arXiv subjects

Shradha Mishra

Publications and source records attributed to Shradha Mishra.

At least 73 records · Page 4Linked to original sources

arXiv2019

Binary phase separation in a collection of self-propelled particle with variable speed

We study the collective behavior of binary mixture of self-propelled particles. Particles moves along their heading direction with {\it variable speed} and interact through short range alignment interaction. A variable speed parameter $γ>0$ is introduced such that for $γ=0.0$ model reduces to {\it constant speed} Vicsek's model. We mix the particles with two different $γ$'s and study the steady state behavior of the mixture for different choice of $γ$'s and noise strength. One of the $γ$ is kept fixed to $1.0$ and another one is varied from small $0.0$ to larger values $8.0$. Properties of system is characterise by two types of order parameters (i) orientation order parameter, which is a measure of ordering in the system and (ii) density order parameter, which measures the phase separation is the system. For all set of $γ$'s, system shows a transition from disorder-to-ordered state on the variation of noise strength. The nature of transition and critical noise is independent of value of $γ$, which is also supported from coarse-grained hydrodynamic study. On the variation of system parameters, ($γ$'s, $η$), we find four distinct phases, (i) ordered phase separated, (ii) ordered mixed, (iii) disordered mixed and (iv) disordered phase segragated. Our study shade light on different phases of mixture of different types of active particles.

cond-mat.soft↗

arXiv2018

Polar flock in the presence of random quenched rotators

We study a collection of polar self-propelled particles (SPPs) on a two-dimensional substrate in the presence of random quenched rotators. These rotators act like obstacles which rotate the orientation of the SPPs by an angle determined by their intrinsic orientations. In the zero self-propulsion limit, our model reduces to the equilibrium $XY$ model with quenched disorder, while for the clean system, it is similar to the Vicsek model for polar flock. We note that a small amount of the quenched rotators destroys the long-range order usually noted in the clean SPPs. The system shows a quasi-long range order state upto some moderate density of the rotators. On further increment in the density of rotators, the system shows a continuous transition from the quasi-long-range order to disorder state at some critical density of rotators. Our linearized hydrodynamic calculation predicts anisotropic higher order fluctuation in two-point structure factors for density and velocity fields of the SPPs. We argue that nonlinear terms probably suppress this fluctuation such that no long-range order but only a quasi-long-range order prevails in the system.

cond-mat.stat-mech↗

arXiv2018

Phase separation in binary mixtures of active and passive particles

We study binary mixtures of small active and big passive athermal particles interacting via soft repulsive forces on a frictional substrate. Athermal self propelled particles are known to phase separate into a dense aggregate and a dilute gas-like phase at fairly low packing fractions. Known as {\emph {motility induced phase separation}}, this phenomenon governs the behaviour of binary mixtures for small to intermediate size ratios of the particle species. An effective attraction between passive particles, due to the surrounding active medium, leads to true phase separation for large size ratios and volume fractions of active particles. The effective interaction between active and passive particles can be attractive or repulsive at short range depending on the size ratio and volume fractions of the particles. This affects the clustering of passive particles. We find three distinct phases based on the spatial distribution of passive particles. The cluster size distribution of passive particles decays exponentially in the {\emph{homogeneous phase}}. It decays as a power law with an exponential cutoff in the {\emph{clustered phase}} and tends to a power law as the system approaches the transition to the {\emph{phase separated state}}. We present a phase diagram in the plane defined by the size ratio and volume fraction of passive particles.

cond-mat.soft↗

arXiv2018

Collection of polar self-propelled particles with a modified alignment interaction

We study the disorder-to-order transition in a collection of polar self-propelled particles interacting through a distance dependent alignment interaction. Strength of the interaction, $a^{d}$ ($0 0$, the system shows a transition from a disordered to an ordered state as a function of noise strength. We calculate the critical noise strength, $η_c(a)$ for different $a$ and compare it with the mean-field result. Nature of the disorder-to-order transition continuously changes from discontinuous to continuous with decreasing $a$. We numerically estimate tri-critical point $a_{TCP}$ at which the nature of transition changes from discontinuous to continuous. The density phase separation is large for ${\it a}$ close to unity, and it decays with decreasing $a$. We also write the coarse-grained hydrodynamic equations of motion for general ${\it a}$, and find that the homogeneous ordered state is unstable to small perturbation as ${\it a}$ approaches to $1$. The instability in the homogeneous ordered state is consistent with the large density phase separation for ${\it a}$ close to unity.

cond-mat.stat-mech↗

arXiv2018

Ordering dynamics of self-propelled particles in an inhomogeneous medium

Ordering dynamics of self-propelled particles in an inhomogeneous medium in two-dimensions is studied. We write coarse-grained hydrodynamic equations of motion for coarse-grained density and velocity fields in the presence of an external random disorder field, which is quenched in time. The strength of inhomogeneity is tuned from zero disorder (clean system) to large disorder. In the clean system, the velocity field grows algebraically as $L_{\rm V} \sim t^{0.5}$. The density field does not show clean power-law growth; however, it follows $L_{\rm ρ} \sim t^{0.8}$ approximately. In the inhomogeneous system, we find a disorder dependent growth. For both the density and the velocity, growth slow down with increasing strength of disorder. The velocity shows a disorder dependent power-law growth $L_{\rm V}(t,Δ) \sim t^{1/\bar z_{\rm V}(Δ)}$ for intermediate times. At late times, there is a crossover to logarithmic growth $L_{\rm V}(t,Δ) \sim (\ln t)^{1/φ}$, where $φ$ is a disorder independent exponent. Two-point correlation functions for the velocity shows dynamical scaling, but the density does not.

cond-mat.stat-mech↗

arXiv2017

Order-disorder transition in active nematic: A lattice model study

We introduce a lattice model for active nematic composed of self-propelled apolar particles,study its different ordering states in the density-temperature parameter space, and compare with the corresponding equilibrium model. The active particles interact with their neighbours within the framework of the Lebwohl-Lasher model, and move anisotropically along their orientation to an unoccupied nearest neighbour lattice site. An interplay of the activity, thermal fluctuations and density gives rise distinct states in the system. For a fixed temperature, the active nematic shows a disordered isotropic state, a locally ordered inhomogeneous mixed state, and bistability between the inhomogeneous mixed and a homogeneous globally ordered state in different density regime. In the low temperature regime, the isotropic to the inhomogeneous mixed state transition occurs with a jump in the order parameter at a density less than the corresponding equilibrium disorder-order transition density. Our analytical calculations justify the shift in the transition density and the jump in the order parameter. We construct the phase diagram of the active nematic in the density-temperature plane.

cond-mat.soft↗

arXiv2017

Flocking in one dimension: effect of update rules

In this study the effect of parallel and random-sequential updates on the dynamical properties of flocks in one dimension is considered. It is found that the frequency of directional switching is increased for random-sequential updates as compared to a parallel update. The nature of disorder to order transition is also affected by the difference of updating mechanism: discontinuous for parallel and continuous for random-sequential updates.

cond-mat.stat-mech↗

arXiv2017

Boundary induced convection in a collection of polar self-propelled particles

We study a collection of polar self-propelled particles confined to a long two-dimensional channel. We write the coupled hydrodynamic equations of motion for density and polarisation order parameter. At two confined boundaries, density is fixed to the mean and orientation is anti-parallel with fixed magnitude of polarisation. Such boundary conditions make our system similar to a sheared suspension of self-propelled particles, which has many practical applications. Antiparallel alignment at the two confined boundaries and alignment inside the channel create rolls of orientation along the long axis of the channel. For zero self-propulsion speed, density and orientation fields are decoupled and density remains homogeneous inside the channel. For finite self-propelled speed, density inhomogeneities develop and these rolls move along the long axis of the channel. Density inhomogeneity increases sharply with increasing the self propulsion speed and then reaches a maximum and again decreases for very large speeds. Formation of rolls is very similar to the classic problem of Rayleigh-Benard convection in fluid dynamics.

physics.flu-dyn↗

arXiv2016

Density phase separation and order-disorder transition in a collection of polar self-propelled particles

We study the order-disorder transition in a collection of polar self-propelled particles, interacting through a distance dependent short range alignment interaction. A distance dependent interaction parameter $a_0$ is introduced such that on decreasing $a_0$ interaction decay faster with distance $d$ and for $a_0=1.0$ model reduces to Vicsek's type. For all $a_0>0.0$, system shows a transition from disorder to long ranged ordered state. We find another phase transition from phase separated to nonphase separated state with decreasing $a_0$: at the same time order-disorder transition changes from discontinuous to continuous type. Hence density phase separation plays an important role in predicting the nature of order-disorder transition. We also calculate the two-point density structure factor using coarse-grained hydrodynamic equations of motion with an introduction of a density dependent alignment term in the equation introduced by Toner and Tu \cite{tonertu}. Density structure factor shows a divergence at a critical wave-vector $q_c$, which decreases with decreasing density dependent alignment term. Alignment term in the coarse-grained equation plays the same role as the distance dependent parameter $a_0$ in the microscopic simulation. Our results can be tested in many biological systems: where particle have tendency to interact strongly with their closest neighbours.

cond-mat.stat-mech↗

arXiv2016

Additivity, density fluctuations, and nonequilibrium thermodynamics for active Brownian particles

Using an additivity property, we study particle-number fluctuations in a system of interacting self-propelled particles, called active Brownian particles (ABPs), which consists of repulsive disks with random self-propulsion velocities. From a fluctuation-response relation - a direct consequence of additivity, we formulate a thermodynamic theory which captures the previously observed features of nonequilibrium phase transition in the ABPs from a homogeneous fluid phase to an inhomogeneous phase of coexisting gas and liquid. We substantiate the predictions of additivity by analytically calculating the subsystem particle-number distributions in the homogeneous fluid phase away from criticality where analytically obtained distributions are compatible with simulations in the ABPs.

cond-mat.stat-mech↗

arXiv2016

Subdiffusion, Anomalous Diffusion and Propagation of a Particle Moving in Random and Periodic Media

We investigate the motion of a single particle moving on a two-dimensional square lattice whose sites are occupied by right and left rotators. These left and right rotators deterministically rotate the particle's velocity to the right or left, respectively and \emph{flip} orientation from right to left or from left to right after scattering the particle. We study three types of configurations of left and right rotators, which we think of as types of media, through with the particle moves. These are completely random (CR), random periodic (RP), and completely periodic (CP) configurations. For CR configurations the particle's dynamics depends on the ratio $r$ of right to left scatterers in the following way. For small $r\simeq0$, when the configuration is nearly homogeneous, the particle subdiffuses with an exponent of 2/3, similar to the diffusion of a macromolecule in a crowded environment. Also, the particle's trajectory has a fractal dimension of $d_f\simeq4/3$, comparable to that of a self-avoiding walk. As the ratio increases to $r\simeq 1$, the particle's dynamics transitions from subdiffusion to anomalous diffusion with a fractal dimension of $d_f\simeq 7/4$, similar to that of a percolating cluster in 2-d. In RP configurations, which are more structured than CR configurations but also randomly generated, we find that the particle has the same statistic as in the CR case. In contrast, CP configurations, which are highly structured, typically will cause the particle to go through a transient stage of subdiffusion, which then abruptly changes to propagation. Interestingly, the subdiffusive stage has an exponent of approximately 2/3 and a fractal dimension of $d_f\simeq4/3$, similar to the case of CR and RP configurations for small $r$.

cond-mat.stat-mech↗

arXiv2015

Density Induced Phases in Active Nematic

We introduce a minimal model for a collection of self-propelled apolar active particles, also called as `active nematic', on a two-dimensional substrate and study the order-disorder transition with the variation of density. The particles interact with their neighbours within the framework of the Lebwohl-Lasher model and move asymmetrically, along their orientation, to unoccupied nearest neighbour lattice sites. At a density lower than the equilibrium isotropic-nematic transition density, the active nematic shows a first order transition from the isotropic state to a banded state. The banded state extends over a range of density, and the scalar order parameter of the system shows a plateau like behaviour, similar to that of the magnetic systems. In the large density limit the active nematic shows a bistable behaviour between a homogeneous ordered state with global ordering and an inhomogeneous mixed state with local ordering. The study of the above phases with density variation is scant and gives significant insight of complex behaviours of many biological systems.

cond-mat.stat-mech↗

arXiv2014

Aspects of the density field in an active nematic

Active nematics are conceptually the simplest orientationally ordered phase of self-driven particles, but have proved to be a perennial source of surprises. We show here through numerical solution of coarse-grained equations for order parameter and density that the growth of the active nematic phase from the isotropic phase is necessarily accompanied by a clumping of the density. The growth kinetics of the density domains is shown to be faster than the 1/3-law expected for variables governed by a conservation law. Other results presented include the suppression of density fluctuations in the stationary ordered nematic by the imposition of an orienting field. We close by posing some open questions.

cond-mat.soft↗

arXiv2013

Mesoscopic theory for fluctuating active nematics

The term active nematics designates systems in which apolar elongated particles spend energy to move randomly along their axis and interact by inelastic collisions in the presence of noise. Starting from a simple Vicsek-style model for active nematics, we derive a mesoscopic theory, complete with effective multiplicative noise terms, using a combination of kinetic theory and Itô calculus approaches. The stochastic partial differential equations thus obtained are shown to recover the key terms argued in EPL \textbf{62} (2003) 196 to be at the origin of anomalous number fluctuations and long-range correlations. Their deterministic part is studied analytically, and is shown to give rise to the long-wavelength instability at onset of nematic order (see arXiv:1011.5408). The corresponding nonlinear density-segregated band solution is given in a closed form.

cond-mat.stat-mech↗

arXiv2013

Electrostatic interactions in concentrated protein solutions

We present an approximate method for calculating the electrostatic free energy of concentrated protein solutions. Our method uses a cell model and accounts for both the coulomb energy and the entropic cost of Donnan salt partitioning. The former term is calculated by linearizing the Poisson-Boltzmann equation around a nonzero average potential, while the second term is calculated using a jellium approximation that is empirically modified to reproduce the dilute solution limit. When combined with a short-ranged binding interaction, calculated using the mean spherical approximation, our model reproduces osmotic pressure measurements of bovine serum albumin solutions. We also use our free energy to calculate the salt-dependent shift in the critical temperature of lysozyme solutions and show why the predicted salt partitioning between the dilute and dense phases has proven experimentally elusive.

physics.bio-ph↗

arXiv2012

Collective dynamics of self-propelled particles with variable speed

Understanding the organization of collective motion in biological systems is an ongoing challenge. In this Paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish, we introduce a power-law dependency of the speed of each particle on the degree of polarization order in its neighborhood. We derive analytically a coarse-grained continuous approximation for this model and find that, while the variable speed rule does not change the details of the ordering transition leading to collective motion, it induces an inverse power-law correlation between the speed or the local polarization order and the local density. Using numerical simulations, we verify the range of validity of this continuous description and explore regimes beyond it. We discover, in disordered states close to the transition, a phase-segregated regime where most particles cluster into almost static groups surrounded by isolated high-speed particles. We argue that the mechanism responsible for this regime could be present in a wide range of collective motion dynamics.

physics.bio-ph↗

arXiv2010

Fluctuations and Pattern Formation in Self-Propelled Particles

We consider a coarse-grained description of a system of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial fluctuations beyond a threshold set by the self-propulsion velocity of the individual units. In this region, the system organizes itself into an inhomogeneous state of well-defined propagating stripes of flocking particles interspersed with low density disordered regions. Further, we find that even in the regime where the homogeneous flocking state is stable, the system exhibits large fluctuations in both density and orientational order. We study the hydrodynamic equations analytically and numerically to characterize both regimes.

cond-mat.stat-mech↗

arXiv2009

A Dynamic Renormalization Group Study of Active Nematics

We carry out a systematic construction of the coarse-grained dynamical equation of motion for the orientational order parameter for a two-dimensional active nematic, that is a nonequilibrium steady state with uniaxial, apolar orientational order. Using the dynamical renormalization group, we show that the leading nonlinearities in this equation are marginally \textit{irrelevant}. We discover a special limit of parameters in which the equation of motion for the angle field of bears a close relation to the 2d stochastic Burgers equation. We find nevertheless that, unlike for the Burgers problem, the nonlinearity is marginally irrelevant even in this special limit, as a result of of a hidden fluctuation-dissipation relation. 2d active nematics therefore have quasi-long-range order, just like their equilibrium counterparts

cond-mat.soft↗