Nonlinear diffusion through large complex networks containing regular subgraphs

Volchenkov D, Blanchard P (2007)
JOURNAL OF STATISTICAL PHYSICS 127(4): 677-697.

Journal Article | Published | English

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Abstract
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 -> infinity. 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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Volchenkov D, Blanchard P. Nonlinear diffusion through large complex networks containing regular subgraphs. JOURNAL OF STATISTICAL PHYSICS. 2007;127(4):677-697.
Volchenkov, D., & Blanchard, P. (2007). Nonlinear diffusion through large complex networks containing regular subgraphs. JOURNAL OF STATISTICAL PHYSICS, 127(4), 677-697.
Volchenkov, D., and Blanchard, P. (2007). Nonlinear diffusion through large complex networks containing regular subgraphs. JOURNAL OF STATISTICAL PHYSICS 127, 677-697.
Volchenkov, D., & Blanchard, P., 2007. Nonlinear diffusion through large complex networks containing regular subgraphs. JOURNAL OF STATISTICAL PHYSICS, 127(4), p 677-697.
D. Volchenkov and P. Blanchard, “Nonlinear diffusion through large complex networks containing regular subgraphs”, JOURNAL OF STATISTICAL PHYSICS, vol. 127, 2007, pp. 677-697.
Volchenkov, D., Blanchard, P.: Nonlinear diffusion through large complex networks containing regular subgraphs. JOURNAL OF STATISTICAL PHYSICS. 127, 677-697 (2007).
Volchenkov, Dimitry, and Blanchard, Philippe. “Nonlinear diffusion through large complex networks containing regular subgraphs”. JOURNAL OF STATISTICAL PHYSICS 127.4 (2007): 677-697.
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