Biomedical subjects

Bikas K Chakrabarti

Publications and source records attributed to Bikas K Chakrabarti.

7 recordsLinked to original sources

PubMed2005

Master equation for a kinetic model of a 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 nu 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.

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PubMed2005

Quantum annealing in a kinetically constrained system.

Classical and quantum annealing is discussed in the case of a generalized kinetically constrained model, where the relaxation dynamics of a system with trivial ground state is retarded by the appearance of energy barriers in the relaxation path, following a local kinetic rule. Effectiveness of thermal and quantum fluctuations in overcoming these kinetic barriers to reach the ground state are studied. It has been shown that for certain barrier characteristics, quantum annealing might by far surpass its thermal counter part in reaching the ground state faster.

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PubMed2005

Crossover behavior in a mixed-mode fiber bundle model.

We introduce a mixed-mode load sharing scheme in a fiber bundle model. This model reduces exactly to equal-load-sharing (ELS) and local-load-sharing (LLS) models at the two extreme limits of a single-load-sharing parameter. We identify two distinct regimes: (a) the mean-field regime where the ELS mode dominates and (b) the short-range regime dominated by the LLS mode. The crossover behavior is explored through a numerical study of the 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, the fiber bundle model shows crossover behavior from mean-field to short-range interactions.

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PubMed2003

Failure due to fatigue in fiber bundles and solids.

We consider first a homogeneous fiber bundle model where all the fibers have got the same stress threshold (sigma(c)) beyond which all fail simultaneously in absence of noise. At finite noise, the bundle acquires a fatigue behavior due to the noise-induced failure probability at any stress sigma. We solve this dynamics of failure analytically and show that the average failure time tau of the bundle decreases exponentially as sigma-->sigma(c) from below and tau=0 for sigma>or=sigma(c). We also determine the avalanche size distribution during such failure and find a power law decay. We compare this fatigue behavior with that obtained phenomenologically for the nucleation of the Griffith cracks. Next we study numerically the fatigue behavior of random fiber bundles having simple distributions of individual fiber strengths, at stress sigma less than the bundle's strength sigma(c); (beyond which it fails instantly). The average failure time tau is again seen to decrease exponentially as sigma-->sigma(c); from below and the avalanche size distribution shows similar power law decay. These results are also in broad agreement with experimental observations on fatigue in solids. We believe, these observations regarding the failure time are useful for quantum breakdown phenomena in disordered systems.

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PubMed2003

Phase transition in fiber bundle models with recursive dynamics.

We study the phase transition in a class of fiber bundle models in which the fiber strengths are distributed randomly within a finite interval and global load sharing is assumed. The dynamics is expressed as recursion relations for the redistribution of the applied stress and the evolution of the surviving fraction of fibers. We show that an irreversible phase transition of second-order occurs, from a phase of partial failure to a phase of total failure, when the initial applied stress just exceeds a critical value. The phase transition is characterized by static and dynamic critical properties. We calculate exactly the critical value of the initial stress for three models of this kind, each with a different distribution of fiber strengths. We derive exact expressions for the order parameter, the susceptibility to changes in the initial applied stress, and the critical relaxation of the surviving fraction of fibers for all the three models. The static and dynamic critical exponents obtained from these expressions are found to be universal.

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PubMed2003

Fluctuation cumulant behavior for the field-pulse-induced magnetization-reversal transition in Ising models.

The universality class of the dynamic magnetization-reversal transition, induced by a competing field pulse, in an Ising model on a square lattice, below its static ordering temperature, is studied here using Monte Carlo simulations. Fourth-order cumulant of the order parameter distribution is studied for different system sizes around the phase boundary region. The crossing point of the cumulant (for different system sizes) gives the transition point and the value of the cumulant at the transition point indicates the universality class of the transition. The cumulant value at the crossing point for low temperature and pulse width range is observed to be significantly less than that for the static transition in the same two-dimensional Ising model. The finite-size scaling behavior in this range also indicates a higher correlation length exponent value. For higher temperature and pulse width range, the transition seems to fall in a mean-field-like universality class.

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PubMed2001

Precursors of catastrophe in the Bak-Tang-Wiesenfeld, Manna, and random-fiber-bundle models of failure.

We have studied precursors of the global failure in some self-organized critical models of sandpile [in Bak-Tang-Wiesenfeld (BTW) and Manna models] and in the random-fiber-bundle model (RFB). In both BTW and Manna model, as one adds a small but fixed number of sand grains (heights) to any central site of the stable pile, the local dynamics starts and continues for an average relaxation time tau and an average number of topplings Delta spread over a radial distance xi. We find that these quantities all depend on the average height h(av) of the pile and they all diverge as h(av) approaches the critical height h(c) from below: Delta approximately (h(c)-h(av))(-delta), tau approximately (h(c)-h(av))(-gamma), and xi approximately (h(c)-h(av))(-nu). Numerically, we find delta approximately 2.0, gamma approximately 1.2, and nu approximately 1.0 for both BTW and Manna model in two dimensions. In the strained RFB model, we find that the breakdown susceptibility chi (giving the differential increment of the number of broken fibers due to increase in external load) and the relaxation time tau, both diverge as the applied load or stress sigma approaches the network failure threshold sigma(c) from below: chi approximately (sigma(c)-sigma)(-1/2) and tau approximately (sigma(c)-sigma)(-1/2). These self-organized dynamical models of failure, therefore, show some definite precursors with robust power laws long before the failure point. Such well-characterized precursors should help predicting the global failure point of the systems in advance.

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