Analytical and spectral characterization of floral patterns in higher-order polynomial pp-waves
Abstract
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.
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BibTeX
@misc{carneiro2026analytical,
title = {{Analytical and spectral characterization of floral patterns in higher-order polynomial pp-waves}},
author = {F. L. Carneiro and H. P. de Carvalho and L. A. Cabral and M. P. Lobo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25459},
eprint = {2609.25459},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25459},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Analytical and spectral characterization of floral patterns in higher-order polynomial pp-waves
AU - F. L. Carneiro
AU - H. P. de Carvalho
AU - L. A. Cabral
AU - M. P. Lobo
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25459
UR - https://arxiv.org/abs/2609.25459
AB - 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.
ER -