1. Jammology Physics of self-driven particles Toward 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. Jammology=Collective 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. ASEP=A toy model for jam
ＡＳＥＰ（Asymmetric Simple Exclusion Process）
Rule：move forward if the front is empty 1 1
This is an exactly solvable model, i.e., we can calculate
density distribution, flux, etc in the stationary state.

11. This research has not been recognized until recently.
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
In the stationary state of TASEP,
flow density relation is
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

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
OV model
Car-following model

14. 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

16. 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
: evaporation rate
: ant density at x

17. Ant trail CA model f f f q q Q One lane, uni-directional flow
Dynamics:
Ants movement
Update Pheromone(creation & diffusion)
q q Q
Parameters: q < Q, f
f f f
D. Chowdhury, V. Guttal, K. Nishinari and A. Schadschneider, J.Phys.A:Math.Gen., Vol. 35 (2002) pp.L573-L577.

18. Bus Route Model ｆ ｆ f f Bus operation system＝In fact the ant CA！ Q Q q
The dynamics is the same as the ant model　
Q Q q
Loose cluster formation = buses bunching up together
ｆ　　　　 ｆ　　　f 　　　f

19. 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)

20. Floor field CA Model Idea： Footprints = Feromone
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“.

21. Details of FF model Floor is devided into cells (a cell=40*40 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 FF・・・footprints of persons
2) Static FF・・・Distance to an exit

22. Dymanic FF (DFF) Number of footprints on each cell
Leave a footprint at each cell whenever a person leave the cell
Dynamics of DFF
　　　　　　　　dissipation＋diffusion
　　 dissipation・・・ diffusion・・・
Herding behaviour =
choose the cell that has more footprints
Store global information to local cells 4 2 1

23. Static FF (SFF) = Dijkstra metric
Distance to the destination is recorded at each cell
One exit with a obstacle
Two exits with four obstacles
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.

24. Problem of “Zone partition”
Application of SFF
Problem of “Zone partition”
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.

25. Probability of movement
Distance between the cell (i,j) and a door.
Number of footprints at the cell (i,j).
Set I=1 if (i,j) is the previous direction of motion.

26. Update procedure Update DFF (dissipation & diffusion)
Initial: Calculate SFF
Update DFF (dissipation & diffusion)
Calculate and determine the target cell
Resolution of conflict　　　　　　　　　　　　
Movement
Add DFF +1
Resolution of conflict
Parameter
All of them cannot move.
One of them can move.

27. 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

28. 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.

29. Simulation Example: Evacuation at Osaka-Sankei Hall
Jams near exits.

30. Hamburg airport in Germany

31. Influence of Obstacle If an obstacle is placed asymmetrically,
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,Phys. Rev. E, vol.67 (2003) p

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

33. 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