Physics
States of matter
Lennard-Jones molecular dynamics: cool a gas until it condenses and freezes, watch the structure sharpen, and meet the potential behind it all.
What happens
A box of Lennard-Jones atoms glowing with their kinetic energy. Start from the hot gas and drag the temperature down: droplets nucleate, merge and finally freeze into a triangular crystal whose g(r) grows sharp shells - the same atoms, three states of matter. Squeeze the box and the virial pressure answers at once; switch the thermostat off and pure Newton remains. The two-atom bench strips it all down to a pair swinging in the V(r) well at exactly the period the curvature dictates, and the substance menu translates the reduced units into kelvins for neon, argon and methane.
Equations used in the module
Equations V(r) = 4ε [(σ/r)¹² − (σ/r)⁶] (Lennard–Jones) m a_i = −Σ_j ∇V(r_ij) T ∝ ⟨½ m v²⟩; gas → liquid → crystal as T falls
