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Crowd Control: A physicist’s approach to collective human behaviour. T. Vicsek Principal collaborators: A.L. Barab á si, A. Czir ó k , I. Farkas , Z. N é da and D. Helbing. Group motion of people: lane formation. Ordered motion (Kaba stone, Mecca).

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crowd control a physicist s approach to collective human behaviour
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

statistical physics of collective behaviour
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*

slide6

MESSAGE

  • - 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)
slide7

bacteria

robots

synchronization
Synchronization
  • Examples: (fire flies, cicada, heart, steps, dancing, etc)
  • “Iron” clapping: collective human behaviour allowing
  • quantitative analysis

Dependence of sound intensity

On time

Nature, 403 (2000) 849

slide9

Fourier-gram of rhythmic applause

Frequency

Time 

Darkness is proportional to the magnitude of the power spectrum

mexican wave la ola
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

mexican wave
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

slide12

Model: excitable medium

Excitable: inactive can be activated (I>c!)

active : active cannot be activated

refractory: inactive cannot be activated

Three states

Examples:

* fire fronts

* cardiac tissue

* Belousov-

Zabotinsky re-

action

* aggregation of

amoebae

simulation demo one inactive and 5 five active refractory stages
Simulation – demoone inactive and 5 five active/refractory stages
slide14

Results

Probability of generating a wave

threshold

Number of initiators

This approach has the potential of interpreting the spreading of excitement in crowds under more complex conditions

group motion of humans theory
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

slide16

Simplest aspect of group motion: flocking, herding

2d

1d

-------------------------------------------------------------------------------------------------

t

         

t+t

        

       

t+2t

swarms flocks and herds
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

slide18

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)

group motion of humans observations
Group motion of humans (observations)

Corridor in stadium: jamming

Pedestrian crossing: Self-organized lanes

escaping from a narrow corridor

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

slide21

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

moving along a wider corridor

Phys. Rev. Lett. (2000)

Moving along a wider corridor
  • Spontaneous segregation (build up of lanes)
  • optimization

Typical situation

crowd

panic
Panic
  • Escaping from a closed area through a door
  • At the exit physical forces are dominant !

Nature, 407 (2000) 487

paradoxial effects
Paradoxial effects
  • obstacle: helps (decreases the presure)
  • widening: harms (results in a jamming-like effect)
effects of herding
Effects of herding

medium

  • Dark room with two exits
  • Changing the level of herding

Total herding

No herding

slide28

http://angel.elte.hu/~vicsek

http://angel.elte.hu/wave

Mexican wave

http://angel.elte.hu/panic

http://www.nd.edu/~networks/clap

collective motion
Collective motion

Patterns of motion of similar, interacting organisms

Flocks, herds, etc

Cells

Humans

slide32

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,..)
acknowledgements
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

major manifestations
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

motion driven by fluctuations
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

translocation of dns through a nuclear pore
Translocation of DNS through a nuclear pore

Transport of a polymer through a narrow hole

Motivation: related experiment, gene therapy, viral infection

Model: real time dynamics (forces, time scales, three dimens.)

duration: 1 ms

Lengt of DNS: 500 nm

duration: 12 s

Length of DNS : 10 mm