**Diffusion with a State Dependent Diffusion Coefficient **

*By Nicole Jinn*

Diffusion is a time-dependent process that arises from deterministic
trajectories appearing to be random. The setup of the experiment consists of
a two-dimensional rectangular lattice partitioned into panels of equal size
that alternate between two diffusion coefficients, one being twice the value
of the other. We are using molecular dynamics to study diffusion.

Two contrary theoretical predictions of the motion of the diffusing particle are available. The first prediction (a dynamical approach) observes that the diffusion coefficient influences how much time is spent on each side of the lattice. This approach uses Brownian motion, a continuous-time stochastic process, to model the motion of the diffusing particle. The second prediction (from statistical mechanics) states that the particle should spend the same amount of time on both sides of the partition. In conducting a numerical simulation, we validated the second prediction.

Two contrary theoretical predictions of the motion of the diffusing particle are available. The first prediction (a dynamical approach) observes that the diffusion coefficient influences how much time is spent on each side of the lattice. This approach uses Brownian motion, a continuous-time stochastic process, to model the motion of the diffusing particle. The second prediction (from statistical mechanics) states that the particle should spend the same amount of time on both sides of the partition. In conducting a numerical simulation, we validated the second prediction.