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

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• 作者：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) (8)
  Massimiliano Viale (1) (2)
  Aleksandra M. Walczak (9)
  
  1. Istituto Sistemi Complessi (ISC-CNR) ; Via dei Taurini 19 ; 00185 ; Rome ; Italy
  2. Dipartimento di Fisica ; 鈥淪apienza鈥?Universit谩 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 Fisicoqu铆micas Te贸ricas y Aplicadas (INIFTA) and Departamento de F铆sica ; 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 Cient铆ficas y T茅cnicas ; La Plata ; Argentina
  6. Laboratoire de Physique Statistique de l鈥櫭塩ole Normale Sup茅rieure ; CNRS and Universites Paris VI and Paris VII ; 24 rue Lhomond ; 75231 ; Paris Cedex 05 ; France
  7. Dipartimento di Informatica ; 鈥淪apienza鈥?Universit谩 di Roma ; 00198 ; Rome ; Italy
  8. Dipartimento di Matematica e Fisica ; Universit谩 Roma Tre ; Via della Vasca Navale ; 84 ; 00146 ; Rome ; Italy
  9. Laboratoire de Physique Th茅orique de l鈥櫭塩ole Normale Sup茅rieure ; CNRS and University Paris VI ; 24 rue Lhomond ; 75231 ; Paris Cedex 05 ; France
  
• 关键词：Collective behavior ; Flocking ; Self ; organization ; Emergent behavior ; Animal groups
• 刊名：Journal of Statistical Physics
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：158
• 期：3
• 页码：601-627
• 全文大小：916 KB
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• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

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.