Tadić Bosiljka, Šuvakov Milovan, Andjelković Miroslav, Rodgers Geoff J
Department of Theoretical Physics, Jožef Stefan Institute, Jamova 39, Ljubljana, Slovenia.
Complexity Science Hub Vienna, Josephstadter Strasse 39, Vienna, Austria.
Phys Rev E. 2020 Sep;102(3-1):032307. doi: 10.1103/PhysRevE.102.032307.
Recently, the importance of higher-order interactions in the physics of quantum systems and nanoparticle assemblies has prompted the exploration of new classes of networks that grow through geometrically constrained simplex aggregation. Based on the model of chemically tunable self-assembly of simplexes [Šuvakov et al., Sci. Rep. 8, 1987 (2018)2045-232210.1038/s41598-018-20398-x], here we extend the model to allow the presence of a defect edge per simplex. Using a wide distribution of simplex sizes (from edges, triangles, tetrahedrons, etc., up to 10-cliques) and various chemical affinity parameters, we investigate the magnitude of the impact of defects on the self-assembly process and the emerging higher-order networks. Their essential characteristics are treelike patterns of defect bonds, hyperbolic geometry, and simplicial complexes, which are described using the algebraic topology method. Furthermore, we demonstrate how the presence of patterned defects can be used to alter the structure of the assembly after the growth process is complete. In the assemblies grown under different chemical affinities, we consider the removal of defect bonds and analyze the progressive changes in the hierarchical architecture of simplicial complexes and the hyperbolicity parameters of the underlying graphs. Within the framework of cooperative self-assembly of nanonetworks, these results shed light on the use of defects in the design of complex materials. They also provide a different perspective on the understanding of extended connectivity beyond pairwise interactions in many complex systems.
最近，量子系统和纳米粒子组装物理学中高阶相互作用的重要性促使人们探索通过几何约束单形聚集生长的新型网络。基于单形化学可调自组装模型[舒瓦科夫等人，《科学报告》8，1987（2018）2045 - 232210.1038/s41598 - 018 - 20398 - x]，在此我们扩展该模型，允许每个单形存在一条缺陷边。使用广泛分布的单形尺寸（从边、三角形、四面体等，直至10 - 团）和各种化学亲和参数，我们研究缺陷对自组装过程和新兴高阶网络的影响程度。它们的基本特征是缺陷键的树状模式、双曲几何和单纯复形，这些使用代数拓扑方法进行描述。此外，我们展示了在生长过程完成后，如何利用图案化缺陷的存在来改变组装结构。在不同化学亲和力下生长的组装体中，我们考虑去除缺陷键，并分析单纯复形层次结构和基础图双曲性参数的渐进变化。在纳米网络协同自组装的框架内，这些结果为复杂材料设计中缺陷的使用提供了启示。它们还为理解许多复杂系统中超越成对相互作用的扩展连通性提供了不同视角。
