Related papers: Discrete Scale Invariance in Scale Free Graphs
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
Inspired by the similarity between the fractal Weierstrass function and quantum systems with discrete scaling symmetry, we establish general conditions under which the dynamics of a quantum system will exhibit fractal structure in the time…
Graphical models for finite-dimensional spin glasses and real-world combinatorial optimization and satisfaction problems usually have an abundant number of short loops. The cluster variation method and its extension, the region graph…
Scale-free networks are ubiquitous in social, biological and technological networked systems. Dynamic Scale-free networks and their synchronizations are important to understand and predict the behavior of social, biological and…
Fractal scale-free networks are empirically known to exhibit disassortative degree mixing. It is, however, not obvious whether a negative degree correlation between nearest neighbor nodes makes a scale-free network fractal. Here we examine…
Standard approximations for the exchange-correlation functional are known to deviate from linear dependence of the energy on the electron and spin numbers (in -space). Violation of this flat-plane condition underlies the failure of all…
We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean field model. Through small coupling series…
In this letter we present numerical and experimental results on the scaling properties of velocity turbulent fields in the range of scales where viscous effects are acting. A generalized version of Extended Self Similarity capable of…
Our numerical simulations with the Cahn-Hilliard equation show that coarsening of fractal clusters (FCs) is not a scale-invariant process. On the other hand, a typical coarsening length scale and interfacial area of the FC exhibit power…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
We introduce a class of stochastic weakly coupled map lattices, as models for studying heat conduction in solids. Each particle on the lattice evolves according to an internal dynamics that depends on its energy, and exchanges energy with…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
We investigate the effect of fragmentation on the homogeneous free cooling of inelastic hard spheres, using Boltzmann kinetic theory and Direct Monte Carlo simulations. We analyze in detail a model where dissipative collisions may…
Using numerical simulations and scaling theory we study the dynamics of the world-wide Web from the growth rules recently proposed in Ref. [1] with appropriate parameters. We demonstrate that the emergence of power-law behavior of the out-…
As a first step towards the understanding of the thermodynamical properties of quasiperiodic structures, we have performed both analytical and numerical calculations associated with succesive hierarchical approximations to multiscale…
We study statistical properties of a zero-range process (ZRP) on random networks. We derive an analytic expression for the distribution of particles (also called node occupation distribution) in the steady state of the ZRP in the ensemble…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine…
In order to understand characteristics common to distributions which have both fractal and non-fractal scale regions in a unified framework, we introduce a concept of typical scale. We employ a model of 2d gravity modified by the $R^2$ term…
The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and…