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Active matter systems - such as a collection of active colloidal particles - operate far from equilibrium with complex inter-particle interactions that govern their collective dynamics. Predicting the collective dynamics of such systems may aid the design of self-shaping structures comprised of active colloidal units with a prescribed dynamical function. Here, using simulations and theory, we study the collective dynamics of a chain consisting of active Brownian particles with internal interactions via trail-mediated chemicals, connected by harmonic springs in two dimensions to obtain design principles for active colloidal molecules. We show that two-dimensional confinement and chemo-repulsive interactions between the freely-jointed particles lead to an emergent rigidity of the chain in the steady-state dynamics. In the chemo-attractive regime, the chain collapses into crystals that abruptly halt their motion. Further, in a chain consisting of a binary mixture of monomers, we show that non-reciprocal chemical affinities between distinct species give rise to novel phenomena, such as chiral molecules with tunable dynamics, sustained undulatory gaits and reversal of the direction of motion. Our results suggest a novel interpretation of the role of trail-mediated interactions, in addition to providing active self-assembly principles arising due to non-reciprocal interactions., Comment: 19 pages. 10 Figures

The field of synthetic active matter has, thus far, been led by efforts to create point-like, isolated (yet interacting) self-propelled objects (\emph{e.g.} colloids, droplets, microrobots) and understanding their collective dynamics. The design of flexible, freely jointed active assemblies from autonomously powered components remains a challenge. Here, we report freely-jointed active polymers created using self-propelled droplets as monomeric units. Our experiments reveal that the self-shaping chemo-hydrodynamic interactions between the monomeric droplets give rise to an emergent rigidity (the acquisition of a stereotypical asymmetric C-shape) and associated ballistic propulsion of the active polymers. The rigidity and propulsion of the chains vary systematically with their lengths. Using simulations of a minimal model, we establish that the emergent polymer dynamics are a generic consequence of quasi two-dimensional confinement and auto-repulsive trail-mediated chemical interactions between the freely jointed active droplets. Finally, we tune the interplay between the chemical and hydrodynamic fields to experimentally demonstrate oscillatory dynamics of the rigid polymer propulsion. Altogether, our work highlights the possible first steps towards synthetic self-morphic active matter., Comment: 15 pages. 8 Figures

An important transition after the origin of life was the first emergence of a Darwinian population, self-reproducing entities exhibiting differential reproduction, phenotypic variation, and inheritance of phenotypic traits. The simplest system we can imagine to have these properties would consist of a compartmentalized autocatalytic reaction system that exhibits two growth states with different chemical compositions. Identifying the chemical composition as the phenotype, this accounts for two of the properties. However, it is not clear what are the necessary conditions for such a chemical system to exhibit inheritance of the compositional states upon growth and division of the compartment. We show that for a general class of autocatalytic chemical systems subject to serial dilution, the inheritance of compositional information only occurs when the time interval between dilutions is below a critical threshold that depends on the efficiency of the catalytic reactions. Further, we show that these thresholds provide rigorous bounds on the properties required for the inheritance of the chemical compositional state for general growth and division cycles. Our result suggests that a serial dilution experiment, which is much easier to set up in a laboratory, can be used to test whether a given autocatalytic chemical system can exhibit heredity. Lastly, we apply our results to a realistic autocatalytic system based on the Azoarcus ribozyme and suggest a protocol to experimentally test whether this system can exhibit heredity., Comment: 30 pages, 22 figures

Since steep declines in a population's size also typically alter its composition, population bottlenecks are considered highly important for evolution. However, despite such significance, the mechanisms governing the impact of a given population bottleneck remain poorly understood. In this context, we show that long-term post-bottleneck outcomes can depend crucially on the rate at which a diminished population grows whilst recovering. That is, two otherwise identical populations, each having undergone the same bottleneck, can fixate on dramatically different demographics due to different rates of post-bottleneck growth. This behaviour is moreover shown to change non-trivially with different levels of mutation. The underlying mechanism can be traced to intrinsic fluctuations whose standard deviation decreases in time with the inverse square root of the growing population size. Crucially, such decreasing fluctuations couple to the underlying dynamics and result in distinct regimes of (non-equilibrium) demographic behaviour, delimited by abrupt transitions at critical population sizes. Seen through this lens, growth and mutation alter evolutionary outcomes by changing the duration and character of dynamical phases; a feature that we speculate may be of generic importance across many systems.

A dilute suspension of active Brownian particles in a dense compressible viscoelastic fluid, forms a natural setting to study the emergence of nonreciprocity during a dynamical phase transition. At these densities, the transport of active particles is strongly influenced by the passive medium and shows a dynamical jamming transition as a function of activity and medium density. In the process, the compressible medium is actively churned up -for low activity, the active particle gets self-trapped in a spherical cavity of its own making, while for large activity, the active particle ploughs through the medium, either accompanied by a moving anisotropic wake, or leaving a porous trail. A hydrodynamic approach makes it evident that the active particle generates a long range density wake which breaks fore-aft symmetry, consistent with the simulations. Accounting for the back reaction of the compressible medium leads to (i) dynamical jamming of the active particle, and (ii) a dynamical non-reciprocal attraction between two active particles moving along the same direction, with the trailing particle catching up with the leading one in finite time. We emphasize that these nonreciprocal effects appear only when the active particles are moving and so manifest in the vicinity of the jamming-unjamming transition., Comment: 11 pages, 6 figures

We study the collective dynamics of groups of whirligig beetles Dineutus discolor (Coleoptera: Gyrinidae) swimming freely on the surface of water. We extract individual trajectories for each beetle, including positions and orientations, and use this to discover (i) a density dependent speed scaling like $v\sim\rho^{-\nu}$ with $\nu\approx0.4$ over two orders of magnitude in density (ii) an inertial delay for velocity alignment of $\sim 13$ ms and (iii) coexisting high and low density phases, consistent with motility induced phase separation (MIPS). We modify a standard active brownian particle (ABP) model to a Corralled ABP (CABP) model that functions in open space by incorporating a density-dependent reorientation of the beetles, towards the cluster. We use our new model to test our hypothesis that a MIPS (or a MIPS like effect) can explain the co-occurrence of high and low density phases we see in our data. The fitted model then successfully recovers a MIPS-like condensed phase for $N=200$ and the absence of such a phase for smaller group sizes $N=50,100$., Comment: To be published in the Journal of the Royal Society Interface on 14 April 2021 - Accepted 23 March 2021

A distinguishing feature of active particles is the nature of the non-equilibrium noise driving their dynamics. Control of these noise properties is, therefore, of both fundamental and applied interest. We demonstrate emergent tuning of the active noise of a granular self-propelled particle by confining it to a quasi one-dimensional channel. We find that this particle, moving like an active Brownian particle (ABP) in two-dimensions, displays run-and-tumble (RTP) characteristics in confinement. We show that the dynamics of the relative orientation co-ordinate of the particle maps to that of a Brownian particle in a periodic potential subject to a constant force, in analogy to the dynamics of a molecular motor. This mapping captures the essential statistical characteristics of the one-dimensional RTP motion. Specifically, our theoretical analysis is in agreement with the empirical distributions of the relative orientation co-ordinate and the run-times (tumble-rates) of the particle. Finally, we explicitly control these emergent run-and-tumble like noise parameters by external driving. Altogether, our work illustrates geometry-induced tuning of the active dynamics of self-propelled units thus suggesting an independent route to harness their internal dynamics.

Active particles, including swimming microorganisms, autophoretic colloids and droplets, are known to self-organize into ordered structures at fluid-solid boundaries. The entrainment of particles in the attractive parts of their spontaneous flows has been postulated as a possible mechanism underlying this phenomenon. Here, combining experiments, theory and numerical simulations, we demonstrate the validity of this flow-induced ordering mechanism in a suspension of active emulsion droplets. We show that the mechanism can be controlled, with a variety of resultant ordered structures, by simply altering hydrodynamic boundary conditions. Thus, for flow in Hele-Shaw cells, metastable lines or stable traveling bands can be obtained by varying the cell height. Similarly, for flow bounded by a plane, dynamic crystallites are formed. At a no-slip wall the crystallites are characterised by a continuous out-of-plane flux of particles that circulate and re-enter at the crystallite edges, thereby stabilising them. At an interface where the tangential stress vanishes the crystallites are strictly two-dimensional, with no out-of-plane flux. We rationalize these experimental results by calculating, in each case, the slow viscous flow produced by the droplets and the dissipative, long-ranged, many-body active forces and torques between them. The results of numerical simulations of motion under the action of the active forces and torques are in excellent agreement with experiments. Our work elucidates the mechanism of flow-induced phase separation (FIPS) in active fluids, particularly active colloidal suspensions, and demonstrates its control by boundaries, suggesting new routes to geometric and topological phenomena in active matter.

Combining high-resolution single cell tracking experiments with numerical simulations, we show that starvation-induced fruiting body (FB) formation in Myxococcus xanthus is a phase separation driven by cells that tune their motility over time. The phase separation can be understood in terms of cell density and a dimensionless Peclet number that captures cell motility through speed and reversal frequency. Our work suggests that M. xanthus take advantage of a self-driven non-equilibrium phase transition that can be controlled at the single cell level.

Two symmetrically coupled populations of N oscillators with inertia $m$ display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendula. In particular, we report the first evidence of intermittent chaotic chimeras, where one population is synchronized and the other jumps erratically between laminar and turbulent phases. These states have finite life-times diverging as a power-law with N and m. Lyapunov analyses reveal chaotic properties in quantitative agreement with theoretical predictions for globally coupled dissipative systems., Comment: 6 pages, 5 figures SUbmitted to Physical Review E, as Rapid Communication

The formation of a collectively moving group benefits individuals within a population in a variety of ways such as ultra-sensitivity to perturbation, collective modes of feeding, and protection from environmental stress. While some collective groups use a single organizing principle, others can dynamically shift the behavior of the group by modifying the interaction rules at the individual level. The surface-dwelling bacterium Myxococcus xanthus forms dynamic collective groups both to feed on prey and to aggregate during times of starvation. The latter behavior, termed fruiting-body formation, involves a complex, coordinated series of density changes that ultimately lead to three-dimensional aggregates comprising hundreds of thousands of cells and spores. This multi-step developmental process most likely involves several different single-celled behaviors as the population condenses from a loose, two-dimensional sheet to a three-dimensional mound. Here, we use high-resolution microscopy and computer vision software to spatiotemporally track the motion of thousands of individuals during the initial stages of fruiting body formation. We find that a combination of cell-contact-mediated alignment and internal timing mechanisms drive a phase transition from exploratory flocking, in which cell groups move rapidly and coherently over long distances, to a reversal-mediated localization into streams, which act as slow-spreading, quasi-one-dimensional nematic fluids. These observations lead us to an active liquid crystal description of the myxobacterial development cycle., Comment: 16 pages, 5 figures

Long-living coupled transverse and longitudinal phonon modes are explored in dense and regular arrangements of flat microfluidic droplets. The collective oscillations are driven by hydrodynamic interactions between the confined droplets and can be excited in a controlled way. Experimental results are quantitatively compared to simulation results obtained by multi-particle collision dynamics. The observed transverse modes are acoustic phonons and can be described by a linearized far-field theory, whereas the longitudinal modes arise from a non-linear mode coupling due to the lateral variation of the flow field under confinement.

The synchronization of coupled oscillators is a fascinating manifestation of self-organization that nature employs to orchestrate essential processes of life, such as the beating of the heart. Although it was long thought that synchrony or disorder were mutually exclusive steady states for a network of identical oscillators, numerous theoretical studies in recent years have revealed the intriguing possibility of `chimera states', in which the symmetry of the oscillator population is broken into a synchronous and an asynchronous part. However, a striking lack of empirical evidence raises the question of whether chimeras are indeed characteristic to natural systems. This calls for a palpable realization of chimera states without any fine-tuning, from which physical mechanisms underlying their emergence can be uncovered. Here, we devise a simple experiment with mechanical oscillators coupled in a hierarchical network to show that chimeras emerge naturally from a competition between two antagonistic synchronization patterns. We identify a wide spectrum of complex states, encompassing and extending the set of previously described chimeras. Our mathematical model shows that the self-organization observed in our experiments is controlled by elementary dynamical equations from mechanics that are ubiquitous in many natural and technological systems. The symmetry breaking mechanism revealed by our experiments may thus be prevalent in systems exhibiting collective behaviour, such as power grids, opto-mechanical crystals or cells communicating via quorum sensing in microbial populations., Comment: Main text, supplementary info and 3 ancillary movies

We study water-in-oil emulsion droplets, running the Belousov-Zhabotinsky reaction, that form a new type of active matter unit. These droplets, stabilised by surfactants dispersed in the oil medium, are capable of internal chemical oscillations and also self-propulsion due to dynamic interfacial instabilities that result from the chemical reactions. The chemical oscillations can couple via the exchange of activator and inhibitor type of reaction intermediates across the droplets under precise conditions of surfactant bilayer formation between the droplets. Here we present the synchronization behaviour of networks of such chemical oscillators and show that the resulting dynamics depend on the network topology. Further, we demonstrate that the motion of droplets can be synchronized with the chemical oscillations inside the droplets, leading to exciting possibilities in future studies of active matter.

We present a scheme of self-propelling liquid droplets which closely mimics the locomotion of some protozoal organisms, so-called squirmers. In contrast to other schemes proposed earlier, locomotion paths are not self-avoiding, since the effect of the squirmer on the surrounding medium is weak. Our results suggest that not only the velocity, but also the mode of operation (i.e., the spherical harmonics of the flow field) can be controlled by appropriate variation of parameters.

We outline a concept of self-assembled soft matter devices based on micro-fluidics, which use surfactant bilayer membranes as their main building blocks, arrested in geometric structures provided by top-down lithography. Membranes form spontaneously when suitable water-in-oil emulsions are forced into micro-fluidic channels at high dispersed-phase volume fractions. They turn out to be remarkably stable even when pumped through the micro-fluidic channel system. Their geometric arrangement is self-assembling, driven by interfacial energy and wetting forces. The ordered membrane arrays thus emerging can be loaded with amphiphilic functional molecules, ion channels, or just be used as they are, exploiting their peculiar physical properties. For wet electronic circuitry, the aqueous droplets then serve as the 'solder points'. Furthermore, the membranes can serve as well-controlled coupling media between chemical processes taking place in adjacent droplets. This is shown for the well-known Belousov-Zhabotinski reaction. Suitable channel geometries can be used to (re-) arrange the droplets, and thereby their contents, in a controlled way by just moving the emulsion through the device. It thereby appears feasible to construct complex devices out of molecular-size components in a self-assembled, but well controlled manner., Comment: 10 pages, 11 figures