Boundary information inflow enhances correlation in flocking

Velocity correlations in jackdaw flocks in different ecological contexts

Velocity correlation is an important feature for animal groups performing collective motions. Previous studies have mostly focused on the velocity correlation in a single ecological context. It is unclear whether correlation characteristics vary in a single species in different contexts. Here, we studied the velocity correlations in jackdaw flocks in two different contexts: transit flocks where birds travel from one location to another, and mobbing flocks where birds respond to an external stimulus. We found that in both contexts, although the interaction rules are different, the velocity correlations remain scale-free, i.e. the correlation length (the distance over which the velocity of two individuals is similar) increases linearly with the group size. Furthermore, we found that the correlation length is independent of the group density for transit flocks, but increases with increasing group density in mobbing flocks. This result confirms a previous observation that birds obey topological interactions in transit flocks, but switch to metric interactions in mobbing flocks. Finally, in both contexts, the impact of group polarization on correlation length is not significant. Our results suggest that wild animals are always able to respond coherently to perturbations regardless of context.

Renormalization group study of marginal ferromagnetism

When studying the collective motion of biological groups, a useful theoretical framework is that of ferromagnetic systems, in which the alignment interactions are a surrogate of the effective imitation among the individuals. In this context, the experimental discovery of scale-free correlations of speed fluctuations in starling flocks poses a challenge to common statistical physics wisdom, as in the ordered phase of standard ferromagnetic models with O(n) symmetry, the modulus of the order parameter has finite correlation length. To make sense of this anomaly, a ferromagnetic theory has been proposed, where the bare confining potential has zero second derivative (i.e., it is marginal) along the modulus of the order parameter. The marginal model exhibits a zero-temperature critical point, where the modulus correlation length diverges, hence allowing us to boost both correlation and collective order by simply reducing the temperature. Here, we derive an effective field theory describing the marginal model close to the T=0 critical point and calculate the renormalization group equations at one loop within a momentum shell approach. We discover a nontrivial scenario, as the cubic and quartic vertices do not vanish in the infrared limit, while the coupling constants effectively regulating the exponents ν and η have upper critical dimension d_{c}=2, so in three dimensions the critical exponents acquire their free values, ν=1/2 and η=0. This theoretical scenario is verified by a Monte Carlo study of the modulus susceptibility in three dimensions, where the standard finite-size scaling relations have to be adapted to the case of d>d_{c}. The numerical data fully confirm our theoretical results.

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. The static one is informative in large enough systems, while the dynamical one requires large observation times to be effective. We believe these criteria may prove useful to detect or confirm the directed nature of collective motion in in vivo experimental observations, which are typically conducted in complex and not fully controlled environments.

From the origin of life to pandemics: emergent phenomena in complex systems

When a large number of similar entities interact among each other and with their environment at a low scale, unexpected outcomes at higher spatio-temporal scales might spontaneously arise. This non-trivial phenomenon, known as emergence, characterizes a broad range of distinct complex systems-from physical to biological and social-and is often related to collective behaviour. It is ubiquitous, from non-living entities such as oscillators that under specific conditions synchronize, to living ones, such as birds flocking or fish schooling. Despite the ample phenomenological evidence of the existence of systems' emergent properties, central theoretical questions to the study of emergence remain unanswered, such as the lack of a widely accepted, rigorous definition of the phenomenon or the identification of the essential physical conditions that favour emergence. We offer here a general overview of the phenomenon of emergence and sketch current and future challenges on the topic. Our short review also serves as an introduction to the theme issue Emergent phenomena in complex physical and socio-technical systems: from cells to societies, where we provide a synthesis of the contents tackled in the issue and outline how they relate to these challenges, spanning from current advances in our understanding on the origin of life to the large-scale propagation of infectious diseases. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Velocity and Speed Correlations in Hamiltonian Flocks

We study a 2D Hamiltonian fluid made of particles carrying spins coupled to their velocities. At low temperatures and intermediate densities, this conservative system exhibits phase coexistence between a collectively moving droplet and a still gas. The particle displacements within the droplet have remarkably similar correlations to those of birds flocks. The center of mass behaves as an effective self-propelled particle, driven by the droplet's total magnetization. The conservation of a generalized angular momentum leads to rigid rotations, opposite to the fluctuations of the magnetization orientation that, however small, are responsible for the shape and scaling of the correlations.

Milling and meandering: Flocking dynamics of stochastically interacting agents with a field of view

We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit nonlinear velocity-alignment interactions with neighbors within their field of view. The stochasticity in the dynamics is spatially heterogeneous and arises implicitly from the nature of the interparticle interactions. We observe long-time spatial cohesion in the emergent flocking dynamics, despite the absence of attractive forces that explicitly depend on the relative positions of particles. The wide array of flocking patterns exhibited by this model are characterized by identifying spatially distinct clusters and computing their corresponding angular momenta.

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

Large collections of autonomously moving agents, such as animals or micro-organisms, are able to flock coherently in space even in the absence of a central control mechanism. While the direction of the flock resulting from this critical behavior is random, this can be controlled by a small subset of informed individuals acting as leaders of the group. In this article we use the Vicsek model to investigate how flocks respond to leadership and make decisions. Using a combination of numerical simulations and continuous modeling we demonstrate that flocks display a linear response to leadership that can be cast in the framework of the fluctuation-dissipation theorem, identifying an effective temperature reflecting how promptly the flock reacts to the initiative of the leaders. The linear response to leadership also holds in the presence of two groups of informed individuals with competing interests, indicating that the flock's behavioral decision is determined by both the number of leaders and their degree of influence.