发表机构
Recognition Physics Institute; Heinrich-Heine-Universität Düsseldorf; Department of Physics, Case Western Reserve University; Theoretical Department, Joint Institute for High Temperatures, RAS（识别物理研究所; 杜塞尔多夫海因里希·海涅大学; 凯斯西储大学物理系; 俄罗斯科学院高温联合研究所理论部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究球面上硬球柱体在切向导向场锁定下的堆积非均匀性，发现倾斜角控制奇点周围贫化区宽度，均匀性受几何而非倾斜限制，方差遵循幂律。
AI 中文摘要
我们研究了球面上的硬球柱体，其轴被刚性锁定在切向导向场中，与经线成固定角度$\tilt$，该导向场在极点处必然奇异。问题由三个长度尺度决定：杆长$\Lrod$、直径$\Drod$和宿主球半径$\Rsph$。针对十五种几何构型和四种覆盖率进行的蒙特卡洛模拟，对于极向边缘分布（即杆中心密度的方位角平均）给出了两个主要结果。首先，倾斜角是控制堆积在每个奇点周围诱导的贫化区域宽度的连续手柄。在经线锁定下，该宽度主要由杆长决定；将导向场转向纬线方向会显著收缩该区域，且收缩在达到纬线锁定之前就已充分完成。其次，极向边缘分布能达到的均匀程度受几何限制，而非倾斜角限制。在采样网格上观察到的最小方差遵循$\Lrod^{2}/(\Rsph\Drod)$的幂律，该量以杆直径为单位衡量直杆两端偏离曲面的距离，有效指数介于$1.1$和$1.3$之间。小宿主球上的长杆在任何采样倾斜角下都无法实现均匀分布；解决方法是几何性的，而非取向性的。极向边缘分布几乎在所有情况下都偏向赤道，仅在高覆盖率和倾斜角下反转；经线锁定是最不均匀的选择，而方差最小化的倾斜角通常位于从$31.7^{\circ}$到$55^{\circ}$的采样带内。黄金比例倾斜角$\arctan(1/\phigold)$是这些角度之一：它是一个基准，而非模型选择的结果。这两个结果都描述了无限锁定的无热系综。
英文摘要
We study hard spherocylinders on a sphere with axes rigidly locked to a tangential director field at fixed angle $\tilt$ to the meridian, necessarily singular at the poles. Three lengths set the problem: the rod length $\Lrod$, the diameter $\Drod$, and the host radius $\Rsph$. Monte Carlo simulations across fifteen geometries and four coverages give two main results for the polar marginal, the azimuthal average of rod-center density. First, the tilt is a continuous handle on the width of the depleted region that packing induces around each singularity. Under meridian locking it is set principally by the rod length; turning the director toward the latitude contracts it substantially, the contraction being spent well before latitude locking. Second, how uniform the polar marginal can be made is limited by geometry, not tilt. The smallest variance on the sampled grid follows a power law in $\Lrod^{2}/(\Rsph\Drod)$, which measures how far a straight rod's ends stand off the curved surface in rod diameters, with an effective exponent between $1.1$ and $1.3$. Long rods on small hosts cannot be made uniform at any sampled tilt; the remedy is geometric, not orientational. The polar marginal is equator-heavy almost everywhere, inverting only at high coverage and tilt; meridian locking is the least uniform choice, and the variance-minimizing tilt usually lies in a sampled band from $31.7^{\circ}$ to $55^{\circ}$. The golden-ratio tilt $\arctan(1/\phigold)$ is one of those angles: a benchmark, not one the model selects. Both results describe the infinitely locked athermal ensemble.
Comments12 pages with 8 figures
