Experiment 04 · Wave Solver

The hypothesis, run against
a real wave equation.

This is a 2D finite-difference time-domain (FDTD) solver for the acoustic wave equation, running directly in the browser on a 128×128staggered Yee grid. The numbers below are not parameterized — they are computed from the simulation as it runs.

→ Compare all five · Tri-Bhaga sweep↗ Planet-scale · /twin Schumann coherence
EXPLAIN LIKE I'M 10
· everyday-language one-paragraph version
Actual waves bouncing around inside a shape, simulated step by step in your browser. Like watching ripples in a pool, but the pool is shaped however you choose. Clean ring-shaped ripples mean the shape is 'singing' on its own note. Messy scattered ripples mean it is leaking. The frequency chart on the side tells you which note it picks.
WHAT YOU ARE LOOKING AT
A live 2D wave equation solved on a grid, showing how a wave actually propagates inside each candidate cavity. This is not a graph of a model — it is the model running step by step in your browser.
WHY THIS MATTERS FOR QUANTUM
A qubit cavity is a resonant chamber for an electromagnetic wave. Whether that wave persists (high Q) or scatters out (low Q) is decided by the geometry alone. This page runs the scalar wave equation — the same one Maxwell wrote — inside whichever shape you pick. What you see on screen is what the qubit would experience.
WHAT TO WATCH
The bright wavefronts. Clean concentric rings means a standing-wave resonance is forming. Chaotic scatter means the cavity is leaking. The frequency spectrum on the side tells you whether one mode dominates — that is the resonance peak.
Swayambhu (self-formed) variants
Reference shapes
Tri-Bhaga proportion · Shilpa Shastra rule
Pressure field · p(x, y)
6.40 cm × 6.40 cm
t = 0.00 ms · step 0/12000
broadband · σ 50µs
FFT · pressure at cavity centre
Energy decay · ∑ p² (log)
Solver record · what is computed here

Update rules: vx, vy on cell faces; p at cell centres. Boundary: Neumann (rigid wall) where the geometry mask=0; graded velocity absorber in the 14-cell border. CFL: dt = 0.729 µs at dx = 0.5 mm. Sampling rate 1372 kHz (Nyquist 686 kHz). Q from −3 dB FFT bandwidth and from linear regression of log E(t).

Geometry
Dhara composite

Five-layer hierarchical cavity: square plinth · octagonal stepped drum · elliptical base with directional outflow channel · Bragg-ring-modulated cylindrical shaft · parabolic cap. The Bragg rings on the shaft give axial frequency selectivity; the directional channel provides a preferred outcoupling axis.

Formation conditions

Architect-prescribed under Shilpa Shastra Tri-Bhaga ratios (Sarvamanika / Vardhamana / Sivadhika). The five-layer arrangement is the canonical consecrated form.

Source mode
Broadband Gaussian pulse · σ = 50 µs

Single Gaussian bump at t = 150 µs. Spectrum is Gaussian centered at 0 Hz with useful content out to ~10.0 kHz. Broadband enough to excite every cavity mode in the band, so the FFT peak is the dominant natural mode of the geometry — not an artefact of the source.

Why this experiment exists

Every other screen on this instrument uses parameterized heuristics that are consistent with cited literature. This one does not. It integrates the acoustic wave equation on a real grid and reports the quantities that come out. The point is to see whether the Helmholtz prediction on the Geometry Arena page survives contact with a numerical wave simulator. If the FFT peak from FDTD lands close to the analytic Helmholtz frequency for the Dhara composite at 3.4 cm, the analytic model is corroborated for this geometry. If it does not, the analytic model is the thing that needs revising.

Honest limits of this build
  • · 2D axisymmetric cross-section, not full 3D — Q values are upper bounds.
  • · Air at STP, lossless interior — wall absorption not modelled.
  • · Grid is 128² (6.40 cm side). Bragg ring count and slit width are quantised by dx.
  • · Source is a soft injection at the cavity centre; mode selection depends on where you couple in.
  • · The acoustic regime is a scale-legible proxy. Geometric rankings transfer up the frequency ladder via the photonic-phononic equivalence; absolute numbers do not.