Geometry-induced nonequilibrium phase transition in sandpiles

Response of the competitive balance model to the external field

The competitive balance model was proposed as an extension of the structural balance theory, aiming to account for heterogeneities observed in real-world networks. In this model, different paradigms lead to form different friendship and enmity. As an example, friendship or enmity between countries can have a political or religious basis. The suggested Hamiltonian is symmetrical between paradigms. Our analyses show that a balanced state can be achieved if just one paradigm prevails in the network and the paradigm shift is possible only by imposing an external field. In this paper, we investigate the influence of the external field on the evolution of the network. We drive the mean-field solutions of the model and verify the accuracy of our analytical solutions by performing Monte-Carlo simulations. We observe that the external field breaks the symmetry of the system. The response of the system to this external field, contingent upon temperature, can be either paramagnetic or ferromagnetic. We observed a hysteresis behavior in the ferromagnetic regime. Once communities are formed based on a certain paradigm, then they resist change. We found that to avoid wasting energy we need to know the level of stochastic behavior in the network. Analogous to magnetic systems, we observe that susceptibility adheres to Curie's law.

Relation between the degree and betweenness centrality distribution in complex networks

The centrality measures, like betweenness b and degree k in complex networks remain fundamental quantities helping to classify them. It is realized from Barthelemy's paper [Eur. Phys. J. B 38, 163 (2004)10.1140/epjb/e2004-00111-4] that the maximal b-k exponent for the scale-free (SF) networks is η_{max}=2, belonging to SF trees, based on which one concludes δ≥γ+1/2, where γ and δ are the scaling exponents for the distribution functions of the degree and the betweenness centralities, respectively. This conjecture was violated for some special models and systems. Here we present a systematic study on this problem for visibility graphs of correlated time series, and show evidence that this conjecture fails in some correlation strengths. We consider the visibility graph of three models: two-dimensional Bak-Tang-Weisenfeld (BTW) sandpile model, one-dimensional (1D) fractional Brownian motion (FBM), and 1D Levy walks, the two latter cases are controlled by the Hurst exponent H and the step index α, respectively. In particular, for the BTW model and FBM with H≲0.5, η is greater than 2, and also δ<γ+1/2 for the BTW model, while the Barthelemy's conjecture remains valid for the Levy process. We assert that the failure of the Barthelemy's conjecture is due to large fluctuations in the scaling b-k relation resulting in the violation of hyperscaling relation η=γ-1/δ-1 and emergent anomalous behavior for the BTW model and FBM. Universal distribution function of generalized degree is found for these models which have the same scaling behavior as the Barabasi-Albert network.

A self-organized critical model and multifractal analysis for earthquakes in Central Alborz, Iran

This paper is devoted to a phenomenological study of the earthquakes in central Alborz, Iran. Using three observational quantities, namely the weight function, the quality factor, and the velocity model in this region, we develop a modified dissipative sandpile model which captures the main features of the system, especially the average activity field over the region of study. The model is based on external stimuli, the location of which is chosen (I) randomly, (II) on the faults, (III) on the low active points, (IV) on the moderately active points, and (V) on the highly active points in the region. We uncover some universal behaviors depending slightly on the method of external stimuli. A multi-fractal detrended fluctuation analysis is exploited to extract the spectrum of the Hurst exponent of the time series obtained by each of these schemes. Although the average Hurst exponent depends slightly on the method of stimuli, we numerically show that in all cases it is lower than 0.5, reflecting the anti-correlated nature of the system. The lowest average Hurst exponent is found to be associated with the case (V), in such a way that the more active the stimulated sites are, the lower the average Hurst exponent is obtained, i.e. the large earthquakes are more anticorrelated. Moreover, we find that the activity field achieved in this study provide information about the depth and topography of the basement, and also the area that can potentially be the location of the future large events. We successfully determine a high activity zone on the Mosha Fault, where the mainshock occurred on May 7th, 2020 (M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_W$$\end{document}W 4.9).

Invasion percolation in short-range and long-range disorder background

In the original invasion percolation model, a random number quantifies the role of necks, or generally the quality of pores, ignoring the structure of pores and impermeable regions (to which the invader cannot enter). In this paper, we investigate invasion percolation (IP), taking into account the impermeable regions, the configuration of which is modeled by ordinary and Ising-correlated site percolation (with short-range interactions, SRI), on top of which the IP dynamics is defined. We model the long-ranged correlations of pores by a random Coulomb potential (RCP). By examining various dynamical observables, we suggest that the critical exponents of Ising-correlated cases change considerably only in the vicinity of the critical point (critical temperature), while for the ordinary percolation case the exponents are robust against the occupancy parameter p. The properties of the model for the long-range interactions [LRI (RCP)] are completely different from the normal IP. In particular, the fractal dimension of the external frontier of the largest hole is nearly 4/3 for SRI far from the critical points, which is compatible with normal IP, while it converges to 1.099±0.04 for RCP. For the latter case, the time dependence of our observables is divided into three parts: the power law (short time), the logarithmic (moderate time), and the linear (long time) regimes. The second crossover time is shown to go to infinity in the thermodynamic limit, whereas the first crossover time is nearly unchanged, signaling the dominance of the logarithmic regime. The average gyration radius of the growing clusters, the length of their external perimeter, and the corresponding roughness are shown to be nearly constant for the long-time regime in the thermodynamic limit.

Self-organized criticality in cumulus clouds

The shape of clouds has proven to be essential for classifying them. Our analysis of images from fair weather cumulus clouds reveals that, in addition to turbulence, they are driven by self-organized criticality. Our observations yield exponents that support the fact the clouds, when projected to two dimensions, exhibit conformal symmetry compatible with c=-2 conformal field theory. By using a combination of the Navier-Stokes equation, diffusion equations, and a coupled map lattice, we successfully simulated cloud formation, and obtained the same exponents.

Superstatistical two-temperature Ising model

The previous approach of the nonequilibrium Ising model was based on the local temperature in which each site or part of the system has its own specific temperature. We introduce an approach of the two-temperature Ising model as a prototype of the superstatistic critical phenomena. The model is described by two temperatures (T_{1},T_{2}) in a zero magnetic field. To predict the phase diagram and numerically estimate the exponents, we develop the Metropolis and Swendsen-Wang Monte Carlo method. We observe that there is a nontrivial critical line, separating ordered and disordered phases. We propose an analytic equation for the critical line in the phase diagram. Our numerical estimation of the critical exponents illustrates that all points on the critical line belong to the ordinary Ising universality class.