Compact Expansion of a Repulsive Suspension.

Short-range repulsion governs the dynamics of matter from atoms to animals. Using theory, simulations, and experiments, we find that an ensemble of repulsive particles spreads compactly with a sharp boundary, in contrast to the diffusive spreading of Brownian particles. Starting from the pair interactions, at high densities, the many-body dynamics follow nonlinear diffusion with a self-similar expansion, growing as t^{1/4}; At longer times, thermal motion dominates with the classic t^{1/2} expansion. A logarithmic growth controlled by nearest-neighbor interactions connects the two self-similar regimes.

Hydrodynamically induced aggregation of two dimensional oriented active particles.

We investigate a system of co-oriented active particles interacting only via hydrodynamic and steric interactions in a two-dimensional fluid. We offer a new method of calculating the flow created by any active particle in such a fluid, focusing on the dynamics of flow fields with a high-order spatial decay, which we analyze using a geometric Hamiltonian. We show that when the particles are oriented and the flow has a single, odd power decay, such systems lead to stable, fractal-like aggregation, with the only exception being the force dipole. We discuss how our results can easily be generalized to more complicated force distributions and to other effective two-dimensional systems.

Hamiltonian Dynamics and Structural States of Two-Dimensional Active Particles.

We show that a two-dimensional system of flocking active particles interacting hydrodynamically can be expressed using a Hamiltonian formalism. The Hamiltonian depends strictly on the angles between the particles and their orientation, thereby restricting their available phase-space. Simulations of co-oriented active particles evolve into "escalators"-sharp lines at a particular tilt along which particles circulate. The conservation of the Hamiltonian and its symmetry germinate the self-assembly of the observed steady-state arrangements as confirmed by stability analysis.

Hyperuniformity and phase enrichment in vortex and rotor assemblies.

Ensembles of particles rotating in a two-dimensional fluid can exhibit chaotic dynamics yet develop signatures of hidden order. Such rotors are found in the natural world spanning vastly disparate length scales - from the rotor proteins in cellular membranes to models of atmospheric dynamics. Here we show that an initially random distribution of either driven rotors in a viscous membrane, or ideal vortices with minute perturbations, spontaneously self assemble into a distinct arrangement. Despite arising from drastically different physics, these systems share a Hamiltonian structure that sets geometrical conservation laws resulting in prominent structural states. We find that the rotationally invariant interactions isotropically suppress long-wavelength fluctuations - a hallmark of a disordered hyperuniform material. With increasing area fraction, the system orders into a hexagonal lattice. In mixtures of two co-rotating populations, the stronger population will gain order from the other and both will become phase enriched. Finally, we show that classical 2D point vortex systems arise as exact limits of the experimentally accessible microscopic membrane rotors, yielding a new system through which to study topological defects.

Rotating Membrane Inclusions Crystallize Through Hydrodynamic and Steric Interactions.

We show that rotating membrane inclusions can crystallize due to combined hydrodynamic and steric interactions. Alone, steric repulsion of unconfined particles, even with thermal fluctuations, does not lead to crystallization, nor do rotational hydrodynamic interactions which allow only a marginally stable lattice. Hydrodynamic interactions enable particles to explore states inaccessible to a nonrotational system, yet, unlike Brownian motion, Hamiltonian conservation confines the ensemble which, when combined with steric interactions, anneals into a stable crystal state.

Effect of Hydrodynamic Interactions on Reaction Rates in Membranes.

The Brownian motion of two particles in three dimensions serves as a model for predicting the diffusion-limited reaction rate, as first discussed by von Smoluchowski. Deutch and Felderhof extended the calculation to account for hydrodynamic interactions between the particles and the target, which results in a reduction of the rate coefficient by about half. Many chemical reactions take place in quasi-two-dimensional systems, such as on the membrane or surface of a cell. We perform a Smoluchowski-like calculation in a quasi-two-dimensional geometry, i.e., a membrane surrounded by fluid, and account for hydrodynamic interactions between the particles. We show that rate coefficients are reduced relative to the case of no interactions. The reduction is more pronounced than the three-dimensional case due to the long-range nature of two-dimensional flows.

Shapeable sheet without plastic deformation.

Randomly crumpled sheets have shape memory. In order to understand the basis of this form of memory, we simulate triangular lattices of springs whose lengths are altered to create a topography with multiple potential energy minima. We then deform these lattices into different shapes and investigate their ability to retain the imposed shape when the energy is relaxed. The lattices are able to retain a range of curvatures. Under moderate forcing from a state of local equilibrium, the lattices deform by several percent but return to their retained shape when the forces are removed. By increasing the forcing until an irreversible motion occurs, we find that the transitions between remembered shapes show cooperativity among several springs. For fixed lattice structures, the shape memory tends to decrease as the lattice is enlarged; we propose ways to counter this decrease by modifying the lattice geometry. We survey the energy landscape by displacing individual nodes. An extensive fraction of these nodes proves to be bistable; they retain their displaced position when the energy is relaxed. Bending the lattice to a stable curved state alters the pattern of bistable nodes. We discuss this shapeability in the context of other forms of material memory and contrast it with the shapeability of plastic deformation. We outline the prospects for making real materials based on these principles.

Why do sleeping nematodes adopt a hockey-stick-like posture?

A characteristic posture is considered one of the behavioral hallmarks of sleep, and typically includes functional features such as support for the limbs and shielding of sensory organs. The nematode C. elegans exhibits a sleep-like state during a stage termed lethargus, which precedes ecdysis at the transition between larval stages. A hockey-stick-like posture is commonly observed during lethargus. What might its function be? It was previously noted that during lethargus, C. elegans nematodes abruptly rotate about their longitudinal axis. Plausibly, these "flips" facilitate ecdysis by assisting the disassociation of the old cuticle from the new one. We found that body-posture during lethargus was established using a stereotypical motor program and that body bends during lethargus quiescence were actively maintained. Moreover, flips occurred almost exclusively when the animals exhibited a single body bend, preferentially in the anterior or mid section of the body. We describe a simple biomechanical model that imposes the observed lengths of the longitudinally directed body-wall muscles on an otherwise passive elastic rod. We show that this minimal model is sufficient for generating a rotation about the anterior-posterior body axis. Our analysis suggests that posture during lethargus quiescence may serve a developmental role in facilitating flips and that the control of body wall muscles in anterior and posterior body regions are distinct.

Anomalously fast kinetics of lipid monolayer buckling.

We reexamine previous observations of folding kinetics of compressed lipid monolayers in light of the accepted mechanical buckling mechanism recently proposed by L. Pocivavsek et al. [Science 320, 912 (2008)]. Using simple models, we set conservative limits on (a) the energy released in the mechanical buckling process and (b) the kinetic energy entailed by the observed folding motion. These limits imply a kinetic energy at least 30 times greater than the energy supplied by the buckling instability. We discuss possible extensions of the accepted picture that might resolve this discrepancy.

In-plane dynamics of membranes with immobile inclusions.

Cell membranes are anchored to the cytoskeleton via immobile inclusions. We investigate the effect of such anchors on the in-plane dynamics of a fluid membrane and mobile inclusions (proteins) embedded in it. The immobile particles lead to a decreased diffusion coefficient of mobile ones and suppress the correlated diffusion of particle pairs. Because of the long-range, quasi-two-dimensional nature of membrane flows, these effects become significant at a low area fraction (below 1%) of immobile inclusions.

Correlated dynamics of inclusions in a supported membrane.

The hydrodynamic theory of heterogeneous fluid membranes is extended to the case of a membrane adjacent to a solid substrate. We derive the coupling diffusion coefficients of pairs of membrane inclusions in the limit of large separation compared to the inclusion size. Two-dimensional compressive stresses in the membrane make the coupling coefficients decay asymptotically as 1/r(2) with interparticle distance r. For the common case, where the distance to the substrate is of submicrometer scale, we present expressions for the coupling between distant disklike inclusions, which are valid for arbitrary inclusion size. We calculate the effect of inclusions on the response of the membrane and the associated corrections to the coupling diffusion coefficients to leading order in the concentration of inclusions. While at short distances the response is modified as if the membrane were a two-dimensional suspension, the large-distance response is not renormalized by the inclusions.

Correlated diffusion of membrane proteins and their effect on membrane viscosity.

We extend the Saffman theory of membrane hydrodynamics to account for the correlated motion of membrane proteins, along with the effect of protein concentration on that correlation and on the response of the membrane to stresses. Expressions for the coupling diffusion coefficients of protein pairs and their concentration dependence are derived in the limit of small protein size relative to the interprotein separation. The additional role of membrane viscosity as determining the characteristic length scale for membrane response leads to unusual concentration effects at large separation-the transverse coupling increases with protein concentration, whereas the longitudinal one becomes concentration-independent.