Despite decades of interdisciplinary research on topologically linked ring polymers, their dynamics remain largely unstudied. These systems represent a major scientific challenge as they are often subject to both topological and hydrodynamic interactions (HI), which render dynamical solutions either mathematically intractable or computationally prohibitive. Here we circumvent these limitations by preaveraging the HI of linked rings. We show that the symmetry of ring polymers leads to a hydrodynamic decoupling of ring dynamics. This decoupling is valid even for nonideal polymers and nonequilibrium conditions. Physically, our findings suggest that the effects of topology and HI are nearly independent and do not act cooperatively to influence polymer dynamics. We use this result to develop highly efficient Brownian dynamics algorithms that offer enormous performance improvements over conventional methods and apply these algorithms to simulate catenated ring polymers at equilibrium, confirming the independence of topological effects and HI. The methods developed here can be used to study and simulate large systems of linked rings with HI, including kinetoplast DNA, Olympic gels, and poly[$n$]catenanes.

中文翻译：

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拓扑连接的环聚合物中的流体动力学相互作用

尽管对拓扑连接的环聚合物进行了数十年的跨学科研究，但仍未对其动力学进行研究。这些系统经常面临拓扑和水动力相互作用（HI），这代表了重大的科学挑战，这使得动力学解决方案在数学上难以处理或在计算上令人望而却步。在这里，我们通过平均链接环的HI来规避这些限制。我们表明，环聚合物的对称性导致环动力学的流体动力学解耦。这种去耦甚至对于非理想的聚合物和非平衡条件也是有效的。从物理上讲，我们的发现表明拓扑结构和HI的影响几乎是独立的，并且不协同作用来影响聚合物动力学。我们使用该结果来开发高效的布朗动力学算法，与传统方法相比，该算法提供了巨大的性能改进，并将这些算法应用于平衡状态下的链状环聚合物模拟，从而确认了拓扑效应和HI的独立性。此处开发的方法可用于研究和模拟与HI相连的大型环，包括动塑料DNA，奥林匹克凝胶和聚[$ñ$] catenanes。