Evolution equation for a model of surface relaxation in complex networks.
C E La Rocca1, L A Braunstein, P A Macri
1Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR)-Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata-CONICET, Funes 3350, 7600 Mar del Plata, Argentina.
Summary
This study analytically derives the surface growth interface equation for the surface with relaxation to the minimum (SRM) model in complex networks. Nonlinear terms emerge in heterogeneous networks, causing logarithmic roughness divergence.
Area of Science:
- Complex networks
- Statistical physics
- Surface growth models
Background:
- Disagreement in scaling results between discrete SRM and Edward-Wilkinson models in scale-free networks (P(k) ~ k^-lambda, lambda<3).
- Euclidean lattices exhibit linear interface evolution equations.
Purpose of the Study:
- To analytically derive the interface evolution equation for the SRM model in complex networks.
- To investigate the emergence of nonlinearities and their impact on surface growth dynamics in heterogeneous networks.
Main Methods:
- Analytical derivation of the interface evolution equation.
- Analysis of surface growth dynamics in complex network structures.
Main Results:
- Nonlinear terms appear in the evolution equation for complex heterogeneous networks, unlike linear behavior in Euclidean lattices.
- These nonlinearities arise from network heterogeneity and asymmetry.
- A logarithmic divergence of saturation roughness with system size is observed, consistent with previous findings for lambda<3.
Conclusions:
- The heterogeneity and asymmetry of complex networks introduce nonlinearities into surface growth models.
- These nonlinearities explain the observed logarithmic divergence in saturation roughness, resolving discrepancies in prior studies.
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