Katsuhiro Nishinari

1
Jammology Physics of self-driven
particlesToward solution of all jams

• Katsuhiro Nishinari
• Faculty of Engineering, University of Tokyo

2
Outline

• Introduction of Jammology
• Self-driven particles, methodology
• Simple traffic model for
• ants and molecular
  motors
• Conclusions

3
Jams Everywhere
4
School, Herd, Flock, etc.
5
What are self-driven particles (SDP)?

• Vehicles, ants, pedestrians, molecular motors
• Non-Newtonian particles,
• which do not satisfy three laws of motion.
• ex. 1) Action Reaction,
• force is
  psychological
• 2) Sudden change of motion

D. Helbing, Rev. Mod. Phys. vol.73 (2001) p.1067.
D. Chowdhury, L. Santen and A. Schadschneider,Phys
. Rep. vol.329 (2000) p.199.
6
JammologyCollective dynamics of SDP
Text book of Jammology

• Conventional mechanics,
• or statistical physics cannot
• be directly applicable.
• Rule-based approach
• (e.g., CA model)
• Numerical computations
• Exactly solvable models
• (ASEP,ZRP)

7
Subjects of Jammology

• Vehicles
• car, bus, bicycle, airplane,etc.
• Humans
• Swarm, animals,
• ant, bee, cockroach, fly, bird,fish,etc.
• Internet packet transportation
• Jams in human body
• Blood, Kinesin, ribosome, etc.
• Infectious disease, forest fire, money, etc.

8
Conventional theory of Jam Queuing theory
Out
In
Service
Breakdown of balance of in and out causes Jam.
9
What is NOT considered in Queuing theory

• Exclusion effect of finite volume of SDP

ASEP model can deal the exclusion!
10
ASEPA toy model for jam

• ASEP(Asymmetric Simple Exclusion Process)

Rulemove forward if the front is empty
0 1 0 1 1 0 0 1 0 1 1 1 0 0 0
0 0 1 1 0 1 0 0 1 1 1 0 1 0 0
This is an exactly solvable model, i.e., we can
calculate density distribution, flux, etc in the
stationary state.
11
Who considered ASEP?

• Macdonald Gibbs, Biopolymers, vol.6 (1968) p.1.
• Protein composition process of Ribosomes on
  mRNA

This research has not been recognized until
recently.
12
Fundamental diagram of ASEP
with periodic boundary condition

• Flow-density Particle-hole symmetry

• Velocity-density monotonic decrease

M.Kanai, K.Nishinari and T.Tokihiro,J. Phys. A
Math. Gen., vol.39 (2006) pp.9071-9079..
13
Ultradiscrete method reveals the relation between
different traffic models!
J.Phys.A, vol.31 (1998) p.5439
Ultradiscrete method
ASEP(Rule 184)
Burgers equation
CA model
Macroscopic model
Euler-Lagrange transformation
Phys.Rev.Lett., vol.90 (2003) p.088701
OV model
Car-following model
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Toward solution of all kind of jams!

• Vehicular traffic
• cars, bus, trains,
• Pedestrians
• Jams in our body

15
Traffic in ant-trail
Ants drop a chemical (generically called
pheromone) as they crawl forward. Other sniffing
ants pick up the smell of the pheromone and
follow the trail.
with periodic boundary conditions
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Ant trail traffic models and experiments

• Experiments and theory
• Differential equations

1) M. Burd, D. Archer, N. Aranwela and D.J.
Stradling, American Natur. (2002) 2) I.D.Couzin
and N.R.Franks, Proc.R.Soc.Lond.B (2002) 3) A.
Dussutour, V. Fourcassie, D.Helbing and J.L.
Deneubourg, Nature (2004)
E.M.Rauch, M.M.Millonas and D.R.Chialvo,
Phys.Lett.A (1995)
Ant
Langevin type equation
pheromonal field
ant density at x
evaporation rate
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Ant trail CA model
One lane, uni-directional flow
Dynamics

1. Ants movement
2. Update Pheromone(creation diffusion)

f f f
Parameters q lt Q, f
D. Chowdhury, V. Guttal, K. Nishinari and A.
Schadschneider,J.Phys.AMath.Gen., Vol. 35
(2002) pp.L573-L577.
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Bus Route Model

• Bus operation systemIn fact the ant CA!

The dynamics is the same as the ant model
Loose cluster formation buses bunching up
together
f f f f
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Modeling of pedestrians

• Basic features of collective behaviours of
  pedestrians
• 1) Arch formation at exit
• 2) Oscillation of flow at bottleneck
• 3) Lane formation of counterflow at corridor
• Models for evacuation

Social force model (Continuous model)
D.Helbing, I.Farkas and T.Vicsek, Nature (2000).
Floor field model (CA model)
C.Burstedde, K.Klauck, A.Schadschneider,J.Zittartz
, Physica A (2001)
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Floor field CA Model
C.Burstedde, K.Klauck, A.Schadschneider,J.Zittartz
, Physica A, vol.295 (2001) p.507.
Pedestrians in evacuation herding behavior
long range interaction
For computational efficiency, can we describe
the behavior of pedestrians by using local
interactions only?
Idea Footprints Feromone
Long range interaction is imitated by local
interaction through memory on a floor.
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Details of FF model

• Floor is devided into cells (a cell4040 cm2)
• Exclusion principle in each cell
• Parallel update
• A person moves to one of nearest cells with the
  probability defined by floor field(FF).
• Two kinds of FF is introduced in each cell
• 1) Dynamic FFfootprints of persons
• 2) Static FFDistance to an exit

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Dymanic FF (DFF)

• Number of footprints on each cell
• Leave a footprint at each cell whenever a person
  leave the cell
• Dynamics of DFF
• dissipationdiffusion
• dissipation diffusion
• Herding behaviour
• choose the cell that has more footprints
• Store global information to local cells

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Static FF (SFF) Dijkstra metric

• Distance to the destination is recorded at each
  cell

Two exits with four obstacles
One exit with a obstacle
This is done by Visibility Graph and Dijkstra
method.
K. Nishinari, A. Kirchner, A. Namazi and A.
Schadschneider,
IEICE Trans. Inf. Syst.,
Vol.E87-D (2004) p.726.
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Problem of Zone partition
Application of SFF
By using SFF
Which door is the nearest?
The ratio of an area to the total area determines
the number of people who use the door in
escaping from this room.
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Probability of movement
Distance between the cell (i,j) and a door.
Number of footprints at the cell (i,j).
Set I1 if (i,j) is the previous direction of
motion.
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Update procedure
Initial Calculate SFF

1. Update DFF (dissipation diffusion)
2. Calculate and determine the target cell
3. Resolution of conflict
4. Movement
5. Add DFF 1

Resolution of conflict
Parameter
All of them cannot move.
One of them can move.
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Meanings of parameters in the model

• kS kD
• kS large Normal (kS small Random walk)
• kD large Panic
• kD / kS Panic degree (panic parameter)
• large competition
• small coorporation

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Simulations using inertia effect

• There is a minimum in the evacuation time when
  the effect of inertia is introduced.

SFF is strongly disturbed.
People become less flexible to form arches. (Do
not care others!)
People become flexible to avoid congestion.
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Simulation Example Evacuation at Osaka-Sankei
Hall
Jams near exits.
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Hamburg airport in Germany
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Influence of Obstacle
Placed an obstacle near exit.
2offset
None
Center
1offset
Intensive competition.
If an obstacle is placed asymmetrically, total
evacuation time is reduced!
D.Helbing, I.Farkas and T.Vicsek, Nature, vol.407
(2000) p.487.
A.Kirchner, K.Nishinari, and A.Schadschneider,Phy
s. Rev. E, vol.67 (2003) p.056122.
32
Conclusions

• Traffic Jams everywhere
• Jammology is interdisciplinary research
• among Math. , Physics and Engineering!
• Examples
• Ant trail CA model is proposed by extending ASEP.
  The model is well analyzed by ZRP.
• Non-monotonic variation of the average speed of
  the ants is confirmed by robots experiment.
• Traffic jam in our body is related to diseases.
• Modelling molecular motors
• Jammology Math. , Physics and Engineering

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Conclusions

• Ant trail CA model is proposed by extending ASEP.
  The model is well analyzed by ZRP.
• Non-monotonic variation of the average speed of
  the ants is confirmed by robots experiment.
• FF model is a local CA model with memory, which
  can emulating grobal behavior.
• FF model is quite efficient tool for simulating
• pedestrian behavior.
• Jammology Math. , Physics and Engineering