发表机构
Jožef Stefan Institute（约瑟夫·斯特凡研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对曲面上粒子组织的有序机制，发现非球面形变可消除球面处的简并性，通过Riesz s-能量与屏蔽库仑势两类相互作用，可利用离子强度调控粒子有序性以探测微观相互作用定律。
AI 中文摘要
球面掩盖了粒子组织的单体特征：面积均匀、导体和曲率加权的测量在球面处重合，因此有序机制在密度中没有留下痕迹。非球面形变消除了这种简并性。在椭球面上，这些有序机制分离为壳中心到其切平面距离的不同幂次。在形变的主导阶，特征指数可从结构因子四极矩和回转半径两者读出。两类相互作用以互补方式实现该指数：Riesz s-能量，其极限测度在边际幂次处急剧切换；以及屏蔽库仑势，其指数由盐浓度连续调节。离子强度因此成为实验旋钮，在固定非球面上转变粒子有序性，跨越导体到堆积的交叉，将宏观形状参数转变为探测微观相互作用定律的探针。
英文摘要
Spherical surfaces conceal the one-body signature of particle organization: area-uniform, conductor, and curvature-weighted measures coincide there, so the ordering mechanism leaves no trace in the density. Hard spheres and Coulomb charges confined to the sphere thus produce identical mean densities, and distinctions between their particle arrangements appear only in many-body correlations. Aspherical deformation lifts this degeneracy, and we show that on an ellipsoid, different ordering mechanisms separate by virtue of a single exponent $p$ of the distance from the shell center to its tangent plane. To leading order in deformation, the characteristic exponent $p$ can be obtained both from the quadrupole of the spherical structure factor and from the radius of gyration. Two interaction families demonstrate how this can be realized in practice: the Riesz $s$-energy, whose limiting measure is determined by the power $s$ and exhibits a transition at $s=d=2$, and the screened Coulomb potential, whose measure and thus the characteristic exponent are tuned continuously by the salt concentration. The value of the characteristic exponent $p$ positions the arrangement of particles between the conductor and packing limits, and its response to a control parameter such as salt concentration can be used experimentally to identify the interaction family.
Comments10 pages, 3 figures
