New Perspectives in Active Systems

I will talk about a study of collective behavior in zebrafish and how modular deep nets can give you insight into the underlying rules. If time permits, I will switch gears and discuss an approach to agents solving simple math problems.

Swarms of insects, schools of fish and flocks of birds display an impressive variety of collective movement patterns that emerge from local interactions among group members. These puzzling phenomena raise a variety of questions about the interactions rules that govern the coordination of individuals’ motions and the emergence of large-scale patterns. While numerous models have been proposed, there is still a strong need for detailed experimental studies to foster the biological understanding of such collective motion phenomena. In the recent years we develop a method to characterize the social interactions between individual fish involved in the coordination of swimming in fish schools from data gathered at the individual scale. We used this method to investigate the interactions involved in the coordination of swimming in groups of Hemigrammus rhodostomus. This species of tropical fish performs burst-and-coast swimming behavior that consists of sudden heading changes combined with brief accelerations followed by quasi-passive, straight decelerations. Our results show that both attraction and alignment behaviors control the reaction of fish to a neighbor. We used these results to build a model of spontaneous burst-and-coast swimming and social interactions of fish, with all parameters being estimated or directly measured from experiments. This model shows that the simple addition of the pairwise interactions with two neighbors quantitatively reproduces the collective behavior observed in groups of fish. Overall, our results suggest that fish have to acquire only a minimal amount of information about their environment to coordinate their movements when swimming in groups.

Crowd movements can be observed across species and scales: from insects to mammals but also in non-cognitive systems such as eukaryotic cells. We are interested in the effect of complex environments on collective movements within a system barely explored so far: macroscopic aquatic agents, i.e. fish. To understand and model the interplay between social behavior and physical forces, we couple experiments in controlled environments, numerical simulations and statistical physics theory. For instance, what happens when gregarious animals have to momentarily adopt an individual behavior? To challenge the balance between herd and individual behaviours, a school of Neons (Paracheirodon innesi) was forced to cross a constriction. This experiment is reminiscent of panic crowd escaping through a narrow door. Using statistical analysis developed for granular matter and applied to crowd evacuation, our results clearly show that contrarily to human crowds or herds of sheep, no clogging is formed at the bottleneck. Fish don’t collide and wait by respecting their social distance and a minimum waiting time between two successive exits. When the constriction starts to be comparable to or smaller than their social distance, the individual domains fixed by this cognitive distance must deform and the fish density is increased. We show that the current of escaping fish indeed behaves as a set of deformable 2D-bubbles, their 2D domain, through a constriction and obeys the same law. With this original biological model, we show that a crowd of agents can indeed escape without a hustle contrary to the scenario often presented as universal so far. These results can lead to interesting progress in more applied topics such as swarm robotics, crowd management or the traffic flow of autonomous cars.

A unidimensional SPP model whit non-reciprocal interactions is studied in detail both, by computational simulations and coarse-grained equations. We demonstrate that by breaking the action-reaction symmetry it is possible to obtain global polar order from non-polar local interactions. This also leads to new ways of coarsening and the formation of aggregates whose speed, larger than the active speed of the particles, is enhanced by noise.

Cells in tissues consume fuel to sustain periodic mechanical deformation [1]. The combination of individual deformation and local interactions yields contraction waves, propagating throughout tissues with only negligible cell displacement [2]. We consider a model of dense repulsive particles whose activity drives periodic change in size of each individual [3]. It reveals that, in dense environments, pulsation of synchronised particles is a generic route to contraction waves. The competition between repulsion and synchronisation triggers an instability which promotes a wealth of dynamical patterns, ranging from spiral waves to defect turbulence. We identify the mechanisms underlying the emergence of patterns, and characterize the corresponding transitions. We derive the hydrodynamics of our model, and propose an analogy with that of reaction-diffusion systems. References: [1] S. Zehnder, M. Suaris, M. Bellaire, and T. Angelini. (2015) Cell volume fluctuations in MDCK monolayers, Biophys. J. [2] X. Serra-Picamal, V. Conte, R. Vincent, E. Anon, D. T. Tambe, E. Bazellieres, J. P. Butler, J. J. Fredberg, and X. Trepat. (2012) Mechanical waves during tissue expansion, Nat. Phys. [3] Y. Zhang and É. Fodor. (2022) Pulsating active matter, arXiv:2208.06831.

Studies of active matter, from molecular assemblies to animal groups, have revealed two broad classes of behavior: alignment interactions yield orientational order and collective motion, whereas repulsive interactions lead to self-trapping and motility-induced phase separation. I will present a third class of behavior: orientational interactions that produce active phase separation. Combining theory and experiments on self-propelled Janus colloids, we show that stronger repulsion on the rear than on the front of these particles produces non-reciprocal torques that reorient particle motion towards high-density regions. Particles thus self-propel towards crowded areas, which leads to phase separation. Because this torque-based aggregation requires no self-trapping, particles in clusters retain substantial speed, and clusters remain dilute and unjammed. Overall, our work identifies a torque-based mechanism for phase separation in active fluids, and it shows that orientational interactions can yield coexisting phases with no internal orientational order.

Collective behavior of animals is a fascinating example of self-organization in biology, which together with the underlying social interactions are believed to have emerged from evolutionary adaptations, and is widely assumed to confer fitness benefits to individuals, for example by enabling exchange of social information, promoting accurate collective decisions, or offering protection from predators. Based on theoretical arguments, it has been argued that distributed information processing systems in biology, including animal groups, should operate in a special parameter region close to a phase transition (critical point), where various aspects of collective computations become optimal. Here, we will investigate this "criticality hypothesis" in the context of animal collectives by combining model simulations and experimental data. We will explore the optimality of the order-disorder transition in collective movement, and whether individual-level evolutionary adaptation can lead to self-organization towards criticality. Further, by combining experimental and modeling work, we will investigate whether animal collectives, do indeed operate at - or close to - a phase transition, and what potential costs and benefits it entails, for example with respect to collective predator avoidance.

Collective motion is generally not a continuous process, and collectives display repeated transitions from static to moving phases. The initiation of collective motion – of an initially static group – is a crucial process to ensure group cohesion and behavioral synchrony that remains largely unexplored. Here, we investigate the statistical properties of the initiation of collective motion. We find that the information propagates as an activation wave, whose speed is modulated by the velocity of the active agents, where both, the magnitude and direction of the agents’ velocity play a crucial role. The analysis reveals a series of distinct dynamic regimes, including a selfish regimes that allow the first informed individuals to avoid predation by swapping position with uninformed individuals. Furthermore, we unravel the existence of a generic and intimate connection between the initiation of collective motion and critical phenomena in systems with an absorbing phase, showing that in a range of agents’ velocities the initiation process displays criticality. The obtained results provide an insight in the way collectives distribute, process, and respond to the local environmental cues.

How do cells respond to curvature? Does curvature has an influence on cell shape and movement? What are the consequences for collective behaviour of interacting cells in tissue? We address these questions using a multiphase field model on different curved surfaces and compare the results with experimental data on pillars, in tubes and other surfaces. The results show a significant influence of curvature and the possibility to effectively model the observed phenomena with classical models and additional curvature terms.

The past 25 years have seen a surge of experimental observations and theoretical progress in the description of phase separation and collective motion in the realm of active liquids. There are however a number of circumstances under which the description in terms of liquids is not suited. One can think of ants building solid bridges out of their bodies, meta-materials made of mechanically connected engines, cohesive cell layers or simply very dense assemblies of self propelled particles forming a glass or a crystal. In such cases a description in terms of elastic solid is likely to be more appropriate. However very little is known about the actuation of an elastic lattice by polar active particles, the orientations of which may couple to the displacement field. In this talk, I will present recent experimental and theoretical works aiming at developing this new path of research in active matter. Doing so, we shall unveil a new type of collective phenomena, namely collective actuation, and discover how the coupling between linear elasticity and activity leads to a rich selection mechanism of the actuated dynamics. We shall further unveil a second type of collective actuation driven by noise. Finally we will discuss the effect of an external polarizing field on the transitions towards collective actuation.

Epithelial cell sheets perform major biological functions by shaping the developing embryo, and they are equally important as barrier tissue in the adult, such as in the gut, or in the case of the corneal epithelium, the surface of the eye. This tissue consists of a thin layer of cells on a spherical cap, where cells are born at the edges (the limbus) and then migrate, divide, and are extruded in a steady-state spiral migration pattern with a vortex at the centre. In this talk, I will present a quantitative soft active matter model of this process. In a minimal approach, we model each cell as an active Brownian particle with a crawling speed, short-range interactions, orientational diffusion and alignment with other particles, as well as density-feedback division and death. First, we consider in in-vitro corneal cell sheets, where we identify a characteristic correlated velocity pattern that emerges from uncorrelated active persistent motion, a very general active effect. Using the fully fitted model to these in-vitro cells as well as corneal explants, we are able to simulate a full, spiralling cornea. The central spiral emerges as a +1 topological defect of the director and velocity fields, and is only present if the system crosses the flocking threshold in polar alignment. Thus we are able to identify the system as belonging to the class of polar systems without density conservation, and write a flux conservation equation for the spiral angle. We match the simulations with data obtained from tracing the stripes of dissected mouse eyes, from which we can infer the velocity field. We obtain good quantitative agreement on spiral angle, and renewal time of the tissue.

Self-organization is a hallmark of complex systems that are far from thermal equilibrium, such as biological systems ranging from sub-cellular constituents to multicellular organisms. Using motile bacteria as a model system, we seek to understand how biological active matter can self-organize in space and time. In this talk I will introduce several remarkable examples of ordering in bacterial active fluids and in biofilm-based active solids mediated by purely physical forces. I will also discuss how bacterial communities and other living systems may benefit from these mechanisms of ordering. The findings are relevant to microbial physiology, non-equilibrium physics, and active matter engineering.

Active solids comprise self-propelled agents embedded in a mechanically stable elastic matrix. They are governed by the interplay between their inherent self-propulsion activity and elasticity. If activity is small enough, vibrational modes of the solid are barely excited, and the network can be considered as effectively rigid. Although in this limit elastic deformations can be neglected, stress propagation can lead to collective motion. In this talk I will discuss a theoretical framework for strictly rigid structures, showing that in the presence of zero modes, any finite amount of activity leads to the emergence of collective steady states, whose stability are governed by the structure's geometry and a single dimensionless parameter. Combining this framework with numerical simulations and with the experimental study of centimetric-model active solids, we show that our predictions are robust to imperfections and to a finite amount of elasticity. In addition, we investigate the effect of noise showing that the dynamics of active solids can be mapped to equilibrium thermodynamic systems, for which exact results exist. In particular, mode selection and the existence of collective motion are determined by the minima of a thermodynamic-like potential.

In this presentation, I discuss purely deterministic aspects of active particle dynamics. First, I discuss how the overactive limit leads to Hamiltonian equations of motion of a particle in an external potential, and what happens at strong but finite activity. Further, I discuss models with different types of coupling between particles (acoustic interaction, coupling potentials, but also non-conservative alignment interaction) and dynamical regimes there. Typically, only small ensembles of particles are considered.

We study the dynamics of a chiral active particle subject to an external torque due to the presence of a gravitational field. Our computer simulations reveal an arbitrarily strong amplification of the long-time diffusivity of the gravitactic particle when the external torque approaches the intrinsic angular drift. We provide analytic expressions for the mean-square displacement in terms of eigenfunctions and eigenvalues of the noisy-driven-pendulum problem. The pronounced maximum in the diffusivity is then rationalized by the vanishing of the lowest eigenvalues of the Fokker-Planck equation for the angular motion as the rotational diffusion decreases. A simple harmonic-oscillator picture for the barrier-dominated motion provides a quantitative description for the onset of the resonance while its range of validity is determined by the crossover to a critical-fluctuation-dominated regime.

The motility patterns exhibited by bacteria on surfaces and in the bulk, i.e. in free 3D swimming are very different. On surfaces, bacteria display noisy circular trajectories, and in the bulk a motility pattern known as run-and-tumble. Each of these motility patterns has associated a characteristic diffusion coefficient. How can we understand and describe their full motion in a tube, combining the two distinct kinds of behaviors, and the transitions between the two? We address these questions first by computing analytically the diffusion coefficient of a random walk, which exhibits exponentially distributed residence times in the bulk and on the surface. In a second step, we generalize these results to arbitrary, residence time distributions. We use these results to estimate the diffusion coefficient of our original model, where the bulk residence times are computed as a firt-passage time problem.

Biological cells are fascinating micromachines capable of moving and performing various tasks. Simple engineered cell-mimicking systems help us not only in learning about their natural counterparts, but also in designing soft-matter microrobots capable of performing cell-like and beyond-nature activities. One interesting model is an active vesicle which combines a soft membrane with enclosed self-propelled particles (SPPs). Due to the forces exerted by SPPs on the membrane, this system exhibits a variety of different non-equilibrium shapes with tether-like protrusions and highly branched, dendritic structures. However, this system does not seem to exhibit a directed motility. An alteration to the system design through the attachment of active particles to the membrane from outside leads to the generation of directed motion. We will discuss the behaviour of active vesicles and physical mechanisms involved. Furthermore, possible strategies for their motility control will be suggested.

Active elastic models can be used to control robot swarms and to describe dense self-propelled physical systems. In this talk, I will present our work with this type of model in both fields. First, I will describe experiments where we used a position-based active elastic model as a distributed control algorithm for a small swarm of the E-puck robots, in order to achieve self-organized translation or rotation. Second, I will show in numerical simulations that, when we use an active-elastic model to describe a dense sheet of self-propelled agents with eccentric rotation, the distance R between the point where elastic forces are applied and the center of the process of each agent controls the transition from alignment-based to attraction-repulsion-based interactions, and that a novel noise-induced state of quenched disorder emerges for large enough R. Building on this previous work, I will then present our ongoing numerical studies of a dense system of active polar disks with linear repulsive interactions, confined by boundaries. Here, an active elastic model describes a set of self-propelled polar disks (each only able to turn about an axis of rotation located behind its geometrical center) that interact through forces and torques with overlapping neighbors. We will characterize the collective states that result from variating the preferred speeds, R values, density, noise, and heterogeneity.

Dense active systems with repulsive interactions can be found in a variety of contexts, from cell sheets to robot swarms in confined spaces. We report and characterize the emergence of a noise-induced state of quenched disorder (QD) in a generic model of a dense sheet of active polar disks with non-isotropic rotational and translational dynamics. In this novel state, the orientations of jammed active agents fluctuate about fixed random directions. The QD phase appears at intermediate noise levels, between the standard disordered state with changing headings and the ordered polar state of collective motion that typically define the flocking transition. In an analytical approximation, we show that the agent fluctuations in the QD state follow an Ornstein–Uhlenbeck process. We then use this result to demonstrate the mechanism that leads to the QD transition and calculate its critical noise, showing that it matches our numerical simulations. Finally, we argue that this state could be observed in a broad range of natural and artificial dense active systems with repulsive interactions.

The use of Active Matter (AM) concepts in robotics to model collective motion has gained popularity in recent years. One such model is the Active Elastic Sheet (AES), in which agents interact only through linear springs, exhibiting rich dynamics mostly in free space. In this study, we extend the AES model by incorporating an anticipation term, resulting in the Active Elastic Anticipation (AEAnt) model. We develop a multi-agent simulator in MATLAB and conduct several experiments to evaluate the performance of AEAnt in different scenarios. We focus on tuning anticipation as a control parameter, comparing order-disorder transitions to understand its gradual effect. Our study includes phase transitions not only in free space but also under environmental changes, which is valuable for swarm robotics applications. We demonstrate the tuning of task-driven parameters under the measure of polarization. To explore the existence of similar behaviors in real robots, we create a kinematic-based embodied simulator in Python, as the multi-agent simulator assumes point particles. Our results suggest that the AEAnt model has potential for practical applications in swarm robotics.

We present experiments with two insects that behave as active materials, fire ants and black soldier fly larvae. Fire ants link their bodies together to form waterproofs rafts that can flow or solidify in response to the fluid forces around them. Black soldier fly larvae can eat an entire pizza in two hours. We rationalize their high feeding rates by visualizing the vortices their swarms create. We use fluidized beds to show that their motion erases any structural memory of their aggregations, which cause them to flow differently than typical inactive granular materials like sand.

Termites build complex nests which are an impressive example of collective behaviour and self-organisation. We know that the coordinated actions involved in the construction of these nests by multiple individuals are primarily mediated by signals and cues embedded in the structure of the nest itself, rather than through direct interactions. However, to date there is still no scientific consensus on the nature of the stimuli that guide termite construction, and how they are sensed by termites. Here, we studied experimentally the building behaviour of Coptotermes formosanus termites by mapping termite positions in the experimental arena, as well as the locations of new pellet collection and deposition events. Pellet collections were evenly distributed across the experimental setup, compatible with a collection mechanism that is not affected by local topography, but only by the distribution of termite occupancy (termites pick pellets at the positions where they are). Conversely, pellet depositions were concentrated at locations of high surface curvature and at the boundaries between different types of substrate. The single feature shared by all pellet deposition regions was that they correspond to local maxima in the evaporation flux. We can show analytically and we confirm experimentally that evaporation flux is directly proportional to the local curvature of nest surfaces. Computer simulations show that a pattern formation mechanism in which structure growth is mediated exclusively by local surface curvature can alone produce many realistic features observed in real termite nests. Taken together, our results indicate that surface curvature is sufficient to organise termite building activity, and that termites likely sense curvature indirectly through substrate evaporation.

Stability analysis of nematic alignment and flow detects shortfalls of the standard theory, which does not ensure relaxation to equilibrium in a passive system, since the common test of Onsager relations [1] mixes variables odd and even with respect to time reversal [2]. The analysis of alignment instabilities [3] demonstrates the inadequacy of the director-based description, which misses a stabilizing effect of perturbations of the modulus and advantages or the vector over tensor representation of the nematic order parameter in 2D. [1] P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993). [2] H. R. Brand, H. Pleiner, and D. Svenšek, Rheol. Acta 57, 773 (2018). [3] L. M. Pismen, PRE 106, 034701 (2022)

One of the main challenges in the research of collective motion phenomena lies in quantitative characterization of the dynamics. Statistical physics provides some widely used tools, such as correlation functions, density fluctuations and approximations to known processes. These can be used, with some partial success, to classify collective states and compare swarming regimes. However, one of the major tools of statistical physics – the entropy – has seldom been used. Entropy is one of the principle thermodynamic variables and its definition can be extended to nonequilibrium systems based on its relation to information (Shannon entropy). However, applying this definition in practice is practically impossible. The reason is essentially “technical” – a crude estimate shows that a system of $N$ individuals moving in $D$ dimensions would require an order of $10^{ND}$ samples. In this talk, I present a new method that relates the entropy to other integrated, macroscopic properties, which are accessible experimentally. The advantage of using entropy to characterize collective motion is demonstrated in examples, including swarming bacteria.

We will consider particles acted on simultaneously by both Brownian and active noise. By performing a Laplace transform of the governing Fokker-Planck equation, we will discuss a direct method to derive exact expressions for all the moments of the relevant dynamical variables in arbitrary dimensions. These are verified via numerical simulations and used to analyze interesting dynamical crossovers. The method is extended for motion in the presence of harmonic trap and inertia. Using illustrative examples, we will show how an interplay of activity, trapping stiffness, and inertia lead to dynamic crossovers between equilibrium-like and purely non-equilibrium distributions. If time permits, we will also discuss how inertial effects modify the non-equilibrium properties of a repulsively interacting active particle bath.

Active matter systems have emerged as a key paradigm for studying non-equilibrium systems, offering unique insights into the rich phenomenology of living matter. In particular, microtubule-motor mixtures and the actin motility assay exemplify how relatively simple constituents can self-organize into complex structures with novel phases of matter, such as polar flocks, active foams, and phases exhibiting topological defects. In this talk, I will review recent advances in understanding the emergence of these collective phenomena based on agent-based simulations and active field theories. Additionally, active systems that self-organize through communication between agents are an area of active research. I will highlight the latest progress in the field and discuss the significance of these findings for fundamental science and potential applications in soft robotics.

The key property of active particles is that they consume energy to generate persistent motion, thereby breaking detailed balance. The resulting nonequilibrium dynamics can create novel nonequilibrium states of matter, a striking example being the motility-induced phase separation that arises as a consequence of an effective attraction between sterically-repelling particles - this emerging as a consequence of persistent motion. In this work we construct the effective pair potentials for persistent particles undergoing two different types of repulsive interaction. When a (passive) hard-core repulsive interaction applies, we find that the jamming of particles until such time that one of them changes direction (tumbles) leads to an effective short-range attraction, characterised by a linear pair potential. In a scaling limit where the persistent motion is ballistic and tumbles occur as a Poisson process, the potential sharpens to a step at the microscopic scale. We further consider an active repulsion, specifically, a sudden recoil of a particle when it impacts another - this is active because the dynamics does not derive from reversible heat exchange with a reservoir, as is the case for passive interactions. We show that the fundamental nature of effective interaction - whether it is attractive or repulsive - can be controlled by tuning the persistence length, suggesting that persistent particles with active contact interactions may be capable of nontrivial collective behaviour. References A B Slowman et al (2016) Jamming and attraction of interacting run-and-tumble random walkers. PRL 116 218101 M J Metson et al (2022) Tuning attraction and repulsion between active particles through persistence. arxiv:2207.01317

Active matter is strongly based on idealized models and processes. The underlying assumption is that, as in equilibrium, “universality classes” depend only on the symmetry and range of the interactions, as well as on the presence or absence of conserved quantities. For example, the emergence of polar order is explained assuming the existence of a short-range velocity alignment mechanism, which is believed to lead generically to active fluids that fall into the Toner-Tu class. Similarly, phase separation in active systems is usually rationalized in the context of short-range repulsive active Brownian particles that are believed to fall into the mobility-induced phase separation (MIPS) class. However, it can be argued that in general the emergence of order and phase separation are closely interconnected in several active systems. For instance, in self-propelled rods the emergence of (local) polar order precludes MIPS and leads to a phase separation process that exhibits statistical features that are different from those reported in MIPS. Similarly, active particles with non-reciprocal attraction interactions phase separate via a distinct process, inconsistent with MIPS, into high-density structures displaying either polar, neutral or nematic order depending on noise value and the non-reciprocity parameter. Here, we investigate the large-scale properties of a system of active particles with short-range velocity alignment that also experience short-range attraction and repulsion. We show that in sharp contrast to what is expected for active polar fluids and Toner-Tu theory, the system undergoes a Bose-Einstein condensation. Furthermore, we indicate that there exist at least two active condensation classes.

We introduce and study a model of active Brownian motion with multiplicative noise describing fluctuations in the self-propulsion or activity. We find that the standard picture of density accumulation in slow regions is qualitatively modified by active fluctuations, as stationary density profiles are generally not determined only by the mean self-propulsion speed landscape. As a result, activity gradients generically correlate the particle self-propulsion speed and orientation, leading to emergent polarization at interfaces pointing either towards dense or dilute regions depending on the amount of noise in the system. Considering a minimal model of active particles with quorum sensing interactions, we moreover discuss how active noise affects the emergence of motility induced phase separation. Our work provides a foundation for systematic studies of active matter self-organization in the presence of activity landscapes and active fluctuations.

The Weissenberg effect, also known as "rod-climbing effect", is a curious phenomenon that occurs when an elastic liquid climb up a rotating rod immersed in it. Contrary to what is commonly observed in Newtonian fluids which are driven away from the spinning rod, this effect results from fluid elasticity which generates a normal stress difference. Here we use a microscopic version of the Weissenberg effect to realize active shakers, namely squirmers that shake the fluid around them without moving. The shakers are magnetic microrotors which collectively organize into large scale zigzag bands and are impossible to observe in a simple Newtonian liquid. These dynamic structures display self-similar growth, generate topological defects in form of cusps that connect vortices of rolling particles with alternating chirality. By combining experimental analysis with particle-based simulation, we show that the special flow field created by shakers is the only ingredient needed to reproduce the observed spatiotemporal pattern. The microscopic version of the Weissenberg effect leads to a novel self-organization scenario for driven particles in elastic fluids and gives us new insight on the collective behavior of shaker particles.

TBA

Interactions between micro-swimmers and solid boundaries play an important role in many biological and technological processes. I will discuss our ongoing work in modeling and simulations that aim to understand the motion of micro-swimmers such as bacteria, micro-algae, spermatozoa or active colloids in various confinements or in structured environments. Our results highlight a complex interplay of the fluidic and contact interactions of the individuals with each-other and the boundaries to give rise to non-trivial individual and collective behavior.

Models of collective motion in animal systems can generate dynamics that display cohesion and co-alignment. These properties are typically encoded into the equations of motion at the outset, in a "top-down" manner and can lack power to explain how and why such properties emerge in the first place. We study instead “bottom-up” models in which agents sense their visual environment and then choose actions that maximise a path entropy in the visual state-space. This is analogous to agents “keeping their options open”, a principle that should confer fitness in an uncertain future for rather general reasons. A variety of phenotypes reminiscent of animal and insect behaviour emerge naturally from our model. We also identify a novel order-disorder transition in which order initially increases with the addition of noise; order is then lost as the noise is increased further, as usual. As a control algorithm for intelligent matter our model has minimal information processing and sensing requirements and can be abstracted to heuristics, e.g. neural networks, that could plausibly operate in real time, either in simple artificial agents or under animal cognition.

We consider self-propelled objects that, if unperturbed, proceed along persistently bent trajectories in discrete steps. Moreover, they try to orient towards a fixed remote target or along an externally imposed fixed direction. It turns out that this combination leads to rather complex nonlinear dynamics. Depending on the tendency of alignment towards the target, different types of trajectory emerge. Specifically, we observe closed polygonal, cycloidal-like, straight, zigzag, double-zigzag, higher-order-zigzag, and chaotic trajectories. In certain chaotic regimes, on shorter time scales, the motion appears rather stochastic. Adding mutual alignment interactions between such objects, here for simplicity of the Vicsek type, orientational ordering results. In the chaotic regime, concentration of the crowd into a spot is observed that then moves as one entity along a chaotic trajectory. Fluctuations in the alignment interaction reduce the degree of orientational ordering and spatial concentration. Similar results are obtained for polydispersity in the tendency of alignment towards the remote target. Our hope is to stimulate corresponding experiments. Suitable objects may be vibrated chiral hoppers on an inclined vibrated surface that introduces a tendency of external alignment through gravity. Other examples may be bacteria that through controlled irradiation can swim along polygon-shaped trajectories, if additional alignment is added, for instance, through nutrient gradients.

Morphogenesis often involves tissue-scale flows (plastic deformations) which require cell rearrangements (cell neighbor exchanges/intercalations). In a passive fluid, these rearrangements are driven by external forces. In contrast, in a living tissue, internal stresses generated by molecular motors can drive active intercalations. Using gastrulation of Drosophila embryos as a model system, imaged, segmented, and tracked in toto, we show how tension inference can be used to distinguish between these two processes purely based on the local geometry of the cell array. Active intercalations are characterized by an increasing (relative) tension on the contracting cell junction, while junctional length changes in passive intercalations take place under constant tension. Geometrically, junctional tensions are reflected by the angles between junctions at each vertex. This suggests a novel decomposition of tissue strain rate into a tension-driven contribution an isogonal (angle-preserving) contribution that reflects cell deformations driven by external stresses. This decomposition systematically links the tissue level dynamics to the cell/junction level dynamics. Moreover, the ensemble statistics of the tensions (i.e. angles) at each vertex allows us to robustly characterize the cell-scale mechanical state of the tissue. Our findings inform a minimal model based on positive tension feedback which reproduces the experimental observations and explains the coordination of subcellular stress generation underlying coherent tissue level-flows.

In this project we study what collective and global patterns emerge when cohesion is used as the low level principle or drive of agents that interact locally in real space and in the behavioral space. We define cohesion defined as the avoidance of losing neighbors. Unlike previous works, we introduce a cone of vision that breaks the symmetry of interactions. Rather than restricting their behavior by introducing forces or potentials we let them choose what direction to choose. Their behavior evolves in time according to their unique experiences and ability to keep cohesion. We study systems with perception based on the velocity of the neighbors on the one hand and their positions, on the other. When noise is applies is starts to disturb the order and the collective learning but not necessarily equally. Lastly, noise leads to behaviors different to the expected ones.

Amplitude (or envelope) equations describe the spatio-temporal dynamics of the essential mode(s) in the vicinity of a linear instability threshold and represent universal equations for spatially extended systems. Cross and Hohenberg have introduced a classification of linear instabilities based on the distinction of monotonic and oscillatory behavior and of small-scale and large-scale spatial structures [4]. Such a classification is useful to identify similarities between different pattern forming systems that share the same weakly nonlinear behavior. However, further studies have revealed that conservation laws may strongly influence the weakly nonlinear dynamics [7, 12] as well as the behavior in the fully nonlinear regime [2, 5]. Since conserved quantities naturally occur in a wide spectrum of pattern forming systems, e.g. in mass-conserving reaction diffusion systems [3] or in an extended Keller-Segel model for chemotactically communicating cells [1], we argue that the widely used Cross-Hohenberg classification should be amended by adding the distinction of conserved and nonconserved dynamics. Here, we use the improved classification and discuss the basic types of linear instabilities in the presence of conservation laws. We emphasize that there exists one relevant case for which the amplitude equation is still unknown. In particular, it is the large-scale oscillatory instability – a conserved-Hopf instability – that naturally occurs in many systems with two conservation laws. Relevant examples include ATP-driven cellular Min oscillations [5], two-species chemotactic systems [13], an active poroelastic model for mechanochemical waves in cytoskeleton and cytosol [11], thin liquid layers covered by self-propelled surfactant particles [8, 10], oscillatory coupled lipid and protein dynamics in cell membranes [6], and heated two-layer liquid films [9]. We derive the corresponding amplitude equation that captures the leading-order dynamics of all these systems close to a conserved-Hopf instability. Thus, we argue that it plays a similar role in the systematics of pattern formation as the complex Ginzburg-Landau equation. Moreover, it generalizes a phenomenological model of considerable recent interest, namely, the nonreciprocal Cahn-Hilliard equation. [1] F. Bergmann, L. Rapp, and W. Zimmermann. Active phase separation: a universal approach. Phys. Rev. E, 98:020603(R), 2018. [2] C. Beta, N. S. Gov, and A. Yochelis. Why a large-scale mode can be essential for understanding intracellular actin waves. Cells, 9:1533, 2020. [3] F. Brauns, J. Halatek, and E. Frey. Phase-space geometry of mass-conserving reaction-diffusion dynamics. Phys. Rev. X, 10:041036, 2020. [4] M. C. Cross and P. C. Hohenberg. Pattern formation outside of equilibrium. Rev. Mod. Phys., 65:851–1112, 1993. [5] J. Halatek and E. Frey. Rethinking pattern formation in reaction-diffusion systems. Nature Phys.,14:507–514, 2018. [6] K. John and M. Bär. Travelling lipid domains in a dynamic model for protein-induced pattern formation in biomembranes. Phys. Biol., 2:123–132, 2005. [7] P. C. Matthews and S. M. Cox. Pattern formation with a conservation law. Nonlinearity, 13:1293–1320, 2000. [8] A. Nepomnyashchy and S. Shklyaev. Longwave oscillatory patterns in liquids: outside the world of the complex Ginzburg-Landau equation. J. Phys. A-Math. Theor., 49:053001, 2016. [9] A. Pototsky, M. Bestehorn, D. Merkt, and U. Thiele. Morphology changes in the evolution of liquid two-layer films. J. Chem. Phys., 122:224711, 2005. [10] A. Pototsky, U. Thiele, and H. Stark. Mode instabilities and dynamic patterns in a colony of self-propelled surfactant particles covering a thin liquid layer. Eur. Phys. J. E, 39:51, 2016. [11] M. Radszuweit, S. Alonso, H. Engel, and M. Bär. Intracellular mechanochemical waves in an active poroelastic model. Phys. Rev. Lett., 110:138102, 2013. [12] D. M. Winterbottom, P. C. Matthews, and S. M. Cox. Oscillatory pattern formation with a conserved quantity. Nonlinearity, 18:1031–1056, 2005. [13] G. Wolansky. Multi-components chemotactic system in the absence of conflicts. Eur. J. Appl. Math., 13:641–661, 2002.