Biophysics

Equipment

• Virtual fluid region with many independent Brownian trajectories
• Sliders for temperature T and particle radius a
• ⟨x²⟩-vs-time plot and D readout

Procedure

1. Observe Brownian trajectories

   In figure 1 "Thermal noise and particle trajectories", watch particles zigzag randomly under molecular collisions — described by the Langevin equation $\gamma\dot{x} = F + \xi(t)$ with random force $\xi$. Let the simulation run long enough for trajectories to wander; smaller particles (lower "Particle radius a") jitter more strongly.

2. Measure the mean-square displacement

   In figure 2 "Diffusion law", the ⟨x²⟩(t) curve is a straight line through the origin — the mark of normal diffusion, unlike ballistic motion (⟨x²⟩ ∝ t²). Read the coefficient D from the readout and check $\langle x^2 \rangle = 2Dt$ at two time points.

3. Verify D = k_BT/(6πηa)

   With a fixed, raise "Temperature T": D grows linearly with T. With T fixed, raise a: D falls like $1/a$ — the readout shows the relative diffusion coefficient $\propto T/a$. Compare with cell scales: a small molecule in a cell ($D \sim 10^{-9}$ m²/s) crosses ~10 μm in ~0.1 s — diffusion is fast enough for biology at cellular sizes.

Simulation

Experiment history

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