arXiv subjects

Rakesh Chatterjee

Publications and source records attributed to Rakesh Chatterjee.

13 recordsLinked to original sources

arXiv2024

Non-equilibrium structure and relaxation in active microemulsions

Microphase separation is common in active biological systems as exemplified by the separation of RNA and DNA-rich phases in the cell nucleus driven by the transcriptional activity of polymerase enzymes acting similarly to amphiphiles in a microemulsion. Here we propose an analytically tractable model of an active microemulsion to investigate how the activity affects its structure and relaxation dynamics. Continuum theory derived from a lattice model exhibits two distinct regimes of the relaxation dynamics and is linked to the broken detailed balance due to intermittent activity of the amphiphiles.

cond-mat.soft↗

arXiv2020

Arrested States in Persistent Active Matter: Gelation without Attraction

We explore phase separation and kinetic arrest in a model active colloidal system consisting of self-propelled, hard-core particles with nonconvex shapes. The passive limit of the model, namely cross-shaped particles on a square lattice, exhibits a first-order transition from a fluid phase to a solid phase with increasing density. Quenches into the two-phase coexistence region exhibit an aging regime. The nonconvex shape of the particles eases jamming in the passive system and leads to strong inhibition of rotations of the active particles. Using numerical simulations and analytical modeling, we quantify the nonequilibrium phase behavior as a function of density and activity. If we view activity as the analog of attraction strength, the phase diagram exhibits strong similarities to that of attractive colloids, exhibiting both aging, glassy states and gel-like arrested states. The two types of dynamically arrested states, glasses and gels, are distinguished by the appearance of density heterogenities in the latter. In the infinitely persistent limit, we show that a coarse-grained model based on the asymmetric exclusion process quantitatively predicts the density profiles of the gel states. The predictions remain qualitatively valid for finite rotation rates. Using these results, we classify the activity-driven phases and identify the boundaries separating them.

cond-mat.soft↗

arXiv2019

Local time of diffusion with stochastic resetting

Diffusion with stochastic resetting has recently emerged as a powerful modeling tool with a myriad of potential applications. Here, we study local time in this model, covering situations of free and biased diffusion with, and without, the presence of an absorbing boundary. Given a Brownian trajectory that evolved for $t$ units of time, the local time is simply defined as the total time the trajectory spent in a small vicinity of its initial position. However, as Brownian trajectories are stochastic --- the local time itself is a random variable which fluctuates round and about its mean value. In the past, the statistics of these fluctuations has been quantified in detail; but not in the presence of resetting which biases the particle to spend more time near its starting point. Here, we extend past results to include the possibility of stochastic resetting with, and without, the presence of an absorbing boundary and/or drift. We obtain exact results for the moments and distribution of the local time and these reveal that its statistics usually admits a simple form in the long-time limit. And yet, while fluctuations in the absence of stochastic resetting are typically non-Gaussian --- resetting gives rise to Gaussian fluctuations. The analytical findings presented herein are in excellent agreement with numerical simulations.

cond-mat.stat-mech↗

arXiv2019

Kinetically constrained model for gravity-driven granular flow and clogging

We add extreme driving to the Kob-Andersen kinetically-constrained lattice-gas model in order to mimic the effect of gravity on dense granular systems. For low particle densities, the current that develops in the system agrees at arbitrary field intensity with a mean field theory. At intermediate densities, spatial correlations give rise to non-monotonic dependence of the current on field intensity. At higher densities, the current ultimately vanishes at a finite, field-dependent jamming density. We supplement the study of this bulk behavior with an investigation of the current through a narrow hole. There, lateral flow decreases the local density in front of the hole. Remarkably, the current through the hole quantitatively agrees with a theoretical prediction based on the bulk current at the measured local density.

cond-mat.soft↗

arXiv2018

Motion of active tracer in a lattice gas with cross-shaped particles

We analyze the dynamics of an active tracer particle embedded in a thermal lattice gas. All particles are subject to exclusion up to third nearest neighbors on the square lattice, which leads to slow dynamics at high densities. For the case with no rotational diffusion of the tracer, we derive an analytical expression for the resulting drift velocity v of the tracer in terms of non-equilibrium density correlations involving the tracer particle and its neighbors, which we verify using numerical simulations. We show that the properties of the passive system alone do not adequately describe even this simple system of a single non-rotating active tracer. For large activity and low density, we develop an approximation for v. For the case where the tracer undergoes rotational diffusion independent of its neighbors, we relate its diffusion coefficient to the thermal diffusion coefficient and v. Finally we study dynamics where the rotation of the tracer is limited by the presence of neighboring particles. We find that the effect of this rotational locking may be quantitatively described in terms of a reduction of the rotation rate.

cond-mat.soft↗

arXiv2018

Identifying long-term precursors of financial market crashes using correlation patterns

The study of the critical dynamics in complex systems is always interesting yet challenging. Here, we choose financial market as an example of a complex system, and do a comparative analyses of two stock markets - the S&P 500 (USA) and Nikkei 225 (JPN). Our analyses are based on the evolution of crosscorrelation structure patterns of short time-epochs for a 32-year period (1985-2016). We identify "market states" as clusters of similar correlation structures, which occur more frequently than by pure chance (randomness). The dynamical transitions between the correlation structures reflect the evolution of the market states. Power mapping method from the random matrix theory is used to suppress the noise on correlation patterns, and an adaptation of the intra-cluster distance method is used to obtain the "optimum" number of market states. We find that the USA is characterized by four market states and JPN by five. We further analyze the co-occurrence of paired market states; the probability of remaining in the same state is much higher than the transition to a different state. The transitions to other states mainly occur among the immediately adjacent states, with a few rare intermittent transitions to the remote states. The state adjacent to the critical state (market crash) may serve as an indicator or a "precursor" for the critical state and this novel method of identifying the long-term precursors may be very helpful for constructing the early warning system in financial markets, as well as in other complex systems.

q-fin.ST↗

arXiv2018

Characterization of catastrophic instabilities: Market crashes as paradigm

Catastrophic events, though rare, do occur and when they occur, they have devastating effects. It is, therefore, of utmost importance to understand the complexity of the underlying dynamics and signatures of catastrophic events, such as market crashes. For deeper understanding, we choose the US and Japanese markets from 1985 onward, and study the evolution of the cross-correlation structures of stock return matrices and their eigenspectra over different short time-intervals or "epochs". A slight non-linear distortion is applied to the correlation matrix computed for any epoch, leading to the emerging spectrum of eigenvalues. The statistical properties of the emerging spectrum display: (i) the shape of the emerging spectrum reflects the market instability, (ii) the smallest eigenvalue may be able to statistically distinguish the nature of a market turbulence or crisis -- internal instability or external shock, and (iii) the time-lagged smallest eigenvalue has a statistically significant correlation with the mean market cross-correlation. The smallest eigenvalue seems to indicate that the financial market has become more turbulent in a similar way as the mean does. Yet we show features of the smallest eigenvalue of the emerging spectrum that distinguish different types of market instabilities related to internal or external causes. Based on the paradigmatic character of financial time series for other complex systems, the capacity of the emerging spectrum to understand the nature of instability may be a new feature, which can be broadly applied.

q-fin.GN↗

arXiv2016

Symmetric exclusion processes on a ring with moving defects

We study symmetric simple exclusion processes (SSEP) on a ring in the presence of uniformly moving multiple defects or disorders - a generalization of the model proposed earlier [Phys. Rev. E 89, 022138 (2014)]. The defects move with uniform velocity and change the particle hopping rates locally. We explore the collective effects of the defects on the spatial structure and transport properties of the system. We also introduce an SSEP with ordered sequential (sitewise) update and elucidate the close connection with our model.

cond-mat.stat-mech↗

arXiv2014

Asymmetric exclusion processes on a closed network with bottlenecks

We study the generic non-equilibrium steady states in asymmetric exclusion processes on a closed network with bottlenecks. To this end we proposes and study closed simple networks with multiply-connected non-identical junctions. Depending upon the parameters that define the network junctions and the particle number density, the models display phase transitions with both static and moving density inhomogeneities. The currents in the models can be tuned by the junction parameters. Our models highlight how extended and point defects may affect the density profiles in a closed directed network. Phenomenological implications of our results are discussed.

cond-mat.stat-mech↗

arXiv2014

Interacting particles in a periodically moving potential: Traveling wave and transport

We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles where the diffusion dynamics is locally modified at a uniformly moving defect site, mimicking the effect of the periodically moving external potential. The model, though simple, exhibits remarkably rich features in particle transport, such as polarity reversal and double peaks in particle current upon variation of defect velocity and particle density. By tuning these variables, the most efficient transport can be achieved in either direction along the ring. These features can be understood in terms of a traveling density wave propagating in the system. Our results could be experimentally tested, e.g., in a system of colloidal particles driven by a moving optical tweezer.

cond-mat.stat-mech↗

arXiv2013

Phase transition and phase coexistence in coupled rings with driven exclusion process

We study one-dimensional exclusion processes in two coupled closed rings consisting of a common diffusive channel and two parallel active (driven) channels. Our model displays bulk-driven phase transition and phase coexistence in the form of a localised domain wall (DW) in one of the active channels in a limit where the diffusive and driven dynamics compete. By controlling a splitting parameter which tunes the in-coming currents into the active channels, the system can be brought to a delocalisation transition, when delocalised DWs are formed in both the active channels. We characterise the DW fluctuations numerically.

cond-mat.stat-mech↗

arXiv2011

Comments on "Critical Study on the Absorbing Phase Transition in a Four-State Predator-Prey Model in One Dimension"

In a recent article [arXiv:1108.5127] Park has shown that the four-state predator-prey model studied earlier in [J. Stat. Mech, L05001 (2011)] belongs to Directed Percolation (DP) universality class. It was claimed that predator density is not a reasonable order parameter, as there are many absorbing states; a suitably chosen order parameter shows DP critical behavior. In this article, we argue that the configuration that does not have any predator is the only dynamically accessible absorbing configuration, and the predator density too settles to DP critical exponents after a long transient.

cond-mat.stat-mech↗

arXiv2011

Absorbing Phase Transition in a Four State Predator Prey Model in One Dimension

The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator, or occupied by a single prey, or by both. Along with the pairwise death of predators and growth of preys, we introduce an interaction where the predators can eat one of the neighboring prey and reproduce a new predator there instantly. The model shows a non-equilibrium phase transition into a unusual absorbing state where predators are absent and the lattice is fully occupied by preys. The critical exponents of the system are found to be different from that of the Directed Percolation universality class and they are robust against addition of explicit diffusion.

cond-mat.stat-mech↗