Glass Transition Phenomena Semiannual Status Report

Multiple glass transitions, heat capacities, and equation of state properties of polymer system

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

Statistical mechanics far from equilibrium: prediction and test for a sheared system

We report the complete statistical treatment of a system of particles interacting via Newtonian forces in continuous boundary-driven flow, far from equilibrium. By numerically time-stepping the force-balance equations of a model fluid we measure occupancies and transition rates in simulation. The high-shear-rate simulation data verify the invariant quantities predicted by our statistical theory, thus demonstrating that a class of non-equilibrium steady states of matter, namely sheared complex fluids, is amenable to statistical treatment from first principles.Comment: 4 pages plus a 3-page pdf supplemen

A Lattice-Boltzmann model for suspensions of self-propelling colloidal particles

We present a Lattice-Boltzmann method for simulating self-propelling (active) colloidal particles in two-dimensions. Active particles with symmetric and asymmetric force distribution on its surface are considered. The velocity field generated by a single active particle, changing its orientation randomly, and the different time scales involved are characterized in detail. The steady state speed distribution in the fluid, resulting from the activity, is shown to deviate considerably from the equilibrium distribution.Comment: 8 pages, 13 figure

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

Pathway Switching Explains the Sharp Response Characteristic of Hypoxia Response Network

Hypoxia induces the expression of genes that alter metabolism through the hypoxia-inducible factor (HIF). A theoretical model based on differential equations of the hypoxia response network has been previously proposed in which a sharp response to changes in oxygen concentration was observed but not quantitatively explained. That model consisted of reactions involving 23 molecular species among which the concentrations of HIF and oxygen were linked through a complex set of reactions. In this paper, we analyze this previous model using a combination of mathematical tools to draw out the key components of the network and explain quantitatively how they contribute to the sharp oxygen response. We find that the switch-like behavior is due to pathway-switching wherein HIF degrades rapidly under normoxia in one pathway, while the other pathway accumulates HIF to trigger downstream genes under hypoxia. The analytic technique is potentially useful in studying larger biomedical networks

Rheology of Active-Particle Suspensions

We study the interplay of activity, order and flow through a set of coarse-grained equations governing the hydrodynamic velocity, concentration and stress fields in a suspension of active, energy-dissipating particles. We make several predictions for the rheology of such systems, which can be tested on bacterial suspensions, cell extracts with motors and filaments, or artificial machines in a fluid. The phenomena of cytoplasmic streaming, elastotaxis and active mechanosensing find natural explanations within our model.Comment: 3 eps figures, submitted to Phys Rev Let