Strong Casimir-like Forces in Flocking Active Matter.

Confining in space the equilibrium fluctuations of statistical systems with long-range correlations is known to result into effective forces on the boundaries. Here we demonstrate the occurrence of Casimir-like forces in the nonequilibrium context provided by flocking active matter. In particular, we consider a system of aligning self-propelled particles in two spatial dimensions that are transversally confined by reflecting or partially reflecting walls.

Signatures of directed and spontaneous flocking.

Collective motion-or flocking-is an emergent phenomena that underlies many biological processes of relevance, from cellular migrations to animal group movements. In this work, we derive scaling relations for the fluctuations of the mean direction of motion and for the static density structure factor (which encodes static density fluctuations) in the presence of a homogeneous, small external field. This allows us to formulate two different and complementary criteria capable of detecting instances of directed motion exclusively from easily measurable dynamical and static signatures of the collective dynamics, without the need to detect correlations with environmental cues.

Quantitative Assessment of the Toner and Tu Theory of Polar Flocks.

We present a quantitative assessment of the Toner and Tu theory describing the universal scaling of fluctuations in polar phases of dry active matter. Using large-scale simulations of the Vicsek model in two and three dimensions, we find the overall phenomenology and generic algebraic scaling predicted by Toner and Tu, but our data on density correlations reveal some qualitative discrepancies. The values of the associated scaling exponents we estimate differ significantly from those conjectured in 1995.

Clustering and anisotropic correlated percolation in polar flocks.

We study clustering and percolation phenomena in the Vicsek model, taken here in its capacity of prototypical model for dry aligning active matter. Our results show that the order-disorder transition is not related in any way to a percolation transition, contrary to some earlier claims. We study geometric percolation in each of the phases at play, but we mostly focus on the ordered Toner-Tu phase, where we find that the long-range correlations of density fluctuations give rise to an anisotropic percolation transition.

Synchronization in time-varying random networks with vanishing connectivity.

A sufficiently connected topology linking the constituent units of a complex system is usually seen as a prerequisite for the emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phase oscillators in which the links mediating the interactions are constantly rearranged with a characteristic timescale and, possibly, an extremely low instantaneous connectivity. We show that with strong coupling and sufficiently fast rewiring the network reaches partial synchronization even in the vanishing connectivity limit.

Desynchronization and pattern formation in a noisy feed-forward oscillator network.

We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is studied in a region of the parameters that would yield deterministic synchronization. Non-normal directed couplings seed a coherent amplification of the perturbation: this latter manifests as a modulation, transversal to the limit cycle, which gains in potency node after node.

Evidence of a Critical Phase Transition in Purely Temporal Dynamics with Long-Delayed Feedback.

Experimental evidence of an absorbing phase transition, so far associated with spatiotemporal dynamics, is provided in a purely temporal optical system. A bistable semiconductor laser, with long-delayed optoelectronic feedback and multiplicative noise, shows the peculiar features of a critical phenomenon belonging to the directed percolation universality class. The numerical study of a simple, effective model provides accurate estimates of the transition critical exponents, in agreement with both theory and our experiment.

Origin and scaling of chaos in weakly coupled phase oscillators.

We discuss the behavior of the largest Lyapunov exponent λ in the incoherent phase of large ensembles of heterogeneous, globally coupled, phase oscillators. We show that the scaling with the system size N depends on the details of the spacing distribution of the oscillator frequencies. For sufficiently regular distributions λ∼1/N, while for strong fluctuations of the frequency spacing λ∼lnN/N (the standard setup of independent identically distributed variables belongs to the latter class).

Noise-driven neuromorphic tuned amplifier.

We study a simple stochastic model of neuronal excitatory and inhibitory interactions. The model is defined on a directed lattice and internodes couplings are modulated by a nonlinear function that mimics the process of synaptic activation. We prove that such a system behaves as a fully tunable amplifier: the endogenous component of noise, stemming from finite size effects, seeds a coherent (exponential) amplification across the chain generating giant oscillations with tunable frequencies, a process that the brain could exploit to enhance, and eventually encode, different signals.

Intertangled stochastic motifs in networks of excitatory-inhibitory units.

A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied. The endogenous component of noise, stemming from finite size corrections, drives robust internode correlations that persist at large distances. Antiphase synchrony at small frequencies is resolved on adjacent nodes and found to promote the spontaneous generation of long-ranged stochastic patterns that invade the network as a whole.

Local equilibrium in bird flocks.

The correlated motion of flocks is an instance of global order emerging from local interactions. An essential difference with analogous ferromagnetic systems is that flocks are active: animals move relative to each other, dynamically rearranging their interaction network. The effect of this off-equilibrium element is well studied theoretically, but its impact on actual biological groups deserves more experimental attention.

Intermittent collective dynamics emerge from conflicting imperatives in sheep herds.

Among the many fascinating examples of collective behavior exhibited by animal groups, some species are known to alternate slow group dispersion in space with rapid aggregation phenomena induced by a sudden behavioral shift at the individual level. We study this phenomenon quantitatively in large groups of grazing Merino sheep under controlled experimental conditions. Our analysis reveals strongly intermittent collective dynamics consisting of fast, avalanche-like regrouping events distributed on all experimentally accessible scales.

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.

Dynamical maximum entropy approach to flocking.

We derive a new method to infer from data the out-of-equilibrium alignment dynamics of collectively moving animal groups, by considering the maximum entropy model distribution consistent with temporal and spatial correlations of flight direction. When bird neighborhoods evolve rapidly, this dynamical inference correctly learns the parameters of the model, while a static one relying only on the spatial correlations fails. When neighbors change slowly and the detailed balance is satisfied, we recover the static procedure.

Boundary information inflow enhances correlation in flocking.

The most conspicuous trait of collective animal behavior is the emergence of highly ordered structures. Less obvious to the eye, but perhaps more profound a signature of self-organization, is the presence of long-range spatial correlations. Experimental data on starling flocks in 3D show that the exponent ruling the decay of the velocity correlation function, C(r)~1/r(γ), is extremely small, γ<<1.

Nonlinear field equations for aligning self-propelled rods.

We derive a set of minimal and well-behaved nonlinear field equations describing the collective properties of self-propelled rods from a simple microscopic starting point, the Vicsek model with nematic alignment. Analysis of their linear and nonlinear dynamics shows good agreement with the original microscopic model. In particular, we derive an explicit expression for density-segregated, banded solutions, allowing us to develop a more complete analytic picture of the problem at the nonlinear level.

Competing ferromagnetic and nematic alignment in self-propelled polar particles.

We study a Vicsek-style model of self-propelled particles where ferromagnetic and nematic alignment compete in both the usual "metric" version and in the "metric-free" case where a particle interacts with its Voronoi neighbors. We show that the phase diagram of this out-of-equilibrium XY model is similar to that of its equilibrium counterpart: The properties of the fully nematic model, studied before by Ginelli et al. [Phys.

Deciphering interactions in moving animal groups.

Collective motion phenomena in large groups of social organisms have long fascinated the observer, especially in cases, such as bird flocks or fish schools, where large-scale highly coordinated actions emerge in the absence of obvious leaders. However, the mechanisms involved in this self-organized behavior are still poorly understood, because the individual-level interactions underlying them remain elusive. Here, we demonstrate the power of a bottom-up methodology to build models for animal group motion from data gathered at the individual scale.

Continuous theory of active matter systems with metric-free interactions.

We derive a hydrodynamic description of metric-free active matter: starting from self-propelled particles aligning with neighbors defined by "topological" rules, not metric zones-a situation advocated recently to be relevant for bird flocks, fish schools, and crowds-we use a kinetic approach to obtain well-controlled nonlinear field equations. We show that the density-independent collision rate per particle characteristic of topological interactions suppresses the linear instability of the homogeneous ordered phase and the nonlinear density segregation generically present near threshold in metric models, in agreement with microscopic simulations.

Chaos in the Hamiltonian mean-field model.

We study the dynamical properties of the canonical ordered phase of the Hamiltonian mean-field (HMF) model, in which N particles, globally coupled via pairwise attractive interactions, form a rotating cluster. Using a combination of numerical and analytical arguments, we first show that the largest Lyapunov exponent remains strictly positive in the infinite-size limit, converging to its asymptotic value with 1/lnN corrections. We then elucidate the scaling laws ruling the behavior of this asymptotic value in the critical region separating the ordered, clustered phase and the disordered phase present at high-energy densities.

Hyperbolic decoupling of tangent space and effective dimension of dissipative systems.

We show, using covariant Lyapunov vectors, that the tangent space of spatially extended dissipative systems is split into two hyperbolically decoupled subspaces: one comprising a finite number of frequently entangled "physical" modes, which carry the physically relevant information of the trajectory, and a residual set of strongly decaying "spurious" modes. The decoupling of the physical and spurious subspaces is defined by the absence of tangencies between them and found to take place generally; we find evidence in partial differential equations in one and two spatial dimensions and even in lattices of coupled maps or oscillators. We conjecture that the physical modes may constitute a local linear description of the inertial manifold at any point in the global attractor.

Extensive and subextensive chaos in globally coupled dynamical systems.

Using a combination of analytical and numerical techniques, we show that chaos in globally coupled identical dynamical systems, whether dissipative or Hamiltonian, is both extensive and subextensive: their spectrum of Lyapunov exponents is asymptotically flat (thus extensive) at the value λ(0) given by a single unit forced by the mean field, but sandwiched between subextensive bands containing typically O(logN) exponents whose values vary as λ≃λ(∞)+c/logN with λ(∞)≠λ(0).

Relevance of metric-free interactions in flocking phenomena.

We show that the collective properties of self-propelled particles aligning with their topological (Voronoi) neighbors are qualitatively different from those of usual models where metric interaction ranges are used. This relevance of metric-free interactions, shown in a minimal setting, indicate that realistic models for the cohesive motion of cells, bird flocks, and fish schools may have to incorporate them, as suggested by recent observations.

Large-scale collective properties of self-propelled rods.

We study, in two space dimensions, the collective properties of constant-speed polar point particles interacting locally by nematic alignment in the presence of noise. This minimal approach to self-propelled rods allows one to deal with large numbers of particles, which exhibit a rich phenomenology distinctively different from all other known models for self-propelled particles. Extensive simulations reveal long-range nematic order, phase separation, and space-time chaos mediated by large-scale segregated structures.

Lyapunov analysis captures the collective dynamics of large chaotic systems.

We show, using generic globally coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting collectively on the trajectory. For globally coupled maps, we show, moreover, a quantitative correspondence between the collective modes and some of the so-called Perron-Frobenius dynamics. Our results imply that the conventional definition of extensivity must be changed as soon as collective dynamics sets in.