球盒中软排斥粒子的堆积--广义汤姆逊问题
Packing of softly repulsive particles in a spherical box - a generalised Thomson problem
摘要：
研究了N个软排斥粒子在球盒中的（接近或接近）基态分布。电荷通过形式为$1/r^γ$的逆幂律势相互作用。我们研究了三种制度，其中的费用形成一个单一的球壳在边缘的盒子（$γ=1$），一系列的同心壳的密度增加（$γ=2$）和$γ=12$的费用形成壳具有更均匀的电荷分布。我们进行数值模拟的集群包含多达5000个电荷和比较整个系统的电荷密度与连续极限的结果。数值（离散）结果和连续极限之间的一致性被发现随着N的增加而改善。
英文摘要：
We study the (near or close to) ground state distribution of N softly repelling particles trapped in the interior of a spherical box. The charges mutually interact via an inverse power law potential of the form $1/r^γ$. We study three regimes in which the charges form an single spherical shell at the edge of the box ($γ=1$), a series of concentric shells of increasing density ($γ=2$) and $γ=12$ for which the charges form shells with a more uniform charge distribution. We conduct numerical simulations for clusters containing up to 5000 charges and compare charge density across the system with continuum limit results. The agreement between numerical (discrete) results and the continuum limit is found to improve with increasing N.
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