Session V35: Active Matter: Collective Phenomena in Living Systems V

Questioning the activity of active matter: the case of bird flocks

Animal flocking is a natural instance of active matter. What makes flocks active is the rearrangement of neighborhoods, which constantly remodels the network of interactions between individuals in the group, keeping the system out of equilibrium. Despite the predicted importance of this reshuffling, its true impact for natural flocks is not well understood. Here we analyse films of flocks of startlings with a novel statistical inference technique based on dynamical maximum entropy to measure the parameters of flock alignment - alignment strength, interaction range, and noise. We show that birds align their flight orientations must faster than they change neighbors. In the statistical mechanics sense, this means that flocks remain adiabatically in equilibrium, allowing for a rigorous analogy with equilibrium systems of interacting spins, and we show that an inference method based on equilibrium assumptions gives fully consistent results.   

Linear response to leadership, effective temperature and decision making in flocks.

The Vicsek model is the prototypical system for studying collective behavior of interacting self propelled particles (SPPs). It has formed the basis for models explaining the collective behavior of many active systems including flocks of birds and swarms of insects. To the standard Vicsek model we introduce a small angular torque to a subset of the particles and observe how this effects the direction of polarisation of the entire swarm. This is analogous to a few informed birds trying to lead the rest of a large flock by initiating a turn. We find a linear response to this perturbation and fluctuations that are in agreement with fluctuation dissipation theorem. This allows the identification of an effective temperature for the Vicsek model that follows a power law with the noise amplitude. The linear response can also be extended to the process of decision-making, wherein flocks must decide between the behaviors of two competing subgroups of individuals.   

Fluctuation Spectra Underlie the Behavior of Non-equilibrium Systems

A diverse set of important physical phenomena, ranging from hydrodynamic turbulence to the collective behaviour of bacteria, are intrinsically far from equilibrium. Despite their ubiquity, there are few general theoretical results that describe these non-equilibrium steady states. Here we argue that a generic signature of non-equilibrium systems is nontrivial fluctuation spectra. Based on this observation, we derive a general relation for the force exerted by a non-equilibrium system on two embedded walls. We find that for a narrow, unimodal spectrum, the force depends solely on the width and the position of the peak in the fluctuation spectrum, and will oscillate between repulsion and attraction. We demonstrate the generality of our framework by examining two apparently disparate examples: the Maritime Casimir effect and recent simulations of active Brownian particles. A key implication of our work is that important non-equilibrium interactions are encoded within the fluctuation spectrum. In this sense the noise becomes the signal.   

Visual perturbations and the collective dynamics of fish schools

We investigate the dynamics of the collective behaviors exhibited in a laboratory fish school. Using an artificial light gradient with varies both spatially and temporally, we investigate the competition between individual locomotion and local polarization arising from social interactions between individuals. We will discuss how our work informs current agent-based models on the interplay between social interactions and heterogeneous environments.   

The influence of following on bidirectional flow through a doorway

Pedestrian dynamics is a subset of the study of self-propelled particles. We simulate two species of pedestrians undergoing bidirectional flow through a narrow doorway. Using the Helbing-Monlár-Farkas-Vicsek Social Force Model, our pedestrians are soft discs that experience psychosocial and physical contact forces. We vary the “following” parameter which determines the degree to which a pedestrian matches its direction of movement to the average of nearby, same-species pedestrians. Current density, efficiency and statistics of bursts and lags are calculated. These indicate that choosing different following parameters for each species affects the efficacy of transport - greater following being associated with lower efficacy. The information entropy associated with velocity and the long time tails of the complementary CDF of lag times are additional indicators of the dynamical consequences of following during bidirectional flow.   

Collective dynamics of sperm in viscoelastic fluid

Collective dynamics in biology is an interesting subject for physicists, in part because of its close relations to emergent behaviors in condensed matter, such as phase separation and criticality. However, the emergence of order is often less drastic in systems composed of the living cells, sometimes due to the natural variability among individual organisms. Here, using bull sperm as a model system, we demonstrate that the cells migrate collectively in viscoelastic fluids, exhibiting behavior similar to “flocking”. This collectiveness is greatly reduced in similarly viscous Newtonian fluids, suggesting that the cell-cell interaction is primarily a result of the elastic property or the memory effect of the fluids, instead of pure hydrodynamic interactions. Unlike bacterial swarming, this collectiveness does not require a change in phenotype of the cells; therefore, it is a better model system for physicists.   

Critical phenomena in active matter

A collection of active agents can organize in phases with structural properties remarkably similar to those of ordinary materials, such as active gases, liquids and glasses. These phases are formed, however, out of equilibrium, where the machinery of equilibrium statistical mechanics cannot be applied. It has recently been shown that models of particles with Gaussian colored noise can capture some of the nonequilibrium behavior of active Brownian particles, including motility-induced phase separation. By using the Unified Gaussian Colored Noise Approximation (UCNA) it has been possible to obtain an equilibrium-like probability distribution function and an effective free energy for active Brownian particles. Here we employ UCNA to examine the effect of colored noise on mean-field order-disorder transitions. Starting with a $\varphi^4$ Landau model that undergoes a second-order phase transition as a function of a tuning parameter, we calculate the shift in transition due to colored noise as a function of the noise amplitude and correlation time $\tau$. We find that the transition line exhibits reentrance as a function of $\tau$. The mean-field theoretical predictions are compared with Molecular Dynamics simulations of active Lennard-Jones particles.   

Long-range Acoustic Interactions in Insect Swarms: An Adaptive Gravity Model

The collective motion of groups of animals emerges from the net effect of the interactions between individual members of the group. In many cases, such as birds, fish, or ungulates, these interactions are mediated by sensory stimuli that predominantly arise from nearby neighbors. But not all stimuli in animal groups are short range. Here, we consider mating swarms of midges, which interact primarily via long-range acoustic stimuli. We exploit the similarity in form between the decay of acoustic and gravitational sources to build a model for swarm behavior. By accounting for the adaptive nature of the midges’ acoustic sensing, we show that our “adaptive gravity” model makes mean-field predictions that agree well with experimental observations of laboratory swarms. Our results highlight the role of sensory mechanisms and interaction range in collective animal behavior. The adaptive interactions that we present here open a new class of equations of motion, which may appear in other biological contexts.   

Synchronization of self-propelled units carrying an internal oscillator

We adress the question of how self-propulsion, and the dynamical patterns emerging from it, affects the synchronization of motile physical entities, like moving cells synchronizing their intracellular genetic oscillators. In order to do that, we introduce a simple model of self-propelled hard disks moving in 2D carrying an internal variable which follows a Kuramoto dynamics. We find that, in the absence of particle-particle interactions, self-propulsion promotes the synchronization of the particles up to a saturation threshold that we identify with the parameters of the model. However, the presence of steric interactions give rise to an optimal self-propulsion for synchronization as a consequence of the clustering of the particles. This new effect shows that the interplay between the oscillators coupling and the topology of the underliying network, arising from particle interactions, plays an important role for the performance of mobile systems. We single out several dynamic regimes controlled by different processes that we describe. We analyse the relaxation of the system and show that synchronization proceeds throught a mechanism that, despite being out-of-equilibrium, verifies the dynamical scaling hypothesis.   

Statistical Mechanics of Collective Transport by Ants

\newline Collective decisions and cooperation within groups are essential for the survival of many species. Conflicts within the group must be suppressed but conformism may render the system unresponsive to new information. Collective transport by ants is therefore an ideal model system to study how animal groups optimize these opposing requirements.\newline We combine experiments and theory to characterize the collective transport. The ants are modeled as binary Ising spins, representing the two roles ants can perform during transport. It turns out that the ants poise themselves collectively near a critical point where the response to a newly attached ant is maximized. We identify the size as being proportional to an inverse effective temperature and thus the system can exhibit a mesoscopic transition between order and disorder by manipulating the size. Constraining the cargo with a string makes the system behave as a strongly non-linear pendulum. Theoretically we predict that a Hopf bifurcation occurs at a critical size followed by a global bifurcation where full swings emerge. Remarkably, these theoretical predictions were verified experimentally.   

Dynamics of fire ant aggregations

Fire ant aggregations are an inherently active system. Each ant harvests its own energy and can convert it into motion. The motion of individual ants contributes non-trivially to the bulk material properties of the aggregation. We have measured some of these properties using plate-plate rheology, where the response to an applied external force or deformation is measured. In this talk, we will present data pertaining to the aggregation behavior in the absence of any external force. We quantify the aggregation dynamics by monitoring the rotation of the top plate and by measuring the normal force. We then compare the results with visualizations of 2D aggregations.   

Extensional Rheology of Fire Ant Aggregates

We explore the extensional rheology and self-healing of fire ant (Solenopsis invicta) aggregations, mechanically entangled ensembles used to form rafts, bivouacs or bridges. Macroscopic experiments create quasi-two dimensional piles and measure the force required to impose a constant end-velocity. This force fluctuates, reminiscent of similar experiments on geometrically cohesive granular materials. Heterogeneous chains develop, with isolated ants often the sole link between top and bottom. Finally, the maximum pile strength scales sub-linearly with the number of ants, with the maximum force per ant decreasing as the pile grows. We reproduce these behaviors with a simple model that represents ants feet as discs connected by a spring (the "leg"). Discs move randomly, and stick to one another when in contact. Discs in contact un-stick at random with a probability that decreases as the spring (leg) is stretched, modeling an ant's tendency to hold on longer when stretched. Simulations qualitatively reproduces the fluctuating force, chain formation and sublinear scaling of maximum force with particle number and give insight into underlying mechanisms that govern the ants' behaviors.