arXiv subjects

Atri Goswami

Publications and source records attributed to Atri Goswami.

3 recordsLinked to original sources

arXiv2024

Defect versus defect: stationary states of single file marching in periodic landscapes with road blocks

Totally asymmetric simple exclusion process (TASEP) sets the paradigm for one-dimensional driven single file motion. We study a periodic TASEP with two ``road blocks'' or defects of different kinds, one point and another extended, across which particle flows are inhibited. We show how the interplay between particle number conservation and competition between the defects lead to inhomogeneous steady states with localised domain walls (LDW). The LDW locations jump discontinuously, indicating a discontinuous transition between these LDW states, as the system passes from being controlled by one defect to the other. When the defects are ``competing'', instead of an LDW a pair of delocalised domain walls appear, none of which can penetrate the extended defect. A minimum current principle can be used to identify the dominant defect that controls the domain wall formations. Our results should be important in diverse systems, ranging from protein synthesis by ribosomes in biological cells to urban traffic networks.

cond-mat.stat-mech↗

arXiv2023

Nonequilibrium steady states in coupled asymmetric and symmetric exclusion processes

We propose and study a one-dimensional (1D) model consisting of two lanes with open boundaries. One of the lanes executes diffusive and the other lane driven unidirectional or asymmetric exclusion dynamics, which are mutually coupled through particle exchanges in the bulk. We elucidate the generic nonuniform steady states in this model. We show that in a parameter regime, where hopping along the TASEP lane, diffusion along the SEP lane and the exchange of particles between the TASEP and SEP lanes compete, the SEP diffusivity $D$ appears as a tuning parameter for both the SEP and TASEP densities for a given exchange rate in the nonequilibrium steady states of this model. Indeed, $D$ can be tuned to achieve phase coexistence in the asymmetric exclusion dynamics together with spatially smoothly varying density in the diffusive dynamics in the steady state. We obtain phase diagrams of the model by using mean field theories, and corroborate and complement the results by stochastic Monte Carlo simulations. This model reduces to an isolated open totally asymmetric exclusion process (TASEP) and an open TASEP with bulk particle nonconserving Langmuir kinetics (LK), respectively, in the limits of vanishing and diverging particle diffusivity in the lane executing diffusive dynamics. Thus this model works as an overarching general model, connecting both pure TASEPs and TASEPs with LK in different asymptotic limits. We further define phases in the SEP and obtain phase diagrams, and show their correspondence with the TASEP phases. In addition to its significance as a 1D driven, diffusive model, this model also serves as a simple reduced model for cell biological transport by molecular motors undergoing diffusive and directed motion inside eukaryotic cells.

cond-mat.stat-mech↗

arXiv2022

Steady states and phase transitions in heterogeneous asymmetric exclusion processes

We study the nonequilibrium steady states in totally asymmetric exclusion processes (TASEP) with open boundary conditions having spatially inhomogeneous hopping rates. Considering smoothly varying hopping rates, we show that the steady states are in general classified by the steady state currents in direct analogy with open TASEPs having uniform hopping rates. We calculate the steady state bulk density profiles, which are now spatially nonuniform. We also obtain the phase diagrams in the plane of the control parameters, which though have phase boundaries that are in general curved lines, have the same topology as their counterparts for conventional open TASEPs, independent of the form of the hopping rate functions. This reveals a type of universality, not encountered in critical phenomena. Surprisingly and in contrast to the phase transitions in an open TASEP with uniform hopping, our studies on the phase transitions in the model reveal that all the three transitions are {\em first order} in nature. { We also demonstrate that this model admits delocalised domain walls (DDWs) on the phase boundaries demarcating the generalised low and high density phases in this model. However, in contrast to the DDWs observed in an open TASEP with uniform hopping, the envelopes of the DDWs in the present model are generally curved lines.}

cond-mat.stat-mech↗