The impact of topology on the structure of a smectic monolayer confined to a sphere is explored by particle-resolved computer simulations of hard rods. The orientations of the particles are tangential to the sphere and either free or restricted to a prescribed director field with a latitude or longitude orderings. Depending on the imprinted topology, a wealth of different states are found including equatorial smectic with isotropic poles, equatorial smectic with empty poles, a broken egg-shell like modulated smectic, a capped nematic with equatorial bald patches, equatorial nematic with empty poles, and a situation with 4 or 8 half-strength topological defects. Potentially these states could be verified in experiments with Pickering emulsions of droplets with colloidal rods. The unique nature of dipolar structures consisting of positive and negative half-strength disclinations is revealed. These structures, classified by their density and interaction with other defects in the system, relieve the strain of the poles by separating closely positioned half-strength defects. The proximity of these structures to the half-strength defects might enhance the structural diffusion of the defects across the system.

中文翻译：

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限制在球体上的近晶单层：粒子尺度上的拓扑

通过硬棒的粒子解析计算机模拟，探索了拓扑对局域单层层限制在一个球体中的结构的影响。粒子的方向与球体相切，并且自由或受限于具有纬度或经度顺序的指定导向器场。根据所刻印的拓扑结构，发现了许多不同的状态，包括具有各向同性极的赤道近晶，具有空极的赤道近晶，像调制近晶的破壳蛋壳，具有赤道秃斑的有盖向列相，带有空极的赤道向列相以及具有4或8个半强度拓扑缺陷的情况。这些状态可能会在使用胶体棒的液滴的Pickering乳液实验中得到验证。揭示了由正负半强度错位构成的偶极结构的独特性质。这些结构按其密度和与系统中其他缺陷的相互作用进行分类，通过分离紧密放置的半强度缺陷来减轻磁极的应变。这些结构与半强度缺陷的接近度可能会增强缺陷在整个系统中的结构扩散。