. The chance of percolation, which is when we see a state in the Bethe lattice where there's at least one continuous path through neighboring conducting nodes all the way across, is similar to the likelihood of a self-sustaining fission chain reaction happening. When this probability hits a critical point, we get a (conditionally) infinite cluster of neutrons forming. The percolation probability, influenced by how long the reactor has been running and its size, is linked to the reactor's criticality. We take a look at how the neutron multiplication factor behaves over time. We especially focus on the early stages of a self-sustaining nuclear fission chain reaction. We also highlight the ways to identify the boundaries of the critical region.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
