Chuck Yeung

Swimming efficiency of bacterium Escherichia coli.

We use measurements of swimming bacteria in an optical trap to determine fundamental properties of bacterial propulsion. In particular, we directly measure the force required to hold the bacterium in the optical trap and determine the propulsion matrix, which relates the translational and angular velocity of the flagellum to the torques and forces propelling the bacterium. From the propulsion matrix, dynamical properties such as torques, swimming speed, and power can be obtained by measuring the angular velocity of the motor. We find significant heterogeneities among different individuals even though all bacteria started from a single colony. The propulsive efficiency, defined as the ratio of the propulsive power output to the rotary power input provided by the motors, is found to be ≈2%, which is consistent with the efficiency predicted theoretically for a rigid helical coil.

Phase separation dynamics in driven diffusive systems

We study phase separation dynamics in a driven diffusive system. Our simulations are based on the Cahn-Hilliard equation with an additional flux term due to an external field. We study the dynamical scaling parallel and perpendicular to the field. A crossover is observed from isotropic domains at early times to extremely anisotropic domains at later times. We find that the inverse interfacial density (an isotropic measure of the domain size) increases astα, with α=1/3, from early times independent of the field strength, even though we do not observe dynamical scaling during these times. Our results indicate that a growth exponent α=1/3 may be more universal than previously expected. We analyze the dynamics in terms of surface driven instabilities and one-dimensional solitary waves.

Universal distribution of centers and saddles in two-dimensional turbulence.

The statistical properties of the local topology of two-dimensional turbulence are investigated using an electromagnetically forced soap film. The local topology of the incompressible 2D flow is characterized by the Jacobian determinant Lambda(x,y) = 1 / 4(omega(2)-sigma(2)), where omega(x,y) is the local vorticity and sigma(x,y) is the local strain rate. For turbulent flows driven by different external force configurations, P(Lambda) is found to be a universal function when rescaled using the turbulent intensity. A simple model that agrees with the measured functional form of P(Lambda) is constructed using the assumption that the stream function, psi(x,y), is a Gaussian random field.

Surface-Driven Instability and Enhanced Relaxation in the Dynamics of a Nonequilibrium Interface

We determine the stability of a nonequilibrium interface between two coexisting solid phases in the presence of a weak external field. Starting at the coarsegrained (Cahn-Hilliard) level, we use the method of matched asymptotics to derive the macroscopic interfacial dynamics. We then show that the external field leads to an instability due to flux along the interface, in contrast with the more common Mullins-Sekerka type instability, which involves fluxes normal to the interface. We also find that the external field produces an important modification of the Gibbs-Thomson relation. With these results, we perform the linear stability analysis for an approximately flat interface. If the field is tangent to the interface, the modification of the Gibbs-Thomson relation is important and the interface is stabilized. If the field is normal to the interface, the surface flux is important, and the effect can be stabilizing or destabilizing, but the orientational dependence is opposite what would be obtained if the Mullins-Sekerka instability dominates. Numerical simulations are performed to study the effect of the surface current and are in agreement with our analytical results.

Modeling reactive compatibilization of a binary blend with interacting particles

We use a multiscale computational approach to study reactive compatibilization in an immiscible binary AB blend that contains A-like and B-like interacting molecules. These molecules are modeled as spherical particles that react at the A/B interface to form A-B dumbbells. Through these simulations, we investigate the reaction kinetics and interfacial morphology of the system as a function of time for different densities of reacting molecules and diffusivities of the dumbbells. The results provide insight into the factors that affect the structural evolution of the interface between the incompatible A and B domains. In particular, we find that for sufficiently high densities of reacting molecules, the initially flat interface is unstable at later times. The instability is initiated by a vanishing of the surface tension, but the amplification of the initial instability is determined by the Brownian motion of the dumbbells. The interfacial width (defined as the root-mean-square variation of the interfacial position) grows as t1/2 and the domains form a lamellar structure at long times.We use a multiscale computational approach to study reactive compatibilization in an immiscible binary AB blend that contains A-like and B-like interacting molecules. These molecules are modeled as spherical particles that react at the A/B interface to form A-B dumbbells. Through these simulations, we investigate the reaction kinetics and interfacial morphology of the system as a function of time for different densities of reacting molecules and diffusivities of the dumbbells. The results provide insight into the factors that affect the structural evolution of the interface between the incompatible A and B domains. In particular, we find that for sufficiently high densities of reacting molecules, the initially flat interface is unstable at later times. The instability is initiated by a vanishing of the surface tension, but the amplification of the initial instability is determined by the Brownian motion of the dumbbells. The interfacial width (defined as the root-mean-square variation of the interfacial p...

METASTABILITY OF A GRANULAR SURFACE IN A SPINNING BUCKET

The surface shape of a spinning bucket of granular material is studied using a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. An experimentally observed central subcritical region is reproduced by the model. The subcritical region occurs when a metastable surface becomes unstable via a nonlinear instability mechanism. The nonlinear instability mechanism destabilizes the surface in large systems while a linear instability mechanism is relevant for smaller systems. The range of angles in which the granular surface is metastable vanishes with increasing system size.

Possibilities and limitations of Gaussian-closure approximations for phase-ordering dynamics

The nonlinear equations describing phase ordering dynamics can be closed by assuming the existence of an underlying Gaussian stochastic field which is nonlinearly related to the observable order parameter field. We discuss the relation between different implementations of the Gaussian assumption and consider the limitations of this assumption for phase ordering dynamics. The fact that the different approaches gives different results is a sign of the breakdown of the Gaussian assumption. We concentrate on the non-conserved order parameter case but also touch on the conserved order parameter case. We demonstrate that the Gaussian assumption is fundamentally flawed in the latter case.

PATTERN FORMATION IN LASER-INDUCED MELTING

A laser focussed onto a semiconductor film can create a disordered lamellae pattern of coexisting molten-solid regions. We present a continuum model based on the higher reflectivity of the molten regions. For large latent heat, this model becomes equivalent to a model of block copolymers. The characteristic wavenumber of the lamellae is that marginally stable to slow variations in the orientation (the zig-zag instability) and is obtained via systematic expansions from two limits. The lamellae can also be unstable to the zig-zag instability and Eckhaus instability simultaneously. This instability is a signal of dynamic steady states. We numerically study the behaviour after a quench. The lamellar size agrees with the analytic results and experiments. For shallow quenches, locally parallel stripes slowly straighten in time. For deep quenches, a disordered lamellae forms. We construct the director field and determine the orientational correlation length. Near onset the correlation is fixed by the system size. Far from onset the correlation length saturates at a finite value. We study the transition to the time-dependent asymptotic states with decreasing latent heat. postScript figures available on request

Theoretical models for grafted homopolymers in poor solvents: Observations of “dimpledrd surfaces

Abstract We introduce two new methods for determining the effect of solvent quality on a layer of end-grafted homopolymers. In the first investigation, we combine the random phase approximation (RPA) with a numerical self-consistent field analysis to examine the structure of the grafted layer. For sufficiently poor solvents, the laterally homogeneous grafted layer is linearly unstable to fluctuations tangential to the grafting plane. In the unstable regime, the grafted layer forms a “dimpled” surface in which the depth of, and the distance between, the dimples depend on chain length, solvent quality and grafting density. We also developed a two-dimensional self-consistent field model for grafted chains. The model allows us to explicitly calculate the density profiles for the grafted layer. These profiles clearly reveal the dimpled surface. Both methods are sufficiently general to be useful in examining a variety of problems involving polymers at interfaces.

Conservative dynamics, phase ordering and stretched exponential decays

The authors discuss the dynamics of an observable field related to a locally conserved field. They show that for a model of phase ordering dynamics and for a variation of model C critical dynamics, that the two-time momentum space correlation function decays asymptotically as a stretched exponential. They show that under some conditions the asymptotic behaviour is experimentally observable and argue that the non-exponential behaviour is not a feature specific to these models but should rather apply for any observable coupled to a locally conserved field.