R. Aditi Simha

Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles

We construct the hydrodynamic equations for suspensions of self-propelled particles (SPPs) with spontaneous orientational order, and make a number of striking, testable predictions: (i) Nematic SPP suspensions are always absolutely unstable at long wavelengths. (ii) SPP suspensions support novel propagating modes at long wavelengths, coupling orientation, flow, and concentration. (iii) In a wave number 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.

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.

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 in dimension d = 2 of primary relevance to experiment, and ii) long-time tails

Statistical hydrodynamics of ordered suspensions of self-propelled particles: waves, giant number fluctuations and instabilities

\sim t^{-d/2}

A dynamic renormalization group study of active nematics

in the autocorrelation of the particle velocities 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.

Traveling Waves in a Drifting Flux Lattice

General principles of symmetry and conservation are used to construct the hydrodynamic equations for orientationally ordered suspensions of self-propelled particles (SPPs). Without knowledge of the microscopic origins of the ordering or the mechanisms of self-propulsion, we are able to make a number of striking, testable predictions for the properties of these nonequilibrium phases of matter. These include: novel wavelike excitations in vectorially ordered suspensions; the absolute instability of nematic SPP suspensions at long wavelengths; the convective instability of low-Reynolds-number vector-ordered suspensions; and giant number fluctuations in vector-ordered SPP suspensions.

Minimal polar swimmer at low Reynolds number

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 irrelevant. We discover a special limit of parameters in which the equation of motion for the angle field 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 a hidden fluctuation-dissipation relation. 2d active nematics therefore have quasi-long-range order, just like their equilibrium counterparts.

Hydrodynamics of soft active matter

Starting from the time-dependent Ginzburg-Landau (TDGL) equations for a type II superconductor, we derive the equations of motion for the displacement field of a moving vortex lattice ignoring pinning and inertia. We show that it is linearly stable and, surprisingly, that it supports wavelike long-wavelength excitations arising not from inertia or elasticity but from the strain-dependent mobility of the moving lattice. It should be possible to image these waves, whose speeds are a few μm/s, using fast scanning tunneling microscopy.

Soft Active Matter

We propose a minimal model for a polar swimmer, consisting of two spheres connected by a rigid slender arm, at low Reynolds number. The propulsive velocity for the proposed model is the maximum for any swimming cycle with the same variations in its two degrees of freedom and its displacement in a cycle is achieved entirely in one step. The stroke averaged flow field generated by the contractile swimmer at large distances is found to be dipolar. In addition, the changing radius of one of the spheres generates the field of a potential doublet centered at its initial position.