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How to use
A simplified pressurised-water reactor plant: the core (centre left) heats the primary water, which boils the secondary side in the steam generator to drive a turbine. The three graphs show thermal power (log scale), fuel and coolant temperatures, and the reactivity in pcm (one pcm is 0.001 percent of reactivity).
Try: use Insert a reactivity step a few times and watch the power rise, then the temperature feedback pull reactivity back. Choose SCRAM: the power falls within seconds to a few percent (decay heat), then slowly. Then Lose primary pumps and watch the fuel temperature climb toward the illustrative limit: why a reactor needs cooling even when shut down. Set the speed to 100x to see hours of decay-heat cooling.
The science
Point reactor kinetics with six delayed-neutron groups (U-235 thermal fission, total delayed fraction beta = 0.65 percent):dn/dt = ((rho - beta)/Lambda) n + sum lambda_i c_i, dc_i/dt = (beta_i/Lambda) n - lambda_i c_in is the relative power, rho the reactivity and Lambda = 20 microseconds the prompt generation time. Delayed neutrons stretch the response time from microseconds to seconds, which is what makes control possible; only when rho exceeds beta (one dollar) is the reactor prompt critical, and the power would change in a few milliseconds.
Prompt jump and period. After a small step rho the power first jumps by beta/(beta - rho), then grows with the stable period given by the inhour equation rho = omega Lambda + sum beta_i omega/(omega + lambda_i). The page checks both against the numerical solution.
Feedback. Temperature changes reactivity: rho = rho_rods + alpha_f (T_fuel - T_0) + alpha_m (T_coolant - T_0) with Doppler alpha_f = -2.5 pcm/K and moderator alpha_m = -20 pcm/K, so the reactor tends to stabilise itself. The control-rod worth follows an S-shaped integral curve with a total worth of 6000 pcm.
Decay heat. After the chain reaction stops, radioactive fission products still release heat. The Way-Wigner approximation gives, as a fraction of the power before shutdown, P_d = 0.066 [(t+1)^-0.2 - (t + T_op)^-0.2] with T_op the operating time (one year here): about 6 percent at once, 1 percent after an hour and 0.5 percent after a day, which is why cooling must continue.
Thermal model. Two lumped heat capacities (fuel and primary coolant) connected by conductances to the secondary side at a fixed 270 C. An educational model with round numbers for a 3000 MW thermal plant: no xenon, no steam-generator dynamics, no pressuriser, no cladding or fuel-melt physics. The 1200 C line is an illustrative threshold, not a licensing limit. This is a generic plant, not a specific design.
What is checked and why you can trust it
Every time the page loads, and whenever you press Re-run check, the simulation evaluates its own mathematics against an independent reference, such as a closed-form formula, a finite-difference derivative or an exhaustive count. Each line above reports PASS or FAIL together with the measured numbers, so you can see by how much it agrees. Results are also published on window.__msChecks for automated testing. The check never uses the same code path as the animation it validates, otherwise it would only confirm itself.
How to read a failure: a FAIL line means the measured discrepancy exceeded the stated tolerance for the current slider values. Try Reset, then move the sliders back toward their defaults; if a check still fails at the defaults it is a bug worth reporting. Tolerances are chosen from the numerical method itself, never tuned to make a test pass: round-off level (1e-9) for exact algebra, about 1e-3 for finite differences and Monte Carlo estimates with a few hundred thousand samples, and a documented margin for stochastic learning runs.
Reproducibility: the particle and pen simulations use the browser random generator for initial positions, so exact pixels differ between visits, but the checks depend only on mathematics and not on those positions. Fixed wave tables (curl noise) and fixed grammars (L-system) are deterministic.
This is an educational model. It shows the mechanism clearly, but it is deliberately simplified; the science panel lists what was left out.