Random Walk Model

If you calculate the the distribution of velocities of particles from MD simulations, the resulting distribution is symmetrical around 0. This means that at a randomly chosen time, any given particle is equally likely to be moving in any direction. This observation allows us to make a huge simplification: instead of modeling our atoms as moving deterministically according to Newton's laws as they do in MD, we will just treat them as taking jumps in random directions.

Imagine taking a snapshot of the MD model every few hundred time steps and connecting the positions of one of the atoms with lines. If we only care about the long term behavior of particles and not their detailed trajectories, this is an adequate and more manageable model! This type of model is known as a Random Walk model, and it greatly simplifies our code and also allows us to simulate much longer time scales with many more atoms.

The model below implements this, along with some extra code that lets you draw "concentration profiles" to determine the concentration of atoms at each position, as shown below: