关键灾难回顾
The critical catastrophe revisited
摘要：
核反应堆原型模型中的中子数可以描述为一组被限制在盒子中的粒子，并经历三种关键的随机机制：扩散、裂变引起的再生和吸收事件引起的死亡。当反应堆在临界点运行，裂变正好被裂变所补偿时，由于出生和死亡引起的剧烈波动，整个中子总数原则上可能会消失。这种现象被称为严重灾难，但在实践中从未观察到：作用于总人口的反馈机制，如人为干预，具有稳定作用。在这项工作中，我们重新审视的关键灾难调查的空间行为的波动在一个封闭的几何形状。当系统自由演化时，中子可能会呈现出一种疯狂的斑块状（群集）。相反，对总人口进行人口控制也会抑制局部波动，从而抑制空间聚集。粒子数控制在淬灭空间涨落中的有效性将被证明取决于中子混合时间之间的竞争（即，粒子探索有限可行空间所花费的平均时间）和灭绝时间。
英文摘要：
The neutron population in a prototype model of nuclear reactor can be described in terms of a collection of particles confined in a box and undergoing three key random mechanisms: diffusion, reproduction due to fissions, and death due to absorption events. When the reactor is operated at the critical point, and fissions are exactly compensated by absorptions, the whole neutron population might in principle go to extinction because of the wild fluctuations induced by births and deaths. This phenomenon, which has been named critical catastrophe, is nonetheless never observed in practice: feedback mechanisms acting on the total population, such as human intervention, have a stabilizing effect. In this work, we revisit the critical catastrophe by investigating the spatial behaviour of the fluctuations in a confined geometry. When the system is free to evolve, the neutrons may display a wild patchiness (clustering). On the contrary, imposing a population control on the total population acts also against the local fluctuations, and may thus inhibit the spatial clustering. The effectiveness of population control in quenching spatial fluctuations will be shown to depend on the competition between the mixing time of the neutrons (i.e., the average time taken for a particle to explore the finite viable space) and the extinction time.
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