Granular Gas Cooling

Inelastic collisions dissipate kinetic energy — Haff's law T ∝ t⁻² describes the cooling.

Parameters

T: —
Collisions: 0
Time: 0
Color = speed
Red = fast, Blue = slow
Clustering appears
at low r values
Haff's law (1983): For a homogeneous granular gas with restitution coefficient r, the granular temperature T = ⟨v²⟩/2 obeys dT/dt = −ξT^(3/2), giving T(t) = T₀/(1 + t/τ)² where τ depends on density and r. This is distinctly non-exponential. At low r, a clustering instability develops — density fluctuations amplify because denser regions cool faster and contract. Watch the particles cluster into clumps at r < 0.7.