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How do update rules affect the dynamical and steady state properties of a flock? In this study, we have explored the active Ising spins (s = +-1) in one dimension, where spin updates its orientation according to the Metropolis algorithm (based on the neighbors) via two different update rules. (i) Parallel, and (ii) Random-sequential. We explore the effect of Parallel and Random-sequential updates on the dynamical properties of flocks in one dimension. Due to the inherent asynchronous nature of the Random-sequential update, the directional switching of the flock is increased compared to the Parallel one. The nature of phase transition is affected by the difference in the updating mechanism: discontinuous for Parallel and continuous for Random-sequential updates., Comment: 7 pages, 6 figures. arXiv admin note: text overlap with arXiv:1704.04041

We perform a comprehensive study on the role of thermal noise on the ordering kinetics of a collection of active Brownian particles modeled using coarse-grained conserved active model B (AMB). The ordering kinetics of the system is studied for the critical mixture when quenched from high to a low temperature. The structure of the growing domains changes from isolated droplet type for AMB without noise to bi-continuous type for active model B with noise (AMBN). Unlike the passive counterpart of the AMB, the noise is relevant for the growth kinetics of the AMB. We use extensive numerical study, as well as dynamic scaling hypothesis to characterize the kinetics of the system. We find that the asymptotic growth law for AMBN is diffusive Lifshitz-Slyozov (LS) type, whereas it was reported previously that the asymptotic growth law for the AMB without noise is slower, with a growth exponent 4. Moreover, the kinetics of the growing domains show a strong time dependent growth for AMBN. The growth law shows a crossover from early time 1/3 value to intermediate time 1/4 value, and it again traverses from 1/4 to 1/3 asymptotically. The two different scaling functions are found for intermediate time and late time with growth law 1/4 and 1/3 respectively., Comment: 9 Pages, 7 figures

We model a binary mixture of passive and active Brownian particles in two dimensions using the effective interaction between passive particles in the active bath. The activity of active particles and the size ratio of two types of particles are two control parameters in the system. The effective interaction is calculated from the average force on two particles generated by the active particles. The effective interaction can be attractive or repulsive, depending on the system parameters. The passive particles form four distinct structural orders for different system parameters viz; disorder (D), disordered cluster (DC), ordered cluster (OC), and poly-crystalline order (P C). The change in structure is dictated by the change in nature of the effective interaction. We further confirm the four structures using full microscopic simulation of active and passive mixture. Our study is useful to understand the different collective behaviour in non-equilibrium systems., Comment: 8-pages and 6-figures

We study the ordering kinetics of an assembly of {\it active Brownian particles} (ABPs) on a two-dimensional substrate. We use a coarse-grained equation for the composition order parameter $\psi ({\bf r},t)$, where ${\bf r}$ and $t$ denote space and time, respectively. The model is similar to the {\it Cahn-Hilliard equation} or {\it Model B} (MB) for a conserved order parameter with an additional activity term of strength $\lambda$. This model has been introduced by Wittkowski et al., Nature Comm. {\bf 5}, 4351 (2014), and is termed {\it Active Model B} (AMB). We study domain growth kinetics and dynamical scaling of the correlation function for the AMB with critical and off-critical compositions. The quantity $P = \mbox{sign}(\lambda \times \psi_0)$ governs the asymptotic growth kinetics for the off-critical AMB, where $\psi_0$ denotes the average order parameter. For negative $P$, the domain growth law is the usual Lifshitz-Slyozov growth law with $L(t,\lambda) \sim t^{1/3}$. For positive $P$, the growth law shows a crossover to a novel growth law $L(t,\lambda) \sim t^{1/4}$. Further, the correlation function shows good dynamical scaling for the off-critical AMB but the scaling function has a dependency on $\psi_0$ and $\lambda$. We also study the effects of both additive and multiplicative noise on the AMB.

We undertake a detailed numerical study of the {\it Active Model B} proposed by Wittkowski et al. [Nature Comm. {\bf 5}, 4351 (2014)]. We find that the introduction of activity has a drastic effect on the ordering kinetics. First, the domain growth law shows a crossover from the usual Lifshitz-Slyozov growth law for phase separation ($L \sim t^{1/3}$, where $t$ is the time) to a novel growth law ($L \sim t^{1/4}$) at late times. Second, the correlation function exhibits dynamical scaling for a given activity strength $\lambda$, but the scaling function depends on $\lambda$.

In this study, we introduce a minimal model for a collection of polar self-propelled particles (SPPs) on a two-dimensional substrate where each particle has a different ability to interact with its neighbours. The SPPs interact through a short-range alignment interaction and interaction strength of each particle is obtained from a uniform distribution. Moreover, the volume exclusion among the SPPs is taken care of by introducing a repulsive interaction among them. We characterise the ordered steady state and kinetics of the system for different strengths of the disorder. We find that the presence of the disorder does not destroy the usual long-range ordering in the system. To our surprise, we note that the density clustering is enhanced in the presence of the disorder. Moreover, the disorder leads to the formation of a random network of different interaction strengths, which makes the alignment weaker and it results in the slower dynamics. Hence, the disorder leads to more cohesion among the particles. Furthermore, we note that the kinetics of the ordered state remains unaffected in the presence of the disorder. Size of orientationally ordered domains and density clusters grow with time with dynamic growth exponents $z_{o} \sim 2$ and $z_{\rho} \sim 4$, respectively.

A collection of self-propelled particles (SPPs) shows coherent motion and exhibits a true long range ordered (LRO) state in two dimensions. Various studies show that the presence of spatial inhomogeneities can destroy the usual long-range ordering in the system. However, the effects of inhomogeneity due to the intrinsic properties of the particles are barely addressed. In this paper we consider a collection of polar SPPs moving with inhomogeneous speed (IS) on a two dimensional substrate, which can arise due to varying physical strength of the individual particle. To our surprise, the IS not only preserves the usual long-range ordering present in the homogeneous speed models but also induces faster ordering in the system. Furthermore, The response of the flock to an external perturbation is also faster, compared to Vicsek like model systems, due to the frequent update of neighbors of each SPP in the presence of the IS. Therefore, our study shows that the IS can help in faster information transfer in the moving flock.

We study the motion of an active Brownian particle (ABP) using overdamped Langevin dynamics on a two-dimensional substrate with periodic array of obstacles and in a quasi-one-dimensional corrugated channel comprised of periodically arrayed obstacles. The periodic arrangement of the obstacles enhances the persistent motion of the ABP in comparison to its motion in the free space. Persistent motion increases with the activity of the ABP. We note that the periodic arrangement induces directionality in ABP motion at late time, and it increases with the size of the obstacles. We also note that the ABP exhibits a super-diffusive dynamics in the corrugated channel. The transport property is independent of the shape of the channel; rather it depends on the packing fraction of the obstacles in the system. However, the ABP shows the usual diffusive dynamics in the quasi-one-dimensional channel with flat boundary.

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, $a^{d}$ ($00$, the system shows a transition from a disordered to an ordered state as a function of noise strength. We calculate the critical noise strength, $\eta_c(a)$ 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., Comment: 17 pages and 7 figures

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., Comment: 7 pages, 7 figures, accepted in Physica A

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., Comment: 10 pages, 7 figures