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Flocking and Turning: a New Model for Self-organized Collective Motion (Articolo in rivista)

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Flocking and Turning: a New Model for Self-organized Collective Motion (Articolo in rivista) (literal)

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Andrea Cavagna (1,2,3); Lorenzo Del Castello (1,2); Irene Giardina (1,2,3); Tomas Grigera (4,5); Asja Jelic (1,2); Stefania Melillo (1,2); Thierry Mora (6); Leonardo Parisi (1,2,7); Edmondo Silvestri (1,2,6); Massimiliano Viale (1,2); Aleksandra M. Walczak (9) (2014)
Flocking and Turning: a New Model for Self-organized Collective Motion
in Journal of statistical physics; Springer Science+Business Media, New York (Stati Uniti d'America)
(literal)

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Andrea Cavagna (1,2,3); Lorenzo Del Castello (1,2); Irene Giardina (1,2,3); Tomas Grigera (4,5); Asja Jelic (1,2); Stefania Melillo (1,2); Thierry Mora (6); Leonardo Parisi (1,2,7); Edmondo Silvestri (1,2,6); Massimiliano Viale (1,2); Aleksandra M. Walczak (9) (literal)

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1. Istituto Sistemi Complessi (ISC-CNR), Via dei Taurini 19, 00185, Rome, Italy 2. Dipartimento di Fisica, \"Sapienza\" Universitá di Roma, P.le Aldo Moro 2, 00185, Rome, Italy 3. Initiative for the Theoretical Sciences, The Graduate Center, 365 Fifth Avenue, New York, NY, 10016, USA 4. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA) and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16, suc. 4, 1900, La Plata, Argentina 5. CONICET La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, La Plata, Argentina 6. Laboratoire de Physique Statistique de l'École Normale Supérieure, CNRS and Universites Paris VI and Paris VII, 24 rue Lhomond, 75231, Paris Cedex 05, France 7. Dipartimento di Informatica, \"Sapienza\" Universitá di Roma, 00198, Rome, Italy 8. Dipartimento di Matematica e Fisica, Universitá Roma Tre, Via della Vasca Navale, 84, 00146, Rome, Italy 9. Laboratoire de Physique Théorique de l'École Normale Supérieure, CNRS and University Paris VI, 24 rue Lhomond, 75231, Paris Cedex 05, France (literal)

Titolo

Flocking and Turning: a New Model for Self-organized Collective Motion (literal)

Abstract

Birds in a flock move in a correlated way, resulting in large polarization of velocities. A good understanding of this collective behavior exists for linear motion of the flock. Yet observing actual birds, the center of mass of the group often turns giving rise to more complicated dynamics, still keeping strong polarization of the flock. Here we propose novel dynamical equations for the collective motion of polarized animal groups that account for correlated turning including solely social forces. We exploit rotational symmetries and conservation laws of the problem to formulate a theory in terms of generalized coordinates of motion for the velocity directions akin to a Hamiltonian formulation for rotations. We explicitly derive the correspondence between this formulation and the dynamics of the individual velocities, thus obtaining a new model of collective motion. In the appropriate overdamped limit we recover the well-known Vicsek model, which dissipates rotational information and does not allow for polarized turns. Although the new model has its most vivid success in describing turning groups, its dynamics is intrinsically different from previous ones in a wide dynamical regime, while reducing to the hydrodynamic description of Toner and Tu at very large length-scales. The derived framework is therefore general and it may describe the collective motion of any strongly polarized active matter system. (literal)

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