This paper introduces the first structural law governing a hybrid Klein–Gordon / Rayleigh–Plesset (KG–RP) model of sonoluminescence, showing that the breathing mode of a nonlinear scalar field and the collapse cycle of a bubble lock into stable integer frequency ratios across thousands of simulations. By nondimensionalizing the system and sweeping a wide parameter space, the work identifies seven fundamental invariants and nine composite dimensionless groups that fully determine the detuning between the two oscillators. Using physically constrained symbolic regression, the study extracts a compact closed‑form detuning law with strong predictive power (R² ≈ 0.72) and demonstrates that this law holds universally across mild, moderate, and strongly nonlinear collapse regimes. The result is not new quantum physics, but a clean, classical structural law that reveals unexpected order in a highly nonlinear system. For the sonoluminescence community, this provides the first mathematically explicit framework linking bubble dynamics to field dynamics, offering a reproducible, empirically validated foundation for future theoretical and experimental work.
David Mulnix (Tue,) studied this question.
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