Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2009-03-09
Physics
Condensed Matter
Soft Condensed Matter
Scientific paper
We consider the Helmholtz problem in the context of the evolution of uniform initial distribution of a physical attribute in general porous media subject to a partially absorbing boundary condition. Its spectral property as a reflection of the boundary geometry has been widely exploited, such as in biological and geophysical applications. We consider the situation where the critical assumptions which enable such applications break down. Specifically, what are the consequences of an inhomogeneous absorption strength? By means of perturbation theory, exact theoretical results, and numerical simulations on random sphere packs, we identify the regions of parameter space in which such inhomogeneity is important and those in which it is not. Our findings shed light on the issue that limits the mapping between the diffusion/relaxation spectrum and the underlying boundary geometry.
Linton Johnson David
Ryu Seungoh
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