Crowd Control: A physicist’s approach to collective human behaviour

1. Crowd Control:A physicist’s approach to collective human behaviour T. Vicsek http://angel.elte.hu/~vicsek Principal collaborators: A.L. Barabási, A. Czirók, I. Farkas, Z.Néda and D. Helbing

2. Collective “action”: Mexican wave

3. Group motion of people: lane formation

4. Ordered motion (Kaba stone, Mecca)

5. The Hajj (Mecca) Stoning of the evil (365 victims in 2006 stampede due to panic)

6. STATISTICAL PHYSICS OF COLLECTIVE BEHAVIOUR Collective behaviour in systems with many similar units selected examples: Physics: ordering in space (crystallization) adopting common directions (spontaneous magetization) Biology: ordered motion (flocking) pattern formation (zebra stripes, seeshells, etc) Society: ordering of “opinions” (fashion, flocking on the stock market, parties, a much studied field in sociology) ordered motion of people (e.g., lane formation) ordering in space (crystallization?) It is typical for such systems (synchronization, networking,etc)

7. Main feature of collective phenomena: the behaviour of the units becomes similar, but very different from what they would exhibit in the absence of the others Main types: (phase) transitions, pattern/network formation, synchronization*, group motion*

8. MESSAGE • - Methods of statistical physics can be successfully used to interpret collective behaviour • - Why? Because the above mentioned behavioural patterns can be observed and quantitatively described/explained for a wide range of phenomena starting from the simplest manifestations of life (bacteria) up to humans. The principle of universality • CONCEPT • Experimentally observed simple behaviour of a very complex system (people) is interpreted with models taking into account details of “reality”. • See, e.g.: Fluctuations and Scaling in Biology, T. Vicsek, ed. (Oxford Univ. Press, 2001)

9. One of the universal patterns

10. bacteria robots

11. Mexican wave Typical Speed: 12 m/sec width: 10 m direction: clockwise Appears usually during less exciting periods of the game Nature, 419 (2002) 131

12. Model: excitable medium Excitable: inactive can be activated (I>c!) active : active cannot be activated refractory: inactive cannot be activated Three states Activated if total calculated exitation/activity level exceeds a threshold Examples: * fire fronts * cardiac tissue * aggregation of amoebae

13. Simulation – demoone inactive and 5 five active/refractory stages

14. Spontaneous symmetry breaking: clockwise or anticlockwise? An example forinstantaneous collective decision making There is always one wave. How is the direction of propagation selected? Within the fraction of a second? Local: an integrated level of excitement of neighbours Global: a decreased tendency to react if the wave as a whole (its centre of actual activity) is moving away, i.e., vx < 0. Global: G(vx ,distance) You want to be with the “winners”. Input excitement level: local  G(vx ,distance) Instability. Taken into account by a sigmoid-like function of width  G(vx ) 1 wherevx > 0 means that the centre of activity is approaching smaller , stronger effect larger sensitivity  0 vx < 0vx > 0

15. Typical situation, “real time” No global interaction, “slow motion”

16. With global interaction, “slow motion” Small “external” bias in the opposite direction “slow motion”

17. Selecting a direction as a function of sensitivity to the global velocity Probability of bidirectional wave less sensitive Probability of choosing a single direction more sensitive Quick “synchronization” of the action: “the nodding “ effect (when you want to guess the other’s intention during board meetings or other voting situations)

18. “External” symmetry breaking Any asymmetry (due to the environment, right handedness, etc. acts as an “external field” As in, e.g., in a suddenly undercooled Ising ferromagnet Level ofasymmetry 1-  Already for 0.05 the difference between clockwise and anticlockwise directions is close to 30%

19. Group motion: from flocking of animals to patterns of collective motion of humans Ordering in velocity space

20. Swarms, flocks and herds • Model:The particles - maintain a given absolute value of the velocity v0 - follow their neighbours - motion is perturbed by fluctuations  • Result:ordering is due to motion

21. Two examples: keratocites (skin cells) and penguins Motion: even skin cells order No motion: no ordering in two dimensions Simulation: rotation in the model with hard core repulsion added

22. Collective motion of keratocites Skin cells obtained from scales of gold fish kept in the lab

23. Modelling the group motion of keratocites

24. simulations

26. Group motion of humans (observations) Corridor in stadium: jamming Pedestrian crossing: Self-organized lanes

27. Group motion of humans (theory) • Model: - Newton’s equations of motion - Forces are of social, psychological or physical origin (herding, avoidance, friction, etc) • Statement: - Realistic models useful for interpretation of practical situations and applications can be constructed

28. EQUATION OF MOTION for the velocity of pedestrian i “psychological / social”, elastic repulsion and sliding friction force terms, and g(x) is zero, if dij > rij , otherwise it is equal to x. MASS BEHAVIOUR: “herding”

29. Social force:”Crystallization” in a pool

30. Panic • Escaping from a closed area • through a door • At the exit physical forces are • dominant ! Nature, 407 (2000) 487

31. Paradoxial effects • obstacle: helps (decreases the presure) • widening: harms (results in a jamming-like effect)

32. The “impatience or anxiety factor” N=3000 N after 50 sec “patient” 95 “impatient” 2

33. Large scale (70,000 particles) and complex geometry: an attempt to simulate how spectators would try to escape from a stadium hosting a rock concert in Belgium • More realistic simulations include taking into account additional factors like: • - herding • choosing an exit with a • probability depending on • * original intention • * exit’s distance • * exit’s size • “patience” • - “injured” block the exit • - etc.

34. Simulation of the Jamarat bridge in Mecca during the Hajj (Helbing et al 2005)

35. Effects of herding • Dark room with two exits • Changing the level of herding medium No herding Total herding

36. http://angel.elte.hu/~vicsek http://angel.elte.hu/wave http://angel.elte.hu/panic http://www.nd.edu/~networks/clap

38. What is displayed in this experimental picture? Directions of prehairs on the wing of a mutant fruitfly (the gene responsible for global directionality is kicked out, wihle the one enforcing local alignment is operational)

39. Collective motion Patterns of motion of similar, interacting organisms Flocks, herds, etc Cells Humans

40. Phys. Rev. Lett. (1999) Escaping from a narrow corridor The chance of escaping (ordered motion) depends on the level of “excitement” (on the level of perturbations relative to the “follow the others” rule) Large perturbatons Smaller perturbations

41. A simple model: Follow your neighbors ! • absolute value of the velocity is equal to v0 • new direction is an average of the directions of • neighbors • plus some perturbation ηj(t) • Simple to implement • analogy with ferromagnets, differences: • for v0 << 1 Heisenberg-model like behavior • for v0>> 1 mean-field like behavior • in between: new dynamic critical phenomena (ordering, grouping, rotation,..)

42. Acknowledgements Principal collaborators: Barabási L.,Czirók A.,Derényi I., Farkas I., Farkas Z., Hegedűs B., D. Helbing, Néda Z., Tegzes P. Grants from: OTKA, MKM FKFP/SZPÖ, MTA, NSF

43. Major manifestations Pattern/network formation : • Patterns: Stripes, morphologies, fractals, etc • Networks: Food chains, protein/gene interactions, social connections, etc Synchronization: adaptation of a common phase during periodic behavior Collective motion: • phase transition from disordered to ordered • applications: swarming (cells, organisms), segregation, panic

50. Fourier-gram of rhythmic applause Frequency Time  Darkness is proportional to the magnitude of the power spectrum