Non-equilibrium systems have steady-state distributions and non-steady dynamics

We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe such systems. In these, the generalisation of a steady state is associated with a stationary probability density of micro-states and a deterministic dynamical system whose trajectories the system follows on average. These trajectories are a manifestation of non-stationary macroscopic currents observed in these systems. We determine precise conditions for the steady state to exist as well as the requirements for it to be stable. We illustrate this with some examples.Comment: 12+ pages, 2 figure

The dynamics of a self-phoretic Janus swimmer near a wall

We study the effect of a nearby planar wall on the propulsion of a phoretic Janus micro-swimmer driven by asymmetric reactions on its surface which absorb reactants and generate products. We show that the behaviour of these swimmers near a wall can be classified ${\bf based \ on \ whether}$ the swimmers are ${\bf mainly}$ absorbing or producing reaction solutes ${\bf and \ whether}$ their swimming directions are such that the inert or active face is at the front. We find that the wall-induced solute gradients always promote swimmer propulsion along the wall while the effect of hydrodynamics leads to re-orientation of the swimming direction away from the wall.Comment: 6 pages, 6 figure

Hydrodynamic interactions in dense active suspensions: from polar order to dynamical clusters

We study the role of hydrodynamic interactions in the collective behaviour of collections of microscopic active particles suspended in a fluid. We introduce a novel calculational framework that allows us to separate the different contributions to their collective dynamics from hydrodynamic interactions on different length scales. Hence we are able to systematically show that lubrication forces when the particles are very close to each other play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that motility-induced phase separation is suppressed by near-field interactions, leading to open gel-like clusters rather than dense clusters. Interestingly, we find a globally polar ordered phase appears for neutral swimmers with no force dipole that is enhanced by near field lubrication forces in which the collision process rather than long-range interaction dominates the alignment mechanism.Comment: 7 pages, 4 figure

Organization and instabilities of entangled active polar filaments

We study the dynamics of an entangled, isotropic solution of polar filaments coupled by molecular motors which generate relative motion of the filaments in two and three dimensions. We investigate the stability of the homogeneous state for constant motor concentration taking into account excluded volume and entanglement. At low filament density the system develops a density instability, while at high filament density entanglement effects drive the instability of orientational fluctuations.Comment: 4pages, 2 eps figure, revtex

Pair creation, motion, and annihilation of topological defects in 2D nematics

We present a novel framework for the study of disclinations in two-dimensional active nematic liquid crystals, and topological defects in general. The order tensor formalism is used to calculate exact multi-particle solutions of the linearized static equations inside a uniformly aligned state. Topological charge conservation requires a fixed difference between the number of half charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parameters of the static solutions, which describes the motion of a half-disclination pair, or of several pairs. Within this formalism, we model defect production and annihilation, as observed in experiments. Our dynamics also provide an estimate for the critical density at which production and annihilation rates are balanced

Hydrodynamic and rheology of active polar filaments

The cytoskeleton provides eukaryotic cells with mechanical support and helps them perform their biological functions. It is a network of semiflexible polar protein filaments and many accessory proteins that bind to these filaments, regulate their assembly, link them to organelles and continuously remodel the network. Here we review recent theoretical work that aims to describe the cytoskeleton as a polar continuum driven out of equilibrium by internal chemical reactions. This work uses methods from soft condensed matter physics and has led to the formulation of a general framework for the description of the structure and rheology of active suspension of polar filaments and molecular motors.Comment: 30 pages, 5 figures. To appear in "Cell Motility", Peter Lenz, ed. (Springer, New York, 2007

Complex Spontaneous Flows and Concentration Banding in Active Polar Films

We study the dynamical properties of active polar liquid crystalline films. Like active nematic films, active polar films undergo a dynamical transitions to spontaneously flowing steady-states. Spontaneous flow in polar fluids is, however, always accompanied by strong concentration inhomogeneities or "banding" not seen in nematics. In addition, a spectacular property unique to polar active films is their ability to generate spontaneously oscillating and banded flows even at low activity. The oscillatory flows become increasingly complicated for strong polarity.Comment: 4 pages, 3 figure

Sheared active fluids: thickening, thinning and vanishing viscosity

We analyze the behavior of a suspension of active polar particles under shear. In the absence of external forces, orientationally ordered active particles are known to exhibit a transition to a state of non-uniform polarization and spontaneous flow. Such a transition results from the interplay between elastic stresses, due to the liquid crystallinity of the suspension, and internal active stresses. In the presence of an external shear we find an extremely rich variety of phenomena, including an effective reduction (increase) in the apparent viscosity depending on the nature of the active stresses and the flow-alignment property of the particles, as well as more exotic behaviors such as a non-monotonic stress/strain-rate relation and yield stress for large activities.Comment: 10 pages, 10 figure