Statistical hydrodynamics of ordered suspensions of self-propelled particles: waves, giant number fluctuations and instabilities

General principles of symmetry and conservation are used to construct the hydrodynamic equations for orientationally ordered suspensions of self-propelled particles (SPPs). Without knowledge of the microscopic origins of the ordering or the mechanisms of self-propulsion, we are able to make a number of striking, testable predictions for the properties of these nonequilibrium phases of matter. These include: novel wavelike excitations in vectorially ordered suspensions; the absolute instability of nematic SPP suspensions at long wavelengths; the convective instability of low-Reynolds-number vector-ordered suspensions; and giant number fluctuations in vector-ordered SPP suspensions

Kardar-Parisi-Zhang universality in a two-component driven diffusive model

We elucidate the universal spatio-temporal scaling properties of the time-dependent correlation functions in a two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion process. By using a perturbative renormalization group framework, we show that the relevant scaling exponents have values same as those for the 1D Kardar-Parisi-Zhang (KPZ) equation. We thus establish that the model belongs to the 1D KPZ universality class.Comment: 13 pages, 2 figure

Classical XY model with conserved angular momentum is an archetypal non-Newtonian fluid

We find that the classical one-dimensional (1D) XY model, with angular-momentum-conserving Langevin dynamics, mimics the non-Newtonian flow regimes characteristic of soft matter when subjected to counter-rotating boundaries. An elaborate steady-state phase diagram has continuous and first-order transitions between states of uniform flow, shear-banding, solid-fluid coexistence and slip-planes. Results of numerically studies and a concise mean-field constitutive relation, offer a paradigm for diverse non-equilibrium complex fluids

Active nematics on a substrate: giant number fluctuations and long-time tails

We construct the equations of motion for the coupled dynamics of order parameter and concentration for the nematic phase of driven particles on a solid surface, and show that they imply (i) giant number fluctuations, with a standard deviation proportional to the mean and (ii) long-time tails $\sim t^{-d/2}$ in the autocorrelation of the particle velocities in $d$ dimensions despite the absence of a hydrodynamic velocity field. Our predictions can be tested in experiments on aggregates of amoeboid cells as well as on layers of agitated granular matter.Comment: Submitted to Europhys Lett 26 Aug 200

Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles

We construct the hydrodynamic equations for {\em suspensions} of self-propelled particles (SPPs) with spontaneous orientational order, and make a number of striking, testable predictions:(i) SPP suspensions with the symmetry of a true {\em nematic} are {\em always} absolutely unstable at long wavelengths.(ii) SPP suspensions with {\em polar}, i.e., head-tail {\em asymmetric}, order support novel propagating modes at long wavelengths, coupling orientation, flow, and concentration. (iii) In a wavenumber regime accessible only in low Reynolds number systems such as bacteria, polar-ordered suspensions are invariably convectively unstable.(iv) The variance in the number N of particles, divided by the mean , diverges as $^{2/3}$ in polar-ordered SPP suspensions.Comment: submitted to Phys Rev Let

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 counterpartsComment: 31 pages 6 figure