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.

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 Vicsekstyle 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

Two-dimensional nonequilibrium nematic steady states, as found in agitated granular-rod monolayers or films of orientable amoeboid cells, were predicted [Europhys. Lett. 62 (2003) 196] to have giant number fluctuations, with standard deviation proportional to the mean. We show numerically that the steady state of such systems is macroscopically phase-separated, yet dominated by fluctuations, as in the Das-Barma model [PRL 85 (2000) 1602]. We suggest experimental tests of our findings in granular and living-cell systems. The ordering or "flocking" [1, 2, 3] of self-propelled particles obeys laws strikingly different from those governing thermal equilibrium systems of the same spatial symmetry. Even in two dimensions, the velocities of particles in such flocks show true longrange order [1,2], despite the spontaneous breaking of continuous rotational invariance. Density fluctuations in the ordered phase are anomalously large [2], and the onset of the ordered phase is discontinuous [4]. The ultimate origin of these nonequilibrium phenomena is that the order parameter is not simply an orientation but a macroscopic velocity. It is thus intriguing that even the nematic phase of a collection of self-driven particles, which is apolar and hence has zero macroscopic velocity, shows [5,6] giant number fluctuations [7], as a result of the manner in which orientational fluctuations drive mass currents. This Letter takes a closer look at these fluctuations and shows that they offer a physical realisation of the remarkable nonequilibrium phenomenon known as fluctuation-dominated phase separation [8], hitherto a theoretical curiosity.Before presenting our results, we make precise the term active nematic. An active particle extracts energy from sources in the ambient medium or an internal fuel tank, dissipates it by the cyclical motion of an internal "motor" coordinate, and moves as a consequence. For the anisotropic particles that concern us here, the direction of motion is determined predominantly by the orientation. Our definition encompasses self-propelled organisms, living cells, molecular motors, and macroscopic rods on a vertically vibrated substrate (where the tilt of the rod * Also with CMTU, JNCASR, Bangalore 560064, India † Electronic address: sriram@physics.iisc.ernet.in serves as the motor coordinate). An active nematic is a collection of such particles with axes on average spontaneously aligned in a directionn, with invariance undern → −n. We know of two realisations of active nematics: collections of living amoeboid cells [10] and granular-rod monolayers [11,12]. We study active nematics in a simple numerical model described in detail below. Our results confirm (see Fig. 1) the giant number fluctuations (standard deviation ∝ mean) [6] predicted by the linearised analysis of [5], but are far richer: (i) A statistically uniform initial distribution of particles, on a well-ordered nematic background, undergoes a delicate "fluctuation-dominated" [8] phase separation, where the system explores many statistically simila...

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 specific variable speed rule used 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.

Antibody solutions are typically much more viscous than solutions of globular proteins at equivalent volume fraction. Here we propose that this is due to molecular entanglements that are caused by the elongated shape and intrinsic flexibility of antibody molecules. We present a simple theory in which the antibodies are modeled as linear polymers that can grow via reversible bonds between the antigen binding domains. This mechanism explains the observation that relatively subtle changes to the interparticle interaction can lead to large changes in the viscosity. The theory explains the presence of distinct power law regimes in the concentration dependence of the viscosity as well as the correlation between the viscosity and the charge on the variable domain in our anti-streptavidin IgG 1 model system.