发表机构
Universidade Federal do Norte do Tocantins（托坎廷斯联邦北部大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过解析和数值方法表征高阶多项式pp波引起的粒子环花型变形，确认角模式主导性并区分位移与速度记忆。
AI 中文摘要
我们解析和数值地研究了由pp波的高阶多项式模式引起的粒子环的花型变形。横向潮汐本征方向决定了$m$个径向拉伸和压缩的交错扇区，而一个弱脉冲解提供了环的完整一阶响应。对$m=2,3,4$的直接测地线积分证实了预测的方向和离散对称性。傅里叶分析表明，响应仍然以角模式$n=m$为主导；特别是，对于$m=4$发现的环状结构源于基本模式的几何折叠，而非强谐波混合。脉冲的时间矩进一步区分了位移记忆与速度记忆，而不改变这一角特征。
英文摘要
We investigate analytically and numerically the floral deformation of particle rings induced by higher-order polynomial modes of pp-waves. The transverse tidal eigendirections determine $m$ interlaced sectors of radial stretching and compression, while a weak-pulse solution provides the complete first-order response of the ring. Direct geodesic integration for $m=2,3,4$ confirms the predicted orientation and discrete symmetry. A Fourier analysis shows that the response remains overwhelmingly dominated by the angular mode $n=m$; in particular, the loops found for $m=4$ arise from geometrical folding of the fundamental mode rather than strong harmonic mixing. The temporal moments of the pulse further distinguish displacement from velocity memory without changing this angular signature.
Comments6 pages, 4 figures
