title: Dynamics of comb-of-comb networks.
abstract: The dynamics of complex networks, a current hot topic in many scientific fields, is often coded through the corresponding Laplacian matrix. The spectrum of this matrix carries the main features of the networks' dynamics. Here we consider the deterministic networks which can be viewed as "comb-of-comb" iterative structures. For their Laplacian spectra we find analytical equations involving Chebyshev polynomials whose properties allow one to analyze the spectra in deep. Here, in particular, we find that in the infinite size limit the corresponding spectral dimension goes as d(s) → 2. The d(s) leaves its fingerprint on many dynamical processes, as we exemplarily show by considering the dynamical properties of polymer networks, including single monomer displacement under a constant force, mechanical relaxation, and fluorescence depolarization.
authors.affiliation: School of Computer Science, Fudan University, Shanghai 200433, China.|Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Hongxiao
authors.initials: H
authors.lastname: Liu
authors.affiliation: School of Computer Science, Fudan University, Shanghai 200433, China.|Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Lin
authors.affiliation: Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany.|Institut Charles Sadron, Université de Strasbourg and CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France.
authors.forename: Maxim
authors.initials: M
authors.lastname: Dolgushev
authors.affiliation: School of Computer Science, Fudan University, Shanghai 200433, China.|Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Zhongzhi
authors.initials: Z
authors.lastname: Zhang