INSTITUTO DE INVESTIGACIONES FISICAS DE MAR DEL PLATA
Unidad Ejecutora - UE
Evolution equation for a model of surface relaxation in complex networks
CRISTIAN E. LA ROCCA; LIDIA A. BRAUNSTEIN; PABLO A. MACRI
PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS
Año: 2008 vol. 77 p. 46120 - 46120
In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the steady state of the fluctuations between the discrete SRM model and the Edward-Wilkinson process found in scale-free networks with degree distribution P(k)~k^(-lambda) for lambda<3 [Pastore y Piontti et al., Phys. Rev. E 76, 046117 (2007)]. Even though for Euclidean lattices the evolution equation is linear, we find that in complex heterogeneous networks non-linear terms appear due to the heterogeneity and the lack of symmetry of the network; they produce a logarithmic divergency of the saturation roughness with the system size as found by Pastore y Piontti et al. for lambda<3.