本文研究了一种模型网络液体，已知该液体通过连续两次液-液相变（LLPTs）实现致密化。研究人员阐明了环（由网络中键合粒子形成的循环路径）及其空间分布对于理解支撑LLPTs过程中密度增加的结构变化的重要性。
分析表明，这些网络的致密化主要由连环的形成驱动，而LLPTs对应于一系列拓扑转变，其中环是基本的构建块。研究人员设想纠缠作为一种普遍的致密化机制出现，这对物理网络的嵌入，尤其是在受限空间中，具有广泛的影响。
据悉，将复杂系统表示为网络已成为科学领域中的一项关键工具。在物理网络（如生物神经网络、血管网络或网络液体，其中节点和边占据三维空间中的体积）的背景下，如何使它们变得密集排列是一个特别重要的问题。
附：英文原文
Title: Hierarchy of topological transitions in a network liquid
Author: Neophytou, Andreas, Starr, Francis W., Chakrabarti, Dwaipayan, Sciortino, Francesco
Issue&Volume: 2024-8-29
Abstract: The representation of complex systems as networks has become a critical tool across many fields of science. In the context of physical networks, such as biological neural networks, vascular networks, or network liquids where the nodes and edges occupy volume in three-dimensional space, the question of how they become densely packed is of special importance. Here, we investigate a model network liquid, which is known to densify via two successive liquid–liquid phase transitions (LLPTs). We elucidate the importance of rings—cyclic paths formed by bonded particles in the networks—and their spatial disposition in understanding the structural changes that underpin the increase in density across the LLPTs. Our analyses demonstrate that the densification of these networks is primarily driven by the formation of linked rings, and the LLPTs correspond to a hierarchy of topological transitions where rings form the fundamental building blocks. We envisage entanglement to emerge as a general mechanism for densification, with wide implications for the embedding of physical networks, especially in confined spaces.
DOI: 10.1073/pnas.2406890121
Source: https://www.pnas.org/doi/abs/10.1073/pnas.2406890121