Collective motion: from 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: 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 algorithm (Craig Reynolds – Sony) . Flocks, , and Schools: A Distributed Behavioral Model Computer Graphics, 21(4), pp. 25-34, 1987 . Defined with simple interaction rules

▪ Separation

▪ Alignment

▪ Cohesion Background: Physics

 Motivation

 The (1995 results)

 Order parameter (alignment/magnetization)

 Main Result  “Novel type” of phase transition

Background: Biology

The “zones” model

- “Insect-like” :

- 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  qR  L w3 L R  R L

 Stationary solutions

 Disordered: 1 L  R  2  Ordered (for low noise or high density): R

0  qR  L w3 L RL  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 / / flocking / active matter

 New big-data experiments with animal groups

 Minimal adaptive network model

 Active solids and active crystals … Fin … Fin