标题： 乘法过程的重要性 显示英文标题

标题： The criticality of multiplicative processes

摘要： 考虑到对核反应堆核心在临界附近的演化进行数值模拟的应用，我们使用一个通用的数学框架来描述乘法过程（涉及粒子生成的过程）在粒子世代和时间上的演化。 该框架使我们能够在同一形式体系中获得两个对应的倍增因子估计值，这些估计值描述了大时间尺度下粒子数量的增长。 我们得到了这两个估计值彼此之间以及与临界状态之间的相对位置。 这些关系在以现实方式模拟次临界状态下核反应堆的监测时可能特别有用，例如加速器驱动系统（ADS）的情况。 更一般地，这项研究适用于自然界中存在的各种乘法过程。 显示英文摘要

摘要： Keeping in view applications to numerical simulations of the evolution of a nuclear reactor core around criticality, we use a general mathematical framework for describing the evolutions of multiplicative processes (processes involving particle creation) both in particle generations and in time. This framework allows us to obtain, within a same formalism, two corresponding estimates of the multiplication factor which describes the growth of particle numbers at large times. We obtain the relative positions of both estimates with respect to each other and to criticality. These relations may show particularly useful when simulating in a realistic way the monitoring of nuclear cores in subcritical states, such as is the case for Accelerator Driven Systems (ADS). More generally, this study applies to various multiplicative processes which can be found in nature.