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