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The physics of the city: pedestrians dynamics and crowding panic equation in Venezia

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Abstract

In this paper we present the physics of the city, a new approach in order to investigate the urban dynamics. In particular we focus on the citizens’ mobility observation and modeling. Being in principle the social dynamics not directly observable, our main idea is that observing the human mobility processes we can deduce some features and characteristics of social dynamics. We define the automata gas paradigm and we write a crowding equation able to predict, in a statistical sense, the threshold between a selforganized crowd and a chaotic one, which we interpret as the emergence of a possible panic scenario. We show also some specific results obtained on the Venezia pedestrian network. Firstly, analyzing the network we estimate the Venice complexity, secondly measuring the pedestrian flow on some bridges we find significant statistical correlations, and by the experimental data we design two different bridges flow profiles depending from the pedestrian populations. Furthermore considering a reduced portion of the city, i.e. Punta della Dogana, we build up a theoretical model via a Markov approach, with a stationary state solution. Finally implementing some individual characteristics of pedestrians, we simulate the flows finding a good agreement with the empirical distributions. We underline that these results can be the basis to construct an E-governance mobility system.

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References

  • Albert R., Barabasi A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)

    Article  Google Scholar 

  • Badii R., Politi A.: Complexity, Hierarchical Structures and Scaling in Physics. Cambridge Nonlinear Science Series, vol. 6. Cambridge University Press, Cambridge (1997)

    Book  Google Scholar 

  • Barrat A., Barthélemy M., Vespignani A.: Dynamical Processes on Complex Networks. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  • Batty M.: Cities and Complexity. MIT Press, Cambridge (2005a)

    Google Scholar 

  • Batty M.: Agents, cells and cities: new representational models for simulating multi-scale urban dynamics. Environ. Plan. A 37(8), 1373–1394 (2005b)

    Article  Google Scholar 

  • Bazzani A. et al.: A chronotopic model of mobility in urban spaces. Physica A 325, 517–530 (2003)

    Article  Google Scholar 

  • Bazzani, A., Giorgini, B., Rambaldi, S. (eds.): Physics and the city. Advances in Complex Systems, 10(2), 255–270 (2007a)

  • Bazzani, A., Giorgini, B., Rambaldi, S., Brambilla, M., Cattelani, L.: Walking between free will and determinism. In: Proceedings of the 2007 Summer Computer Simulation Conference (2007b)

  • Bazzani, A., Giorgini, B., Zanlungo, F., Rambaldi, S.: Cognitive dynamics in a automata gas. In: Serra, R., Villani, M., Poli, I. (eds.) Artificial Life and Evolutionary Computation: Proceedings of Wivace. World Scientific, Singapore (2008)

  • Bazzani, A., Giorgini, B., Rambaldi, S.: Traffic and Crowd Dynamics: the physics of the city. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, Part 20. Springer, New York (2009)

  • Bazzani A., Giorgini B., Rambaldi S.: Modeling urban mobility for e-governance with low energy complexity. J. Green Eng. 1, 1–32 (2010)

    Google Scholar 

  • Berk R.A.: A gaming approach to crowd behavior. Am. Sociol. Rev. 39(3), 355–373 (1974)

    Article  Google Scholar 

  • Blumer H.: Collective Behavior (first publishing 1951). Irvington Publishers, New York (1993)

    Google Scholar 

  • Bonfiglioli, S.: Che cosa è un cronotopo. Urbanistica Quaderni INU, Roma (1997) (ibidem)

  • Braudel F.: Memory and the Mediterranean. Vintage Books, New York (2002)

    Google Scholar 

  • Caldarelli G.: Scale-Free Networks. Oxford University Press, Oxford (2007)

    Book  Google Scholar 

  • Canetti E.: Crowds and Power. The Noonday Press (Farrar, Strauss & Giroux), New York (1984)

    Google Scholar 

  • Cascetta E.: Transportation System Engineering: Theory and Methods. Kluwer, Boston (2001)

    Book  Google Scholar 

  • Crucitti P., Latora W., Porta S.: Centrality measures in spatial networks of urban streets. Phys. Rev. E 73, 036125 (2006)

    Article  Google Scholar 

  • Domencich T., McFadden D.: Urban Travel Demand: A Behavioral Analysis. North-Holland Publishing Co, Amsterdam (1975)

    Google Scholar 

  • Eckmann J.P., Ruelle D.: Ergodic theory of chaos and strangers attractors. Rev. Mod. Phys. 57, 617–656 (1985)

    Article  Google Scholar 

  • Federici, M.L.: Agent-based modelling and micro-simulation of pedestrian dynamics and crowd phenomena in public environments. Ph.D. Thesis, Università degli Studi di Milano Bicocca, Anno Accademico (2006–2007)

  • Garnsey, E., McGlade, J. (eds.): Complexity and Co-Evolution, Continuity and Change in Socio-Economic Systems. Edward Elgar Publisher, Cheltenham (2006)

  • Giorgini, B.: The time of chaos, in Il tempo e la città tra natura e storia. In: Bonfiglioli, S., Mareggi, M. (eds.) Atlante dei progetti sui tempi della città. Urbanistica Quaderni INU, Roma (1997)

  • Giorgini, B., Turchetti, G.: From Newton–Boltzmann paradigms to complexity: a bridge to biosystems. In: Freguglia, P. (ed.) The Science of Complexity: Chimera or Reality, Milan Research for Industrial and Applied Mathematics. Esculapio, Bologna (2006)

  • Hayles N.K.: How We Became Posthuman. Virtual Bodies in Cybernetics, Literature, and Information. The University of Chicago Press, Chicago (1999)

    Book  Google Scholar 

  • Helbing D.: A fluid-dynamic model for the movement of pedestrians. Complex Syst. 6, 391–415 (1992)

    Google Scholar 

  • Helbing D.: Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73, 1067–1141 (2001)

    Article  Google Scholar 

  • Le Bon, G.: The Crowd: A Study of the Popular Mind (first publishing 1895). Dover, Mineola (2002)

  • Mamoli, M., Michieletto, P., Bazzani, A., Giorgini, B.: Venice as pedestrian city and tourist magnet. In: Proceedings of the Venice Transport International (2010)

  • Martinotti G.: Gone with the Wind: physical spaces in the third generation metropolis. Adv. Complex Syst. 10(2), 233–253 (2007)

    Article  Google Scholar 

  • Melchiorre, G., Bazzani, A., Giorgini, B., Rambaldi, S.: Walking in Venezia carnival: crowd dynamics and pedestrian trajectories. In: Pezzanio, M., Chiafa, E. (eds.) Space for Public Shows and Trade Fairs. Codice SIAE pbx003, Brescia. www.polibrixia.it (2007)

  • Nicolis G., Prigogine I.: Exploring Complexity. W. H. Freeman & Co. Ltd, New York (1989)

    Google Scholar 

  • Nuvolati, G.: Lo sguardo vagabondo. Il flâneur e la città da Baudelaire ai postmoderni, il Mulino, Bologna (2006)

  • Nuvolati G.: Le Flâneur Dans l’Espace Urbain. Géographie et Culture Dans L’Espace Urbain 70, 7–20 (2009)

    Article  Google Scholar 

  • Progetto di Ricerca di Interesse Nazionale (PRIN). (2005–2007). Individui e gruppi in movimento: strumenti sociologici e nuove tecnologie per lo studio della mobilità di eventi turistici e delle trasformazioni urbane, National Coordinator: Prof. Guido Martinotti—Università Milano Bicocca

  • Progetto di Ricerca di Interesse Nazionale (PRIN). (2007–2009). Individui e gruppi in movimento: strumenti sociologici e nuove tecnologie per lo studio della mobilità di eventi turistici e delle trasformazioni urbane, National Coordinator: Prof. Guido Martinotti—Università Milano Bicocca

  • Rizzolatti G., Craighero L.: The Mirror Neuron System. Annu. Rev. Neurosci. 27, 169–192 (2004)

    Article  Google Scholar 

  • Scott, A. (ed.): Encyclopedia of Nonlinear Science. Routledge Taylor & Francis Group New York (2005)

  • Shannon C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)

    Article  Google Scholar 

  • Shannon C.E., Weaver W.: The Mathematical Theory of Communication. University of Illinois Press, Urbana (1949)

    Google Scholar 

  • Taylor M.C.: The Moment of Complexity Emerging Network Culture. The University of Chicago Press, Chicago and London (2001)

    Google Scholar 

  • Turchetti G., Zanlungo F., Giorgini B.: Dynamics and thermodynamics of a gas of automata. Europhys. Lett. 78-5, 58003 (2007)

    Article  Google Scholar 

  • Parisi, G.: Complex systems: a physicist’s view point. Stat. Mech. arXiv: cond-mat/0205297 (2002)

  • Turner J.: Social Identity in Social Identity Theory: Where are We Now. Blackwell, Oxford (1999)

    Google Scholar 

  • Gelder T.: The dinamica hypothesis in cognitive science. Behav. Brain Sci. 21, 615 (1998)

    Google Scholar 

  • Von Neumann J.: The General and Logical Theory of Automata. Collected Works, vol. V, pp. 288–328. Pergamon Press, Oxford (1963)

    Google Scholar 

  • Walmsley G.: Emergence and reduction in dynamical cognitive science. New Ideas Psychol. 28, 274–282 (2010)

    Article  Google Scholar 

  • Wiener N.: Cybernetics, or Control and Communication in the Animal and Machine. Wiley, New York (1948)

    Google Scholar 

  • Yamori K.: Going with the flow: micro–macro dynamics in the macro behavioral patterns of pedestrian crowds. Psychol. Rev. 105(3), 530–557 (1998)

    Article  Google Scholar 

  • Yates F.E.: Self-Organizing Systems: The Emergence of Order. Plenum, New York (1997)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Laboratorio di Fisica della Città, CIG and CIRI, Università di Bologna, Bologna, Italy

    Elisa Omodei, Armando Bazzani, Sandro Rambaldi & Bruno Giorgini

  2. Dipartimento di Fisica and INFN, Sezione di Bologna, Bologna, Italy

    Elisa Omodei, Armando Bazzani, Sandro Rambaldi & Bruno Giorgini

  3. IUAV Università di Venezia, Venice, Italy

    Paolo Michieletto

  4. Laboratoire LaTTice (CNRS, ENS and Paris 3) and Institut des Systèmes Complexes (ISC-PIF), Paris, France

    Elisa Omodei

  5. IMéRA, Marseille, France

    Bruno Giorgini

Authors
  1. Elisa Omodei
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  2. Armando Bazzani
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  3. Sandro Rambaldi
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  4. Paolo Michieletto
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  5. Bruno Giorgini
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Correspondence to Elisa Omodei.

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Omodei, E., Bazzani, A., Rambaldi, S. et al. The physics of the city: pedestrians dynamics and crowding panic equation in Venezia. Qual Quant 48, 347–373 (2014). https://doi.org/10.1007/s11135-012-9773-5

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