arXiv subjects

Tirthankar Banerjee

Publications and source records attributed to Tirthankar Banerjee.

At least 19 recordsLinked to original sources

arXiv2025

Contraction waves in pulsating active liquids: From pacemaker to aster dynamics

We propose a hydrodynamic theory to examine the emergence of contraction waves in dense active liquids composed of pulsating deformable particles. Our theory couples the liquid density with a chemical phase that determines the periodic deformation of the particles. This mechanochemical coupling regulates the interplay between the flow induced by local deformation, and the resistance to pulsation stemming from steric interaction. We show that this interplay leads the emergent contraction waves to spontaneously organize into a packing of pacemakers. We reveal that the dynamics of these pacemakers is governed by a complex feedback between slow and fast topological defects that form asters in velocity flows. In fact, our defect analysis is a versatile platform for investigating the self-organization of waves in a wide range of contractile systems. Our results shed light on the key mechanisms that control the rich phenomenology of pulsating liquids, with relevance for biological systems such as tissues made of confluent pulsating cells.

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arXiv2025

Shape-specific fluctuations of an active colloidal interface

Motivated by a recently synthesizable class of active interfaces formed by linked self--propelled colloids, we investigate the dynamics and fluctuations of a phoretically (chemically) interacting active interface with roto--translational coupling. We enumerate all steady--state shapes of the interface across parameter space and identify a regime where the interface acquires a finite curvature, leading to a characteristic ''C--shaped'' topology, along with persistent self--propulsion. In this phase, the interface height fluctuations obey Family--Vicsek scaling but with novel exponents: a dynamic exponent $z_h \approx 0.5$, a roughness exponent $\alpha_h \approx 0.9$ and a super--ballistic growth exponent $\beta_h \approx 1.7$. In contrast, the orientational fluctuations of the colloidal monomers exhibit a negative roughness exponent, reflecting a surprising smoothness law, where steady--state fluctuations diminish with increasing system size. Together, these findings point towards a unique non--equilibrium universality class associated with self--propelled interfaces of non--standard shape.

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arXiv2024

Hydrodynamics of pulsating active liquids

Inspired by dense contractile tissues, where cells are subject to periodic deformation, we formulate and study a generic hydrodynamic theory of pulsating active liquids. Combining mechanical and phenomenological arguments, we postulate that the mechanochemical feedback between the local phase, which describes how cells deform due to autonomous driving, and the local density can be described in terms of a free energy. We demonstrate that such a feedback is compatible with the coarse-graining of a broad class of microscopic models. Our hydrodynamics captures the three main states emerging in its particle-based counterparts: a globally cycling state, a homogeneous arrested state with constant phase, and a state with propagating radial waves. Remarkably, we show that the competition between these states can be rationalized intuitively in terms of an effective landscape, and argue that waves can be regarded as secondary instabilities. Linear stability analysis of the arrested and cycling states, including the role of fluctuations, leads to predictions for the phase boundaries. Overall, our results demonstrate that our minimal, yet non-trivial model provides a relevant platform to study the rich phenomenology of pulsating liquids.

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arXiv2022

Role of initial conditions in $1D$ diffusive systems: compressibility, hyperuniformity and long-term memory

We analyse the long-lasting effects of initial conditions on fluctuations in one-dimensional diffusive systems. We consider both the fluctuations of current for non-interacting diffusive particles starting from a step-like initial density profile, and the mean-square displacement of tracers in homogeneous systems with single-file diffusion. For these two cases, we show analytically (via the propagator and Macroscopic Fluctuation Theory, respectively) that the long-term memory of initial conditions is mediated by a single static quantity: a generalized compressibility that quantifies the density fluctuations of the initial state. We thereby identify a universality class of hyperuniform initial states whose dynamical variances coincide with the `quenched' cases studied previously; we also describe a continuous family of other classes among which equilibrated (or `annealed') initial conditions are but one family member. We verify our predictions through extensive Monte Carlo simulations.

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arXiv2021

Tracer dynamics in one dimensional gases of active or passive particles

We consider one-dimensional systems comprising either active run-and-tumble particles (RTPs) or passive Brownian random walkers. These particles are either noninteracting or have hardcore exclusions. We study the dynamics of a single tracer particle embedded in such a system - this tracer may be either active or passive, with hardcore exclusion from environmental particles. In an active hardcore environment, both active and passive tracers show long-time subdiffusion: displacements scale as $t^{1/4}$ with a density-dependent prefactor that is independent of tracer type, and differs from the corresponding result for passive-in-passive subdiffusion. In an environment of noninteracting active particles, the passive-in-passive results are recovered at low densities for both active and passive tracers, but transient caging effects slow the tracer motion at higher densities, delaying the onset of any $t^{1/4}$ regime. For an active tracer in a passive environment, we find more complex outcomes, which depend on details of the dynamical discretization scheme. We interpret these results by studying the density distribution of environmental particles around the tracer. In particular, sticking of environment particles to the tracer cause it to move more slowly in noninteracting than in interacting active environments, while the anomalous behaviour of the active-in-passive cases stems from a `snowplough' effect whereby a large pile of diffusive environmental particles accumulates in front of a RTP tracer during a ballistic run.

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arXiv2020

Active gating: rocking diffusion channels

When the contacts of an open system flip between different reservoirs, the resulting nonequilibrium shows increased dynamical activity. We investigate such active gating for one-dimensional symmetric (SEP) and asymmetric (ASEP) exclusion models where the left/right boundary rates for entrance and exit of particles are exchanged at random times. Such rocking makes SEP spatially symmetric and on average there is no boundary driving; yet the entropy production increases in the rocking rate. For ASEP a non-monotone density profile can be obtained with particles clustering at the edges. In the totally asymmetric case, there is a bulk transition to a maximal current phase as the rocking exceeds a finite threshold, depending on the boundary rates. We study the resulting density profiles and current as functions of the rocking rate.

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arXiv2020

Smooth or shock: universality in closed inhomogeneous driven single file motions

We study the nonequilibrum steady states in a unidirectional {or driven} single file motion (DSFM) of a collection of particles with hard-core repulsion in a closed system. For driven propulsion that is {spatially} smoothly varying with a few discontinuities, we show that the steady states are broadly classified into two classes, independent of any system detail: (i) when the steady state current depends explicitly on the {conserved} number density $n$, and (ii) when it is independent of $n$. This manifests itself in the universal topology of the phase diagrams {and fundamental diagrams (i.e., the current versus density curves) } for DSFM, which are determined solely by the interplay between {two control parameters} $n$ and the minimum propulsion speed along the chain. Our theory can be tested in laboratory experiments on driven particles in a closed geometry.

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arXiv2020

Current fluctuations in non-interacting run-and-tumble particles in one-dimension

We present a general framework to study the distribution of the flux through the origin up to time $t$, in a non-interacting one-dimensional system of particles with a step initial condition with a fixed density $ρ$ of particles to the left of the origin. We focus principally on two cases: (i) when the particles undergo diffusive dynamics (passive case) and (ii) run-and-tumble dynamics for each particle (active case). In analogy with disordered systems, we consider the flux distribution both for the annealed and the quenched initial conditions, for the passive and active particles. In the annealed case, we show that, for arbitrary particle dynamics, the flux distribution is a Poissonian with a mean $μ(t)$ that we compute exactly in terms of the Green's function of the single particle dynamics. For the quenched case, we show that, for the run-and-tumble dynamics, the quenched flux distribution takes an anomalous large deviation form at large times $P_{\rm qu}(Q,t) \sim \exp\left[-ρ\, v_0\, γ\, t^2 ψ_{\rm RTP}\left(\frac{Q}{ρv_0\,t} \right) \right]$, where $γ$ is the rate of tumbling and $v_0$ is the ballistic speed between two successive tumblings. In this paper, we compute the rate function $ψ_{\rm RTP}(q)$ and show that it is nontrivial. Our method also gives access to the probability of the rare event that, at time $t$, there is no particle to the right of the origin. For diffusive and run-and-tumble dynamics, we find that this probability decays with time as a stretched exponential, $\sim \exp(-c\, \sqrt{t})$ where the constant $c$ can be computed exactly. We verify our results for these large deviations by using an importance sampling Monte-Carlo method.

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arXiv2019

Active velocity processes with suprathermal stationary distributions and long-time tails

When a particle moves through a spatially-random force field, its momentum may change at a rate which grows with its speed. Suppose moreover that a thermal bath provides friction which gets weaker for large speeds, enabling high-energy localization. The result is a unifying framework for the emergence of heavy tails in the velocity distribution, relevant for understanding the power-law decay in the electron velocity distribution of space plasma or more generally for explaining non-Maxwellian behavior of driven gases. We also find long-time tails in the velocity autocorrelation, indicating persistence at large speeds for a wide range of parameters and implying superdiffusion of the position variable.

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arXiv2019

Rolled up or crumpled: phases of asymmetric tethered membranes

We show that inversion-asymmetric tethered membranes exhibit a new double-spiral phase with long range orientational order not present in symmetric membranes. We calculate the universal algebraic spiral shapes of these membranes in this phase. Asymmetry can trigger the crumpling of these membranes as well. In-vitro experiments on lipid, red blood cell membrane extracts, and on graphene coated on one side, could test these predictions.

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arXiv2019

Statistical mechanics of asymmetric tethered membranes: spiral and crumpled phases

We develop the elastic theory for inversion-asymmetric tethered membranes and use it to identify and study their possible phases. Asymmetry in a tethered membrane causes spontaneous curvature, which in general depends upon the local in-plane dilation of the tethered network. This in turn leads to long-ranged interactions between the local mean and Gaussian curvatures, which is not present in symmetric tethered membranes. This interplay between asymmetry and Gaussian curvature leads to a new {\em double-spiral} phase not found in symmetric tethered membranes. At temperature $T=0$, tethered membranes of arbitrarily large size are always rolled up tightly into a conjoined pair of Archimedes' spirals. At finite $T$ this spiral structure swells up significantly into algebraic spirals characterized by universal exponents which we calculate. These spirals have long range orientational order, and are the asymmetric analogs of statistically flat symmetric tethered membranes. We also find that sufficiently strong asymmetry can trigger a structural instability leading to crumpling of these membranes as well. This provides a new route to crumpling for asymmetric tethered membranes. We calculate the maximum linear extent $L_c$ beyond which the membrane crumples, and calculate the universal dependence of $L_c$ on the membrane parameters. By tuning the asymmetry parameter, $L_c$ can be continuously varied, implying a {\em scale-dependent} crumpling. Our theory can be tested on controlled experiments on lipids with artificial deposits of spectrin filaments, in-vitro experiments on %\sout{artificial deposition of spectrin filaments on} red blood cell membrane extracts, %\sout{after %depletion of adenosine-tri-phosphate molecules} and on graphene coated on one side.

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arXiv2018

Perspectives on scaling and multiscaling in passive scalar turbulence

We revisit the well-known problem of multiscaling in substances passively advected by homogeneous and isotropic turbulent flows or passive scalar turbulence. To that end we propose a two-parameter continuum hydrodynamic model for an advected substance concentration $θ$, parametrised jointly by $y$ and $\overline y$, that characterise the spatial scaling behaviour of the variances of the advecting stochastic velocity and the stochastic additive driving force, respectively. We analyse it within a one-loop dynamic renormalisation group method to calculate the multiscaling exponents of the equal-time structure functions of $θ$. We show how the interplay between the advective velocity and the additive force may lead to simple scaling or multiscaling. In one limit, our results reduce to the well-known results from the Kraichnan model for passive scalar. Our framework of analysis should be of help for analytical approaches for the still intractable problem of fluid turbulence itself.

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arXiv2017

Active processes make mixed lipid membranes either flat or crumpled

Whether live cell membranes show miscibility phase transitions (MPTs), and if so, how they fluctuate near the transitions remain outstanding unresolved issues in physics and biology alike. Motivated by these questions we construct a generic hydrodynamic theory for lipid membranes {that are active, due for instance, to the molecular motors in the surrounding cytoskeleton, or active protein components in the membrane itself}. We use this to uncover a direct correspondence between membrane fluctuations and MPTs. Several testable predictions are made: (i) generic {\em active stiffening} with orientational long range order (flat membrane) or {\em softening} with crumpling of the membrane, controlled by the {\em active tension} and (ii) for mixed lipid membranes, capturing the nature of putative MPTs by measuring the membrane conformation fluctuations. Possibilities of both first and second order MPTs in mixed active membranes are argued for. Near second order MPTs, active stiffening (softening) manifests as a {\em super-stiff (super-soft) membrane}. Our predictions are testable in a variety of {\em in-vitro} systems, e.g., live cytoskeletal extracts deposited on liposomes and lipid membranes containing active proteins embedded in a passive fluid.

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arXiv2017

Symmetries and scaling in generalised coupled conserved Kardar-Parisi-Zhang equations

We study the noisy nonequilibrium dynamics of a conserved density that is driven by a fluctuating surface governed by the conserved Kardar-Parisi-Zhang equation. We uncover the universal scaling properties of the conserved density. We consider two separate minimal models where the surface fluctuations couple (i) with the spatial variation of the conserved density, and (ii) directly with the magnitude of the conserved density. Both these two models conserve the density, but differ from symmetry stand point. We use our result to highlight the dependence of nonequilibrium universality classes on the interplay between symmetries and conservation laws.

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arXiv2017

Active hydrodynamics of synchronization and ordering in moving oscillators

The nature of emergent collective behaviors of moving physical agents interacting with their neighborhood is a long-standing open issue in physical and biological systems alike. This calls for studies on the control of synchronization and the degree of order in a collection of diffusively moving noisy oscillators. We address this by constructing a generic hydrodynamic theory for active phase fluctuations in a collection of large number of nearly phase-coherent moving oscillators in two dimensions. Our theory describes the general situation where phase fluctuations and oscillator mobility mutually affect each other. We show that the interplay between the active effects and the mobility of the oscillators leads to a variety of phenomena, ranging from synchronization with long range, nearly long range and quasi long range orders to instabilities and desynchronization with short range order of the oscillator phases. We highlight the complex dependences of synchronization on the active effects. These should be testable in wide ranging systems, e.g., oscillating chemical reactions in the presence of different reaction inhibitors/facilitators, live oriented cytoskeletal extracts, or vertebrate segmentation clocks.

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arXiv2016

Tethered membranes do not remain flat for strong structural asymmetry

We set up the statistical mechanics for a nearly flat, thermally equilibrated fluid membrane, attached to an elastic network through one of its sides. We predict that the resulting structural (inversion) asymmetry of the membrane, notably due to the elastic network attached to one of its sides, can generate a local spontaneous curvature $C_0$, that may in turn destabilize the otherwise flat membrane. As $C_0$ rises above a threshold at a fixed temperature, a flat tethered membrane in the thermodynamic limit becomes structurally unstable, signaling {\em crumpling} of the flat membrane. In-vitro experiments on red blood cell membranes after depletion of adenosine-tri-phosphate molecules and artificial deposition of spectrin filaments on lipid bilayers may be used to verify our results.

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arXiv2016

Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with particle nonconservation

We study asymmetric exclusion processes (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or {\em defects}. We allow weak particle nonconservation via Langmuir kinetics (LK), that are parameterised by generic unequal attachment and detachment rates. For an extended defect, in the thermodynamic limit the system generically displays inhomogeneous density profiles in the steady state - the faster segment is either in a phase with spatially varying density having no density discontinuity, or a phase with a discontinuous density changes. Nonequilibrium phase transitions between them are controlled by the inhomogeneity and LK. The slower segment displays only macroscopically uniform bulk density profiles in the steady states, reminiscent of the maximal current phase of TASEP but with a bulk density generally different from half. With a point defect, there are low and high density spatially uniform phases as well, in addition to the inhomogeneous density profiles observed for an extended defect. In all the cases, it is argued that the the mean particle density in the steady state is controlled only by the ratio of the LK attachment and detachment rates.

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arXiv2015

Phase transitions and order in two-dimensional generalized nonlinear $σ$-models

We study phase transitions and the nature of order in a class of classical generalized $O(N)$ nonlinear $σ$-models (NLS) constructed by minimally coupling pure NLS with additional degrees of freedom in the form of (i) Ising ferromagnetic spins, (ii) an advective Stokesian velocity and (iii) multiplicative noises. In examples (i) and (ii), and also (iii) with the associated multiplicative noise being not sufficiently long-ranged, we show that the models may display a class of unusual phase transitions between {\em stiff} and {\em soft phases}, where the effective spin stiffness, respectively, diverges and vanishes in the long wavelength limit at two dimensions ($2d$), unlike in pure NLS. In the stiff phase, in the thermodynamic limit the variance of the transverse spin (or, the Goldstone mode) fluctuations are found to scale with the system size $L$ in $2d$ as $\ln\ln L$ with a model-dependent amplitude, that is markedly weaker than the well-known $\ln L$-dependence of the variance of the broken symmetry modes in models that display quasi-long range order in $2d$. Equivalently, for $N=2$ at $2d$ the equal-time spin-spin correlations decay in powers of inverse logarithm of the spatial separation with model-dependent exponents. These transitions are controlled by the model parameters those couple the $O(N)$ spins with the additional variables. In the presence of long-range noises in example (iii), true long-range order may set in $2d$, depending upon the specific details of the underlying dynamics. Our results should be useful in understanding phase transitions in equilibrium and nonequilibrium low-dimensional systems with continuous symmetries in general.

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