<Dd> ∂ ρ ∂ t = ∂ 2 ρ ∂ x 2 ⋅ ∫ − ∞ + ∞ Δ 2 2 τ ⋅ φ (Δ) d Δ + higher - order even moments (\ displaystyle (\ frac (\ partial \ rho) (\ partial t)) = (\ frac (\ partial ^ (2) \ rho) (\ partial x ^ (2))) \ cdot \ int _ (- \ infty) ^ (+ \ infty) (\ frac (\ Delta ^ (2)) (2 \, \ tau)) \ cdot \ varphi (\ Delta) \, \ mathrm (d) \ Delta + (\ text (higher - order even moments))) </Dd> <P> Where the coefficient before the Laplacian, the second moment of probability of displacement Δ (\ displaystyle \ Delta), is interpreted as mass diffusivity D: </P> <Dl> <Dd> D = ∫ − ∞ + ∞ Δ 2 2 τ ⋅ φ (Δ) d Δ (\ displaystyle D = \ int _ (- \ infty) ^ (+ \ infty) (\ frac (\ Delta ^ (2)) (2 \, \ tau)) \ cdot \ varphi (\ Delta) \, \ mathrm (d) \ Delta) </Dd> </Dl> <Dd> D = ∫ − ∞ + ∞ Δ 2 2 τ ⋅ φ (Δ) d Δ (\ displaystyle D = \ int _ (- \ infty) ^ (+ \ infty) (\ frac (\ Delta ^ (2)) (2 \, \ tau)) \ cdot \ varphi (\ Delta) \, \ mathrm (d) \ Delta) </Dd>

State three different material that can be used to demonstrate brownian motion