Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs

Details Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs

2006-06-30

arxiv.org/abs/cond-mat/0606797v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

21 pages, 2 figures included

Scientific paper

10.1007/s10955-007-9313-1

Transport through generalized trees is considered. Trees contain the simple nodes and supernodes, either well-structured regular subgraphs or those with many triangles. We observe a superdiffusion for the highly connected nodes while it is Brownian for the rest of the nodes. Transport within a supernode is affected by the finite size effects vanishing as $N\to\infty.$ For the even dimensions of space, $d=2,4,6,...$, the finite size effects break down the perturbation theory at small scales and can be regularized by using the heat-kernel expansion.

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