Open-channel radiation zeros and nonlinear damping of a critical-bubble internal mode
Abstract
We study radiation and nonlinear damping of a spherically symmetric localized mode of an O(3) thermal critical bubble. The leading second-harmonic radiation amplitude is determined by the overlap between a nonlinear source and a continuum scattering wave. This overlap can vanish through destructive interference as the supercooling is varied, even when the second harmonic lies above the continuum threshold. A signed-overlap scan resolves five zeros in a finite parameter interval, including three on the thinner-wall side of the two representative roots studied in detail. For these representative roots, half-line Jost--Green calculations, threshold-preserving wall deformations, and constrained radial evolution verify the cancellation and its robustness. Near a selected root, fourth-order perturbation theory predicts an A2 displacement of the finite-amplitude radiation minimum and an A-linear width of the third-harmonic-dominated region; radial evolution quantitatively tests both relations. At the selected zero, third-harmonic loss predicts A∼τ−1/4, instead of the generic A∼τ−1/2 law. Measured harmonic powers and a slow-envelope reconstruction support this hierarchy. Independent center-stable shooting recovers the unprojected third-harmonic coefficient, which differs from the fixed-projector value. The results connect a tunable radiation form factor to nonlinear relaxation of an internal mode on an unstable nucleation saddle.
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BibTeX
@misc{inagaki2026openchannel,
title = {{Open-channel radiation zeros and nonlinear damping of a critical-bubble internal mode}},
author = {Tomohiro Inagaki and Yuko Murakami},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15056},
eprint = {2609.15056},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15056},
}
RIS
TY - UNPB
TI - Open-channel radiation zeros and nonlinear damping of a critical-bubble internal mode
AU - Tomohiro Inagaki
AU - Yuko Murakami
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15056
UR - https://arxiv.org/abs/2609.15056
AB - We study radiation and nonlinear damping of a spherically symmetric localized mode of an O(3) thermal critical bubble. The leading second-harmonic radiation amplitude is determined by the overlap between a nonlinear source and a continuum scattering wave. This overlap can vanish through destructive interference as the supercooling is varied, even when the second harmonic lies above the continuum threshold. A signed-overlap scan resolves five zeros in a finite parameter interval, including three on the thinner-wall side of the two representative roots studied in detail. For these representative roots, half-line Jost--Green calculations, threshold-preserving wall deformations, and constrained radial evolution verify the cancellation and its robustness. Near a selected root, fourth-order perturbation theory predicts an A^2 displacement of the finite-amplitude radiation minimum and an A-linear width of the third-harmonic-dominated region; radial evolution quantitatively tests both relations. At the selected zero, third-harmonic loss predicts A∼τ^−1/4, instead of the generic A∼τ^−1/2 law. Measured harmonic powers and a slow-envelope reconstruction support this hierarchy. Independent center-stable shooting recovers the unprojected third-harmonic coefficient, which differs from the fixed-projector value. The results connect a tunable radiation form factor to nonlinear relaxation of an internal mode on an unstable nucleation saddle.
ER -