Related papers: Discrete Scale Invariance in Scale Free Graphs
Coordinate scaling of each spin density separately is considered in spin density functional theory. A virial theorem relates the spin-scaled correlation energy to the spin-scaled correlation potentials. An adiabatic connection formula…
Circulant graphs are an important class of interconnection networks in parallel and distributed computing. Integral circulant graphs play an important role in modeling quantum spin networks supporting the perfect state transfer as well. The…
The study of random graphs has become very popular for real-life network modeling such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice $\mathbb Z^d$, $d\ge1$, is a…
Scale free dynamics are observed in a variety of physical and biological systems. These include neural activity in which evidence for scale freeness has been reported using a range of imaging modalities. Here, we derive the ways in which…
The calculation of the band-gap by density-functional theory (DFT) methods is examined by considering the behavior of the energy as a function of number of electrons. It is found that the incorrect band-gap prediction with most approximate…
City is proved to be a scale-free phenomenon, and spatial autocorrelation is often employed to analyze spatial redundancy of cities. Unfortunately, spatial analysis results deviated practical requirement in many cases due to fractal nature…
In this work, we demonstrate that a functional modeling the self-aggregation of stochastically distributed lipid molecules can be obtained as the $\Gamma$-limit of a family of discrete energies driven by a sequence of independent and…
The large-scale structure of the magnetic field in the solar corona provides the energy to power large-scale solar eruptive events. Our physical understanding of this structure, and hence our ability to predict these events, is limited by…
We investigate analytically and numerically eigenfunction statistics in a disordered system on a finite Bethe lattice (Cayley tree). We show that the wave function amplitude at the root of a tree is distributed fractally in a large part of…
We study the scaling properties of two-dimensional turbulence using dimensional analysis. In particular, we consider the energy spectrum both at large and small scales and in the "inertial ranges" for the cases of freely decaying and forced…
A contribution is presented to the study of hadron spectroscopy through the use of fractals and discrete scale invariance implying log-periodic corrections to continuous scaling. The masses of mesons and baryons, reported by the Particle…
This is a brief introduction to fractals, multifractals and wavelets in an accessible way, in order that the founding ideas of those strange and intriguing newcomers to science as fractals may be communicated to a wider public. Fractals are…
We have developed different network approaches to complex patterns of frictional interfaces (contact areas developments). Here, we analyze the dynamics of static friction. We found, under the correlation measure, the fraction of triangles…
We investigate the contact process on four different types of scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where each potential edge is updated with a rate depending on the strength of the adjacent…
We find that transport on scale-free random networks depends strongly on degree-correlated network topologies whereas transport on Erd$\ddot{o}$s-R$\acute{e}$nyi networks is insensitive to the degree correlation. An approach for the tuning…
The scope of the paper is the theoretical analysis of the time rate in which a dynamical system reaches a stable stationary state or stable oscillations. The method used for the analysis is based on the so-called iterative time profiles,…
We consider a random graph model evolving in discrete time-steps that is based on 3-interactions among vertices. Triangles, edges and vertices have different weights; objects with larger weight are more likely to participate in future…
We introduce a deterministic model for scale-free networks, whose degree distribution follows a power-law with the exponent $\gamma$. At each time step, each vertex generates its offsprings, whose number is proportional to the degree of…
The free energy of a multi-component scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys non-linear functional differential equations which are turned into…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…