论文标题
曲线上粒子的动力学
Dynamics of Particles on a Curve with Pairwise Hyper-singular Repulsion
论文作者
论文摘要
我们调查了$ n $颗粒的巨大时间行为，仅限于$ \ mathbb {r}^d $的平滑封闭曲线，并在欧几里得超单星的偏见riesz $ s $ syergy方面呈梯度流，并带有$ s>1。 $ n $ - 最小。此外，相对于沿曲线的弧度测量，此类颗粒的分布将接近均匀。
We investigate the large time behavior of $N$ particles restricted to a smooth closed curve in $\mathbb{R}^d$ and subject to a gradient flow with respect to Euclidean hyper-singular repulsive Riesz $s$-energy with $s>1.$ We show that regardless of their initial positions, for all $N$ and time $t$ large, their normalized Riesz $s$-energy will be close to the $N$-point minimal possible. Furthermore, the distribution of such particles will be close to uniform with respect to arclength measure along the curve.
