Virtual walks and phase transitions in the two-dimensional Biswas-Chatterjee-Sen model with extreme switches.

In kinetic exchange models of opinion formation, one considers pairwise interactions to update the states of the agents. We have studied a kinetic exchange model with three opinion states 0,±1, by considering a walk in a one-dimensional virtual space which evolves according to the dynamical states of the agents. The model involves two noise parameters p and q; p represents the fraction of negative interactions and q corresponds to the probability of a stronger interaction with the other agent, which may result in extreme switches (change of state from +1 to -1 or vice versa).

Avalanche shapes in the fiber bundle model.

We study the temporal evolution of avalanches in the fiber bundle model of disordered solids, when the model is gradually driven towards the critical breakdown point. We use two types of loading protocols: (i) quasistatic loading and (ii) loading by a discrete amount. In the quasistatic loading, where the load is increased by the minimum amount needed to initiate an avalanche, the temporal shapes of avalanches are asymmetric away from the critical point and become symmetric as the critical point is approached.

Opinion formation models with extreme switches and disorder: Critical behavior and dynamics.

In a three-state kinetic exchange opinion formation model, the effect of extreme switches was considered in a recent paper. In the present work, we study the same model with disorder. Here disorder implies that negative interactions may occur with a probability p.

Nonequilibrium dynamics in a three-state opinion-formation model with stochastic extreme switches.

We investigate the nonequilibrium dynamics of a three-state kinetic exchange model of opinion formation, where switches between extreme states are possible, depending on the value of a parameter q. The mean field dynamical equations are derived and analyzed for any q. The fate of the system under the evolutionary rules used in S.

Kinetic exchange models of societies and economies.

The statistical nature of collective human behaviour in a society is a topic of broad current interest. From formation of consensus through exchange of ideas, distributing wealth through exchanges of money, traffic flows, growth of cities to spread of infectious diseases, the application range of such collective responses cuts across multiple disciplines. Kinetic models have been an elegant and powerful tool to explain such collective phenomena in a myriad of human interaction-based problems, where an energy consideration for dynamics is generally inaccessible.

Virtual walks inspired by a mean-field kinetic exchange model of opinion dynamics.

We propose two different schemes of realizing a virtual walk corresponding to a kinetic exchange model of opinion dynamics. The walks are either Markovian or non-Markovian in nature. The opinion dynamics model is characterized by a parameter [Formula: see text] which drives an order disorder transition at a critical value [Formula: see text].

Nonequilibrium dynamics in Ising-like models with biased initial condition.

We investigate the dynamical fixed points of the zero temperature Glauber dynamics in Ising-like models. The stability analysis of the fixed points in the mean field calculation shows the existence of an exponent that depends on the coordination number z in the Ising model. For the generalized voter model, a phase diagram is obtained based on this study.

Long route to consensus: Two-stage coarsening in a binary choice voting model.

Formation of consensus, in binary yes-no type of voting, is a well-defined process. However, even in presence of clear incentives, the dynamics involved can be incredibly complex. Specifically, formations of large groups of similarly opinionated individuals could create a condition of "support-bubbles" or spontaneous polarization that renders consensus virtually unattainable (e.

Effect of bias in a reaction-diffusion system in two dimensions.

We consider a single species reaction diffusion system on a two-dimensional lattice where the particles A are biased to move towards their nearest neighbors and annihilate as they meet. Allowing the bias to take both negative and positive values parametrically, any nonzero bias is seen to drastically affect the behavior of the system compared to the unbiased (simple diffusive) case. For positive bias, a finite number of dimers, which are isolated pairs of particles occurring as nearest neighbors, exist while for negative bias, a finite density of particles survives.

Virtual walks in spin space: A study in a family of two-parameter models.

We investigate the dynamics of classical spins mapped as walkers in a virtual "spin" space using a generalized two-parameter family of spin models characterized by parameters y and z [de Oliveira et al., J. Phys.

Critical noise can make the minority candidate win: The U.S. presidential election cases.

A national voting population, when segmented into groups such as, for example, different states, can yield a counterintuitive scenario in which the winner may not necessarily get the highest number of total votes. A recent example is the 2016 presidential election in the United States. We model the situation by using interacting opinion dynamics models, and we look at the effect of coarse graining near the critical points where the spatial fluctuations are high.

Zero-temperature coarsening in the Ising model with asymmetric second-neighbor interactions in two dimensions.

We consider the zero-temperature coarsening in the Ising model in two dimensions where the spins interact within the Moore neighborhood. The Hamiltonian is given by H=-∑_{〈i,j〉}S_{i}S_{j}-κ∑_{〈i,j^{'}〉}S_{i}S_{j^{'}}, where the two terms are for the first neighbors and second neighbors, respectively, and κ≥0. The freezing phenomenon, already noted in two dimensions for κ=0, is seen to be present for any κ.

Interplay of interfacial noise and curvature-driven dynamics in two dimensions.

We explore the effect of interplay of interfacial noise and curvature-driven dynamics in a binary spin system. An appropriate model is the generalized two-dimensional voter model proposed earlier [M. J.

An empirical analysis of the Ebola outbreak in West Africa.

The data for the Ebola outbreak that occurred in 2014-2016 in three countries of West Africa are analysed within a common framework. The analysis is made using the results of an agent based Susceptible-Infected-Removed (SIR) model on a Euclidean network, where nodes at a distance l are connected with probability P(l) ∝ l, δ determining the range of the interaction, in addition to nearest neighbors. The cumulative (total) density of infected population here has the form , where the parameters depend on δ and the infection probability q.

Minority-spin dynamics in the nonhomogeneous Ising model: Diverging time scales and exponents.

We investigate the dynamical behavior of the Ising model under a zero-temperature quench with the initial fraction of up spins 0≤x≤1. In one dimension, the known results for persistence probability are verified; it shows algebraic decay for both up and down spins asymptotically with different exponents. It is found that the conventional finite-size scaling is valid here.

Condensation transition in a conserved generalized interacting zero-range process.

A conserved generalized zero-range process is considered in which two sites interact such that particles hop from the more populated site to the other with a probability p. The steady-state particle distribution function P(n) is obtained using both analytical and numerical methods. The system goes through several phases as p is varied.

Continuous utility factor in segregation models.

We consider the constrained Schelling model of social segregation in which the utility factor of agents strictly increases and nonlocal jumps of the agents are allowed. In the present study, the utility factor u is defined in a way such that it can take continuous values and depends on the tolerance threshold as well as the fraction of unlike neighbors. Two models are proposed: in model A the jump probability is determined by the sign of u only, which makes it equivalent to the discrete model.

Maximizing the Strength of Fiber Bundles under Uniform Loading.

The collective strength of a system of fibers, each having a failure threshold drawn randomly from a distribution, indicates the maximum load carrying capacity of different disordered systems ranging from disordered solids, power-grid networks, to traffic in a parallel system of roads. In many of the cases where the redistribution of load following a local failure can be controlled, it is a natural requirement to find the most efficient redistribution scheme, i.e.

A+A→∅ model with a bias towards nearest neighbor.

We have studied the A+A→∅ reaction-diffusion model on a ring, with a bias ε(0≤ε≤0.5) of the random walkers A to hop towards their nearest neighbor. Though the bias is local in space and time, we show that it alters the universality class of the problem.

Exit probability in inflow dynamics: nonuniversality induced by range, asymmetry, and fluctuation.

Probing deeper into the existing issues regarding the exit probability (EP) in one-dimensional dynamical models, we consider several models where the states are represented by Ising spins and the information flows inwards. At zero temperature, these systems evolve to either of two absorbing states. The EP, E(x), which is the probability that the system ends up with all up spins starting with x fraction of up spins, is found to have the general form E(x)=xα/xα+(1-x)α.

Opinion dynamics model with weighted influence: exit probability and dynamics.

We introduce a stochastic model of binary opinion dynamics in which the opinions are determined by the size of the neighboring domains. The exit probability here shows a step function behavior, indicating the existence of a separatrix distinguishing two different regions of basin of attraction. This behavior, in one dimension, is in contrast to other well known opinion dynamics models where no such behavior has been observed so far.

Nonconservative kinetic exchange model of opinion dynamics with randomness and bounded confidence.

The concept of a bounded confidence level is incorporated in a nonconservative kinetic exchange model of opinion dynamics model where opinions have continuous values ∈[-1,1]. The characteristics of the unrestricted model, which has one parameter λ representing conviction, undergo drastic changes with the introduction of bounded confidence parametrized by δ. Three distinct regions are identified in the phase diagram in the δ-λ plane and the evidences of a first order phase transition for δ ≥ 0.

Effect of the nature of randomness on quenching dynamics of the Ising model on complex networks.

Randomness is known to affect the dynamical behavior of many systems to a large extent. In this paper we investigate how the nature of randomness affects the dynamics in a zero-temperature quench of the Ising model on two types of random networks. In both networks, which are embedded in a one-dimensional space, the first-neighbor connections exist and the average degree is 4 per node.

Antipersistent dynamics in kinetic models of wealth exchange.

We investigate the detailed dynamics of gains and losses made by agents in some kinetic models of wealth exchange. An earlier work suggested that a walk in an abstract gain-loss space can be conceived for the agents. For models in which agents do not save, or save with uniform saving propensity, the walk has diffusive behavior.

Phase transitions in a two-parameter model of opinion dynamics with random kinetic exchanges.

Recently, a model of opinion formation with kinetic exchanges has been proposed in which a spontaneous symmetry-breaking transition was reported [M. Lallouache, A. S.