Physics
Brownian motion
Random walks and diffusion: the Einstein relation.
What happens
The amber tracer moves through impacts from visible molecules. Its cyan trail records one trajectory. The graph measures unbounded copies of the bath molecules: walls and tracer collisions do not affect those copies. Compare the measured mean squared displacement with the OU curve including inertia; 6Dt is its long-time limit. Changing temperature, friction or particle count resets the experiment.
Equations used in the module
Equations τ = m/γ; D = kT/γ ⟨r²⟩ = 6D[t − τ(1 − exp(−t/τ))] t/τ → 0: ⟨r²⟩ ≈ 3(kT/m)t² t/τ → ∞: ⟨r²⟩ ≈ 6Dt
