Velocity correlations in an active nematic

Active Model H: Scalar Active Matter in a Momentum-Conserving Fluid

We present a continuum theory of self-propelled particles, without alignment interactions, in a momentum-conserving solvent. To address phase separation, we introduce a dimensionless scalar concentration field ϕ with advective-diffusive dynamics. Activity creates a contribution Σ_{ij}=-κ[over ^][(∂_{i}ϕ)(∂_{j}ϕ)-(∇ϕ)^{2}δ_{ij}/d] to the deviatoric stress, where κ[over ^] is odd under time reversal and d is the number of spatial dimensions; this causes an effective interfacial tension contribution that is negative for contractile swimmers. We predict that domain growth then ceases at a length scale where diffusive coarsening is balanced by active stretching of interfaces, and confirm this numerically. Thus, there is a subtle interplay of activity and hydrodynamics, even without alignment interactions.

Celebrating Soft Matter's 10th Anniversary: Cell division: a source of active stress in cellular monolayers

We introduce the notion of cell division-induced activity and show that the cell division generates extensile forces and drives dynamical patterns in cell assemblies. Extending the hydrodynamic models of lyotropic active nematics we describe turbulent-like velocity fields that are generated by the cell division in a confluent monolayer of cells. We show that the experimentally measured flow field of dividing Madin-Darby Canine Kidney (MDCK) cells is reproduced by our modeling approach. Division-induced activity acts together with intrinsic activity of the cells in extensile and contractile cell assemblies to change the flow and director patterns and the density of topological defects. Finally we model the evolution of the boundary of a cellular colony and compare the fingering instabilities induced by cell division to experimental observations on the expansion of MDCK cell cultures.

Turbulence of swarming sperm

Collective motion of self-sustained swarming flows has recently provided examples of small-scale turbulence arising where viscous effects are dominant. We report the first observation of universal enstrophy cascade in concentrated swarming sperm consistent with a body of evidence built from various independent measurements. We found a well-defined k^{-3} power-law decay of a velocity field power spectrum and relative dispersion of small beads consistent with theoretical predictions in 2D turbulence. Concentrated living sperm displays long-range, correlated whirlpool structures of a size that provides an integral scale of turbulence. We propose a consistent explanation for this quasi-2D turbulence based on self-structured laminated flow forced by steric interactions and alignment, a state of active matter that we call "swarming liquid crystal." We develop scaling arguments consistent with this interpretation.

Active viscoelastic matter: from bacterial drag reduction to turbulent solids

A paradigm for internally driven matter is the active nematic liquid crystal, whereby the equations of a conventional nematic are supplemented by a minimal active stress that violates time-reversal symmetry. In practice, active fluids may have not only liquid-crystalline but also viscoelastic polymer degrees of freedom. Here we explore the resulting interplay by coupling an active nematic to a minimal model of polymer rheology. We find that adding a polymer can greatly increase the complexity of spontaneous flow, but can also have calming effects, thereby increasing the net throughput of spontaneous flow along a pipe (a "drag-reduction" effect). Remarkably, active turbulence can also arise after switching on activity in a sufficiently soft elastomeric solid.

Multiscale polar theory of microtubule and motor-protein assemblies

Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new "bioactive" liquid-crystalline fluids that are intrinsically out of equilibrium and which display complex flows and defect dynamics. It is not yet well understood how microscopic activity, which involves polarity-dependent interactions between motor proteins and microtubules, yields such larger-scale dynamical structures. In our multiscale theory, Brownian dynamics simulations of polar microtubule ensembles driven by cross-linking motors allow us to study microscopic organization and stresses. Polarity sorting and cross-link relaxation emerge as two polar-specific sources of active destabilizing stress. On larger length scales, our continuum Doi-Onsager theory captures the hydrodynamic flows generated by polarity-dependent active stresses. The results connect local polar structure to flow structures and defect dynamics.

Biphasic, lyotropic, active nematics

We perform dynamical simulations of a two-dimensional active nematic fluid in coexistence with an isotropic fluid. Drops of active nematic become elongated, and an effective anchoring develops at the nematic-isotropic interface. The activity also causes an undulatory instability of the interface. This results in defects of positive topological charge being ejected into the nematic, leaving the interface with a diffuse negative charge. Quenching the active lyotropic fluid results in a steady state in which phase-separating domains are elongated and then torn apart by active stirring.

Active nematic materials with substrate friction

Active turbulence in dense active systems is characterized by high vorticity on a length scale that is large compared to that of individual entities. We describe the properties of active turbulence as momentum propagation is screened by frictional damping. As friction is increased, the spacing between the walls in the nematic director field decreases as a consequence of the more rapid velocity decays. This leads to, first, a regime with more walls and an increased number of topological defects, and then to a jammed state in which the walls deliminate bands of opposing flow, analogous to the shear bands observed in passive complex fluids.

Defect dynamics in active nematics

Topological defects are distinctive signatures of liquid crystals. They profoundly affect the viscoelastic behaviour of the fluid by constraining the orientational structure in a way that inevitably requires global changes not achievable with any set of local deformations. In active nematic liquid crystals, topological defects not only dictate the global structure of the director, but also act as local sources of motion, behaving as self-propelled particles. In this article, we present a detailed analytical and numerical study of the mechanics of topological defects in active nematic liquid crystals.

Tunable dynamics of microtubule-based active isotropic gels

We investigate the dynamics of an active gel of bundled microtubules (MTs) that is driven by clusters of kinesin molecular motors. Upon the addition of ATP, the coordinated action of thousands of molecular motors drives the gel to a highly dynamical turbulent-like state that persists for hours and is only limited by the stability of constituent proteins and the availability of the chemical fuel. We characterize how enhanced transport and emergent macroscopic flows of active gels depend on relevant molecular parameters, including ATP, kinesin motor and depletant concentrations, MT volume fraction, as well as the stoichiometry of the constituent motor clusters. Our results show that the dynamical and structural properties of MT-based active gels are highly tunable. They also indicate existence of an optimal concentration of molecular motors that maximize far-from-equilibrium activity of active isotropic MT gels.

Aspects of the density field in an active nematic

Active nematics are conceptually the simplest orientationally ordered phase of self-driven particles, but have proved to be a perennial source of surprises. We show here through numerical solution of coarse-grained equations for the order parameter and density that the growth of the active nematic phase from the isotropic phase is necessarily accompanied by a clumping of the density. The growth kinetics of the density domains is shown to be faster than the [Formula: see text] law expected for variables governed by a conservation law. Other results presented include the suppression of density fluctuations in the stationary ordered nematic by the imposition of an orienting field. We close by posing some open questions.

Vorticity, defects and correlations in active turbulence

We describe a numerical investigation of a continuum model of an active nematic, concentrating on the regime of active turbulence. Results are presented for the effect of three parameters, activity, elastic constant and rotational diffusion constant, on the order parameter and flow fields. Defects and distortions in the director field act as sources of vorticity, and thus vorticity is strongly correlated to the director field. In particular, the characteristic length of decay of vorticity and order parameter correlations is controlled by the defect density. By contrast, the decay of velocity correlations is determined by a balance between activity and dissipation. We highlight the role of microscopic flow generation mechanisms in determining the flow patterns and characteristic scales of active turbulence and contrast the behaviour of extensile and contractile active nematics.

Topology and dynamics of active nematic vesicles

Engineering synthetic materials that mimic the remarkable complexity of living organisms is a fundamental challenge in science and technology. We studied the spatiotemporal patterns that emerge when an active nematic film of microtubules and molecular motors is encapsulated within a shape-changing lipid vesicle. Unlike in equilibrium systems, where defects are largely static structures, in active nematics defects move spontaneously and can be described as self-propelled particles. The combination of activity, topological constraints, and vesicle deformability produces a myriad of dynamical states. We highlight two dynamical modes: a tunable periodic state that oscillates between two defect configurations, and shape-changing vesicles with streaming filopodia-like protrusions. These results demonstrate how biomimetic materials can be obtained when topological constraints are used to control the non-equilibrium dynamics of active matter.

Large-scale chaos and fluctuations in active nematics

We show that dry active nematics, e.g., collections of shaken elongated granular particles, exhibit large-scale spatiotemporal chaos made of interacting dense, ordered, bandlike structures in a parameter region including the linear onset of nematic order. These results are obtained from the study of both the well-known (deterministic) hydrodynamic equations describing these systems and of the self-propelled particle model they were derived from. We prove, in particular, that the chaos stems from the generic instability of the band solution of the hydrodynamic equations. Revisiting the status of the strong fluctuations and long-range correlations in the particle model, we show that the giant number fluctuations observed in the chaotic phase are a trivial consequence of density segregation. However anomalous, curvature-driven number fluctuations are present in the homogeneous quasiordered nematic phase and characterized by a nontrivial scaling exponent.

Topological structure dynamics revealing collective evolution in active nematics

Topological defects frequently emerge in active matter like bacterial colonies, cytoskeleton extracts on substrates, self-propelled granular or colloidal layers and so on, but their dynamical properties and the relations to large-scale organization and fluctuations in these active systems are seldom touched. Here we reveal, through a simple model for active nematics using self-driven hard elliptic rods, that the excitation, annihilation and transportation of topological defects differ markedly from those in non-active media. These dynamical processes exhibit strong irreversibility in active nematics in the absence of detailed balance. Moreover, topological defects are the key factors in organizing large-scale dynamic structures and collective flows, resulting in multi-spatial temporal effects. These findings allow us to control the self-organization of active matter through topological structures.

Topological defects are observed in a range of active systems, but their dynamical properties are largely unknown. Here, the authors use a simulation of self-propelled hard-rods to generate topological defects in active nematics, finding that their anomalous dynamics may lead to large-scale collective motions.

Nonequilibrium structure and dynamics in a microscopic model of thin-film active gels

In the presence of adenosine triphosphate, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modeling can help to quantify the relationship between individual motors plus filaments to organization and dynamics on molecular and supramolecular length scales. Here, we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between filaments are included. A systematic variation of rates for motor motion, attachment, and detachment, including a differential detachment rate from filament ends, reveals a range of nonequilibrium behavior. Strong motor binding produces structured filament aggregates that we refer to as asters, bundles, or layers, whose stability depends on motor speed and differential end detachment. The gross features of the dependence of the observed structures on the motor rate and the filament concentration can be captured by a simple one-filament model. Loosely bound aggregates exhibit superdiffusive mass transport, where filament translocation scales with lag time with nonunique exponents that depend on motor kinetics. An empirical data collapse of filament speed as a function of motor speed and end detachment is found, suggesting a dimensional reduction of the relevant parameter space. We conclude by discussing the perspectives of microscopic modeling in the field of active gels.

Living liquid crystals

Collective motion of self-propelled organisms or synthetic particles, often termed "active fluid," has attracted enormous attention in the broad scientific community because of its fundamentally nonequilibrium nature. Energy input and interactions among the moving units and the medium lead to complex dynamics. Here, we introduce a class of active matter--living liquid crystals (LLCs)--that combines living swimming bacteria with a lyotropic liquid crystal. The physical properties of LLCs can be controlled by the amount of oxygen available to bacteria, by concentration of ingredients, or by temperature. Our studies reveal a wealth of intriguing dynamic phenomena, caused by the coupling between the activity-triggered flow and long-range orientational order of the medium. Among these are (i) nonlinear trajectories of bacterial motion guided by nonuniform director, (ii) local melting of the liquid crystal caused by the bacteria-produced shear flows, (iii) activity-triggered transition from a nonflowing uniform state into a flowing one-dimensional periodic pattern and its evolution into a turbulent array of topological defects, and (iv) birefringence-enabled visualization of microflow generated by the nanometers-thick bacterial flagella. Unlike their isotropic counterpart, the LLCs show collective dynamic effects at very low volume fraction of bacteria, on the order of 0.2%. Our work suggests an unorthodox design concept to control and manipulate the dynamic behavior of soft active matter and opens the door for potential biosensing and biomedical applications.

Dynamics of defects in an active nematic layer

Defect dynamics in a thin active nematic layer is studied by asymptotic matching of solutions in the defect core and the far field. The analysis is facilitated by the correspondence between the two-dimensional nematic and complex scalar field models. Self-propulsion and topological interactions are identified as the primary drivers of the defect motion, surpassing the influence of both passive backflow and active flow induced by other defects.