Orientational Correlations in Active and Passive Nematic Defects

We investigate the emergence of orientational order among +1/2 disclinations in active nematic liquid crystals. Using a combination of theoretical and experimental methods, we show that +1/2 disclinations have short-range antiferromagnetic alignment, as a consequence of the elastic torques originating from their polar structure. The presence of intermediate -1/2 disclinations, however, turns this interaction from antialigning to aligning at scales that are smaller than the typical distance between like-sign defects. No long-range orientational order is observed. Strikingly, these effects are insensitive to material properties and qualitatively similar to what is found for defects in passive nematic liquid crystals.

Geometrical Control of Active Turbulence in Curved Topographies

We investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal constrained to a curved surface. Using a combination of hydrodynamic and particle-based simulations, we demonstrate that the fundamental structural features of the fluid, such as the topological charge density, the defect number density, the nematic order parameter, and defect creation and annihilation rates, are approximately linear functions of the substrate Gaussian curvature, which then acts as a control parameter for the chaotic flow. Our theoretical predictions are then compared with experiments on microtubule-kinesin suspensions confined on toroidal droplets, finding excellent qualitative agreement.

Cellular geometry controls the efficiency of motile sperm aggregates

Sperm that swim collectively to the fertilization site have been observed across several vertebrate and invertebrate species, with groups ranging in size from sperm pairs to massive aggregates containing hundreds of cells. Although the molecular mechanisms that regulate sperm-sperm adhesion are still unclear, aggregation can enhance sperm motility and thus offer a fertilization advantage. Here, we report a thorough computational investigation on the role of cellular geometry in the performance of sperm aggregates. The sperm head is modelled as a persistent random walker characterized by a non-trivial three-dimensional shape and equipped with an adhesive region where cell-cell binding occurs. By considering both, a simple parametric head shape and a computer reconstruction of a real head shape based on morphometric data, we demonstrate that the geometry of the head and the structure of the adhesive region crucially affects both the stability and motility of the aggregates. Our analysis further suggests that the apical hook commonly found in the sperm of muroid rodents might serve to shield portions of the adhesive region and promote efficient alignment of the velocities of the interacting cells.

Turbulent Dynamics of Epithelial Cell Cultures

We investigate the large length and long time scales collective flows and structural rearrangements within in vitro human bronchial epithelial cell (HBEC) cultures. Activity-driven collective flows result in ensembles of vortices randomly positioned in space. By analyzing a large population of vortices, we show that their area follows an exponential law with a constant mean value and their rotational frequency is size independent, both being characteristic features of the chaotic dynamics of active nematic suspensions. Indeed, we find that HBECs self-organize in nematic domains of several cell lengths. Nematic defects are found at the interface between domains with a total number that remains constant due to the dynamical balance of nucleation and annihilation events. The mean velocity fields in the vicinity of defects are well described by a hydrodynamic theory of extensile active nematics.

Swarming, swirling and stasis in sequestered bristle-bots

The collective ability of organisms to move coherently in space and time is ubiquitous in any group of autonomous agents that can move and sense each other and the environment. Here, we investigate the origin of collective motion and its loss using macroscopic self-propelled bristle-bots, simple automata made from a toothbrush and powered by an onboard cell phone vibrator-motor, that can sense each other through shape-dependent local interactions, and can also sense the environment non-locally via the effects of confinement and substrate topography. We show that when bristle-bots are confined to a limited arena with a soft boundary, increasing the density drives a transition from a disordered and uncoordinated motion to organized collective motion either as a swirling cluster or a collective dynamical stasis. This transition is regulated by a single parameter, the relative magnitude of spinning and walking in a single automaton. We explain this using quantitative experiments and simulations that emphasize the role of the agent shape, environment and confinement via boundaries. Our study shows how the behavioural repertoire of these physically interacting automatons controlled by one parameter translates into the mechanical intelligence of swarms.

Minimal surfaces bounded by elastic lines

In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution to the Plateau problem. But what happens if a soap film spans a loop of inextensible but flexible wire? We consider this simple query that couples Plateau's problem to Euler's Elastica : a special class of twist-free curves of given length that minimize their total squared curvature energy. The natural marriage of two of the oldest geometrical problems linking physics and mathematics leads to a quest for the shape of a minimal surface bounded by an elastic line: the Euler–Plateau problem. We use a combination of simple physical experiments with soap films that span soft filaments and asymptotic analysis combined with numerical simulations to explore some of the richness of the shapes that result. Our study raises questions of intrinsic interest in geometry and its natural links to a range of disciplines, including materials science, polymer physics, architecture and even art.

Multi-stability of free spontaneously curved anisotropic strips

Multi-stable structures are objects with more than one stable conformation, exemplified by the simple switch. Continuum versions are often elastic composite plates or shells, such as the common measuring tape or the slap bracelet, both of which exhibit two stable configurations: rolled and unrolled. Here, we consider the energy landscape of a general class of multi-stable anisotropic strips with spontaneous Gaussian curvature. We show that while strips with non-zero Gaussian curvature can be bistable, and strips with positive spontaneous curvature are always bistable, independent of the elastic moduli, strips of spontaneous negative curvature are bistable only in the presence of spontaneous twist and when certain conditions on the relative stiffness of the strip in tension and shear are satisfied. Furthermore, anisotropic strips can become tristable when their bending rigidity is small. Our study complements and extends the theory of multi-stability in anisotropic shells and suggests new design criteria for these structures.

Excitable patterns in active nematics

We analyze a model of mutually propelled filaments suspended in a two-dimensional solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations, and the nematic order parameter is allowed to vary in space and time. We show that the interplay between nonuniform nematic order, activity, and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media. In this regime the dynamics consists of nearly stationary periods separated by "bursts" of activity in which the system is elastically distorted and solvent is pumped throughout. At even higher activity, the dynamics becomes chaotic.

Statistical mechanics of developable ribbons

We investigate the statistical mechanics of long developable ribbons of finite width and very small thickness. The constraint of isometric deformations in these ribbonlike structures that follows from the geometric separation of scales introduces a coupling between bending and torsional degrees of freedom. Using analytical techniques and Monte Carlo simulations, we find that the tangent-tangent correlation functions always exhibit an oscillatory decay at any finite temperature implying the existence of an underlying helical structure even in the absence of a preferential zero-temperature twist. In addition, the persistence length is found to be over 3 times larger than that of a wormlike chain having the same bending rigidity. Our results are applicable to many ribbonlike objects in polymer physics and nanoscience that cannot be described by the classical wormlike chain model.

Pak3 inhibits local actin filament formation to regulate global cell polarity

Lamellipodia are broad actin-based structures that define the protruding edge of many motile animal cells. Here we identify a Drosophila homolog of the p21-activated kinases (Paks) as a novel inhibitor of Rac-mediated lamellipodial formation: Pak3 overexpression mimics a loss of Rac activity, while Pak3 RNAi-mediated silencing enhances lamellipodial dynamics. Strikingly, the depletion of Pak3 also polarizes the cellular distribution of actin filaments, is sufficient to induce nonmotile cells to migrate, and, in cells firmly attached to the substrate, gives rise to a wave of high actin filament density that encircles the cell periphery at a steady pace. To better understand these systems level phenomena, we developed a model of the cortical actin network as an active gel whose behavior is dominated by the rate of actin filament bundling and polymer synthesis. In the presence of filament treadmilling, this system generates a propagating density wave of actin filaments like that seen in Pak3 RNAi cells. This analysis reveals an intimate relationship between local regulation of actin filament dynamics and global cytoskeletal polarity, and suggests a role for negative regulators of lamellipodial formation, like Pak3, in the maintenance of a poised state, in which regulated directional cell movement can occur.

Elastic theory of defects in toroidal crystals

We report a comprehensive analysis of the ground-state properties of axisymmetric toroidal crystals based on the elastic theory of defects on curved substrates. The ground state is analyzed as a function of the aspect ratio of the torus, which provides a non-local measure of the underlying Gaussian curvature, and the ratio of the defect core energy to the Young modulus. Several structural features are discussed, including a spectacular example of curvature-driven amorphization in the limit of the aspect ratio approaching one. The outcome of the elastic theory is then compared with the results of a numerical study of a system of point-like particles constrained on the surface of a torus and interacting via a short-range potential.