Anisotropic diffusion in a two-dimensional model with obstruction and a comparison of mean first passage time...

The disagreement between two different studies of the diffusion equation for two hard disks to diffuse past each other in a narrow channel remains unresolved. Two different values for the divergence exponent of the mean first passage time (MFPT) were obtained. This has motivated the proposal that the difference arises from the use of different and nonequivalent definitions for the MFPT. Doubt was raised regarding the validity of the numerical solution of the diffusion equation as an explanation for the disagreement with the dimensional reduction method. In this paper, a one disk model which partially mimics the two disks problem is studied in the infinitely anisotropic diffusion limits. Although analytical arguments predict the exact exponent to be 1/2, it has not been probed in numerical studies. Using the two algorithms, we obtain exponents from numerical solutions which are consistent with each other and the proposed exact value.