圆盘内汤姆孙问题的全局极小值：一种带固定边界电荷的分子动力学方法
Global Minima of the Thomson Problem in a Disk: A Molecular Dynamics Approach with Fixed Border Charges
- Dzhelepov Laboratory of Nuclear Problems, JINR（杰列波夫核问题实验室，JINR）
- Dubna State University（杜布纳国立大学）
- Meshcheryakov Laboratory of Information Technologies, JINR（梅什恰里亚科夫信息技术实验室，JINR）
- HSE University（高等经济学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文结合淬火分子动力学与固定边界启发式方法，为圆盘内N=60、61、92、99的汤姆孙问题找到能量更低的全局极小值构型，并确认或改进其对称性，结果高度可重复。
AI中文摘要：
我们报告了经典汤姆孙问题中N=60、61、92和99个排斥库仑电荷被限制在圆盘内的改进全局极小值构型。通过将淬火分子动力学（QMD）方法与Amore和Zarate引入的固定边界启发式方法相结合，我们系统地获得了能量E_QMD(60)=2159.3584240930、E_QMD(61)=2237.19264190、E_QMD(92)=5358.35353314和E_QMD(99)=6254.83029083的构型，这些能量优于先前已知的最佳值。对于N=60，我们构型的Voronoi图与先前报道的不同。N=61（C_2）和N=99（D_1）的对称性得到确认，并与这些构型的已知对称模式一致。对于N=92，尽管先前报道的Voronoi图具有较低的对称性，但我们的解表现出清晰的D_1（轴向）缺陷对称性。结果在多次独立运行中高度可重复，提供了强有力的证据表明这些构型是稳健的全局极小值候选。
英文摘要：
We report improved global-minimum configurations for the classical Thomson problem of $N=60$, $61$, $92$, and $99$ repulsive Coulomb charges confined to a disk. By combining the quenched molecular dynamics (QMD) method with the fixed-border heuristic introduced by Amore and Zarate, we systematically obtain configurations with energies $E_{\mathrm{QMD}}(60)=2159.3584240930$, $E_{\mathrm{QMD}}(61)=2237.19264190$, $E_{\mathrm{QMD}}(92)=5358.35353314$, and $E_{\mathrm{QMD}}(99)=6254.83029083$, which improve upon the previously best-known values. For $N=60$, the Voronoi diagram of our configuration differs from the one reported earlier. The symmetries for $N=61$ $(C_{2})$ and $N=99$ $(D_{1})$ are confirmed and are consistent with the known symmetry patterns for these configurations. For $N=92$, whereas the previously reported Voronoi diagram has lower symmetry, our solution exhibits a clear $D_{1}$ (axial) symmetry of defects. The results are highly reproducible across multiple independent runs, providing strong evidence that these configurations are robust global-minimum candidates.
