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

2. Group motion of people: lane formation

3. Ordered motion (Kaba stone, Mecca)

4. Collective “action”: Mexican wave

5. STATISTICAL PHYSICS OF COLLECTIVE BEHAVIOUR Collective behaviour is a typical feature of living systems consisting of many similar units 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*

6. - Methods of statistical physics can be successfully used to interpret collective behaviour - 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 because of 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) MESSAGE

7. bacteria robots

8. Synchronization Dependence of sound intensity On time Examples: (fire flies, cicada, heart, steps, dancing, etc) “Iron” clapping: collective human behaviour allowing quantitative analysis Nature, 403 (2000) 849

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

10. Mexican wave (La Ola) Phenomenon : A human wave moving along the stands of a stadium One section of spectators stands up, arms lifting, then sits down as the next section does the same. Interpretation: using modified models originally proposed for excitable media such as heart tissue or amoeba colonies Nature, 419 (2002) 131

11. Mexican wave Typical Speed: 12 m/sec width: 10 m/sec 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 Examples: * fire fronts * cardiac tissue * Belousov- Zabotinsky re- action * aggregation of amoebae Three states

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

14. Results Number of initiators threshold Probability of generating a wave This approach has the potential of interpreting the spreading of excitement in crowds under more complex conditions

15. 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

16.                            2d 1d t t+  t t+2  t ------------------------------------------------------------------------------------------------- Simplest aspect of group motion: flocking, herding

17. Swarms, flocks and herds Model: The particles - maintain a given velocity - follow their neighbours - motion is perturbed by fluctuations Result: ordering is due to motion

18. 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)

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

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

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

22. Social force:”Crystallization” in a pool

23. Moving along a wider corridor Typical situation crowd Spontaneous segregation (build up of lanes) optimization Phys. Rev. Lett. (2000)

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

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

26. “Panic at the rock concert in Brussels”

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

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

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

32. A simple model: Follow your neighbors ! absolute value of the velocity is equal to v 0 new direction is an average of the directions of neighbors plus some perturbation η j (t) Simple to implement analogy with ferromagnets, differences: for v 0 << 1 Heisenberg-model like behavior for v 0 >> 1 mean-field like behavior in between: new dynamic critical phenomena (ordering, grouping, rotation,..)

33. 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

34. Social force:”Crystallization” in a pool

36. 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

44. Motion driven by fluctuations Molecular motors: Protein molecules moving in a strongly fluctuatig environment along chains of complementary proteins Our model: Kinesin moving along microtubules (transporting cellular organelles). „scissors” like motion in a periodic, sawtooth shaped potential

45. Transport of a polymer through a narrow hole Motivation: related experiment, gene therapy, viral infection Model: real time dynamics (forces, time scales, three dimens.) Translocation of DNS through a nuclear pore duration: 1 ms Lengt of DNS: 500 nm duration: 12 s Length of DNS : 10  m

47. Collective motion Humans

48. Ordered motion (Kaba stone, Mecca)