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

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 $\ell$. Cells actively regulate $\ell$ via the activity of force generating molecules, such as myosin II. Here we develop a general theory for such systems through 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 $\ell$, 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 show good agreement

Spinodals with Disorder: from Avalanches in Random Magnets to Glassy Dynamics

We revisit the phenomenon of spinodals in the presence of quenched disorder and develop a complete theory for it. We focus on the spinodal of an Ising model in a quenched random field (RFIM), which has applications in many areas from materials to social science. By working at zero temperature in the quasi-statically driven RFIM, thermal fluctuations are eliminated and one can give a rigorous content to the notion of spinodal. We show that the latter is due to the depinning and the subsequent expansion of rare droplets. We work out the associated critical behavior, which, in any finite dimension, is very different from the mean-field one: the characteristic length diverges exponentially and the thermodynamic quantities display very mild nonanalyticities much like in a Griffith phenomenon. From the recently established connection between the spinodal of the RFIM and glassy dynamics, our results also allow us to conclusively assess the physical content and the status of the dynamical transition predicted by the mean-field theory of glass-forming liquids.Comment: Published version: Total 7 pages including 2 pages of supplemental materia

Comment on "Layering transition in confined molecular thin films: Nucleation and growth"

When fluid is confined between two molecularly smooth surfaces to a few molecular diameters, it shows a large enhancement of its viscosity. From experiments it seems clear that the fluid is squeezed out layer by layer. A simple solution of the Stokes equation for quasi-two-dimensional confined flow, with the assmption of layer-by-layer flow is found. The results presented here correct those in Phys. Rev. B, 50, 5590 (1994), and show that both the kinematic viscosity of the confined fluid and the coefficient of surface drag can be obtained from the time dependence of the area squeezed out. Fitting our solution to the available experimental data gives the value of viscosity which is ~7 orders of magnitude higher than that in the bulk.Comment: 4 pages, 2 figure

How Do Glassy Domains Grow?

We construct the equations for the growth kinetics of a structural glass within mode-coupling theory, through a non-stationary variant of the 3-density correlator defined in Phys. Rev. Lett. 97}, 195701 (2006). We solve a schematic form of the resulting equations to obtain the coarsening of the 3-point correlator $\chi_3(t,t_w)$ as a function of waiting time $t_w$. For a quench into the glass, we find that $\chi_3$ attains a peak value $\sim t_w^{0.5}$ at $t -t_w \sim t_w^{0.8}$, providing a theoretical basis for the numerical observations of Parisi [J. Phys. Chem. B 103, 4128 (1999)] and Kob and Barrat [Phys. Rev. Lett. 78, 4581 (1997)]. The aging is not "simple": the $t_w$ dependence cannot be attributed to an evolving effective temperature.Comment: 6 pages, 5 figure