Crowd Control: A physicist’s approach to collective human behaviour
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Transcript of Crowd Control: A physicist’s approach to collective human behaviour
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Crowd Control:A physicist’s approach to collective
human behaviour
T. Vicsek
in collaboration with:
A.L. Barabási, A. Czirók, I. Farkas, Z. Néda and D. Helbing
http://angel.elte.hu/~vicsek
EPS12, Budapest, Aug. 2002
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Group motion of humans (observations)
Pedestrian crossing: Self-
organized lanes
Corridor in stadium: jamming
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Ordered motion (Kaba stone, Mecca)
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Collective “action”: Mexican wave
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STATISTICAL PHYSICS OF COLLECTIVE BEHAVIOUR
Collective behavior is a typical feature of living systems consisting of many similar units
- We consider systems in which the global behaviour does not depend on the fine details of its units (“particles”)
- 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*
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- Methods of statisical 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 common underlying principles
•See, e.g.: Fluctuations and Scaling in Biology, T. Vicsek, ed. (Oxford Univ. Press, 2001)
MESSAGES
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Synchronization
Dependence of sound intensityOn time
• Examples: (fire flies, cicada, heart, steps, dancing, etc) • “Iron” clapping: collective human behaviour allowing quantitative analysis
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Time
Frequency
Fourier-gram of rhythmic applause
Darkness is proportional to the magnitude of the power spectrum
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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
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flocking, herding
2d
1dt
t+tt+2t
-------------------------------------------------------------------------------------------------
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Escaping from a narrow corridor
Large perturbatons Smaller 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)
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EQUATION OF MOTION for the velocity of pedestrian i
, exp
, )()()( 00
ijtjiijijijijijiijijiij
iWij
iji
iiii
ii
tvdrgndrkgBdrAf
fftvtetv
mdt
dvm
“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
, )(1 )( 00
jjiiii tepepNte
. ofion normalizat denotes )( where zzzzN
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Social force:”Crystallization” in a pool
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Moving along a wider corridor
Typical situation crowd
• Spontaneous segregation (build up of lanes)• optimization
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Panic
• Escaping from a closed area through a door• At the exit physical forces are dominant !
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Paradoxial effects
•obstacle: helps (decreases the presure)•widening: harms (results in a jamming-like effect)
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Effects of herding
• Dark room with two exits• Changing the level of herding
medium
No herding
Total herding
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Collective motion
Patterns of motion of similar, interacting organisms
Humans
Cells Flocks, herds, etc
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A simple model: Follow your neighbors !
)()(
)()1( 0 t
tv
tvvtv j
Ri
Rij
•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,..)
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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 amoebea colonies
Model:
• three states: excitable, refractory, inactive
• triggering, bias
• realistic parameters lead to agreement with observations
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Swarms, flocks and herds
• Model: The particles
- maintain a given velocity
- follow their neighbours
- motion is perturbed by
fluctuations
• Result: oredering is due to motion
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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
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Social force:”Crystallization” in a pool
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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
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Nincs követés
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Közepes követés
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Teljes követés
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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
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Transport of a polymer through a narrow holeMotivation: related experiment, gene therapy, viral infectionModel: real time dynamics (forces, time scales, three dimens.)
Translocation of DNS through a nuclear pore
duration: 1 msLengt of DNS: 500 nm
duration: 12 sLength of DNS : 10 m
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Collective motion
Humans
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Ordered motion (Kaba stone, Mecca)