Universal Critical Phase Diagram Using Gini Index
Journal of the Physical Society of Japan, 2025, DOI Link
View abstract ⏷
The critical phase surface of a system, in general, can depend on one or more parameters. We show that by calculating the Gini index (g) of any suitably defined response function of a system, the critical phase surface can always be reduced to that of a single parameter, starting from g = 0 and terminating at g = gf, where gf is a universal number for a chosen response function in a given universality class. We demonstrate the construction with analytical and numerical calculations of mean field transverse field Ising model and site diluted Ising model on the Bethe lattice, respectively. Both models have two parameter critical phase surfaces – transverse field and temperature for the first case and site dilution and temperature in the second case. Both can be reduced to single parameter transition points in terms of the Gini index. We have additionally demonstrated the validity of the method for a mean field two parameter opinion dynamics model that includes a tri-critical point. The method is generally applicable for any multi-parameter critical transition.
Quantum annealing in SK model employing Suzuki–Kubo–deGennes quantum Ising mean field dynamics
Das S., Biswas S., Chakrabarti B.K.
European Physical Journal B, 2025, DOI Link
View abstract ⏷
Abstract: We study a quantum annealing approach for estimating the ground state energy of the Sherrington–Kirpatrick mean field spin glass model using the Suzuki–Kubo–deGennes dynamics applied for individual local magnetization components. The solutions of the coupled differential equations, in discretized state, give a fast annealing algorithm (cost N3) in estimating the ground state of the model: classical (E0=-0.7629±0.0002), quantum (E0=-0.7623±0.0001), and mixed (E0=-0.7626±0.0001), all of which are to be compared with the best known estimate E0=-0.763166726⋯. We infer that the continuous nature of the magnetization variable used in the dynamics here is the reason for reaching close to the ground state quickly and also the reason for not observing the de-Almeida–Thouless line in this approach.
Inequalities of energy release rates in compression of nanoporous materials predict its imminent breakdown
Physical Review E, 2025, DOI Link
View abstract ⏷
We show that the inequality in the divergent acoustic energy release rate in quasistatically compressed nanoporous materials can be used as a precursor to failure. A quantification of the inequality in the evolution of the energy release rate using social inequality (such as Gini and Kolkata) indices can predict large bursts of energy release. We also verify similar behavior for simulations of viscoelastic fiber bundle models that mimic the strain-hardening dynamics of the samples. The results demonstrate experimental applicability of the precursory signal for fracture with a diverging energy release rate using social inequality indices.
Classical annealing of the Sherrington-Kirkpatrick spin glass using Suzuki-Kubo mean-field Ising dynamics
Das S., Biswas S., Chakrabarti B.K.
Physical Review E, 2025, DOI Link
View abstract ⏷
We propose and demonstrate numerically a fast classical annealing scheme for the Sherrington-Kirkpatrick (SK) spin glass model, employing the Suzuki-Kubo mean-field Ising dynamics (supplemented by a modified Thouless-Anderson-Palmer reaction field). The resultant dynamics, starting from any arbitrary paramagnetic phase (with local magnetizations mi=±1, for the ith spin, and the global magnetization m=0), takes the system quickly to an appropriate state with small local values of magnetization (mi) commensurate with the (frustrated) interactions. As the temperature decreases with the annealing, the configuration practically remains (in an effective adiabatic way) close to a low-energy configuration as the magnitudes of mi's and the spin glass order parameter q grow to unity. While the configuration reached by the procedure is not the ground state, for an N-spin SK model (with N up to 10 000), the deviation in the energy per spin EN0-E0 found by the annealing procedure scales as N-2/3, with E0=-0.7629±0.0002, suggesting that in the thermodynamic limit the energy per spin of the low-energy configurations converges to the ground state of the SK model (analytical estimate being E0=-0.7631667265 »), fluctuation σN in EN0 decreases as ∼N-3/4, and the annealing time τN∼N, making this protocol highly efficient in estimating the ground state energy of the SK model.
Does Excellence Correspond to Universal Inequality Level?
Biswas S., Chakrabarti B.K., Ghosh A., Ghosh S., Jozsa M., Neda Z.
Entropy, 2025, DOI Link
View abstract ⏷
We study the inequality of citations received for different publications of various researchers and Nobel laureates in Physics, Chemistry, Medicine and Economics using Google Scholar data from 2012 to 2024. Citation distributions are found to be highly unequal, with even greater disparity among Nobel laureates. Measures of inequality, such as the Gini and Kolkata indices, emerge as useful indicators for distinguishing Nobel laureates from others. Such high inequality corresponds to growing critical fluctuations, suggesting that excellence aligns with an imminent (self-organized dynamical) critical point. Additionally, Nobel laureates exhibit systematically lower values of the Tsallis–Pareto parameter b and Shannon entropy, indicating more structured citation distributions. We also analyze the inequality in Olympic medal tallies across countries and find similar levels of disparity. Our results suggest that inequality measures can serve as proxies for competitiveness and excellence.
Signature of maturity in cryptocurrency volatility
Ghosh A., Biswas S., Chakrabarti B.K.
Physica A: Statistical Mechanics and its Applications, 2025, DOI Link
View abstract ⏷
We study the fluctuations, particularly the inequality of fluctuations, in cryptocurrency prices over the last ten years. We calculate the inequality in the price fluctuations through different measures, such as the Gini and Kolkata indices, and also the Q factor (given by the ratio between the highest value and the average value) of these fluctuations. We compare the results with the equivalent quantities in some of the more prominent national currencies and see that while the fluctuations (or inequalities in such fluctuations) for cryptocurrencies were initially significantly higher than national currencies, over time the fluctuation levels of cryptocurrencies tend towards the levels characteristic of national currencies. We also compare similar quantities for a few prominent stock prices.
A Fiber Bundle Model of Systemic Risk in Financial Networks
New Economic Windows, 2025, DOI Link
View abstract ⏷
Failure statistics of banks in the US show that their sizes are highly unequal (ranging from a few tens of thousands to over a billion dollars) and also, they come in “waves” of intermittent activities. This motivates a self-organized critical picture for the interconnected banking network. For such dynamics, recent developments in studying the inequality of the events, measured through the well-known Gini index and the more recently introduced Kolkata index, have been proved to be fruitful in anticipating large catastrophic events. In this chapter we review such developments for catastrophic failures using a simple model called the fiber bundle model. We then analyse the failure data of banks in terms of the inequality indices and study a simple variant of the fiber bundle model to analyse the same. It appears, both from the data and the model, that coincidence of these two indices signal a systemic risk in the network.
Order–disorder–order transitions and winning margins’ scaling in kinetic exchange opinion model
Biswas S., Annapurna M.S., Jakkampudi V., Yarlagadda D., Thota B.
International Journal of Modern Physics C, 2025, DOI Link
View abstract ⏷
The kinetic exchange opinion model shows a well-studied order–disorder transition as the noise parameter, representing discord between interacting agents, is increased. A further increase in the noise drives the model, in low dimensions, to an extreme segregation ordering through a transition of similar nature. The scaling behavior of the winning margins has distinct features in the ordered and disordered phases that are similar to the observations noted recently in election data in various countries, explaining the qualitative differences in such scaling between tightly contested and land-slide election victories.
Prediction of depinning transitions in interface models using Gini and Kolkata indices
Physical Review E, 2024, DOI Link
View abstract ⏷
The intermittent dynamics of driven interfaces through disordered media and its subsequent depinning for large enough driving force is a common feature for a myriad of diverse systems, starting from mode-I fracture, vortex lines in superconductors, and magnetic domain walls to invading fluid in a porous medium, to name a few. In this work, we outline a framework that can give a precursory signal of the imminent depinning transition by monitoring the variations in sizes or the inequality of the intermittent responses of a system that are seen prior to the depinning point. In particular, we use measures traditionally used to quantify economic inequality, i.e., the Gini index and the Kolkata index, for the case of the unequal responses of precritical systems. The crossing point of these two indices serves as a precursor to imminent depinning. Given a scale-free size distribution of the responses, we calculate the expressions for these indices, evaluate their crossing points, and give a recipe for forecasting depinning transitions. We apply this method to the Edwards-Wilkinson, Kardar-Parisi-Zhang, and fiber bundle model interface with variable interaction strengths and quenched disorder. The results are applicable for any interface dynamics undergoing a depinning transition. The results also explain previously observed near-universal values of Gini and Kolkata indices in self-organized critical systems.
Inequality of creep avalanches can predict imminent breakdown
Kanuri T.R., Roy S., Biswas S.
Physica A: Statistical Mechanics and its Applications, 2024, DOI Link
View abstract ⏷
We have numerically studied a mean-field fiber bundle model of fracture at a non-zero temperature and acted upon by a constant external tensile stress. The individual fibers fail due to creep-like dynamics that lead up to a catastrophic breakdown. We quantify the variations in sizes of the resulting avalanches by calculating the Lorenz function and two inequality indices – Gini (g) and Kolkata (k) indices – derived from the Lorenz function. We show that the two indices cross just prior to the failure point when the dynamics goes through intermittent avalanches. For a continuous failure dynamics (finite numbers of fibers breaking at each time step), the crossing does not happen. However, in that phase, the usual prediction method i.e., linear relation between the time of minimum strain-rate (time at which rate of fiber breaking is the minimum) and failure time, holds. The boundary between continuous and intermittent dynamics is very close to the boundary between crossing and non-crossing of the two indices in the temperature-stress phase space, both drawn from independent analytical calculations and are verified by numerical simulations.
Avalanche shapes in the fiber bundle model
Bodaballa N.K., Biswas S., Sen P.
Physical Review E, 2024, DOI Link
View abstract ⏷
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. A measure of asymmetry (A) follows a universal form A∼(σ-σc)θ, with θ≈0.25, where σ is the load per fiber and σc is the critical load per fiber. This behavior is independent of the disorder present in the system in terms of the individual failure threshold values. Thus it is possible to use this asymmetry measure as a precursor to imminent failure. For the case of discrete loading, the load is always increased by a fixed amount. The dynamics of the model in this case can be solved in the mean field limit. It shows that the avalanche shapes always remain asymmetric. We also present a variable range load sharing version of this case, where the results remain qualitatively similar.
Finding critical points and correlation length exponents using finite size scaling of Gini index
Das S., Biswas S., Chakraborti A., Chakrabarti B.K.
Physical Review E, 2024, DOI Link
View abstract ⏷
The order parameter for a continuous transition shows diverging fluctuation near the critical point. Here we show, through numerical simulations and scaling arguments, that the inequality (or variability) between the values of an order parameter, measured near a critical point, is independent of the system size. Quantification of such variability through the Gini index (g) therefore leads to a scaling form g=G[|F-Fc|N1/dν], where F denotes the driving parameter for the transition (e.g., temperature T for ferromagnetic to paramagnetic transition, or lattice occupation probability p in percolation), N is the system size, d is the spatial dimension and ν is the correlation length exponent. We demonstrate the scaling for the Ising model in two and three dimensions, site percolation on square lattice, and the fiber bundle model of fracture.
Critical Scaling through Gini Index
Physical Review Letters, 2023, DOI Link
View abstract ⏷
In the systems showing critical behavior, various response functions have a singularity at the critical point. Therefore, as the driving field is tuned toward its critical value, the response functions change drastically, typically diverging with universal critical exponents. In this Letter, we quantify the inequality of response functions with measures traditionally used in economics, namely by constructing a Lorenz curve and calculating the corresponding Gini index. The scaling of such a response function, when written in terms of the Gini index, shows singularity at a point that is at least as universal as the corresponding critical exponent. The critical scaling, therefore, becomes a single parameter fit, which is a considerable simplification from the usual form where the critical point and critical exponents are independent. We also show that another measure of inequality, the Kolkata index, crosses the Gini index at a point just prior to the critical point. Therefore, monitoring these two inequality indices for a system where the critical point is not known can produce a precursory signal for the imminent criticality. This could be useful in many systems, including that in condensed matter, bio- and geophysics to atmospheric physics. The generality and numerical validity of the calculations are shown with the Monte Carlo simulations of the two dimensional Ising model, site percolation on square lattice, and the fiber bundle model of fracture.
Social dynamics through kinetic exchange: the BChS model
Biswas S., Chatterjee A., Sen P., Mukherjee S., Chakrabarti B.K.
Frontiers in Physics, 2023, DOI Link
View abstract ⏷
This review presents an overview of the current research in kinetic exchange models for opinion formation in a society. The review begins with a brief introduction to previous models and subsequently provides an in-depth discussion of the progress achieved in the Biswas-Chatterjee-Sen model proposed in 2012, also known as the BChS model in some later research publications. The unique feature of the model is its inclusion of negative interaction between agents. The review covers various topics, including phase transitions between different opinion states, critical behavior dependent on various parameters, and applications in realistic scenarios such as the United States presidential election and Brexit.
Evolutionary dynamics of social inequality and coincidence of Gini and Kolkata indices under unrestricted competition
Banerjee S., Biswas S., Chakrabarti B.K., Challagundla S.K., Ghosh A., Guntaka S.R., Koganti H., Kondapalli A.R., Maiti R., Mitra M., Ram D.R.S.
International Journal of Modern Physics C, 2023, DOI Link
View abstract ⏷
Social inequalities are ubiquitous, and here we show that the values of the Gini (g) and Kolkata (k) indices, two generic inequality indices, approach each other (starting from g=0 and k=0.5 for equality) as the competitions grow in various social institutions like markets, universities and elections. It is further shown that these two indices become equal and stabilize at a value (at g=kâ 0.87) under unrestricted competitions. We propose to view this coincidence of inequality indices as a generalized version of the (more than a) century old 80-20 law of Pareto. Furthermore, the coincidence of the inequality indices noted here is very similar to the ones seen before for self-organized critical (SOC) systems. The observations here, therefore, stand as a quantitative support toward viewing interacting socio-economic systems in the framework of SOC, an idea conjectured for years.
Sandpile Universality in Social Inequality: Gini and Kolkata Measures
Banerjee S., Biswas S., Chakrabarti B.K., Ghosh A., Mitra M.
Entropy, 2023, DOI Link
View abstract ⏷
Social inequalities are ubiquitous and evolve towards a universal limit. Herein, we extensively review the values of inequality measures, namely the Gini (g) index and the Kolkata (k) index, two standard measures of inequality used in the analysis of various social sectors through data analysis. The Kolkata index, denoted as k, indicates the proportion of the ‘wealth’ owned by (Formula presented.) fraction of the ‘people’. Our findings suggest that both the Gini index and the Kolkata index tend to converge to similar values (around (Formula presented.), starting from the point of perfect equality, where (Formula presented.) and (Formula presented.)) as competition increases in different social institutions, such as markets, movies, elections, universities, prize winning, battle fields, sports (Olympics), etc., under conditions of unrestricted competition (no social welfare or support mechanism). In this review, we present the concept of a generalized form of Pareto’s 80/20 law ((Formula presented.)), where the coincidence of inequality indices is observed. The observation of this coincidence is consistent with the precursor values of the g and k indices for the self-organized critical (SOC) state in self-tuned physical systems such as sand piles. These results provide quantitative support for the view that interacting socioeconomic systems can be understood within the framework of SOC, which has been hypothesized for many years. These findings suggest that the SOC model can be extended to capture the dynamics of complex socioeconomic systems and help us better understand their behavior.
Inequality of avalanche sizes in models of fracture
Physical Review E, 2023, DOI Link
View abstract ⏷
Prediction of an imminent catastrophic event in a driven disordered system is of paramount importance - from the laboratory scale controlled fracture experiment to the largest scale of mechanical failure, i.e., earthquakes. It has long been conjectured that the statistical regularities in the energy emission time series mirror the "health"of such driven systems and hence have the potential for forecasting imminent catastrophe. Among other statistical regularities, a measure of how unequal avalanche sizes are is potentially a crucial indicator of imminent failure. The inequalities of avalanche sizes are quantified using inequality indices traditionally used in socioeconomic systems: the Gini index g, the Hirsch index h, and the Kolkata index k. It is shown analytically (for the mean-field case) and numerically (for the non-mean-field case) with models of quasi-brittle materials that the indices show universal behavior near the breaking points in such models and hence could serve as indicators of imminent breakdown of stressed disordered systems.
Prediction of imminent failure using supervised learning in a fiber bundle model
Physical Review E, 2022, DOI Link
View abstract ⏷
Prediction of a breakdown in disordered solids under external loading is a question of paramount importance. Here we use a fiber bundle model for disordered solids and record the time series of the avalanche sizes and energy bursts. The time series contain statistical regularities that not only signify universality in the critical behavior of the process of fracture, but also reflect signals of proximity to a catastrophic failure. A systematic analysis of these series using supervised machine learning can predict the time to failure. Different features of the time series become important in different variants of training samples. We explain the reasons for such a switch over of importance among different features. We show that inequality measures for avalanche time series play a crucial role in imminent failure predictions, especially for imperfect training sets, i.e., when simulation parameters of training samples differ considerably from those of the testing samples. We also show the variation of predictability of the system as the interaction range and strengths of disorders are varied in the samples, varying the failure mode from brittle to quasibrittle (with interaction range) and from nucleation to percolation (with disorder strength). The effectiveness of the supervised learning is best when the samples just enter the quasibrittle mode of failure showing scale-free avalanche size distributions.
Scaling behavior of the Hirsch index for failure avalanches, percolation clusters, and paper citations
Ghosh A., Chakrabarti B.K., Ram D.R.S., Mitra M., Maiti R., Biswas S., Banerjee S.
Frontiers in Physics, 2022, DOI Link
View abstract ⏷
A popular measure for citation inequalities of individual scientists has been the Hirsch index (h). If for any scientist the number nc of citations is plotted against the serial number np of the papers having those many citations (when the papers are ordered from the highest cited to the lowest), then h corresponds to the nearest lower integer value of np below the fixed point of the non-linear citation function (or given by nc = h = np if both np and nc are a dense set of integers near the h value). The same index can be estimated (from h = s = ns) for the avalanche or cluster of size (s) distributions (ns) in the elastic fiber bundle or percolation models. Another such inequality index called the Kolkata index (k) says that (1 − k) fraction of papers attract k fraction of citations (k = 0.80 corresponds to the 80–20 law of Pareto). We find, for stress (σ), the lattice occupation probability (p) or the Kolkata Index (k) near the bundle failure threshold (σc) or percolation threshold (pc) or the critical value of the Kolkata Index kc a good fit to Widom–Stauffer like scaling (Formula presented.) = (Formula presented.), (Formula presented.) or (Formula presented.), respectively, with the asymptotically defined scaling function f, for systems of size N (total number of fibers or lattice sites) or Nc (total number of citations), and α denoting the appropriate scaling exponent. We also show that if the number (Nm) of members of parliaments or national assemblies of different countries (with population N) is identified as their respective h − indexes, then the data fit the scaling relation (Formula presented.), resolving a major recent controversy.
Success of social inequality measures in predicting critical or failure points in some models of physical systems
Ghosh A., Biswas S., Chakrabarti B.K.
Frontiers in Physics, 2022, DOI Link
View abstract ⏷
Statistical physicists and social scientists both extensively study some characteristic features of the unequal distributions of energy, cluster, or avalanche sizes and of income, wealth, etc., among the particles (or sites) and population, respectively. While physicists concentrate on the self-similar (fractal) structure (and the characteristic exponents) of the largest (percolating) cluster or avalanche, social scientists study the inequality indices such as Gini and Kolkata, given by the non-linearity of the Lorenz function representing the cumulative fraction of the wealth possessed by different fractions of the population. Here, using results from earlier publications and some new numerical and analytical results, we reviewed how the above-mentioned social inequality indices, when extracted from the unequal distributions of energy (in kinetic exchange models), cluster sizes (in percolation models), or avalanche sizes (in self-organized critical or fiber bundle models) can help in a major way in providing precursor signals for an approaching critical point or imminent failure point. Extensive numerical and some analytical results have been discussed.
Machine learning predictions of COVID-19 second wave end-times in Indian states
Kondapalli A.R., Koganti H., Challagundla S.K., Guntaka C.S.R., Biswas S.
Indian Journal of Physics, 2022, DOI Link
View abstract ⏷
The estimate of the remaining time of an ongoing wave of epidemic spreading is a critical issue. Due to the variations of a wide range of parameters in an epidemic, for simple models such as Susceptible-Infected-Removed (SIR) model, it is difficult to estimate such a time scale. On the other hand, multidimensional data with a large set attributes are precisely what one can use in statistical learning algorithms to make predictions. Here we show, how the predictability of the SIR model changes with various parameters using a supervised learning algorithm. We then estimate the condition in which the model gives the least error in predicting the duration of the first wave of the COVID-19 pandemic in different states in India. Finally, we use the SIR model with the above mentioned optimal conditions to generate a training data set and use it in the supervised learning algorithm to estimate the end-time of the ongoing second wave of the pandemic in different states in India.
Near universal values of social inequality indices in self-organized critical models
Manna S.S., Biswas S., Chakrabarti B.K.
Physica A: Statistical Mechanics and its Applications, 2022, DOI Link
View abstract ⏷
We have studied few social inequality measures associated with the sub-critical dynamical features (measured in terms of the avalanche size distributions) of four self-organized critical models while the corresponding systems approach their respective stationary critical states. It has been observed that these inequality measures (specifically the Gini and Kolkata indices) exhibit nearly universal values though the models studied here are widely different, namely the Bak–Tang–Wiesenfeld sandpile, the Manna sandpile and the quenched Edwards–Wilkinson interface, and the fiber bundle interface. These observations suggest that the self-organized critical systems have broad similarity in terms of these inequality measures. A comparison with similar earlier observations in the data of socio-economic systems with unrestricted competitions suggest the emergent inequality as a result of the possible proximity to the self-organized critical states.
Correlation Between Avalanches and Emitted Energies During Fracture With a Variable Stress Release Range
Bodaballa N.K., Biswas S., Roy S.
Frontiers in Physics, 2022, DOI Link
View abstract ⏷
We observe the failure process of a fiber bundle model with a variable stress release range, γ, and higher the value of γ, lower the stress release range. By tuning γ from low to high, it is possible to go from the mean-field (MF) limit of the model to the local load-sharing (LLS) limit where local stress concentration plays a crucial role. In the MF limit, individual avalanches (number of fibers breaking in going from one stable state to the next, s) and the corresponding energies E emitted during those avalanches have one-to-one linear correlation. This results in the same size distributions for both avalanches (P(s)) and energy bursts (Q(E)): a scale-free distribution with a universal exponent value of −5/2. With increasing γ, the model enters the LLS limit beyond some γc. In this limit, due to the presence of local stress concentrations around a damaged region, such correlation C(γ) between s and E decreases, i.e., a smaller avalanche can emit a large amount of energy or a large avalanche may emit a small amount of energy. The nature of the decrease in the correlation between s and E depends highly on the dimension of the bundle. In this work, we study the decrease in the correlation between avalanche size and the corresponding energy bursts with an increase in the load redistribution localization in the fiber bundle model in one and two dimensions. Additionally, we note that the energy size distribution remains scale-free for all values of γ, whereas the avalanche size distribution becomes exponential for γ > γc.
Opinion dynamics: public and private
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2022, DOI Link
View abstract ⏷
We study here the dynamics of opinion formation in a society where we take into account the internally held beliefs and externally expressed opinions of the individuals, which are not necessarily the same at all times. While these two components can influence one another, their difference, both in dynamics and in the steady state, poses interesting scenarios in terms of the transition to consensus in the society and characterizations of such consensus. Here we study this public and private opinion dynamics and the critical behaviour of the consensus forming transitions, using a kinetic exchange model. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.
Kinetic exchange models of societies and economies
Toscani G., Sen P., Biswas S.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2022, DOI Link
View abstract ⏷
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. Nonetheless, in this age of Big Data, seeking empirical regularities emerging out of collective responses is a prominent and essential approach, much like the empirical thermodynamic principles preceding quantitative foundations of statistical mechanics. In this introductory article of the theme issue, we will provide an overview of the field of applications of kinetic theories in different socio-economic contexts and its recent boosting topics. Moreover, we will put the contributions to the theme issue in an appropriate perspective. This article is part of the theme issue ‘Kinetic exchange models of societies and economies’.
Parallel Minority Game and it’s application in movement optimization during an epidemic
Physica A: Statistical Mechanics and its Applications, 2021, DOI Link
View abstract ⏷
We introduce a version of the Minority Game where the total number of available choices is D>2, but the agents only have two available choices to switch. For all agents at an instant in any given choice, therefore, the other choice is distributed between the remaining D−1 options. This brings in the added complexity in reaching a state with the maximum resource utilization, in the sense that the game is essentially a set of MG that are coupled and played in parallel. We show that a stochastic strategy, used in the MG, works well here too. We discuss the limits in which the model reduces to other known models. Finally, we study an application of the model in the context of population movement between various states within a country during an ongoing epidemic. we show that the total infected population in the country could be as low as that achieved with a complete stoppage of inter-region movements for a prolonged period, provided that the agents instead follow the above mentioned stochastic strategy for their movement decisions between their two choices. The objective for an agent is to stay in the lower infected state between their two choices. We further show that it is the agents moving once between any two states, following the stochastic strategy, who are less likely to be infected than those not having (or not opting for) such a movement choice, when the risk of getting infected during the travel is not considered. This shows the incentive for the moving agents to follow the stochastic strategy.
Optimization strategies of human mobility during the COVID-19 pandemic: A review
Mathematical Biosciences and Engineering, 2021, DOI Link
View abstract ⏷
The impact of the ongoing COVID-19 pandemic is being felt in all spheres of our lives – cutting across the boundaries of nation, wealth, religions or race. From the time of the first detection of infection among the public, the virus spread though almost all the countries in the world in a short period of time. With humans as the carrier of the virus, the spreading process necessarily depends on the their mobility after being infected. Not only in the primary spreading process, but also in the subsequent spreading of the mutant variants, human mobility plays a central role in the dynamics. Therefore, on one hand travel restrictions of varying degree were imposed and are still being imposed, by various countries both nationally and internationally. On the other hand, these restrictions have severe fall outs in businesses and livelihood in general. Therefore, it is an optimization process, exercised on a global scale, with multiple changing variables. Here we review the techniques and their effects on optimization or proposed optimizations of human mobility in different scales, carried out by data driven, machine learning and model approaches.
Cooperative Dynamics in the Fiber Bundle Model
Chakrabarti B.K., Biswas S., Pradhan S.
Frontiers in Physics, 2021, DOI Link
View abstract ⏷
We discuss the cooperative failure dynamics in the fiber bundle model where the individual elements or fibers are Hookean springs that have identical spring constants but different breaking strengths. When the bundle is stressed or strained, especially in the equal-load-sharing scheme, the load supported by the failed fiber gets shared equally by the rest of the surviving fibers. This mean-field-type statistical feature (absence of fluctuations) in the load-sharing mechanism helped major analytical developments in the study of breaking dynamics in the model and precise comparisons with simulation results. We intend to present a brief review on these developments.
The Ising universality class of kinetic exchange models of opinion dynamics
Mukherjee S., Biswas S., Chatterjee A., Chakrabarti B.K.
Physica A: Statistical Mechanics and its Applications, 2021, DOI Link
View abstract ⏷
We show using scaling arguments and Monte Carlo simulations that a class of binary interacting models of opinion evolution belong to the Ising universality class in presence of an annealed noise term of finite amplitude. While the zero noise limit is known to show an active-absorbing transition, addition of annealed noise induces a continuous order–disorder transition with Ising universality class in the infinite-range (mean field) limit of the models.
Social inequality analysis of fiber bundle model statistics and prediction of materials failure
Physical Review E, 2021, DOI Link
View abstract ⏷
Inequalities are abundant in a society with a number of agents competing for a limited amount of resources. Statistics on such social inequalities are usually represented by the Lorenz function , where fraction of the population possesses fraction of the total wealth, when the population is arranged in ascending order of their wealth. Similarly, in scientometrics, such inequalities can be represented by a plot of the citation count versus the respective number of papers by a scientist, again arranged in ascending order of their citation counts. Quantitatively, these inequalities are captured by the corresponding inequality indices, namely, the Kolkata and the Hirsch indices, given by the fixed points of these nonlinear (Lorenz and citation) functions. In statistical physics of criticality, the fixed points of the renormalization group generator functions are studied in their self-similar limit, where their (fractal) structure converges to a unique form (macroscopic in size and lone). The statistical indices in social science, however, correspond to the fixed points where the values of the generator function (wealth or citation sizes) are commensurately abundant in fractions or numbers (of persons or papers). It has already been shown that under extreme competitions in markets or at universities, the index approaches a universal limiting value, as the dynamics of competition progresses. We introduce and study these indices for the inequalities of (prefailure) avalanches, given by their nonlinear size distributions in fiber bundle models of nonbrittle materials. We show how prior knowledge of the terminal and (almost) universal value of the index for a wide range of disorder parameters can help in predicting an imminent catastrophic breakdown in the model. This observation is also complemented by noting a similar (but not identical) behavior of the Hirsch index (), redefined for such avalanche statistics.
Size Distribution of Emitted Energies in Local Load Sharing Fiber Bundles
Frontiers in Physics, 2021, DOI Link
View abstract ⏷
We study the local load sharing fiber bundle model and its energy burst statistics. While it is known that the avalanche size distribution of the model is exponential, we numerically show here that the avalanche size (s) and the corresponding average energy burst (〈E〉) in this version of the model have a non-linear relation (〈E〉 ~ sγ). Numerical results indicate that γ ≈ 2.5 universally for different failure threshold distributions. With this numerical observation, it is then possible to show that the energy burst distribution is a power law, with a universal exponent value of −(γ + 1).
Block size dependence of coarse graining in discrete opinion dynamics model: Application to the US presidential elections
Biswas K., Biswas S., Sen P.
Physica A: Statistical Mechanics and its Applications, 2021, DOI Link
View abstract ⏷
The electoral college of voting system for the US presidential election is analogous to a coarse graining procedure commonly used to study phase transitions in physical systems. In a recent paper, opinion dynamics models manifesting a phase transition, were shown to be able to explain the cases when a candidate winning more number of popular votes could still lose the general election on the basis of the electoral college system. We explore the dependence of such possibilities on various factors like the number of states and total population (i.e., system sizes) and get an interesting scaling behavior. In comparison with the real data, it is shown that the probability of the minority win, calculated within the model assumptions, is indeed near the highest possible value. In addition, we also implement a two step coarse graining procedure, relevant for both opinion dynamics and information theory.
Flory-like statistics of fracture in the fiber bundle model as obtained via Kolmogorov dispersion for turbulence: A conjecture
Physical Review E, 2020, DOI Link
View abstract ⏷
It has long been conjectured that (rapid) fracture propagation dynamics in materials and turbulent motion of fluids are two manifestations of the same physical process. The universality class of turbulence (Kolmogorov dispersion, in particular) is conjectured to be identifiable with the Flory statistics for linear polymers (self-avoiding walks on lattices). These help us to relate fracture statistics to those of linear polymers (Flory statistics). The statistics of fracture in the fiber bundle model (FBM) are now well studied and many exact results are now available for the equal-load-sharing (ELS) scheme. Yet, the correlation length exponent in this model was missing and we show here how the correspondence between fracture statistics and the Flory mapping of Kolmogorov statistics for turbulence helps us to make a conjecture about the value of the correlation length exponent for fracture in the ELS limit of FBM and, also, about the upper critical dimension. In addition, the fracture avalanche size exponent values at lower dimensions (as estimated from such mapping to Flory statistics) also compare well with the observations.
Prediction of creep failure time using machine learning
Biswas S., Fernandez Castellanos D., Zaiser M.
Scientific Reports, 2020, DOI Link
View abstract ⏷
A subcritical load on a disordered material can induce creep damage. The creep rate in this case exhibits three temporal regimes viz. an initial decelerating regime followed by a steady-state regime and a stage of accelerating creep that ultimately leads to catastrophic breakdown. Due to the statistical regularities in the creep rate, the time evolution of creep rate has often been used to predict residual lifetime until catastrophic breakdown. However, in disordered samples, these efforts met with limited success. Nevertheless, it is clear that as the failure is approached, the damage become increasingly spatially correlated, and the spatio-temporal patterns of acoustic emission, which serve as a proxy for damage accumulation activity, are likely to mirror such correlations. However, due to the high dimensionality of the data and the complex nature of the correlations it is not straightforward to identify the said correlations and thereby the precursory signals of failure. Here we use supervised machine learning to estimate the remaining time to failure of samples of disordered materials. The machine learning algorithm uses as input the temporal signal provided by a mesoscale elastoplastic model for the evolution of creep damage in disordered solids. Machine learning algorithms are well-suited for assessing the proximity to failure from the time series of the acoustic emissions of sheared samples. We show that materials are relatively more predictable for higher disorder while are relatively less predictable for larger system sizes. We find that machine learning predictions, in the vast majority of cases, perform substantially better than other prediction approaches proposed in the literature.
Failure processes of cemented granular materials
Yamaguchi Y., Biswas S., Hatano T., Goehring L.
Physical Review E, 2020, DOI Link
View abstract ⏷
The mechanics of cohesive or cemented granular materials is complex, combining the heterogeneous responses of granular media, like force chains, with clearly defined material properties. Here we use a discrete element model simulation, consisting of an assemblage of elastic particles connected by softer but breakable elastic bonds, to explore how this class of material deforms and fails under uniaxial compression. We are particularly interested in the connection between the microscopic interactions among the grains or particles and the macroscopic material response. To this end, the properties of the particles and the stiffness of the bonds are matched to experimental measurements of a cohesive granular medium with tunable elasticity. The criterion for breaking a bond is also based on an explicit Griffith energy balance, with realistic surface energies. By varying the initial volume fraction of the particle assembles we show that this simple model reproduces a wide range of experimental behaviors, both in the elastic limit and beyond it. These include quantitative details of the distinct failure modes of shear-banding, ductile failure, and compaction banding or anticracks, as well as the transitions between these modes. The present work, therefore, provides a unified framework for understanding the failure of porous materials such as sandstone, marble, powder aggregates, snow, and foam.
Long route to consensus: Two-stage coarsening in a binary choice voting model
Mukherjee S., Biswas S., Sen P.
Physical Review E, 2020, DOI Link
View abstract ⏷
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.g., the question of the UK exiting the EU). There have been earlier attempts in capturing the dynamics of consensus formation in societies through simple Z2-symmetric models hoping to capture the essential dynamics of average behavior of a large number of individuals in a statistical sense. However, in absence of external noise, they tend to reach a frozen state with fragmented and polarized states, i.e., two or more groups of similarly opinionated groups with frozen dynamics. Here we show in a kinetic exchange opinion model considered on L×L square lattices, that while such frozen states could be avoided, an exponentially slow approach to consensus is manifested. Specifically, the system could either reach consensus in a time that scales as L2 or a long-lived metastable state (termed a "domain-wall state") for which formation of consensus takes a time scaling as L3.6. The latter behavior is comparable to some voterlike models with intermediate states studied previously. The late-time anomaly in the timescale is reflected in the persistence probability of the model. Finally, the interval of zero crossing of the average opinion, i.e., the time interval over which the average opinion does not change sign, is shown to follow a scale-free distribution, which is compared with that seen in the opinion surveys regarding Brexit and associated issues since the late 1970s. The issue of minority spreading is also addressed by calculating the exit probability.
Avalanche dynamics in hierarchical fiber bundles
Physical Review E, 2019, DOI Link
View abstract ⏷
Heterogeneous materials are often organized in a hierarchical manner, where a basic unit is repeated over multiple scales. The structure then acquires a self-similar pattern. Examples of such structure are found in various biological and synthetic materials. The hierarchical structure can have significant consequences for the failure strength and the mechanical response of such systems. Here we consider a fiber bundle model with hierarchical structure and study the avalanche dynamics exhibited by the model during the approach to failure. We show that the failure strength of the model generally decreases in a hierarchical structure, as opposed to the situation where no such hierarchy exists. However, we also report a special arrangement of the hierarchy for which the failure threshold could be substantially above that of a nonhierarchical reference structure.
Load dependence of power outage statistics
EPL, 2019, DOI Link
View abstract ⏷
Dynamics of power outages remain an unpredictable hazard in spite of expensive consequences. While the operations of the components of power grids are well understood, the emergent complexity due to their interconnections gives rise to intermittent outages, and power-law statistics. Here we demonstrate that there are additional patterns in the outage size distributions that indicate the proximity of a grid to a catastrophic failure point. Specifically, the analysis of the data for the U.S. between 2002 and 2017 shows a significant anti-correlation between the exponent value of the power-law outage size distribution and the load carried by the grid. The observation is surprisingly similar to dependences noted for failure dynamics in other multi-component complex systems such as sheared granulates and earthquakes, albeit under much different physical conditions. This inspires a generic threshold-activated model, simulated in realistic network topologies, which can successfully reproduce the exponent variation in a similar range. Given sufficient data, the methods proposed here can be used to indicate proximity to failure points and forecast probabilities of major blackouts with a non-intrusive measurement of intermittent grid outages.
Statistical physics of fracture and earthquakes
Biswas S., Goehring L., Chakrabarti B.K.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2019, DOI Link
View abstract ⏷
Manifestations of emergent properties in stressed disordered materials are often the result of an interplay between strong perturbations in the stress field around defects. The collective response of a long-ranged correlated multi-component system is an ideal playing field for statistical physics. Hence, many aspects of such collective responses in widely spread length and energy scales can be addressed by the tools of statistical physics. In this theme issue, some of these aspects are treated from various angles of experiments, simulations and analytical methods, and connected together by their common base of complex-system dynamics.
Failure time in heterogeneous systems
Physical Review Research, 2019, DOI Link
View abstract ⏷
We show that the failure time τf in the fiber bundle model, taken as a prototype of heterogeneous materials, depends crucially on the strength of the disorder δ and the stress release range R in the model. In the mean-field limit, the distribution of τf is log-normal. In this limit, the average failure time shows the variation τf∼Lα(δ), where L is the system size. The exponent α has a constant value above a critical disorder δc (=1/6), while it is an increasing function of δ in the region δ<δc. On the other hand, in the limit where the local stress concentration plays a crucial role, we observe the scaling τf∼Lα(δ)φ(R/L1-α(δ)), where R is the stress release range. We find that the crossover length scale Rc, between the above two limiting cases, scales as Rc∼L1-α(δ).
Mapping heterogeneities through avalanche statistics
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2019, DOI Link
View abstract ⏷
Avalanche statistics of various threshold-activated dynamical systems are known to depend on the magnitude of the drive, or stress, on the system. Such dependences exist for earthquake size distributions, in sheared granular avalanches, laboratory-scale fracture and also in the outage statistics of power grids. In this work, we model threshold-activated avalanche dynamics and investigate the time required to detect local variations in the ability of model elements to bear stress. We show that the detection time follows a scaling law where the scaling exponents depend on whether the feature that is sought is either weaker, or stronger, than its surroundings. We then look at earthquake data from Sumatra and California, demonstrate the trade-off between the spatial resolution of a map of earthquake exponents (i.e. the b-values of the Gutenberg-Richter Law) and the accuracy of those exponents, and suggest a means to maximize both.
Drying and percolation in correlated porous media
Biswas S., Fantinel P., Borgman O., Holtzman R., Goehring L.
Physical Review Fluids, 2018, DOI Link
View abstract ⏷
We study how the dynamics of a drying front propagating through a porous medium are affected by small-scale correlations in material properties. For this, we first present drying experiments in microfluidic micromodels of porous media. Here, the fluid pressures develop more intermittent dynamics as local correlations are added to the structure of the pore spaces. We also consider this problem numerically, using a model of invasion percolation with trapping, and find that there is a crossover in invasion behavior associated with the length scale of the disorder in the system. The critical exponents that describe large enough events are similar to the classic invasion percolation problem, while the addition of a finite correlation length significantly affects the exponent values of avalanches and bursts, up to some characteristic size. We find that even a weak local structure can interfere with the universality of invasion percolation phenomena. This has implications for a variety of multiphase flow problems, such as drying, drainage, and fluid invasion.
Effect of localized loading on failure threshold of fiber bundles
Physica A: Statistical Mechanics and its Applications, 2018, DOI Link
View abstract ⏷
We investigate the global failure threshold of an interconnected set of elements, when a finite fraction of the elements initially share an externally applied load. The study is done under the framework of random fiber bundle model, where the fibers are linear elastic objects attached between two plates. The failure threshold of the system varies non-monotonically with the fraction of the system on which the load is applied initially, provided the load sharing mechanism following a local failure is sufficiently wide. In this case, there exists a finite value for the initial loading fraction, for which the damage on the system will be maximum, or in other words the global failure threshold will be minimum for a finite value of the initial loading fraction. This particular value of initial loading fraction, however, goes to zero when the load sharing is sufficiently local. Such crossover behavior, seen for both one and two dimensional versions of the model, can give very useful information about stability of interconnected systems with random failure thresholds.
Record-breaking statistics near second-order phase transitions
Kundu M., Mukherjee S., Biswas S.
Physical Review E, 2018, DOI Link
View abstract ⏷
When a quantity reaches a value higher (or lower) than its value at any time before, it is said to have made a record. We numerically study the statistical properties of records in the time series of order parameters in different models near their critical points. Specifically, we choose the transversely driven Edwards-Wilkinson model for interface depinning in (1+1) dimensions and the Ising model in two dimensions, as paradigmatic and simple examples of nonequilibrium and equilibrium critical behaviors, respectively. The total number of record-breaking events in the time series of the order parameters of the models show maxima when the system is near criticality. The number of record-breaking events and associated quantities, such as the distribution of the waiting time between successive record events, show power-law scaling near the critical point. The exponent values are specific to the universality classes of the respective models. Such behaviors near criticality can be used as a precursor to imminent criticality, i.e., abrupt and catastrophic changes in the system. Due to the extreme nature of the records, its measurements are relatively free of detection errors and thus provide a clear signal regarding the state of the system in which they are measured.
Critical noise can make the minority candidate win: The U.S. presidential election cases
Physical Review E, 2017, DOI Link
View abstract ⏷
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. We establish that the sole effect of coarse graining, which mimics the "winner take all" electoral college system in the United States, can give rise to finite probabilities of events in which a minority candidate wins even in the large size limit near the critical point. The overall probabilities of victory of the minority candidate can be predicted from the models, which indicate that one may expect more instances of minority candidate winning in the future.
Modes of failure in disordered solids
Physical Review E, 2017, DOI Link
View abstract ⏷
The two principal ingredients determining the failure modes of disordered solids are the strength of heterogeneity and the length scale of the region affected in the solid following a local failure. While the latter facilitates damage nucleation, the former leads to diffused damage - the two extreme natures of the failure modes. In this study, using the random fiber bundle model as a prototype for disordered solids, we classify all failure modes that are the results of interplay between these two effects. We obtain scaling criteria for the different modes and propose a general phase diagram that provides a framework for understanding previous theoretical and experimental attempts of interpolation between these modes. As the fiber bundle model is a long-standing model for interpreting various features of stressed disordered solids, the general phase diagram can serve as a guiding principle in anticipating the responses of disordered solids in general.
Interface propagation in fiber bundles: Local, mean-field and intermediate range-dependent statistics
New Journal of Physics, 2016, DOI Link
View abstract ⏷
The fiber bundle model is essentially an array of elements that break when sufficient load is applied on them. With a local loading mechanism, this can serve as a model for a one-dimensional interface separating the broken and unbroken parts of a solid in mode-I fracture. The interface can propagate through the system depending on the loading rate and disorder present in the failure thresholds of the fibers. In the presence of a quasi-static drive, the intermittent dynamics of the interface mimic front propagation in disordered media. Such situations appear in diverse physical systems such as mode-I crack propagation, domain wall dynamics in magnets, charge density waves, contact lines in wetting etc. We study the effect of the range of interaction, i.e. the neighborhood of the interface affected following a local perturbation, on the statistics of the intermittent dynamics of the front. There exists a crossover from local to global behavior as the range of interaction grows and a continuously varying 'universality' in the intermediate range. This means that the interaction range is a relevant parameter of any resulting physics. This is particularly relevant in view of the fact that there is a scatter in the experimental observations of the exponents, in even idealized experiments on fracture fronts, and also a possibility in changing the interaction range in real samples.
Nucleation versus percolation: Scaling criterion for failure in disordered solids
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2015, DOI Link
View abstract ⏷
One of the major factors governing the mode of failure in disordered solids is the effective range R over which the stress field is modified following a local rupture event. In a random fiber bundle model, considered as a prototype of disordered solids, we show that the failure mode is nucleation dominated in the large system size limit, as long as R scales slower than Lζ, with ζ=2/3. For a faster increase in R, the failure properties are dominated by the mean-field critical point, where the damages are uncorrelated in space. In that limit, the precursory avalanches of all sizes are obtained even in the large system size limit. We expect these results to be valid for systems with finite (normalizable) disorder.
Statistical physics of fracture, beakdown, and earthquake: Effects of disorder and heterogeneity
Biswas S., Ray P., Chakrabarti B.K.
Statistical Physics of Fracture, Beakdown, and Earthquake: Effects of Disorder and Heterogeneity, 2015, DOI Link
View abstract ⏷
In this book, the authors bring together basic ideas from fracture mechanics and statistical physics, classical theories, simulation and experimental results to make the statistical physics aspects of fracture more accessible. They explain fracture-like phenomena, highlighting the role of disorder and heterogeneity from a statistical physical viewpoint. The role of defects is discussed in brittle and ductile fracture, ductile to brittle transition, fracture dynamics, failure processes with tension as well as compression: experiments, failure of electrical networks, self-organized critical models of earthquake and their extensions to capture the physics of earthquake dynamics. The text also includes a discussion of dynamical transitions in fracture propagation in theory and experiments, as well as an outline of analytical results in fiber bundle model dynamics With its wide scope, in addition to the statistical physics community, the material here is equally accessible to engineers, earth scientists, mechanical engineers, and material scientists. It also serves as a textbook for graduate students and researchers in physics.
Maximizing the Strength of Fiber Bundles under Uniform Loading
Physical Review Letters, 2015, DOI Link
View abstract ⏷
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., following which system can carry the maximum load. We address the question here and find that the answer depends on the mode of loading. We analytically find the maximum strength and corresponding redistribution schemes for sudden and quasistatic loading. The associated phase transition from partial to total failure by increasing the load has been studied. The universality class is found to be dependent on the redistribution mechanism.
Self-organized dynamics in local load-sharing fiber bundle models
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2013, DOI Link
View abstract ⏷
We study the dynamics of a local load-sharing fiber bundle model in two dimensions under an external load (which increases with time at a fixed slow rate) applied at a single point. Due to the local load-sharing nature, the redistributed load remains localized along the boundary of the broken patch. The system then goes to a self-organized state with a stationary average value of load per fiber along the (increasing) boundary of the broken patch (damaged region) and a scale-free distribution of avalanche sizes and other related quantities are observed. In particular, when the load redistribution is only among nearest surviving fiber(s), the numerical estimates of the exponent values are comparable with those of the Manna model. When the load redistribution is uniform along the patch boundary, the model shows a simple mean-field limit of this self-organizing critical behavior, for which we give analytical estimates of the saturation load per fiber values and avalanche size distribution exponent. These are in good agreement with numerical simulation results. © 2013 American Physical Society.
Equivalence of the train model of earthquake and boundary driven Edwards-Wilkinson interface
Biswas S., Ray P., Chakrabarti B.K.
European Physical Journal B, 2013, DOI Link
View abstract ⏷
A discretized version of the Burridge-Knopoff train model with (non-linear friction force replaced by) random pinning is studied in one and two dimensions. A scale free distribution of avalanches and the Omori law type behaviour for after-shocks are obtained. The avalanche dynamics of this model becomes precisely similar (identical exponent values) to the Edwards-Wilkinson (EW) model of interface propagation. It also allows the complimentary observation of depinning velocity growth (with exponent value identical with that for EW model) in this train model and Omori law behaviour of after-shock (depinning) avalanches in the EW model. © 2013 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.
Crossover behaviors in one and two dimensional heterogeneous load sharing fiber bundle models
European Physical Journal B, 2013, DOI Link
View abstract ⏷
We study the effect of heterogeneous load sharing in the fiber bundle models of fracture. The system is divided into two groups of fibers (fraction p and 1 - p) in which one group follows the completely local load sharing mechanism and the other group follows global load sharing mechanism. Patches of local disorders (weakness) in the loading plate can cause such a situation in the system. We find that in 2d a finite crossover (between global and local load sharing behaviours) point comes up at a finite value of the disorder concentration (near p c ∼ 0.53), which is slightly below the site percolation threshold. We numerically determine the phase diagrams (in 1d and 2d) and identify the critical behavior below p c with the mean field behavior (completely global load sharing) for both dimensions. This crossover can occur due to geometrical percolation of disorders in the loading plate. We also show how the critical point depends on the loading history, which is identified as a special property of local load sharing. © 2013 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.
Kolkata Paise Restaurant Problem: An Introduction
Ghosh A., Biswas S., Chatterjee A., Chakrabarti A.S., Naskar T., Mitra M., Chakrabarti B.K.
New Economic Windows, 2013, DOI Link
View abstract ⏷
We discuss several stochastic optimization strategies in games with many players having large number of choices (Kolkata Paise Restaurant Problem) and two choices (minority game problem). It is seen that a stochastic crowd avoiding strategy gives very efficient utilization in KPR problem. A slightly modified strategy in the minority game problem gives full utilization but the dynamics stops after reaching full efficiency, thereby making the utilization helpful for only about half of the population (those in minority). We further discuss the ways in which the dynamics may be continued and the utilization becomes effective for all the agents keeping fluctuation arbitrarily small. © Springer-Verlag Italia 2013.
Disorder induced phase transition in kinetic models of opinion dynamics
Biswas S., Chatterjee A., Sen P.
Physica A: Statistical Mechanics and its Applications, 2012, DOI Link
View abstract ⏷
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 calculation of a discrete version and numerical simulations of the continuous version of the model indicate the existence of a universal continuous phase transition at p=pc below which a consensus is reached. Although the orderdisorder transition is analogous to a ferromagneticparamagnetic phase transition with comparable critical exponents, the model is characterized by some distinctive features relevant to a social system. © 2012 Elsevier B.V. All rights reserved.
Statistical physics of fracture, friction, and earthquakes
Kawamura H., Hatano T., Kato N., Biswas S., Chakrabarti B.K.
Reviews of Modern Physics, 2012, DOI Link
View abstract ⏷
The present status of research and understanding regarding the dynamics and the statistical properties of earthquakes is reviewed, mainly from a statistical physical viewpoint. Emphasis is put both on the physics of friction and fracture, which provides a microscopic basis for our understanding of an earthquake instability, and on the statistical physical modelling of earthquakes, which provides macroscopic aspects of such phenomena. Recent numerical results from several representative models are reviewed, with attention to both their critical and their characteristic properties. Some of the relevant notions and related issues are highlighted, including the origin of power laws often observed in statistical properties of earthquakes, apparently contrasting features of characteristic earthquakes or asperities, the nature of precursory phenomena and nucleation processes, and the origin of slow earthquakes, etc. © 2012 American Physical Society.
Continuous transition of social efficiencies in the stochastic-strategy minority game
Biswas S., Ghosh A., Chatterjee A., Naskar T., Chakrabarti B.K.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2012, DOI Link
View abstract ⏷
We show that in a variant of the minority game problem, the agents can reach a state of maximum social efficiency, where the fluctuation between the two choices is minimum, by following a simple stochastic strategy. By imagining a social scenario where the agents can only guess about the number of excess people in the majority, we show that as long as the guessed value is sufficiently close to the reality, the system can reach a state of full efficiency or minimum fluctuation. A continuous transition to less efficient condition is observed when the guessed value becomes worse. Hence, people can optimize their guess for excess population to optimize the period of being in the majority state. We also consider the situation where a finite fraction of agents always decide completely randomly (random trader) as opposed to the rest of the population who follow a certain strategy (chartist). For a single random trader the system becomes fully efficient with majority-minority crossover occurring every 2 days on average. For just two random traders, all the agents have equal gain with arbitrarily small fluctuations. © 2012 American Physical Society.
Mean-field solutions of kinetic-exchange opinion models
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2011, DOI Link
View abstract ⏷
We present here the exact solution of an infinite range, discrete, opinion formation model. The model shows an active-absorbing phase transition, similar to that numerically found in its recently proposed continuous version. Apart from the two-agent interactions here we also report the effect of having three-agent interactions. The phase diagram has a continuous transition line (two-agent interaction dominated) and a discontinuous transition line (three-agent interaction dominated) separated by a tricritical point. © 2011 American Physical Society.
Erratum: Dynamical percolation transition in the Ising model studied using a pulsed magnetic field (Physical Review E – Statistical, Nonlinear, and Soft Matter Physics)
Biswas S., Kundu A., Chandra A.K.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2011, DOI Link
Dynamical percolation transition in the Ising model studied using a pulsed magnetic field
Biswas S., Kundu A., Chandra A.K.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2011, DOI Link
View abstract ⏷
We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature and pulse width and are different from the (static) percolation transition associated with the thermal transition. For a different model that belongs to the Ising universality class, the exponents are found to be same, confirming that the behavior is a common feature of the Ising class. These observations, along with a universal critical Binder cumulant value, characterize the dynamical percolation of the Ising universality class. © 2011 American Physical Society.
Phase transitions and non-equilibrium relaxation in kinetic models of opinion formation
Biswas S., Chandra A.K., Chatterjee A., Chakrabarti B.K.
Journal of Physics: Conference Series, 2011, DOI Link
View abstract ⏷
We review in details some recently proposed kinetic models of opinion dynamics. We discuss several variants including a generalised model. We provide mean field estimates for the critical points, which are numerically supported with reasonable accuracy. Using non-equilibrium relaxation techniques, we also investigate the nature of phase transitions observed in these models. We also study the nature of correlations as the critical points are approached.
Erratum: Publisher’s Note: Effect of fractal disorder on static friction in the Tomlinson model (Physical Review E – Statistical, Nonlinear, and Soft Matter Physics (2010) 82 (041124))
Eriksen J.A., Biswas S., Chakrabarti B.K.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2010, DOI Link
Effect of fractal disorder on static friction in the Tomlinson model
Eriksen J.A., Biswas S., Chakrabarti B.K.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2010, DOI Link
View abstract ⏷
We propose a modified version of the Tomlinson model for static friction between two chains of beads. We introduce disorder in terms of vacancies in the chain, and distribute the remaining beads in a scale invariant way. For this we utilize a generalized random Cantor set. We relate the static friction force to the overlap distribution of the chains, and discuss how the distribution of the static friction force depends on the distribution of the remaining beads. For the random Cantor set we find a scaled distribution which is independent on the generation of the set. © 2010 The American Physical Society.
