This is an independent 2D model, not a flattened version of the 3D scene. Instead of a rigid static cylinder, the gluon flux tube here is discretized into a chain of mass beads connected by segments under a real, constant string tension σ — the same physical picture (a relativistic-string-like object) that the Cornell potential's linear term describes, but now with genuine transverse dynamics:
m·d²y_i/dt² = σ·(y_{i+1} − 2y_i + y_{i-1}) − damping·v_i
L = Σ segment lengths (≥ r, grows when the string is vibrating)
V(r) = -(4/3)·α_s·ħc/r + σ·L
Hit Pluck String and a real transverse wave is numerically integrated outward from the middle of the tube, reflects off the quark and antiquark ends, and dies down under a small damping term — exactly the discretized wave equation that governs a string under tension, with wave speed σ ∝ (speed)². A vibrating string is also longer than a straight one, so the extra contour length feeds directly into the same stored-energy budget the 3D sim uses for its snap threshold: pluck hard enough near the breaking point and you can nudge the string into snapping early, just as quantum fluctuations of a near-critical flux tube can trigger early string breaking in lattice QCD.
- Separation slider / Auto-Pull — sets or animates the quark–antiquark distance r; the wave pattern already on the string persists and stretches with it.
- Pluck String — kicks the midpoint of the tube sideways and lets the string ring, visualising the same transverse gluon-field dynamics a real flux tube supports.
- σ, αs — σ sets both the confining force and the wave speed on the string (stiffer tension = faster waves); αs only affects the short-range Coulomb term between the endpoints.
- Energy bar — total stored string energy (straight-line stretch + any extra length from vibration) vs. the pair-production threshold. Cross it and the tube snaps at whichever point is currently displaced furthest — a fresh quark–antiquark pair pops out of the vacuum there and the two halves fly apart as separate color-neutral mesons.