App 19 — Energy & Forces Sandbox

Drag atoms in a small toy crystal and watch predicted energy and force vectors update live — forces are computed as F = −∂E/∂r, never written by hand

Drag any atom to displace it

Atomic positions & force vectors

Green arrows show the force on each atom — they always point toward lower energy (steepest descent direction)

Live metrics

Total energy E
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Max force magnitude
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The relation in action

# Lennard-Jones-style toy potential
E = Σ_pairs 4ε[(σ/r)¹² − (σ/r)⁶]

# Force on atom i — autodiff, never hand-coded
F_i = −∂E/∂r_i