Editing Fick's laws of diffusion (section)

=== Example solution 2: Brownian particle and mean squared displacement ===
Another simple case of diffusion is the [[Brownian motion]] of one particle. The particle's [[Mean squared displacement]] from its original position is:
<math display="block">\text{MSD} \equiv \left \langle (\mathbf{x}-\mathbf{x_0})^2 \right \rangle=2nDt , </math>
where <math>n</math> is the [[dimension]] of the particle's Brownian motion. For example, the diffusion of a molecule across a [[cell membrane]] 8&nbsp;nm thick is 1-D diffusion because of the spherical symmetry; However, the diffusion of a molecule from the membrane to the center of a [[Eukaryotic Cell|eukaryotic cell]] is a 3-D diffusion. For a cylindrical [[cactus]], the diffusion from photosynthetic cells on its surface to its center (the axis of its cylindrical symmetry) is a 2-D diffusion.

The square root of MSD, <math>\sqrt{2nDt}</math>, is often used as a characterization of how far the particle has moved after time <math>t</math> has elapsed. The MSD is symmetrically distributed over the 1D, 2D, and 3D space. Thus, the probability distribution of the magnitude of MSD in 1D is Gaussian and 3D is a Maxwell-Boltzmann distribution.