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When animal groups move coherently in the form of a flock, their trajectories are not all parallel, the individuals exchange their position in the group. In this Letter we introduce a measure of this mixing dynamics, which we quantify as…
We present a 2D lattice model of self-propelled spins that can only change direction upon collision with another spin. We show that even with ballistic motion and minimal cooperativity, these spins display robust flocking behavior at nearly…
Collective motion is abundant in nature, producing a vast amount of phenomena which have been studied in recent years, including the landing of flocks of birds. We investigate the collective decision making scenario where a flock of birds…
The most conspicuous trait of collective animal behaviour 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…
The purpose of this paper is to consider flocking formations of a second order dynamic system on a sphere with a Cucker-Smale type flocking operator and cooperative control. The flocking operator consists of a weighted control parameter and…
Flocking and vortical are two typical motion modes in active matter. Although it is known that the two modes can spontaneously switch between each other in a finite-size system, the switching dynamics remain elusive. In this work, by…
Large animal groups -- bird flocks, fish schools, insect swarms -- are often assumed to form by gradual aggregation of sparsely distributed individuals. Using a mathematically precise framework based on time-varying directed interaction…
The nature of the phase transition in a system of self-propelling particles has been extensively studied during the last few decades. A theoretical model was proposed by T. Vicsek, {\it et. al.} [Phys. Rev. Lett. {\bf 75}, 1226 (1995)] with…
The hypothesis of molecular chaos plays the central role in kinetic theory, which provides a closure leading to the Boltzmann equation for quantitative description of classic fluids. Yet how to properly extend it to active systems is still…
In this paper, we examine how to build coarse-grain transport models consistently from the kinetic to fluid regimes. The internal energy of the gas particles is described through a state-to-state approach. A kinetic equation allows us to…
We establish sufficient conditions for the quick relaxation to kinetic equilibrium in the classic Vicsek-Cucker-Smale model of bird flocking. The convergence time is polynomial in the number of birds as long as the number of flocks remains…
Flocking is a paradigmatic example of collective animal behaviour, where decentralized interaction rules give rise to a globally ordered state. In the emergence of order out of self-organization we find similarities between biological…
We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…
We consider flocks of artificial birds and study the emergence of V-like formations during flight. We introduce a small set of fully distributed positioning rules to guide the birds' movements and demonstrate, by means of simulations, that…
Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. Microbial communities are…
Transitions from reversible to irreversible or fluctuating states above a critical density and shear amplitude have been extensively studied in non-thermal cyclically sheared suspensions and amorphous solids. Here, we propose that the same…
Production of energy (metabolism) and its distribution is vital for living organisms, both at individual level - between different functions of an organism, as well as between species of communities at different organizational levels,…
The ability of migratory birds to orient relative to the Earth's magnetic field is believed to involve a coherent superposition of two spin states of a radical electron pair. However, the mechanism by which this coherence can be maintained…
A Collision-Avoiding flocking particle system proposed in [8] is studied in this paper. The global wellposedness of its corresponding Vlasov-type kinetic equation is proved. As a corollary of the global stability result, the mean field…
Non-equilibrium active matter made up of self-driven particles with short-range repulsive interactions is a useful minimal system to study active matter as the system exhibits collective motion and nonequilibrium order-disorder transitions.…