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. 

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