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Bikas K. Chakrabarti

Publications and source records attributed to Bikas K. Chakrabarti.

At least 109 records · Page 6Linked to original sources
arXiv2006

Analysis of the long-range random field quantum antiferromagnetic Ising model

We introduce a solvable quantum antiferromagnetic model. The model, with Ising spins in a transverse field, has infinite range antiferromagnetic interactions with random fields on each site, following an arbitrary distribution. As is well-known, frustration in the random field Ising model gives rise to a many-valley structure in the spin-configuration space. In addition, the antiferromagnetism also induces a regular frustration even for the ground state. In this paper, we investigate analytically the critical phenomena in the model, having both randomness and frustration and we report some analytical results for it.

cond-mat.dis-nn↗
arXiv2006

A Fiber Bundle Model of Traffic Jams

We apply the equal load-sharing fiber bundle model of fracture failure in composite materials to model the traffic failure in a system of parallel road network in a city. For some special distributions of traffic handling capacities (thresholds) of the roads, the critical behavior of the jamming transition can be studied analytically. This has been compared with that for the asymmetric simple exclusion process in a single channel or road.

cond-mat.stat-mech↗
arXiv2006

Precursors and prediction of catastrophic avalanches

In this work we review the precursors of catastrophic avalanches (global failures) in several failure models, namely (a) Fiber Bundle Model (FBM), (b) Random Fuse Model (RFM), (c) Sandpile Models and (d) Fractal Overlap Model. The precursor parameters identified here essentially reflect the growing correlations within such systems as they approach their respective failure points. As we show, often they help us to predict the global failure points in advance.

cond-mat.soft↗
arXiv2005

Master equation for a kinetic model of trading market and its analytic solution

We analyze an ideal gas like model of a trading market with quenched random saving factors for its agents and show that the steady state income ($m$) distribution $P(m)$ in the model has a power law tail with Pareto index $ν$ exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of $P(m)$. Precise solutions are then obtained in some special cases.

cond-mat.other↗
arXiv2005

A solvable quantum antiferromagnet model

We introduce a quantum antiferromagnet model, having exactly soluble thermodynamic properties. It is an infinite range antiferromagnetic Ising model put in a transverse field. The free energy gives the ground state energy in the zero temperature limit and it also gives the low temperature behaviour of the specific heat, the exponential variation of which gives the precise gap magnitude in the excitation spectrum of the system. The detailed behaviour of the (random sublattice) staggard magnetisation and susceptibilities are obtained and studied near the Néel temperature and the zero temperature quantum critical point.

cond-mat.stat-mech↗
arXiv2005

Analyzing money distributions in `ideal gas' models of markets

We analyze an ideal gas like models of a trading market. We propose a new fit for the money distribution in the fixed or uniform saving market. For the marketwith quenched random saving factors for its agents we show that the steady state income ($m$) distribution $P(m)$ in the model has a power law tail with Pareto index $ν$ exactly equal to unity, confirming the earlier numerical studies on this model. We analyze the distribution of mutual money difference and also develop a master equation for the time development of $P(m)$. Precise solutions are then obtained in some special cases.

physics.soc-ph↗
arXiv2005

Quantum Annealing in a Kinetically Constrained System

Classical and quantum annealing is discussed for a kinetically constrained chain of $N$ non-interacting asymmetric double wells, represented by Ising spins in a longitudinal field $h$. It is shown that in certain cases, where the kinetic constraints may arise from infinitely high but vanishingly narrow barriers appearing in the relaxation path of the system, quantum annealing exploiting the quantum-mechanical penetration of sufficiently narrow barriers may be far more efficient than its thermal counterpart. We have used a semiclassical picture of scattering dynamics to do our simulation for the quantum system.

cond-mat.stat-mech↗
arXiv2004

Crossover behavior in a mixed mode fiber bundle model

We introduce a mixed-mode load sharing scheme in fiber bundle model. This model reduces exactly to equal load sharing (ELS) and local load sharing (LLS) models at the two extreme conditions of the load sharing rule. We identify two distinct regimes: a) Mean-field regime where ELS mode dominates and b) short range regime dominated by LLS mode. The crossover behavior is explored through the numerical study of strength variation, the avalanche statistics, susceptibility and relaxation time variations, the correlations among the broken fibers and their cluster analysis. Analyzing the moments of the cluster size distributions we locate the crossover point of these regimes. We thus conclude that even in one dimension, fiber bundle model shows crossover behavior from mean-field to short range interactions.

cond-mat.stat-mech↗
arXiv2004

Competition between ferro-retrieval and anti-ferro orders in a Hopfield-like network model for plant intelligence

We introduce a simple cellular-network model to explain the capacity of the plants as memory devices. Following earlier observations (Bose \cite{Bose} and others), we regard the plant as a network in which each of the elements (plant cells) are connected via negative (inhibitory) interactions. To investigate the performance of the network, we construct a model following that of Hopfield, whose energy function possesses both Hebbian spin glass and anti-ferromagnetic terms. With the assistance of the replica method, we find that the memory state of the network decreases enormously due to the effect of the anti-ferromagnetic order induced by the inhibitory connections. We conclude that the ability of the plant as a memory device is rather weak.

cond-mat.dis-nn↗
arXiv2004

Pareto Law in a Kinetic Model of Market with Random Saving Propensity

We have numerically simulated the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving two-body collision. Unlike in the ideal gas, we introduce (quenched) saving propensity of the agents, distributed widely between the agents ($0 \le λ< 1$). The system remarkably self-organizes to a critical Pareto distribution of money $P(m) \sim m^{-(ν+ 1)}$ with $ν\simeq 1$. We analyse the robustness (universality) of the distribution in the model. We also argue that although the fractional saving ingredient is a bit unnatural one in the context of gas models, our model is the simplest so far, showing self-organized criticality, and combines two century-old distributions: Gibbs (1901) and Pareto (1897) distributions.

cond-mat.stat-mech↗
arXiv2004

Competing field pulse induced dynamic transition in Ising models

The dynamic magnetization-reversal phenomena in the Ising model under a finite-duration external magnetic field competing with the existing order for $T<T_c^0$ has been discussed. The nature of the phase boundary has been estimated from the mean-field equation of motion. The susceptibility and relaxation time diverge at the MF phase boundary. A Monte Carlo study also shows divergence of relaxation time around the phase boundary. Fluctuation of order parameter also diverge near the phase boundary. The behavior of the fourth order cumulant shows two distinct behavior: for low temperature and pulse duration region of the phase boundary the value of the cumulant at the crossing point for different system sizes is much less than that corersponding to the static transition in the same dimension which indicate a new universality class for the dynamic transition. Also, for higher temperature and pulse duration, the transition seem to fall in a mean-field like weak-singularity universality class.

cond-mat.stat-mech↗
arXiv2003

Money in Gas-Like Markets: Gibbs and Pareto Laws

We consider the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving (two-body) collision. Unlike in the ideal gas, we introduce saving propensity $λ$ of agents, such that each agent saves a fraction $λ$ of its money and trades with the rest. We show the steady-state money or wealth distribution in a market is Gibbs-like for $λ=0$, has got a non-vanishing most-probable value for $λ\ne 0$ and Pareto-like when $λ$ is widely distributed among the agents. We compare these results with observations on wealth distributions of various countries.

cond-mat.stat-mech↗
arXiv2003

Precursors of catastrophic failures

We review here briefly the nature of precursors of global failures in three different kinds of many-body dynamical systems. First, we consider the lattice models of self-organised criticality in sandpiles and investigate numerically the effect of pulsed perturbations to the systems prior to reaching their respective critical points. We consider next, the random strength fiber bundle models, under global load sharing approximation, and derive analytically the partial failure response behavior at loading level less than its global failure or critical point. Finally, we consider the two-fractal overlap model of earthquake and analyse numerically the overlap time series data as one fractal moves over the other with uniform velocity. The precursors of global or major failure in all three cases are shown to be very well characterized and prominent.

cond-mat.stat-mech↗
arXiv2003

Quantum Spin Glass Phase Boundary in (+/-)J Transverse Field Ising Systems

Here we study zero temperature quantum phase transition driven by the transverse field for random $\pm J$ Ising model on chain and square lattice. We present some analytical results for one dimension and some numerical results for very small square lattice under periodic boundary condition. The numerical results are obtained employing exact diagonalization technique following Lanczos method.

cond-mat.stat-mech↗
arXiv2003

The Mean Distance to the n-th Neighbour in a Uniform Distribution of Random Points: An Application of Probability Theory

We study different ways of determining the mean distance $ < r_n >$ between a reference point and its $n$-th neighbour among random points distributed with uniform density in a $D$-dimensional Euclidean space. First we present a heuristic method; though this method provides only a crude mathematical result, it shows a simple way of estimating $ < r_n >$. Next we describe two alternative means of deriving the exact expression of $ $: we review the method using absolute probability and develop an alternative method using conditional probability. Finally we obtain an approximation to $ < r_n >$ from the mean volume between the reference point and its $n$-th neighbour and compare it with the heuristic and exact results.

math.PR↗
arXiv2003

Prediction Possibility in the Fractal Overlap Model of Earthquakes

The two-fractal overlap model of earthquake shows that the contact area distribution of two fractal surfaces follows power law decay in many cases and this agrees with the Guttenberg-Richter power law. Here, we attempt to predict the large events (earthquakes) in this model through the overlap time-series analysis. Taking only the Cantor sets, the overlap sizes (contact areas) are noted when one Cantor set moves over the other with uniform velocity. This gives a time series containing different overlap sizes. Our numerical study here shows that the cumulative overlap size grows almost linearly with time and when the overlapsizes are added up to a pre-assigned large event (earthquake) and then reset to `zero' level, the corresponding cumulative overlap sizes grows upto some discrete (quantised) levels. This observation should help to predict the possibility of `large events' in this (overlap) time series.

cond-mat.stat-mech↗
arXiv2003

Failure properties of fiber bundle models

We study the failure properties of fiber bundles when continuous rupture goes on due to the application of external load on the bundles. We take the two extreme models: equal load sharing model (democratic fiber bundles) and local load sharing model. The strength of the fibers are assumed to be distributed randomly within a finite interval. The democratic fiber bundles show a solvable phase transition at a critical stress (load per fiber). The dynamic critical behavior is obtained analytically near the critical point and the critical exponents are found to be universal. This model also shows elastic-plastic like nonlinear deformation behavior when the fiber strength distribution has a lower cut-off. We solve analytically the fatigue-failure in a democratic bundle, and the behavior qualitatively agrees with the experimental observations. The strength of the local load sharing bundles is obtained numerically and compared with the existing results. Finally we map the failure phenomena of fiber bundles in terms of magnetic model (Ising model) which may resolve the ambiguity of studying the failure properties of fiber bundles in higher dimensions.

cond-mat.stat-mech↗