We show that there is a common mode of origin for the power laws observed in two different models: (i) the Pareto law for the distribution of money among the agents with random-saving propensities in an ideal gas-like market model and (ii) the Gutenberg–Richter law for the distribution of...

Following the observations of the self-similarity in various length scales in the roughness of the fractured solid surfaces, we propose here a new model for the earthquake. We demonstrate rigorously that the contact area distribution between two fractal surfaces follows a unique power law. This...

We determine the geometrical properties of the most probable paths at finite temperatures T, between two points separated by a distance r, in one-dimensional lattices with positive energies of interaction εi associated with bond i. The most probable path-length tmp in a homogeneous medium...

A one-dimensional probabilistic cellular automaton that models a transition from elementary rule 4 to elementary rule 22 (following Wolfram's nomenclature scheme) is studied here. The evolution of the automaton follows rule 4 with probability 1 − p and rule 22 with probability p. In course of...

The characteristics of the distribution of transient times of a one-dimensional probabilistic cellular automaton are studied by computer simulation. The mean and width of the distribution are found to diverge by the same power-law at each of the two critical points, pc1 = 0 and pc2 0.75, of the...

We report an exact analysis of a discrete form of the Chakrabarti–Stinchcombe model for earthquakes (Physica A 270 (1999) 27), which considers a pair of dynamically overlapping finite generations of the Cantor set as a prototype of geological faults. In this model the nth generation of the...

Social inequality manifested across different strata of human existence can be quantified in several ways. Here we compute non-entropic measures of inequality such as Lorenz curve, Gini index and the recently introduced k index analytically from known distribution functions. We characterize the...

We propose a model of continuous opinion dynamics, where mutual interactions can be both positive and negative. Different types of distributions for the interactions, all characterized by a single parameter p denoting the fraction of negative interactions, are considered. Results from exact...

The biased link occupation rule in the Achlioptas process (AP) discourages the large clusters from growing much ahead of others and encourages faster growth of clusters which lag behind. In this paper we propose a model where this tendency is sharply reflected in the Gamma distribution of the...

We have numerically simulated the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving two-body collision. Unlike in the ideal gas, we introduce (quenched) saving propensity of the agents, distributed widely...