Collective motion: from active matter to swarms in natural and engineered systems

Transcription

1 Collective motion: from active matter to swarms in natural and engineered systems Cristián Huepe Unaffiliated NSF Grantee: Cristian Huepe Labs Inc Chicago IL Supported by the National Science Foundation under Grants No. DMS & PHY Yael Katz, Christos Ioannou, Kolbjørn Tunstrøm, Iain Couzin Dept. of Ecology & Evolutionary Biology Princeton University USA Gerd Zschaler, Li Chen, Anne-Ly Do, Thilo Gross Max-Planck Institute for the Physics of Complex Systems Dresden, Germany Eliseo Ferrante, Ali Emre Turgut IRIDIA, CoDE Université Libre de Bruxelles Belgium

2 Outline Background: Collective motion in biology, engineering, and complex systems Data-driven analysis of fish schooling experiments Adaptive-network analysis of universal features in collective motion Elasticity-based mechanism for collective motion in active solids

3 from: Collective Minds (documentary by Jacob Kneser) Background: Biological motivation

4 Background: Computer graphics Intuitive flocking algorithm (Craig Reynolds Sony) Flocks, Herds, and Schools: A Distributed Behavioral Model Computer Graphics, 21(4), pp , 1987 Defined Boids with simple interaction rules Separation Alignment Cohesion

5 Background: Physics Motivation The Vicsek model (1995 results) Order parameter (alignment/magnetization) Main Result Novel type of phase transition

6 Background: Biology The zones model - Insect-like swarm: - Torus, milling : Journal of Theoretical Biology (2002) 218, 1-11 I. D. Couzin, J. Krause, R. James, G. D. Ruxton & N. R. Franks - Migration, flocking:

7 Background: Robotics Deploying sensor networks Parallel tasks Micro-robotics Decentralized, Scalable, Robust Small processing power & bandwidth Limited communication (nearby neighbors, line-of-sight, direct contact)

8 Data-driven analysis of fish schooling experiments Dr. Yael Katz Dr. Kolbjørn Tunstrøm Dr. Christos Ioannou Publications: Collective states, multistability and transitional behavior in schooling fish, PLoS Computational Biology Feb [9(2), e ] Prof. Iain Couzin Inferring the structure and dynamics of interactions in schooling fish, PNAS July 2011 [doi: /pnas ]

9 Experimental System

10 1000 fish dynamics Polarized state Rotating state Swarming state

11 Dynamics of state transition State transitions Persistence-time statistics for states

12 The two-fish system Mean effective forces (social) on 2-fish & 3-fish systems 14 experiments of 56 minutes each Zero force high density Higher speed larger front-back distance Higher left-right distance larger turning force

13 Adaptive-network analysis of universal features in collective motion Dr. Gerd Zschaler Dr. Anne-Ly Do Publications: Adaptive-network models of swarm dynamics, New J. Phys. July 2011 [doi: / /13/7/073022] Prof. Thilo Gross

14 The locust experiment Buhl et al. - Science 2 June 2006: Cannibalistic interactions! (equivalent to alignment?) - A more generic approach needed?

15 Mean-field solution Consider left-going and right-going populations R & L: R L 1 Rate equation: 2 2 d t L q R q L w L R w R L w L R w R q L R R L R L w 3 L Stationary solutions Disordered: L R 1 2 Ordered (for low noise or high density): R L w L RL R 0 q 3 q w L R R q w 3 R q / w 3

16 The adaptive network approach Adaptive Networks: collective motion States direction of motion Links mutual awareness

17 Adaptive networks: results Subcritical or supercritical pitchfork bifurcation 1 st or 2 nd order transition Identified processes behind each transition type Intermittent dynamics and collective memory Heading persistence-time distribution Non-Poissonian direction switching Same power-law as in agent-based simulations

18 when you talk about Twitter the media goes nuts

19 Elasticity-based mechanism for collective motion in active solids DILBERT Eliseo Ferrante Publications: Elasticity-based mechanism for collective motion in active solids and active crystals. Submitted to Phys. Rev. Lett., March 2013 Prof. Ali-Emre Turgut Collective motion dynamics of active solids and active crystals. To appear in New Journal of Physics, 2013

20 Toy model with only attraction-repulsion interactions

21 Simulation dynamics Spring-mass model of elastic sheet Active crystals: Rotational ordered state Translational ordered state (metastable) (preferred heading direction) Ordered states develop below critical noise

22 Self-propelled agents steer away from highenergy modes Energy cascades towards low-energy modes Agents self-organize into growing regions of coherent motion

23 Stability matrix = Characteristic polynomial: Routh s stability criterion: C0 C3 C1 C2 < 0 Characteristic polynomial:

24 Active solid setup Random positions Neighbors connected by linear springs Agents here colored by angle Coherent regions grow Energy flows to lower modes

25 Recap & The End Collective motion / swarming / flocking / active matter New big-data experiments with animal groups Minimal adaptive network model Active solids and active crystals Fin

26 Fin