arXiv subjects

Abhik Basu

Publications and source records attributed to Abhik Basu.

At least 73 records · Page 4Linked to original sources

arXiv2015

Phase coexistences and particle non-conservation in a closed asymmetric exclusion process with inhomogeneities

We construct a one-dimensional totally asymmetric simple exclusion process (TASEP) on a ring with two segments having unequal hopping rates, coupled to particle non-conserving Langmuir kinetics (LK) characterized by equal attachment and detachment rates. In the steady state, in the limit of competing LK and TASEP, the model is always found in states of phase coexistence. We uncover a nonequilibrium phase transition between a three-phase and a two-phase coexistence in the faster segment, controlled by the underlying inhomogeneity configurations and LK. The model is always found to be half-filled on average in the steady state, regardless of the hopping rates and the attachment/detachment rate.

cond-mat.stat-mech↗

arXiv2015

Generic nonequilibrium steady states in an exclusion process on an inhomogeneous ring

We consider a one-dimensional totally asymmetric exclusion process on a ring with extended inhomogeneities, consisting of several segments with different hopping rates. Depending upon the underlying inhomogeneity configurations and for moderate densities, our model displays both localised (LDW) and delocalised (DDW) domain walls and delocalisation transitions of LDWs in the steady states. Our results allow us to construct the possible steady state density profiles for an arbitrary number of segments with unequal hopping rates. We explore the scaling properties of the fluctuations of LDWs and DDWs.

cond-mat.stat-mech↗

arXiv2014

Thermal fluctuations and stiffening of heterogeneous fluid membranes

We study the effects of thermal fluctuations on symmetric tensionless heterogeneous (two-component) fluid membranes in a simple minimal model. Close to the critical point $T_c$ of the associated miscibility phase transition of the composition and for sufficiently strong curvature-composition interactions, mediated through a composition-dependent bending modulus, thermal fluctuations lead to enhancement of the effective bending modulus. Thus, the membrane conformation fluctuations will be {\em suppressed} near $T_c$, in comparison with a pure fluid membrane, for which thermal fluctuations are known to reduce the effective bending modulus at all non-zero temperatures.

cond-mat.stat-mech↗

arXiv2014

Active to absorbing state phase transition in the presence of a fluctuating environment: Feedback and universality

We construct and analyse a simple {\em reduced} model to study the effects of the interplay between a density undergoing an active-to-absorbing state phase transition (AAPT) and a fluctuating environment in the form of a broken symmetry mode coupled to the density field in any arbitrary dimension. We show, by using perturbative renormalisation group calculations, that {\em both} the effects of the environment on the density and the latter's feedback on the environment influence the ensuing universal scaling behaviour of the AAPT at its extinction transition. Phenomenological implications of our results in the context of more realistic natural examples are discussed.

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

Nonequilibrium steady states in asymmetric exclusion processes on a ring with bottlenecks

Generic inhomogeneous steady states in an asymmetric exclusion process on a ring with a pair of point bottlenecks are studied. We show that, due to an underlying universal feature, measurements of coarse-grained steady-state densities in this model resolve the bottleneck structures only partially. Unexpectedly, it displays localization-delocalization transitions and confinement of delocalized domain walls, controlled by the interplay between particle number conservation and bottleneck competition for moderate particle densities.

cond-mat.stat-mech↗

arXiv2014

Acoustic horizons in nuclear fluids

We consider a hydrodynamic description of the spherically symmetric outward flow of nuclear matter, accommodating dispersion in it as a very weak effect. About the resulting stationary conditions in the flow, we apply an Eulerian scheme to derive a fully nonlinear equation of a time-dependent radial perturbation. In its linearized limit, with no dispersion, this equation implies the static acoustic horizon of an analogue gravity model. We, however, show that time-dependent nonlinear effects destabilize the static horizon. We also model the perturbation as a high-frequency travelling wave, and perform a {\it WKB} analysis, in which the effect of weak dispersion is studied iteratively. We show that even arbitrarily small values of dispersion make the horizon fully opaque to any acoustic disturbance propagating against the bulk flow, with the amplitude and the energy flux of the radial perturbation undergoing a discontinuity at the horizon, and decaying exponentially just outside it.

nucl-th↗

arXiv2013

Phases and fluctuations in a model for asymmetric inhomogeneous fluid membranes

We propose and analyze a model for phase transitions in an inhomogeneous fluid membrane, that couples local composition with curvature nonlinearly. For asymmetric membranes, our model shows generic non-Ising behavior and the ensuing phase diagram displays either a first- or a second-order phase transition through a critical point (CP) or a tricritical point (TP), depending upon the bending modulus. It predicts generic nontrivial enhancement in fluctuations of asymmetric membranes that scales with system size in a power law fashion at the CP and TP in two dimensions, not observed in symmetric membranes. It also yields two-dimensional Ising universality class for symmetric membranes, in agreement with experimental results.

cond-mat.soft↗

arXiv2013

Generic instabilities in a fluid membrane coupled to a thin layer of ordered active polar fluid

We develop an effective two-dimensional coarse-grained description for the coupled system of a planar fluid membrane anchored to a thin layer of polar ordered active fluid below. The macroscopic orientation of the active fluid layer is assumed to be perpendicular to the attached membrane. We demonstrate that {\em activity} or nonequilibrium drive of the active fluid makes such a system generically linearly unstable for either signature of a model parameter $Δμ$ that characterises the strength of activity. Depending upon boundary conditions and within a range of the model parameters, underdamped propagating waves may be present in our model. We discuss the phenomenological significance of our results.

cond-mat.soft↗

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↗

arXiv2013

Phase transitions and continuously variable scaling in a chiral quenched disordered model

We elucidate the effects of chiral quenched disorder on the scaling properties of pure systems by considering a reduced model that is a variant of the quenched disordered cubic anisotropic O(N) model near its second order phase transition. A generic short-ranged Gaussian disorder distribution is considered. For distributions not invariant under spatial inversion ({hence chiral}), the scaling exponents are found to depend continuously on a model parameter that describes the extent of inversion symmetry breaking. Experimental and phenomenological implications of our results are discussed.

cond-mat.stat-mech↗

arXiv2012

Instabilities and diffusion in a hydrodynamic model of a fluid membrane coupled to a thin active fluid layer

We construct a coarse-grained effective two-dimensional (2d) hydrodynamic theory as a theoretical model for a coupled system of a fluid membrane and a thin layer of a polar active fluid in its ordered state that is anchored to the membrane. We show that such a system is prone to generic instabilities through the interplay of nonequilibrium drive, polar order and membrane fluctuation. We use our model equations to calculate diffusion coefficients of an inclusion in the membrane and show that their values depend strongly on the system size, in contrast to their equilibrium values. Our work extends the work of S. Sankararaman and S. Ramaswamy [Phys. Rev. Lett., 102, 118107 (2009)] to a coupled system of a fluid membrane and an ordered active fluid layer. Our model is broadly inspired by and should be useful as a starting point for theoretical descriptions of the coupled dynamics of a cell membrane and a cortical actin layer anchored to it.

cond-mat.soft↗

arXiv2012

Active-to-absorbing state phase transition in the presence of fluctuating environments: Weak and strong dynamic scaling

We investigate the scaling properties of phase transitions between survival and extinction (active-to-absorbing state phase transition, AAPT) in a model, that by itself belongs to the directed percolation (DP) universality class, interacting with a spatio-temporally fluctuating environment having its own non-trivial dynamics. We model the environment by (i) a randomly stirred fluid, governed by the Navier-Stokes (NS) equation, and (ii) a fluctuating surface, described either by the Kardar-Parisi-Zhang (KPZ) or the Edward-Wilkinson (EW) equations. We show, by using a one-loop perturbative field theoretic set up, that depending upon the spatial scaling of the variance of the external forces that drive the environment (i.e., the NS, KPZ or EW equations), the system may show {\em weak} or {\em strong dynamic scaling} at the critical point of active to absorbing state phase transitions. In the former case AAPT displays scaling belonging to the DP universality class, whereas in the latter case the universal behavior is different.

cond-mat.stat-mech↗

arXiv2012

Continuous Universality in non-equilibrium relaxational dynamics of O(2) symmetric systems

We elucidate a non-conserved relaxational nonequilibrium dynamics of a O(2) symmetric model. We drive the system out of equilibrium by introducing a non-zero noise cross-correlation of amplitude $D_\times$ in a stochastic Langevin description of the system, while maintaining the O(2) symmetry of the order parameter space. By performing dynamic renormalization group calculations in a field-theoretic set up, we analyze the ensuing nonequilibrium steady states and evaluate the scaling exponents near the critical point, which now depend explicitly on $D_\times$. Since the latter remains unrenormalized, we obtain universality classes varying continuously with $D_\times$. More interestingly, by changing $D_\times$ continuously from zero, we can make our system move away from its equilibrium behavior (i.e., when $D_\times=0$) continuously and incrementally.

cond-mat.stat-mech↗

arXiv2011

Fluctuating hydrodynamics and turbulence in a rotating fluid: Universal properties

We analyze the statistical properties of three-dimensional ($3d$) turbulence in a rotating fluid. To this end we introduce a generating functional to study the statistical properties of the velocity field $\bf v$. We obtain the master equation from the Navier-Stokes equation in a rotating frame and thence a set of exact hierarchical equations for the velocity structure functions for arbitrary angular velocity $\mathbf Ω$. In particular we obtain the {\em differential forms} for the analogs of the well-known von Karman-Howarth relation for $3d$ fluid turbulence. We examine their behavior in the limit of large rotation. Our results clearly suggest dissimilar statistical behavior and scaling along directions parallel and perpendicular to $\mathbf Ω$. The hierarchical relations yield strong evidence that the nature of the flows for large rotation is not identical to pure two-dimensional flows. To complement these results, by using an effective model in the small-$Ω$ limit, within a one-loop approximation, we show that the equal-time correlation of the velocity components parallel to $\mathbf Ω$ displays Kolmogorov scaling $q^{-5/3}$, where as for all other components, the equal-time correlators scale as $q^{-3}$ in the inertial range where $\bf q$ is a wavevector in $3d$. Our results are generally testable in experiments and/or direct numerical simulations of the Navier-Stokes equation in a rotating frame.

cond-mat.stat-mech↗

arXiv2011

Universality of scaling and multiscaling in turbulent symmetric binary fluids

We elucidate the universal scaling and multiscaling properties of the nonequilibrium steady states (NESS) in a driven symmetric binary fluid (SBF) mixture in its homogeneous miscible phase in three dimensions (3d). We show, for the first time, via Direct Numerical Simulations (DNS) that structure functions of the velocity and the concentration gradient exhibit multiscaling in 3d and extended self-similarity (ESS). We also find that, in contrast to the well-known passive scalar turbulence problem, structure functions of the concentration show simple scaling. We propose a new shell model for SBF turbulence which preserve all the invariances in the ideal limit of the SBF equations and which reduces to a well-known shell model for fluid turbulence in the zero concentration field limit. We show that the shell model has the same scaling properties as the 3d SBF equations. Our combined results from our DNS of the SBF equations and shell-model studies consistently bring out the multiscaling of the velocity and concentration gradient fields and simple scaling of the concentration field.

nlin.CD↗

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↗