  We present an efficient method to compute the eigenvalues and eigenmodes of
the diffusion operator $\nabla(D\nabla)$ on one-dimensional heterogeneous
structures with multiple semi-permeable barriers. This method allows us to
calculate the diffusion propagator and related quantities such as diffusion MRI
signal or first exit time distribution analytically for regular geometries and
numerically for arbitrary ones. The effect of the barriers and the transition
from infinite permeability (no barriers) to zero permeability (impermeable
barriers) are investigated.

Computational Physics;Statistical Mechanics