arXiv subjects

Parna Roy

Publications and source records attributed to Parna Roy.

11 recordsLinked to original sources

arXiv2025

Stationary densities and delocalized domain walls in asymmetric exclusion processes competing for finite pools of resources

We explore the stationary densities and domain walls in the steady states of a pair of asymmetric exclusion processes (TASEP) antiparallelly coupled to two particle reservoirs without any spatial extent by using the model in Haldar et al., Phys. Rev. E {\bf 111}, 014154 (2025). We show that the model admits a pair of {\em delocalized} domain walls, which exist for some choices of the model parameters that define the effective entry and exit rates into the TASEP lanes. Surprisingly, in the parameter space spanned by these model parameters, the region corresponding to delocalized domain walls covers an {\em extended} region, in contrast to the delocalized domain walls that appear only along a line in the relevant parameter space of the other known variants of TASEP. This implies large fluctuations in the TASEP particle numbers even in the thermodynamic limit that can be found over a range of the control parameters. The corresponding phase diagrams in the plane of the control parameters have different topology from those for an open TASEP or other models with multiple TASEPs connected to two reservoirs.

cond-mat.stat-mech↗

arXiv2024

Availability versus carrying capacity: Phases of asymmetric exclusion processes competing for finite pools of resources

We address how the interplay between the finite availability and carrying capacity of particles at different parts of a spatially extended system can control the steady state currents and density profiles in the one-dimensional current-carrying lanes connecting the different parts of the system. To study this, we set up a minimal model consisting of two particle reservoirs of the same finite carrying capacity connected by two equally sized anti-parallel asymmetric exclusion processes (TASEP). We focus on the steady-state currents and particle density profiles in the two TASEP lanes. The ensuing phases and the phase diagrams, which can be remarkably complex, are parametrized by the model parameters defining particle exchange between the TASEP lanes and the reservoirs and the filling fraction of the particles that determine the total resources available. These parameters may be tuned to make the densities of the two TASEP lanes globally uniform or piece-wise continuous in the form of a combination of a single localized domain wall and a spatially constant density or a pair of delocalized domain walls. Our model reveals that the two reservoirs can be preferentially populated or depopulated in the steady states.

cond-mat.stat-mech↗

arXiv2024

Distributed fixed resources exchanging particles: Phases of an asymmetric exclusion process connected to two reservoirs

We propose and study a conceptual one-dimensional model to explore how the combined interplay between fixed resources and particle exchanges between different parts of an extended system can affect the stationary densities in a current carrying channel connecting different parts of the system. To this end, we consider a model composed of a totally asymmetric simple exclusion process (TASEP) connecting two particle reservoirs without any internal dynamics but which can directly exchange particles between each other, ensuring nonvanishing currents in the steady states. The total particle number in the system that defines the "resources" available, although is kept constant by the model dynamics, can take any value independent of the model parameters that define the dynamics of the model. We show how the resulting phase diagrams of the model are controlled by the parameters, which define the various dynamical update rules together with the total available resources. These control parameters can be tuned to make the density on the TASEP lane globally uniform or piecewise continuous with localized domain walls, and can also control populations of the two reservoirs. In general, the phase diagrams are quite different from a TASEP with open boundaries. In the limit of large amount of resources, the phase diagrams in the plane of the control parameters become topologically identical to that for an open TASEP together with delocalization of domain walls.

cond-mat.stat-mech↗

arXiv2023

Availability, storage capacity, and diffusion: Stationary states of an asymmetric exclusion process connected to two reservoirs

We explore how the interplay of finite availability, carrying capacity of particles at different parts of a spatially extended system and particle diffusion between them control the steady state currents and density profiles in a one-dimensional current-carrying channel connecting the different parts of the system. To study this, we construct a minimal model consisting of two particle reservoirs of finite carrying capacities connected by a totally asymmetric simple exclusion process (TASEP). In addition to particle transport via TASEP between the reservoirs, the latter can also directly exchange particles, modeling particle diffusion between them that can maintain a steady current in the system. We investigate the steady state density profiles and the associated particle currents in the TASEP lane. The resulting phases and the phase diagrams are quite different from an open TASEP, and are characterised by the model parameters defining particle exchanges between the TASEP and the reservoirs, direct particle exchanges between the reservoirs, and the filling fraction of the particles that determines the total resources available. These parameters can be tuned to make the density on the TASEP lane globally uniform or piecewise continuous, and can make the two reservoirs preferentially populated or depopulated.

cond-mat.stat-mech↗

arXiv2020

Asymmetric exclusion processes with fixed resources: Reservoir crowding and steady states

We study the nonequilibrium steady states of an asymmetric exclusion process (TASEP) coupled to a reservoir of unlimited capacity. We elucidate how the steady states are controlled by the interplay between the reservoir population that dynamically controls both the entry and exit rates of the TASEP, and the total particle number in the system. The TASEP can be in the low density, high density, maximal current and shock phases. We show that such a TASEP is different from an open TASEP for all values of available resources: here, the TASEP can support only localised domain walls for any (finite) amount of resources as opposed to delocalised domain walls in open TASEPs. Furthermore, in the limit of infinite resources, the TASEP can be found in its high density phase only for any finite values of the control parameters, in contrast to an open TASEP.

cond-mat.stat-mech↗

arXiv2019

Pinned or moving: states of a single shock in a ring

Totally asymmetric exclusion processes (TASEP) with open boundaries are known to exhibit moving shocks or delocalised domain walls (DDW) for sufficiently small equal injection and extraction rates. In contrast TASEPs in an inhomogeneous ring have been shown to display pinned shocks or localised domain walls (LDW) under similar conditions [see, e.g., H. Hinsch and E. Frey, {\em Phys. Rev. Lett.} {\bf 97}, 095701 (2006)]. By studying periodic exclusion processes composed of a driven (TASEP) and a diffusive segments, we uncover smooth transitions between LDW and DDW; the latter mimics DDWs in an open TASEP, controlled essentially by the fluctuations in the diffusive segment. Mean-field theory together with Monte Carlo simulations are employed to characterize the emerging nonequilibrium steady states. Our studies provide an explicit route to control the degree of shock fluctuations in periodic systems, and should be relevant in cell biological transport where the availability of molecular motors is the rate limiting constraint.

cond-mat.stat-mech↗

arXiv2017

Interplay of interfacial noise and curvature driven dynamics in two dimensions

We explore the effect of interplay of interfacial noise and curvature driven dynamics in a binary spin system. An appropriate model is the generalised two dimensional voter model proposed earlier (J. Phys. A: Math. Gen. {\bf 26}, 2317 (1993)), where the flipping probability of a spin depends on the state of its neighbours and is given in terms of two parameters $x$ and $y$. $x = 0.5, y =1$ corresponds to the conventional voter model which is purely interfacial noise driven while $x = 1 $ and $y = 1$ corresponds to the Ising model, where coarsening is fully curvature driven. The coarsening phenomena for $0.5< x < 1$ keeping $y=1$ is studied in detail. The dynamical behaviour of the relevant quantities show characteristic differences from both $x=0.5$ and $1$. The most remarkable result is the existence of two time scales for $x\ge x_c$ where $x_c \approx 0.7$. On the other hand, we have studied the exit probability which shows Ising like behaviour with an universal exponent for any value of $x > 0.5$; the effect of $x$ appears in altering the value of the parameter occurring in the scaling function only.

cond-mat.stat-mech↗

arXiv2016

Continuous utility factor in segregation models

We consider the constrained Schelling model of social segregation in which the utility factor of agents strictly increases and non-local jumps of the agents are allowed. In the present study, the utility factor u is defined in a way such that it can take continuous values and depends on the tolerance threshold as well as the fraction of unlike neighbours. Two models are proposed: in model A the jump probability is determined by the sign of u only which makes it equivalent to the discrete model. In model B the actual values of u are considered. Model A and model B are shown to differ drastically as far as segregation behaviour and phase transitions are concerned. In model A, although segregation can be achieved, the cluster sizes are rather small. Also, a frozen state is obtained in which steady states comprise of many unsatisfied agents. In model B, segregated states with much larger cluster sizes are obtained. The correlation function is calculated to show quantitatively that larger clusters occur in model B. Moreover for model B, no frozen states exist even for very low dilution and small tolerance parameter. This is in contrast to the unconstrained discrete model considered earlier where agents can move even when utility remains same. In addition, we also consider a few other dynamical aspects which have not been studied in segregation models earlier.

physics.soc-ph↗

arXiv2015

Exit Probability in Generalised Kinetic Ising Model

In this paper we study generalised Ising Glauber models with inflow of informa- tion in one dimension and derive expressions for the exit probability using well established analytical methods. The analytical expressions agree very well with the results obtained from numerical simulation only when the interaction is restricted to the nearest neighbor. But as the range of interaction is increased the analytical results deviate from simulation results systematically. The reasons for the deviation as well as some related open questions are discussed.

cond-mat.stat-mech↗

arXiv2014

Universal features of exit probability in opinion dynamics models with domain size dependent dynamics

We study the exit probability for several binary opinion dynamics models in one dimension in which the opinion state (represented by $\pm 1$) of an agent is determined by dynamical rules dependent on the size of its neighbouring domains. In all these models, we find the exit probability behaves like a step function in the thermodynamic limit. In a finite system of size $L$, the exit probability $E(x)$ as a function of the initial fraction $x$ of one type of opinion is given by $E(x) = f[(x-x_c)L^{1/ν}]$ with a universal value of $ν= 2.5 \pm 0.03$. The form of the scaling function is also universal: $f(y) = [\tanh(λy +c) +1]/2$, where $λ$ is found to be dependent on the particular dynamics. The variation of $λ$ against the parameters of the models is studied. $c$ is non-zero only when the dynamical rule distinguishes between $\pm 1$ states; comparison with theoretical estimates in this case shows very good agreement.

cond-mat.stat-mech↗

arXiv2014

Exit probability in inflow dynamics: nonuniversality induced by range, asymmetry and fluctuation

Probing deeper into the existing issues regarding the exit probability (EP) in one dimensional dynamical models, we consider several models where the states are represented by Ising spins and the information flows inwards. At zero temperature, these systems evolve to either of two absorbing states. The exit probability $E(x)$, which is the probability that the system ends up with all spins up starting with $x$ fraction of up spins is found to have the general form $E(x) = x^α/\left[x^α+ (1-x)^α\right]$. The exit probability exponent $α$ strongly depends on $r$, the range of interaction, the symmetry of the model and the induced fluctuation. Even in a nearest neighbour model, nonlinear form of EP can be obtained by controlling the fluctuations and for the same range, different models give different results for $α$. Non-universal behaviour of the exit probability is thus clearly established and the results are compared to existing studies in models with outflow dynamics to distinguish the two dynamical scenarios.

cond-mat.stat-mech↗