Radial Distribution Function in a 2D Lennard-Jones Fluid

This is the 2D counterpart to the 3D Lennard-Jones molecular-dynamics simulator — not that box flattened onto a plane, but an independently derived 2-dimensional statistical model. 100 disks interact through the truncated Lennard-Jones potential in a periodic square box, integrated with velocity-Verlet, while the radial distribution function g(r) is rebuilt live from the running pairwise-distance histogram using the correct 2D ring-shell normalization (2πr dr instead of 4πr² dr). Because a 2D solid packs as a triangular lattice rather than a 3D FCC/HCP crystal, the coordination number, pressure virial coefficient and even the character of melting all differ numerically from the 3D version at matched temperature and density — drag the sliders or jump to a gas/liquid/solid preset to see the 2D g(r), coordination number, instantaneous temperature and virial pressure update in real time.