arXiv subjects

Bikas K Chakrabarti

Publications and source records attributed to Bikas K Chakrabarti.

23 records · Page 2Linked to original sources

arXiv2005

A two-fractal overlap model of earthquakes

We introduce here the two-fractal model of earthquake dynamics. As the fractured surfaces have self-affine properties, we consider the solid-solid interface of the earth's crust and the tectonic plate below as fractal surfaces. The overlap or contact area between the two surfaces give a measure of the stored elastic energy released during a slip. The overlap between two fractals change with time as one moves over the other and we show that the time average of the overlap distribution follows a Gutenberg-Richter like power-law, with similar exponent value.

cond-mat.stat-mech↗

arXiv2005

A common origin of the power law distributions in models of market and earthquake

We show that there is a common mode of origin for the power laws observed in two different models: (i) the Pareto law for the distribution of money among the agents with random saving propensities in an ideal gas-like market model and (ii) the Gutenberg-Richter law for the distribution of overlaps in a fractal-overlap model for earthquakes. We find that the power laws appear as the asymptotic forms of ever-widening log-normal distributions for the agents' money and the overlap magnitude respectively. The identification of the generic origin of the power laws helps in better understanding and in developing generalized views of phenomena in such diverse areas as economics and geophysics.

physics.soc-ph↗

arXiv2005

Ideal-Gas Like Markets: Effect of Savings

We discuss the ideal gas like models of a trading market. The effect of savings on the distribution have been thoroughly reviewed. The market with fixed saving factors leads to a Gamma-like distribution. In a market with 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 $ν$ equal to unity. We also discuss the detailed numerical results 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↗

arXiv2000

Mean field and Monte Carlo studies of the magnetization-reversal transition in the Ising model

Detailed mean field and Monte Carlo studies of the dynamic magnetization-reversal transition in the Ising model in its ordered phase under a competing external magnetic field of finite duration have been presented here. Approximate analytical treatment of the mean field equations of motion shows the existence of diverging length and time scales across this dynamic transition phase boundary. These are also supported by numerical solutions of the complete mean field equations of motion and the Monte Carlo study of the system evolving under Glauber dynamics in both two and three dimensions. Classical nucleation theory predicts different mechanisms of domain growth in two regimes marked by the strength of the external field, and the nature of the Monte Carlo phase boundary can be comprehended satisfactorily using the theory. The order of the transition changes from a continuous to a discontinuous one as one crosses over from coalescence regime (stronger field) to nucleation regime (weaker field). Finite size scaling theory can be applied in the coalescence regime, where the best fit estimates of the critical exponents are obtained for two and three dimensions.

cond-mat.stat-mech↗

arXiv1998

Dynamic transitions and hysteresis

When an interacting many-body system, such as a magnet, is driven in time by an external perturbation, such as a magnetic field,the system cannot respond instantaneously due to relaxational delay. The response of such a system under a time-dependent field leads to many novel physical phenomena with intriguing physics and important technological applications. For oscillating fields, one obtains hysteresis that would not occur under quasistatic conditions in the presence of thermal fluctuations. Under some extreme conditions of the driving field, one can also obtain a non-zero average value of the variable undergoing such dynamic hysteresis. This non-zero value indicates a breaking of symmetry of the hysteresis loop, around the origin. Such a transition to the spontaneously broken symmetric phase occurs dynamically when the driving frequency of the field increases beyond its threshold value which depends on the field amplitude and the temperature. Similar dynamic transitions also occur for pulsed and stochastically varying fields. We present an overview of the ongoing researches in this not-so-old field of dynamic hysteresis and transitions.

cond-mat.stat-mech↗