A Unified Structural Law for Single–Bubble Sonoluminescence

This paper introduces the first unified mathematical model of single-bubblesonoluminescence (SL), showing that the entire collapse process—geometricfocusing, KG-mode activation, plasma formation, temperature scaling, and lightemission—is governed by a small set of dimensionless invariants and a nestedmanifold hierarchy. For decades, SL research has been fragmented across RP dynamics, plasmaphysics, thermal models, and quantum-field analogues. This work connects theseregimes into a single structure. The hybrid RP–KG–plasma system reduces tothree upstream invariants (IKG, ISP, IₚE), with temperature and lightemerging as downstream invariants (IT = IKG, IL = IₚE). These form a strictcascade: Geometry → IKG → IₚE → IT, IL and a nested manifold structure Mₚ ⊂ MKG. The paper derives closed-form expressions for all invariants, a universallocking law for detuning, and a Master Structural Theorem proving that everydimensionless scalar in the system is a function of (IKG, ISP, IₚE). Thousands of hybrid simulations confirm the theory: the invariants collapse thedata, reproduce KG activation and detuning behavior, and match plasma-energyscaling. The same structure explains multiple experimental datasets thatpreviously lacked a unified interpretation. In summary, the work provides the first complete structural law for SL, showing that its complex dynamics reduce to a simple, hierarchical invariantarchitecture.