Driven active matter: Fluctuations and a hydrodynamic instability

Wet active matter in the presence of an imposed temperature gradient, or chemical potential gradient, is considered. It is shown that there is a type of convective instability that is caused by a (negative) activity parameter. Physically this corresponds to active fluids with contractual stress. In this nonequilibrium steady state the singular generic long-ranged correlations are computed and compared and contrasted with the analogous results in a passive fluid. In addition, the singular nonequilibrium Casimir pressure or force is determined. The fluid motion above the instability is determined by generalizing the Lorenz equations for the Rayleigh-Benard problem in a passive fluid to Lorenz-like equations to describe this instability.

Figure 1

(a) The cellular flow pattern after the onset of the instability using the generalized Lorenz equations. (b) Typical concentration contours in a single cell.

Figure 2

The concentration flux from one plate to another as a function of the parameter $\epsilon =r-1$. The saturation at high values and the nonanalytic behavior near the threshold are distinctive features of the present model. In contrast, the standard Lorenz model shows a linear dependence.

Figure 3

The hysteretic limit cycle just below the threshold of the Hopf bifurcation. Inside the unshaded elliptic region of the figure there is a closed curve which is the locus of initial conditions which separate the basin of attraction of the stable fixed point from the basin of the limit cycle.