Journal of Scientific Computing

, Volume 81, Issue 3, pp 1630–1654 | Cite as

Diffusion Across Semi-permeable Barriers: Spectral Properties, Efficient Computation, and Applications

  • Nicolas MoutalEmail author
  • Denis Grebenkov


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.


Diffusion Semi-permeable barriers Laplacian spectrum Multilayer Composite medium Diffusion MRI First-passage phenomena 



We acknowledge the support under Grant No. ANR-13-JSV5-0006-01 of the French National Research Agency.

Supplementary material

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Supplementary material 1 (pdf 708 KB)


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Authors and Affiliations

  1. 1.Laboratoire de Physique de la Matiere Condensee, Ecole Polytechnique, CNRS, IP ParisPalaiseauFrance

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