Abstract

Processes of coalescence and fragmentation are used to understand the time-evolution of the mass distribution of various systems and may result in a steady state or in stable deterministic or stochastic cycles. Motivated by applications in insurgency warfare we investigate coalescence-fragmentation systems. We begin with a simple model of size-biased coalescence accompanied by shattering into monomers. Depending on the parameters this model has an approximately power-law-distributed steady state or stochastic cycles of alternating gelation and shattering. We conduct stochastic simulations of this model and its generalizations to include different kernel types, accretion and erosion, and various distributions of non-shattering fragmentation. Our central aim is to explore the robustness of the steady state and gel-shatter stochastic cycles to these variations. We show that an approximate power-law steady state persists with the addition of accretion and erosion, and with partial rather than total shattering. However, broader distributions of fragment sizes typically vitiate both the power law steady state and gel-shatter cyclicity. This work clarifies features shown in coalescence/fragmentation model simulations and elucidates the relationship between the microscopic dynamics and observed phenomena in this widely applicable interdisciplinary model type.

Graphical abstract

中文翻译：

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广义聚结断裂模型中稳态和随机循环的鲁棒性

摘要

合并和分裂过程用于了解各种系统的质量分布的时间演化，并可能导致稳态或稳定的确定性或随机循环。受叛乱战争应用的启发，我们研究了聚结-碎片系统。我们从一个简单的尺寸偏向聚结模型开始，并伴随着破碎成单体。根据参数，该模型具有近似幂律分布的稳态或交替凝胶化和破碎的随机循环。我们对该模型及其概括进行了随机模拟，包括不同的内核类型、吸积和侵蚀以及非破碎碎片的各种分布。我们的中心目标是探索稳态和凝胶破碎随机循环对这些变化的鲁棒性。我们表明，随着吸积和侵蚀的增加，以及部分而不是全部破碎，近似幂律稳态持续存在。然而，碎片尺寸的更广泛分布通常会破坏幂律稳态和凝胶破碎循环。这项工作阐明了聚结/破碎模型模拟中显示的特征，并阐明了这种广泛适用的跨学科模型类型中微观动力学与观察到的现象之间的关系。

图形概要