Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E6, Canada.
Phys Rev E. 2019 Oct;100(4-1):042413. doi: 10.1103/PhysRevE.100.042413.
Determination of optimal arrangements of N particles on a sphere is a well-known problem in physics. A famous example of such is the Thomson problem of finding equilibrium configurations of electrical charges on a sphere. More recently, however, similar problems involving other potentials and nonspherical domains have arisen in biophysical systems. Many optimal configurations have previously been computed, especially for the Thomson problem; however, few results exist for potentials that correspond to more applied problems. Here we numerically compute optimal configurations corresponding to the narrow escape and narrow capture problems in biophysics. We provide comprehensive tables of global energy minima for N≤120 and local energy minima for N≤65, and we exclude all saddle points. Local minima up to N=120 are available online.
在物理学中，确定 N 个粒子在球面上的最佳排列是一个众所周知的问题。这样的著名例子是汤姆孙问题，即在球面上找到电荷的平衡配置。然而，最近在生物物理系统中也出现了涉及其他势和非球形域的类似问题。以前已经计算了许多最佳配置，特别是对于汤姆孙问题；然而，对于更适用于实际问题的势，几乎没有结果。在这里，我们数值计算了生物物理学中狭窄逃逸和狭窄捕获问题的最佳配置。我们提供了 N≤120 的全局能量最小值和 N≤65 的局部能量最小值的综合表格，并排除了所有鞍点。局部最小值至 N=120 的结果可在线获取。
