arXiv subjects

Soumyajyoti Biswas

Publications and source records attributed to Soumyajyoti Biswas.

At least 37 records · Page 2Linked to original sources

arXiv2024

Inequalities of energy release rates in compression of nano-porous materials predict its imminent breakdown

We show that the divergent acoustic energy release rate in a quasi-statically compressed nano-porous material can be used as a precursor to failure in such materials. A quantification of the inequality of the energy release rate using social inequality measure indices help constructing a warning signal for 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 formulation for any diverging response function near a transition point using social inequality indices.

cond-mat.stat-mech↗

arXiv2024

Inequality indices for heterogeneous systems: a tool for failure prediction

We have numerically studied a mean-field fiber bundle model of fracture at a non-zero temperature and acted by a constant external tensile stress. The individual fibers fail (local damage) due to creep-like dynamics that lead up to a catastrophic breakdown (global failure). 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 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.

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arXiv2024

Finding critical points and correlation length exponents using finite size scaling of Gini index

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 Gini index ($g$), therefore, leads to a scaling form $g=G\left[|F-F_c|N^{1/dν}\right]$, where $F$ denotes the driving parameter for the transition (e.g., temperature $T$ for ferromagnetic to paramagnetic transition transition, or lattice occupation probability $p$), $N$ 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.

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arXiv2024

A Fiber Bundle Model of Systemic Risk in Financial Networks

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 analyze the failure data of banks in terms of the inequality indices and study a simple variant of the fiber bundle model to analyze the same. It appears, both from the data and the model, that coincidence of these two indices signal a systemic risk in the network.

physics.soc-ph↗

arXiv2023

Avalanche shapes in 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) the quasi-static loading, and (ii) loading by a discrete amount. In the quasi-static 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 follows a universal form $A\sim (σ-σ_c)^θ$, with $θ\approx 0.25$, where $σ$ is the load per fiber and $σ_c$ 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.

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arXiv2023

Prediction of depinning transitions in interface models using Gini and Kolkata indices

The dynamics of driven interfaces through disordered media is a common framework for a myriad of diverse systems starting from mode-I fracture, vortex lines in superconductors, magnetic domain walls to invading fluid in a porous medium to name a few. The dynamics, for a slow enough drive, progress through punctuated equilibria, showing an intermittent, scale free response statistics that are characterized by only a few parameters. For a strong enough driving, on the other hand, the interface is depinnind i.e., can move continuously through the embedded medium. This depinning transition, often characterized as a critical phenomenon, is a crucial point for the system in question, since it often represent a drastic change in the system (catastrophic failure in the case of fracture, magnetisation switching in the case of domain walls, breakthrough point in the case of fluid invasion etc.). 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 seen prior to the depinning point. In particular, we use measures traditionally used to quantify economic inequality, the Gini index and the Kolkata index, for the case of the unequal responses of pre-critical systems. The crossing point of these two indices serves as a precursor to imminent depinning. Given a scale free size distributions of the responses, we calculate the expressions for these indices, evaluate their crossing points and give a recipe for forecasting depinning transitions. We compare these with simulation results from the Edwards-Wilkindon, KPZ and fiber bundle model interface with variable interaction strength. The results are applicable for any interface dynamics undergoing depinning transition.

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arXiv2023

Critical scaling through Gini index

In the systems showing critical behavior, various response functions have a singularity at the critical point. Therefore, as the driving field is tuned towards its critical value, the response functions change drastically, typically diverging with universal critical exponents. In this work, 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.

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arXiv2023

Inequality of avalanche sizes in models of fracture

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 been long conjectured that the statistical regularities in the energy emission time series mirrors the "health" of such driven systems and hence have the potential for forecasting imminent catastrophe. Among other statistical regularities, a measure of how unequal the avalanche sizes are, is potentially a crucial indicator of imminent failure. The inequalities of avalanche sizes are quantified using inequality indices traditionally used in socio-economic systems: the Gini index (g), the Hirsch index (h) and the Kolkata index (k). It is then shown analytically (for mean field) and numerically (for non mean field) in 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.

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arXiv2023

Social dynamics through kinetic exchange: The BChS model

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.

physics.soc-ph↗

arXiv2023

Sandpile Universality in Social Inequality: Gini and Kolkata Measures

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 $(1-k)$ fraction of the `people'. Our findings suggest that both the Gini index and the Kolkata index tend to converge to similar values (around $g=k \approx 0.87$, starting from the point of perfect equality, where $g=0$ and $k=0.5$) 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 ($k=0.80$), 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.

physics.soc-ph↗

arXiv2022

Scaling Behavior of the Hirsch Index for Failure Avalanches, Percolation Clusters and Paper Citations

A popular measure for citation inequalities of individual scientists has been the Hirsch index ($h$). If for any scientist the number $n_c$ of citations is plotted against the serial number $n_p$ of the paper having those many citations (when the papers are ordered from highest cited to lowest) then $h$ corresponds to the nearest lower integer value of $n_p$ below the fixed point of the non-linear citation function (or given by $n_c = h = n_p$ if both $n_p$ and $n_c$ are dense set of integers near the $h$ value). The same index can be estimated (from $h=s=n_{s}$) for the avalanche or cluster of size ($s$) distributions ($n_s$) in 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 ($σ$), lattice occupation probability ($p$) or Kolkata index ($k$) near the bundle failure threshold ($σ_c$) or percolation threshold ($p_c$) or critical value of Kolkata index $k_c$, good fit to Widom-Stauffer like scaling $h/[\sqrt{N}/log N]$ = $f(\sqrt{N}[σ_c -σ]^α)$, $h/[\sqrt{N}/log N]=f(\sqrt{N}|p_c -p|^α)$ or $h/[\sqrt{N_c}/log N_c]=f(\sqrt{N_c}|k_c -k|^α)$ respectively, with asymptotically defined scaling function $f$, for systems of size $N$ (total number of fibers or lattice sites) or $N_c$ (total number of citations), and $α$ denoting the appropriate scaling exponent. We also show that if the number ($N_m$) of members of parliaments or national assemblies of different countries (with population $N$) is identified as their respective $h-$index, then the data fit the scaling relation $N_m \sim \sqrt N /log N$, resolving a major recent controversy.

physics.soc-ph↗

arXiv2022

Evolutionary Dynamics of Social Inequality and Coincidence of Gini and Kolkata indices under Unrestricted Competition

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, elections, etc. It is further showed that these two indices become equal and stabilize at a value (at $g = k \simeq 0.87$) 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 towards viewing interacting socio-economic systems in the framework of SOC, an idea conjectured for years.

physics.soc-ph↗

arXiv2022

Success of Social Inequality Measures in Predicting Critical or Failure Points in Some Models of Physical Systems

Statistical physicists and social scientists both study extensively 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 like Gini and Kolkata etc given by the non-linearity of the Lorenz function representing the cumulative fraction of the wealth possessed by different fraction of the population. We review here, using results from earlier publications and some new numerical as well as analytical results, 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.

physics.soc-ph↗

arXiv2022

Prediction of imminent failure using supervised learning in fiber bundle model

Prediction of breakdown in disordered solids under external loading in 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 contains 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 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 quasi-brittle (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 quasi-brittle mode of failure showing scale-free avalanche size distributions.

cond-mat.stat-mech↗

arXiv2022

Near universal values of social inequality indices in self-organized critical models

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.

cond-mat.stat-mech↗

arXiv2021

Opinion dynamics: Public and private

We study here the dynamics of opinion formation in a society where we take into account of 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 behavior of the consensus forming transitions, using a kinetic exchange model.

physics.soc-ph↗

arXiv2021

Social Inequality Analysis of Fiber Bundle Model Statistics and Prediction of Materials Failure

Inequalities are abundant in a society with a number of agents competing for a limited amount of resource. Statistics of such social inequalities are usually represented by the Lorenz function $L(p)$, where $p$ fraction of the population possesses $L(p)$ fraction of the total wealth, when the population is arranged in the ascending order of their wealth. Similarly, in scientometrics, such inequalities can be represented by a plot of the citation count against the respective number of papers by a scientist, again arranged in the ascending order of their citation counts. Quantitatively, these inequalities are captured by the corresponding inequality indices, namely the Kolkata $k$ and the Hirsch $h$ indices, given by the fixed points of these nonlinear functions. In statistical physics of criticality, the fixed points of the Renormalization Group generator functions are studied in their self-similar limit, where its (fractal) structure converges to a unique form. The statistical indices in the 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). We introduce and study these indices for the inequalities of (pre-failure) avalanches, given by their size distributions in the Fiber Bundle Models (FBM) of non-brittle materials. We show how a prior knowledge of the terminal and almost universal value of the $k$ index for a wide range of disorder parameter, can help in predicting an imminent catastrophic breakdown in the model. This observation has also been complemented by noting a similar (but not identical) behavior of the Hirsch index ($h$), redefined for such avalanche statistics.

cond-mat.stat-mech↗

arXiv2021

Correlation between avalanches and emitted energies during fracture with variable stress release range

We observe the failure process of a fiber bundle model with a variable stress release range, $γ$, 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 local load sharing (LLS) where local stress concentration plays a crucial role. In the MF limit, the avalanche size $s$ and energy $E$ emitted during the avalanche are highly correlated producing the same distribution for both $P(s)$ and $Q(E)$: a scale-free distribution with a universal exponent -5/2. With increasing $γ$, the model enters the LLS limit. In this limit, due to the presence of local stress concentration such correlation $C(γ)$ between $s$ and $E$ decreases where the nature of the decreases depends highly on the dimension of the bundle. In 1d, the $C(γ)$ stars from a high value for low $γ$ and decreases towards zero when $γ$ is increased. As a result, $Q(E)$ and $P(s)$ are similar at low $γ$, an exponential one, and then $Q(E)$ becomes power-law for high-stress release range though $P(s)$ remains exponential. On the other hand, in 2d, the $C(γ)$ decreases slightly with $γ$ but remains at a high value. Due to such a high correlation, the distribution of both $s$ and $E$ is exponential in the LLS limit independent of how large $γ$ is.

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