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Cellular Automata Modelling of Traffic in Human and Biological Systems Andreas Schadschneider Institute for Theoretical Physics University of Cologne www.thp.uni-koeln.de/~as www.thp.uni-koeln.de/ant-traffic
Introduction ,[object Object],[object Object],[object Object]
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object]
Cellular Automata ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Asymmetric Simple Exclusion Process
Asymmetric Simple Exclusion Process ,[object Object],[object Object],[object Object],Caricature of traffic: For applications: different modifications necessary q q
Influence of Boundary Conditions ,[object Object],Applications:  Protein synthesis Surface growth Boundary induced phase transitions exactly solvable!
Phase Diagram Low-density phase J=J(p,  ) High-density phase J=J(p,  ) Maximal current phase J=J(p)
Highway Traffic
Cellular Automata Models ,[object Object],[object Object],[object Object],[object Object],velocity
Update Rules ,[object Object],[object Object],[object Object],[object Object],[object Object],(d j  = # empty cells  in front of car j)
Example Configuration at time t: Acceleration (v max  = 2): Braking: Randomization (p = 1/3): Motion (state at time t+1):
Interpretation of  the Rules ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Simulation of  NaSch  Model ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Fundamental Diagram Relation:  current (flow)  $  density
Metastable States ,[object Object],[object Object],[object Object]
VDR Model ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Simulation of VDR Model NaSch model VDR-model: phase separation   Jam stabilized by J out  < J max VDR model
Dynamics on Ant Trails
Ant trails ants build “road” networks: trail system
Chemotaxis ,[object Object],[object Object],[object Object],[object Object],[object Object]
Ant trail model ,[object Object],[object Object],Dynamics: f  f  f parameters:   q < Q, f q q Q q   q   Q
Fundamental diagram of ant trails different from highway traffic: no egoism velocity vs. density Experiments: Burd et al. (2002, 2005) non-monotonicity  at small evaporation rates!!
Spatio-temporal organization ,[object Object],early times steady state coarsening dynamics
Pedestrian Dynamics
Collective Effects ,[object Object],[object Object],[object Object],[object Object]
Pedestrian Dynamics ,[object Object],[object Object],[object Object],[object Object]
Pedestrian model ,[object Object],[object Object],[object Object],[object Object],idea:  Virtual chemotaxis chemical trace :  long-ranged   interactions are translated into   local   interactions with  ‘‘ memory “
Floor field cellular automaton ,[object Object],[object Object],Interaction:  virtual chemotaxis   (not measurable!) dynamic  +  static  floor fields interaction with  pedestrians  and  infrastructure
Transition Probabilities ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Transition Probabilities ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Lane Formation velocity profile
Intracellular Transport
Intracellular Transport ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],Fuel: ATP ATP  ADP + P  Kinesin Dynein Kinesin and Dynein: Cytoskeletal motors
Practical importance in bio-medical research Goldstein, Aridor, Hannan, Hirokawa, Takemura,……………. Blindness KIF3A  kinesin Retinitis pigmentosa Sinus and Lung disease, male infertility Dynein Primary ciliary diskenesia/  Kartageners’ syndrome Pigmentation defect Myosin V Griscelli disease Hearing loss Myosin VII Usher’s syndrome Neurological disease; sensory loss KIF1B  kinesin Charcot-Marie tooth disease Symptom Motor/Track Disease
ASEP-like Model of Molecular Motor-Traffic   q D A Parmeggiani, Franosch and Frey, Phys. Rev. Lett. 90, 086601 (2003) ASEP  +  Langmuir-like adsorption-desorption Also, Evans, Juhasz and Santen, Phys. Rev.E. 68, 026117 (2003)
position of  domain wall  can be measured as a function of controllable parameters. Nishinari,  Okada,  Schadschneider, Chowdhury,  Phys. Rev. Lett. (2005) KIF1A (Red) MT (Green) 10 pM 100 pM 1000pM 2 mM of ATP 2   m Spatial organization of KIF1A motors: experiment
Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Collaborators ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Thanx to: Rest of the World: Debashish Chowdhury (Kanpur) Ambarish Kunwar (Kanpur) Katsuhiro Nishinari (Tokyo) T. Okada (Tokyo) + many others

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Traffic human-ca

  • 1. Cellular Automata Modelling of Traffic in Human and Biological Systems Andreas Schadschneider Institute for Theoretical Physics University of Cologne www.thp.uni-koeln.de/~as www.thp.uni-koeln.de/ant-traffic
  • 2.
  • 3.
  • 4.
  • 6.
  • 7.
  • 8. Phase Diagram Low-density phase J=J(p,  ) High-density phase J=J(p,  ) Maximal current phase J=J(p)
  • 10.
  • 11.
  • 12. Example Configuration at time t: Acceleration (v max = 2): Braking: Randomization (p = 1/3): Motion (state at time t+1):
  • 13.
  • 14.
  • 15. Fundamental Diagram Relation: current (flow) $ density
  • 16.
  • 17.
  • 18. Simulation of VDR Model NaSch model VDR-model: phase separation Jam stabilized by J out < J max VDR model
  • 19. Dynamics on Ant Trails
  • 20. Ant trails ants build “road” networks: trail system
  • 21.
  • 22.
  • 23. Fundamental diagram of ant trails different from highway traffic: no egoism velocity vs. density Experiments: Burd et al. (2002, 2005) non-monotonicity at small evaporation rates!!
  • 24.
  • 26.
  • 27.
  • 28.
  • 29.
  • 30.
  • 31.
  • 34.
  • 35.
  • 36. Practical importance in bio-medical research Goldstein, Aridor, Hannan, Hirokawa, Takemura,……………. Blindness KIF3A kinesin Retinitis pigmentosa Sinus and Lung disease, male infertility Dynein Primary ciliary diskenesia/ Kartageners’ syndrome Pigmentation defect Myosin V Griscelli disease Hearing loss Myosin VII Usher’s syndrome Neurological disease; sensory loss KIF1B kinesin Charcot-Marie tooth disease Symptom Motor/Track Disease
  • 37. ASEP-like Model of Molecular Motor-Traffic   q D A Parmeggiani, Franosch and Frey, Phys. Rev. Lett. 90, 086601 (2003) ASEP + Langmuir-like adsorption-desorption Also, Evans, Juhasz and Santen, Phys. Rev.E. 68, 026117 (2003)
  • 38. position of domain wall can be measured as a function of controllable parameters. Nishinari, Okada, Schadschneider, Chowdhury, Phys. Rev. Lett. (2005) KIF1A (Red) MT (Green) 10 pM 100 pM 1000pM 2 mM of ATP 2  m Spatial organization of KIF1A motors: experiment
  • 39.
  • 40.

Notas del editor

  1. cellular automaton model
  2. no intelligence on the level of individual dynamics, but for decision making etc.