# Vortex Splitting Interactive Lab By greenlig Topic: Physics & Chemistry [Open the interactive Jig](https://ask.jig.com/j/jW9QAgiKQhBj) ## Guide ### 1. A lab for splitting whirlpools This bench turns one physics paper into a lab you can play with\. The white ball is a model world where tiny whirlpools of phase, called vortices, live\. Two of them sit on top as dark beads\. By the end you will see how scientists can tell whether they are fused or split, even when no camera is sharp enough to see\. Source: Baek, Tajima and Nam, “Spectral Crossings Diagnose Multiply Quantized Vortex Splitting”, pages 1–5 and supplement\. ### 2. Twice around, two ways The colours on the ball show phase, like the hands of a clock painted on the surface\. Walk around the top and the colours cycle twice: a winding of two\. That winding can sit in one fused knot, or in two separate knots that each wind once\. Watch the beads part and rejoin while the total stays the same\. Fused order\-2 zero versus two unit zeros: same total winding and same dark\-state count \(paper p\.1–2, Fig\. 1b\)\. ### 3. Too small to see The thin dark ring on the ball is the magnetic length: the smallest detail this world can resolve\. Slide the right\-hand carriage to raise the flux N, the number of magnetic flux units through the ball\. More flux shrinks the ring, so two close beads stop looking like one\. The ring grows with the size of the ball and shrinks with the square root of the flux \(p\.1\)\. At N = 20 it spans about 18 degrees of the ball; at N = 640, about 3\. ### 4. Listen instead of look Instead of taking a picture, the lab tunes a dial called the detuning until an energy level crosses zero\. How that crossing shrinks as the flux grows is the clue\. Press Sweep to run the flux from 20 to 640 and watch the bead on the lower plot trace the answer\. Fused: each doubling of the flux makes the crossing about 8 times smaller\. Split: about 4 times smaller \(p\.1, Eq\. 1\)\. ### 5. Three agents, one bench Three stations each work out the answer by a different method\. They share the same two carriages as inputs and the same measurement: how steeply the crossing falls, from 3 for fused to 2 for split\. Press a station's round button to send its result to the big gauge\. A: the paper's endpoint laws\. B: the analytic two\-zero crossover\. C: a numerical sum over oscillator states, built as an independent check\. ### 6. Pull the pair apart Slide the left\-hand carriage to move the two beads apart\. Watch the needles swing from 3 down toward 2 as the gap grows past the ring\. The bead on the upper plot rides the same curve the paper draws, and briefly dips below 2 before settling\. The paper puts the halfway knees at x = 1\.093 and 2\.233 for its two branches \(p\.4, Fig\. 3b\); our methods B and C both find 1\.093 and 2\.233\. ### 7. Inside each result Station C shows its working: each pin is one oscillator level, and its height is how much of the state lives there\. As the beads part, the hump of pins slides right\. The comb has only 18 pins, so far apart the hump runs off the end, the pins turn amber and C drifts away from B: a recorded limit, not a discovery\. Our 18\-level truncation agrees with the closed form to better than 0\.01 up to about x = 5; beyond that it is marked unverified\. ### 8. What we checked Method A matches the paper's own table: at N = 640 its numbers land within 1 to 4 percent of the exact values\. Methods B and C agree with each other and with the paper's knees\. One worked example in the paper uses a rounded formula and comes out about 9 percent high\. Anything we could not reproduce stays marked unverified, like the amber comb on station C\. Unverified: the paper's full monopole\-harmonic numerics and the finite\-N split crossover\. Details in the package's verification notes\. ### 9. Measuring the unseeable Two vortices closer than any picture can show still change how a signal shifts as the flux grows\. The knee in that curve tells you how far apart they are\. Play with both carriages and all three stations: every needle on this bench comes from the same inputs, so you can compare them fairly\. The knee appears where the ring shrinks to about the gap between the beads \(p\.3, Eq\. 12\)\.