Lennard-Jones Molecular Dynamics (2D)

This simulation numerically integrates the equations of motion for a 2D gas of particles interacting through the real Lennard-Jones pair potential V(r)=4ε[(σ/r)^12-(σ/r)^6], the same functional form used in real molecular dynamics codes to model van der Waals interactions. Every particle pair repels steeply the instant it gets closer than about one sigma, and attracts weakly across a wider medium-range band — the balance that gives real gases their equation of state and drives condensation into liquid-like clusters when the temperature is low enough. Velocity Verlet integration keeps the total energy (kinetic + potential) nearly constant, which the live energy chart makes visible: a good integrator holds that white line flat even as the pair colors flicker between attraction and repulsion. Adjust particle count, well depth, particle size and initial temperature to explore gas, liquid and clustering regimes.