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Diffusion models (intro)

General · Mathematics

Study notes

Q: Drop of ink in water spreads. If D = 10⁻⁹ m²/s, how far in 1 hour? Diffusion length: L ≈ √(Dt). L = √(10⁻⁹×3600) = √(3.6×10⁻⁶) ≈ 1.9×10⁻³ m ≈ 2 mm. Ink spreads only ~2 mm/hour (slow!)! Heat: D ~ 10⁻⁷: faster! Fundamental solution: (4πDt)^(-1/2)e^(-x²/4Dt)! (Diffusion: slow spreading!)

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