# 851-0585-15L From Crowds to Crises

Semester | Autumn Semester 2014 |

Lecturers | D. Helbing |

Periodicity | yearly course |

Language of instruction | English |

Comment | Prerequisites: solid mathematical skills. |

Abstract | This course presents a problem analysis and mathematical models of subjects like - pedestrian, evacuation, and crowd dynamics (including "panic"); - disaster spreading and response management; - bubbles and crashes in financial markets; - bankruptcy cascades; - the outbreak and breakdown of cooperation; - the formation of social norms; - the occurence of conflict and societal instabilities. |

Objective | Participants should learn to get an overview of the state of the art in the field, to present it in a well understandable way to an interdisciplinary scientific audience, to develop novel mathematical models for open problems, to analyze them with computers, and to defend their results in response to critical questions. In essence, participants should improve their scientific skills and learn to work scientifically. |

Content | The course discusses models of collective behaviors emerging in complex socio-economic and traffic systems. It covers subjects such as - pedestrian, evacuation, and crowd dynamics (including crowd disasters); - traffic dynamics; - the outbreak and breakdown of cooperation; - the formation of social norms; - the occurence of conflict and societal instabilities; Further subjects might be - disaster spreading and response management; - integrated risk management; - bubbles and crashes in financial markets; - bankruptcy cascades. The course builds on a broad scope of approaches such as (social) force models, network models, complexity theory, and evolutionary game theory. It discusses the relevance of, for example, self-organization phenomena, cascading effects, phase transitions, spatial and network interactions. Moreover, the course gives an idea of how mechanisms underlying the spreading of cooperation, norms, conflicts, or disasters may be modeled. The course stresses in particular the importance of interactions for the resulting system behavior, and the implications for mechanism design, such as traffic light (self-)control or traffic assistance systems. |

Lecture notes | A summary of the subjects is provided by the following papers: D. Helbing (2012) Social Self-Organization (Springer, Berlin). D. Helbing, A. Johansson (2010) Pedestrian, Crowd and Evacuation Dynamics. Encyclopedia of Complexity and Systems Science 16, 6476-6495. D. Helbing and K. Nagel (2004) The physics of traffic and regional development. Contemporary Physics 45(5), 405-426. D. Helbing (2013): Globally networked risks and how to respond. Nature 497, 51-59. Further reading: D. Helbing (2010) Quantitative Sociodynamics. Stochastic Methods and Models of Social Interaction Processes (Springer, Berlin). D. Helbing (2001) Traffic and related self-driven many-particle systems. Reviews of Modern Physics 73, 1067-1141. D. Helbing, H. Ammoser, and C. Kühnert (2005) Disasters as extreme events and the importance of network interactions for disaster response management. Pages 319-348. in: S. Albeverio, V. Jentsch, and H. Kantz (eds.) Extreme Events in Nature and Society (Springer, Berlin). D. Helbing (2004) Dynamic decision behavior and optimal guidance through information services: Models and experiments. Pages 47-95 in: M. Schreckenberg and R. Selten (eds.) Human Behaviour and Traffic Networks (Springer, Berlin). D. Helbing and S. Lämmer (2005) Supply and production networks: From the bullwhip effect to business cycles. Page 33-66 in: D. Armbruster, A. S. Mikhailov, and K. Kaneko (eds.) Networks of Interacting Machines: Production Organization in Complex Industrial Systems and Biological Cells (World Scientific, Singapore). |

Literature | Student presentations are based, for example, on the following papers: Pedestrians and Crowds M. Moussaïd, D. Helbing, and G. Theraulaz (2011) How simple rules determine pedestrian behavior and crowd disasters. PNAS 108 (17) 6884-6888. D. Helbing, A. Johansson, J. Mathiesen, M.H. Jensen, and A. Hansen (2006) Analytical approach to continuous and intermittent bottleneck flows. Physical Review Letters 97, 168001. D. Helbing, R. Jiang, and M. Treiber (2005) Analytical investigation of oscillations in intersecting flows of pedestrian and vehicle traffic. Physical Review E 72, 046130. D. Helbing and T. Vicsek (1999) Optimal self-organization. New Journal of Physics 1, 13.1-13.17. D. Helbing, F. Schweitzer, J. Keltsch, and P. Molnár (1997) Active walker model for the formation of human and animal trail systems. Physical Review E 56, 2527-2539. H. Löwen (2010) Particle-resolved instabilities in colloidal dispersions. Soft Matter 6, 3133-3142 as well as J. Dzubiella and H. Löwen (2002) Pattern formation in driven colloidal mixtures: tilted driving forces and re-entrant crystal freezing. J. Phys.: Condens. Matter 14, 9383-9395. K. Aoki (2000) Mathematical model of a saline oscillator. Physica D 147, 187-203 or N. Okamura and K. Yoshikawa (2000) Rhythm in a saline oscillator. Physical Review E 61, 2445-2452. Vehicular Traffic D. Helbing (2009) Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models. European Physical Journal B 69(4), 539-548. D. Helbing and A. Johansson (2009) On the controversy around Daganzo's requiem for and Aw-Rascle's resurrection of second-order traffic flow models. European Physical Journal B 69(4), 549-562. D. Helbing and M. Moussaid (2009) Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model. European Physical Journal B 69(4), 571-581. D. Helbing, M. Treiber, A. Kesting, and M. Schönhof (2009) Theoretical vs. empirical classification and prediction of congested traffic states. European Physical Journal B 69(4), 583-598. D. Helbing and B. Tilch (2009) A power law for the duration of high-flow states and its interpretation from a heterogeneous traffic flow perspective. European Physical Journal B 68(4), 577-586. M. Treiber and D. Helbing (2009) Hamilton-like statistics in onedimensional driven dissipative many-particle systems. European Physical Journal B 68(4), 607-618. D. Helbing (2009) Derivation of a fundamental diagram for urban traffic flow. European Physical Journal B 70(2), 229-241. D. Helbing and A. Mazloumian (2009) Operation regimes and slower-is-faster effect in the control of traffic intersections. European Physical Journal B 70(2), 257-274. S. Lämmer and D. Helbing (2008) Self-control of traffic lights and vehicle flows in urban road networks. JSTAT P04019 as well as S. Lämmer and D. Helbing (2010) Self-stabilizing decentralized signal control of realistic, saturated network traffic, SFI Working Paper 2010-09-019, see http://www.santafe.edu/media/workingpapers/10-09-019.pdf M. Treiber, A. Kesting, and D. Helbing (2007) Influence of reaction times and anticipation on stability of vehicular traffic flow. Transportation Research Record 1999, 23-29. D. Helbing, J. Siegmeier, and S. Lämmer (2007) Self-organized network flows. Networks and Heterogeneous Media 2(2), 193-210. M. Krbalek and D. Helbing (2004) Determination of interaction potentials in freeway traffic from steady-state statistics. Physica A 333, 370-378. D. Helbing (2003) A section-based queueing-theoretical traffic model for congestion and travel time analysis in networks. Journal of Physics A: Mathematical and General 36, L593-L598. R. Kölbl and D. Helbing (2003) Energy laws in human travel behaviour. New Journal of Physics 5, 48.1-48.12. V. Shvetsov and D. Helbing (1999) Macroscopic dynamics of multilane |

Prerequisites / Notice | The number of participants is limited due to the small size of the lecture hall. Solid mathematical skills are useful to prepare the 10 minute student presentations. |