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-0507745 & PHY-0848755 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 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 Background: Biological motivation from: Collective Minds (documentary by Jacob Kneser) Background: Computer graphics Intuitive flocking algorithm (Craig Reynolds – Sony) . Flocks, Herds, and Schools: A Distributed Behavioral Model Computer Graphics, 21(4), pp. 25-34, 1987 . Defined Boids with simple interaction rules ▪ Separation ▪ Alignment ▪ Cohesion Background: Physics Motivation The Vicsek model (1995 results) Order parameter (alignment/magnetization) Main Result “Novel type” of phase transition Background: Biology The “zones” model - “Insect-like” swarm: - Torus, “milling”: Journal of Theoretical - Migration, flocking: Biology (2002) 218, 1-11 I. D. Couzin, J. Krause, R. James, G. D. Ruxton & N. R. Franks 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) 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. 2013 [9(2), e1002915] • Inferring the structure and dynamics of interactions in schooling fish, PNAS July 2011 [doi:10.1073/pnas.1107583108] Prof. Iain Couzin . Experimental System . 1000 fish dynamics Polarized state Rotating state Swarming state . Dynamics of state transition State transitions Persistence-time statistics for states . 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 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:10.1088/1367-2630/13/7/073022] Prof. Thilo Gross – The locust experiment Buhl et al. - Science 2 June 2006: 1402-1406 -Cannibalistic interactions! - A more generic approach needed? (equivalent to alignment?) – “Mean-field” solution Consider left-going and right-going populations R & L: R L 1 Rate equation: 2 2 dt L q R q L w2 L R w2 R L w3 L R w3 R L 2 2 qR L w3 L R R L Stationary solutions Disordered: 1 L R 2 Ordered (for low noise or high density): R 0 qR L w3 L RL R q 1 1 q L R R w3 2 4 w3 q / w3 – The adaptive network approach . Adaptive Networks: . collective motion States direction of motion Links mutual awareness – Adaptive networks: results Subcritical or supercritical pitchfork bifurcation 1st or 2nd 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 …when you talk about Twitter… … the media goes nuts 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 • Collective motion dynamics of active solids and active crystals. Prof. Ali-Emre Turgut To appear in New Journal of Physics, 2013 – Toy model with only attraction-repulsion interactions – 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 Self-propelled agents steer away from high- energy modes Energy cascades towards low-energy modes Agents self-organize into growing regions of coherent motion Stability matrix = Characteristic polynomial: Routh’s stability criterion: C0 C3 – C1 C2 < 0 Characteristic polynomial: Active solid setup . Random positions . Neighbors connected by linear springs Agents here colored by angle . Coherent regions grow . Energy flows to lower modes 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 … Fin .