Tanniemola B. Liverpool

Propulsion of a molecular machine by asymmetric distribution of reaction products

A simple model for the reaction-driven propulsion of a small device is proposed as a model for (part of) a molecular machine in aqueous media. The motion of the device is driven by an asymmetric distribution of reaction products. The propulsive velocity of the device is calculated as well as the scale of the velocity fluctuations. The effects of hydrodynamic flow as well as a number of different scenarios for the kinetics of the reaction are addressed.

Instabilities of isotropic solutions of active polar filaments.

We study the dynamics of an entangled, isotropic solution of polar filaments coupled by molecular motors which generate relative motion of the filaments in two and three dimensions. We investigate the stability of the homogeneous state for constant motor concentration taking into account excluded volume and entanglement. At low filament density the system develops a density instability, while at high filament density entanglement effects drive the instability of orientational fluctuations.

Collapse of Stiff Polyelectrolytes due to Counterion Fluctuations

The effective elasticity of highly charged stiff polyelectrolytes is studied in the presence of counterions, with and without added salt. The rigid polymer conformations may become unstable due to an effective attraction induced by counterion density fluctuations. Instabilities at the longest, or intermediate length scales may signal collapse to globule, or necklace states, respectively. In the presence of added-salt, a generalized electrostatic persistence length is obtained, which has a nontrivial dependence on the Debye screening length.

Sheared active fluids: thickening, thinning, and vanishing viscosity.

We analyze the behavior of a suspension of active polar particles under shear. In the absence of external forces, orientationally ordered active particles are known to exhibit a transition to a state of nonuniform polarization and spontaneous flow. Such a transition results from the interplay between elastic stresses, due to the liquid crystallinity of the suspension, and internal active stresses. In the presence of an external shear, we find an extremely rich variety of phenomena, including an effective reduction (increase) in the apparent viscosity depending on the nature of the active stresses and the flow-alignment property of the particles, as well as more exotic behaviors such as a nonmonotonic stress-strain-rate relation and yield stress for large activities.

Mobility of extended bodies in viscous films and membranes

We develop general methods to calculate the mobilities of extended bodies in (or associated with) membranes and films. We demonstrate a striking difference between in-plane motion of rodlike inclusions and the corresponding case of bulk (three-dimensional) fluids: for rotations and motion perpendicular to the rod axis, we find purely local drag, in which the drag coefficient is purely algebraic in the rod dimensions. These results as well as the calculational methods are applicable to such problems as the diffusion of objects in or associated with Langmuir films and lipid membranes. These methods can also be simply extended to treat viscoelastic systems.

Statistical mechanics of double-stranded semiflexible polymers

We study the statistical mechanics of double-stranded semi-flexible polymers using both analytical techniques and simulation. We find a transition at some finite temperature, from a type of short range order to a fundamentally different sort of short range order. In the high temperature regime, the 2-point correlation functions of the object are identical to worm-like chains, while in the low temperature regime they are different due to a twist structure. In the low temperature phase, the polymers develop a kink-rod structure which could clarify some recent puzzling experiments on actin.

Dynamics of Rigid and Flexible Extended Bodies in Viscous Films and Membranes

We study the dynamics of extended rodlike bodies in (or associated with) membranes and films. We demonstrate a striking difference between the mobilities in films and bulk fluids, even when the dissipation is dominated by the fluid stress: For large inclusions, we find that rotation and motion perpendicular to the rod axis exhibit purely local drag, in which the drag coefficient is algebraic in the rod dimensions. We also study the dynamics of the internal modes of a semiflexible inclusion and find two dynamical regimes in the relaxation spectrum.

Dynamics of a meandering river

We present a statistical model of a meandering river on an alluvial plane which is motivated by the physical non-linear dynamics of the river channel migration and by describing heterogeneity of the terrain by noise. We study the dynamics analytically and numerically. The motion of the river channel is unstable and we show that by inclusion of the formation of ox-bow lakes, the system may be stabilised. We then calculate the steady state and show that it is in agreement with simulations and measurements of field data.

Short-time inertial response of viscoelastic fluids measured with Brownian motion and with active probes

We have directly observed short-time stress propagation in viscoelastic fluids using two optically trapped particles and a fast interferometric particle-tracking technique. We have done this both by recording correlations in the thermal motion of the particles and by measuring the response of one particle to the actively oscillated second particle. Both methods detect the vortexlike flow patterns associated with stress propagation in fluids. This inertial vortex flow propagates diffusively for simple liquids, while for viscoelastic solutions the pattern spreads superdiffusively, depending on the shear modulus of the medium.

Swimmers in Thin Films: From Swarming to Hydrodynamic Instabilities

We investigate theoretically the collective dynamics of a suspension of low Reynolds number swimmers that are confined to two dimensions by a thin fluid film. Our model swimmer is characterized by internal degrees of freedom which locally exert active stresses on the fluid. We find that hydrodynamic interactions mediated by the film can give rise to spontaneous continuous symmetry breaking (swarming), to states with either polar or nematic homogeneous order. For dipolar swimmers, the stroke averaged dynamics are enough to determine the leading contributions to the collective behavior. In contrast, for quadrupolar swimmers, details of the internal dynamics are important in determining the bulk behavior. In the broken symmetry phases, fluctuations of hydrodynamic variables destabilize order. Interestingly, this instability is not generic and depends on the length scale.