BET Adsorption: Master-Equation Population Dynamics

The 3D BET simulator watches individual surface sites randomly gain and lose molecular layers and lets the BET isotherm emerge from statistical noise across a grid. This 2D counterpart takes the opposite, exact route: it integrates the birth–death master equation for the population fraction pₙ(t) — the probability that a site holds exactly n layers — directly as a continuous system of ODEs, using 4th-order Runge–Kutta with no random sampling at all. Watch the population bars redistribute in real time as probability flows up the layer ladder under strong pressure and back down as it relaxes, and see the resulting mean layer count n̄ converge smoothly (not noisily) to the same closed-form BET isotherm equation used industrially to measure surface area from a single adsorption experiment.