有向级联生成新的临界普适类
Directed Cascades Generate New Critical Universality Classes
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中文总结 AI 辅助
该研究证明有向级联的结构可控制瞬态放大与临界统计，连接多个临界子系统会产生新的临界普适类，还为前震-主震序列的高丰度提供了稳态机制。
中文摘要 AI 辅助
谱稳定的级联在最终消失前可经历巨大的瞬态增长。我们证明，这种放大由相互作用的有向结构控制，与决定渐近稳定性的本征值无关。更值得注意的是，当多个临界子系统依次连接时，它们的深度成为临界涨落的新控制参数：每个额外的临界阶段都会产生新的级联大小指数，形成无限的普适类层级。该结果源于一个阶段产生的涨落种群成为下一阶段的随机输入。该机制对有限方差和重尾繁殖均成立，且会大幅提升罕见终端事件的概率。将其应用于多类型地震触发时，它为前震-主震序列异常高的丰度提供了一种稳态机制。因此，即使有向结构未改变谱稳定性，它也能控制级联过程中的瞬态放大和临界统计。
英文摘要
Spectrally stable cascades can undergo enormous transient growth before eventually dying out. We show that this amplification is controlled by the directed architecture of the interactions, independently of the eigenvalues that determine asymptotic stability. More remarkably, when several critical subsystems are connected sequentially, their depth becomes a new control parameter for critical fluctuations: each additional critical stage generates a new cascade-size exponent, producing an infinite hierarchy of universality classes. This result follows because the fluctuating population produced at one stage becomes the random input to the next. The mechanism persists for both finite-variance and heavy-tailed reproduction and strongly enhances the probability of rare terminal events. Applied to multitype earthquake triggering, it provides a stationary mechanism for the anomalously large abundance of foreshock-mainshock sequences. Directed architecture can therefore control both transient amplification and critical statistics in cascade processes even when it leaves spectral stability unchanged.
