Philip H. Jones, Onofrio M. Maragò & Giovanni Volpe
Fig. 7.3 — Theories of Brownian motion: Trajectories and probability distributions
Trajectories and probability distributions. Brownian motion can be modelled by focusing on (a) the stochastic trajectories r(t) of single particles (random walks and Langevin equations) or on (b) the deterministic evolution of the probability density function ρ(r, t) of an ensemble of particles (diffusion equations). The data shown correspond to 0.53 μm radius particles in water, released at t = 0 s from r = 0 μm. The trajectories in (a) were obtained by a Brownian dynamics simulation and the probability distributions in (b) are the solution of a free diffusion equation.
Fig. 7.3 — Theories of Brownian motion: Trajectories and probability distributions