TY - JOUR
T1 - Nonlinear diffusion through large complex networks containing regular subgraphs
AU - Volchenkov, Dimitri
AU - Blanchard, Ph
PY - 2007/5/1
Y1 - 2007/5/1
N2 - 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 → ∞. 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. © Springer Science+Business Media, LLC 2007.
AB - 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 → ∞. 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. © Springer Science+Business Media, LLC 2007.
M3 - Article
SP - 677
EP - 697
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
ER -