Understanding the approximations of mode-coupling theory for sheared steady states of colloids

Mean-field theory for the structure of strongly interacting active liquids

Active systems, which are driven out of equilibrium by local non-conservative forces, exhibit unique behaviors and structures with potential utility for the design of novel materials. An important and difficult challenge along the path towards such a goal is to precisely predict how the structure of active systems is modified as their driving forces push them out of equilibrium. Here, we use tools from liquid-state theories to approach this challenge for a classic minimal isotropic active matter model. First, we construct a nonequilibrium mean-field framework which can predict the structure of systems of weakly interacting particles. Second, motivated by equilibrium solvation theories, we modify this theory to extend it with surprisingly high accuracy to strongly interacting particles, distinguishing it from most existing similarly tractable approaches. Our results provide insight into spatial organization in strongly interacting out-of-equilibrium systems and strategies to control them.

Activity-dependent self-regulation of viscous length scales in biological systems

The cellular cortex, which is a highly viscous thin cytoplasmic layer just below the cell membrane, controls the cell's mechanical properties, which can be characterized by a hydrodynamic length scale ℓ. Cells actively regulate ℓ via the activity of force-generating molecules, such as myosin II. Here we develop a general theory for such systems through a coarse-grained hydrodynamic approach including activity in the static description of the system providing an experimentally accessible parameter and elucidate the detailed mechanism of how a living system can actively self-regulate its hydrodynamic length scale, controlling the rigidity of the system. Remarkably, we find that ℓ, as a function of activity, behaves universally and roughly inversely proportional to the activity of the system. Our theory rationalizes a number of experimental findings on diverse systems, and comparison of our theory with existing experimental data shows good agreement.

Glass susceptibility: Growth kinetics and saturation under shear

We study the growth kinetics of glassy correlations in a structural glass by monitoring the evolution, within mode-coupling theory, of a suitably defined three-point function χ_{C}(t,t_{w}) with time t and waiting time t_{w}. From the complete wave-vector-dependent equations of motion for domain growth, we pass to a schematic limit to obtain a numerically tractable form. We find that the peak value χ_{C}^{P} of χ_{C}(t,t_{w}), which can be viewed as a correlation volume, grows as t_{w}^{0.5}, and the relaxation time as t_{w}^{0.8}, following a quench to a point deep in the glassy state. These results constitute a theoretical explanation of the simulation findings of Parisi [J. Phys. Chem. B 103, 4128 (1999)JPCBFK1520-610610.1021/jp983967m] and Kob and Barrat [Phys. Rev. Lett. 78, 4581 (1997)PRLTAO0031-900710.1103/PhysRevLett.78.4581], and they are also in qualitative agreement with Parsaeian and Castillo [Phys. Rev. E 78, 060105(R) (2008)PLEEE81539-375510.1103/PhysRevE.78.060105]. On the other hand, if the quench is to a point on the liquid side, the correlation volume grows to saturation. We present a similar calculation for the growth kinetics in a p-spin spin glass mean-field model where we find a slower growth, χ_{C}^{P}∼t_{w}^{0.13}. Further, we show that a shear rate γ[over ̇] cuts off the growth of glassy correlations when t_{w}∼1/γ[over ̇] for quench in the glassy regime and t_{w}=min(t_{r},1/γ[over ̇]) in the liquid, where t_{r} is the relaxation time of the unsheared liquid. The relaxation time of the steady-state fluid in this case is ∝γ[over ̇]^{-0.8}.