# Light, matter and bubble dynamics — v1.42.0

Two browser experiments inspired by the user's three reference screenshots. They are simulations, not new laboratory observations. The two sonoluminescence screenshots describe one phenomenon. The atom screenshot has no original calibration, source or apparatus; its headline is not evidence that atoms are confined light. Exact provenance of its two pictures has not been established.

## Hydrogen and a separate light cavity

Fixed-nucleus, nonrelativistic, field-free hydrogen 1s/2s/3s. Let x=r/a0. Spatial wavefunctions in a0^(-3/2):

- 1s: exp(-x)/sqrt(pi)
- 2s: (2-x) exp(-x/2)/(4 sqrt(2pi))
- 3s: (27-18x+2x²) exp(-x/3)/(81 sqrt(3pi))

Position samples use the radial Jacobian 4πr²|ψ|² and uniform solid angle, a seeded LCG and an inverse discretized radial CDF (Δr=.01 a0, r<100 a0). Each point represents an independent position measurement of an identically prepared atom, not a trajectory or multiple electrons in one atom. Accumulation is display order, not time evolution of stationary density. A density slice is not the detector image of photoionization microscopy. Its brightness uses a power transform to expose faint shells. Gold rings locate exact radial nodes. The nuclear marker is schematic.

Checks: normalization <1e-7; mean radius against 3n²/2 within 1e-5 a0; sample mean within 6 standard errors + .01 a0; exact nodal zeros. The independent finer radial integration uses Δr=.005 a0. E_n=-13.605693122994/n² eV in the fixed-nucleus approximation. No field ionization, Stark states, fine structure or electron optics are computed.

The separate ideal one-dimensional vacuum cavity has perfect reflectors: E_y/E0=sin(mπx/L)cos(ωt), cB_z/E0=−cos(mπx/L)sin(ωt), ω=cmπ/L, λ=2L/m. Fields have a common relative amplitude scale. Cross-sectional wireframes are an illustration, not a 3D cavity eigenmode solution. Its length in micrometres is independent of the atom's a0 scale. Similar-looking standing patterns do not imply identical physical systems.

## Driven spherical bubble

Keller–Miksis–Parlitz isolated-bubble equation with a hard-core polytropic closure. R0=4.5 μm; h=R0/8.86; f=26.5 kHz; rho=1000 kg/m³; mu=.001 Pa·s; sigma=.073 N/m; c=1481 m/s; P0=101325 Pa; kappa=5/3. R(0)=R0, U(0)=0. Vapor pressure, diffusion, heat transport, chemistry, nonspherical instabilities and photon emission are omitted.

p∞=P0−Pa sin(2πft); pg=(P0+2sigma/R0)[(R0³−h³)/(R³−h³)]^kappa; q=pg−2sigma/R−4mu U/R−p∞.

The implementation solves Rdot=U and

Udot = {[(1+U/c)q + (R/c)((pg′+2sigma/R²)U+4mu U²/R²−p∞dot)]/rho − (3/2)(1−U/(3c))U²} / [R(1−U/c)+4mu/(rho c)].

The viscosity derivative contributes to the denominator. Integration uses nondimensional R/R0 and t*f; adaptive RK4 step doubling, maximum step 1/512 cycle. The last requested cycle is returned, after 2–8 finite startup cycles; periodic steady state is not assumed. Linear interpolation is for display only. The sampled extrema are retained near collapse. The radius chart and surface use this same trajectory.

Freeze criteria before solving: refine tolerance 2e-7 to 2e-8; extrema and peak Mach must agree within .003 relative error; equilibrium at zero drive; full requested duration; exact replay and parameter binding. Stop on nonfinite integration, iteration budget, R≤1.02h or |U|/c>0.3. This Mach limit is a conservative application guard, not a proof of model accuracy.

The broad glow marks strong compression for visibility. It is not a calculated optical pulse, brightness, spectrum or claim of sonoluminescence onset. A collapse need not produce observable light. No temperature value is inferred from the screenshot.

## Sources, checked 2026-09-29

- Stodolna et al., PRL 110, 213001 (2013): https://ir.amolf.nl/pub/6240/15739OA.pdf — related photoionization microscopy, not a proven match to the screenshot. Our field-free low-n model does not reproduce this experiment.
- NIST fundamental constants: https://physics.nist.gov/cuu/Constants/Table/allascii.txt
- Suslov, Ooi & Manasseh (2012): https://arxiv.org/abs/1204.5285 — isolated-bubble limit of the radial equation; no wall term here.
- Hilgenfeldt et al. (1998): https://arxiv.org/abs/chao-dyn/9805016 — hard-core closure and bubble-dynamics background.
- Brenner, Hilgenfeldt & Lohse (2002): https://ris.utwente.nl/ws/portalfiles/portal/6684678/single-bubble_sonoluminescence.pdf — physical mechanisms and limits.

Workers are fixed local computational roles. Their replay is a numerical check, not independent scientific replication. Browser evidence enters the existing local signed-task graph; no external agent, payment, production database migration or laboratory affiliation is asserted by this release.