Toward a mathematical theory of behavioral-social dynamics for pedestrian crowds

Mathematical Models and Methods in Applied Sciences

Volumn 25, Issue 13, 2015, Pages 2417-2437

  Bellomo, Nicola ^a   Gibelli, Livio ^b  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

active particles; crowd dynamics; kinetic theory; pedestrian segregation; Scaling

Indexed keywords

KINETIC THEORY;

ACTIVE PARTICLES; CROWD DYNAMICS; EMERGING BEHAVIORS; MATHEMATICAL THEORY; MATHEMATICAL TOOLS; PREDICTIVE ABILITIES; SCALING; UNUSUAL BEHAVIORS;

BEHAVIORAL RESEARCH;

EID: 84942198791     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202515400138     Document Type: Article

References (31)

1. J.-P. Agnelli, F. Colasuonno and D. Knopoff, A kinetic theory approach to the dynamics of crowd evacuation from bounded domains, Math. Models Methods Appl. Sci. 25 (2015) 109-129.
2. M. G. Ajmone, M. N. Bellomo and M. Egidi, Towards a mathematical theory of complex socio-economical systems by functional subsystems representation, Kinet. Relat. Models 1 (2008) 249-278.
3. G. Albi and L. Pareschi, Modeling of self-organized systems interacting with a few individuals: From microscopic to macroscopic dynamics, Appl. Math. Lett. 26 (2013) 397-401.
4. V. V. Aristov, Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows (Springer-Verlag 2001)
5. M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale and V. Zdravkovic, Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, Proc. Natl. Acad. Sci. USA 105 (2008) 1232-1237.
6. N. Bellomo and A. Bellouquid, On multiscale models of pedestrian crowds -From mesoscopic to macroscopic, Commun. Math. Sci. 13 (2015).
7. N. Bellomo, A. Bellouquid and D. Knopoff, From the micro-scale to collective crowd dynamics, SIAM Multiscale Model. Simulat. 11 (2013) 943-963.
8. N. Bellomo, A. Bellouquid, J. Nieto and J. Soler, Multicellular biological growing systems: Hyperbolic limits towards macroscopic description, Math. Models Methods Appl. Sci. 17 (2007) 1675-1692.
9. N. Bellomo, A. Bellouquid, J. Nieto and J. Soler, On the asymptotic theory from microscopic to macroscopic growing tissue models: An overview with perspectives, Math. Models Methods Appl. Sci. 22 (2012) 1130001.
10. N. Bellomo, M. A. Herrero and A. Tosin, On the dynamics of social conflicts looking for the black swan, Kinet. Relat. Models 6 (2013) 459-479.
11. N. Bellomo, D. Knopoff and J. Soler, On the difficult interplay between life, "complexity", and mathematical sciences, Math. Models Methods Appl. Sci. 23 (2013) 1861-1913.
12. N. Bellomo, B. Piccoli and A. Tosin, Modeling crowd dynamics from a complex system viewpoint, Math. Models Methods Appl. Sci. 22 (2012) 1230004.
13. N. Bellomo and J. Soler, On the mathematical theory of the dynamics of swarms viewed as complex systems, Math. Models Methods Appl. Sci. 22 (2012) 1140006.
14. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford Univ. Press, 1994).
15. W. Daamen and S. P. Hoogedorn, Experimental research of pedestrian walking behavior, TRB Annual Meeting CD-ROM (2006).
16. P. Degond, L. Pareschi and G. Russo, Modeling and Computational Methods for Kinetic Equations (Birkhauser, 2004).
17. M. Dolfin and M. Lachowicz, Modeling altruism and selfishness in welfare dynamics: The role of nonlinear interactions, Math. Models Methods Appl. Sci. 24 (2014) 2469-2482.
18. S. Faure and B. Maury, Crowd motion from the granular standpoint, Math. Models Methods Appl. Sci. 25 (2015) 463-493.
19. G. P. Ghiroldi and L. Gibelli, A direct method for the Boltzmann equation based on a pseudo-spectral velocity space discretization, J. Comput. Phys. 258 (2014) 568-584.
20. D. Helbing, Traffic and related self-driven many-particle systems, Rev. Mod. Phys. 73 (2001) 1067-1141.
21. D. Helbing, I. Farkas and T. Vicsek, Simulating dynamical feature of escape panic, Nature 407 (2000) 487-490.
22. D. Helbing and A. Johansson, Pedestrian crowd and evacuation dynamics, in Encyclopedia of Complexity and System Science (Springer, 2009), pp. 6476-6495.
23. D. Helbing, A. Johansson and H. Z. Al-Abideen, Dynamics of crowd disasters: An empirical study, Phys. Rev. E 75 (2007) 046109.
24. D. Helbing and P. Molnar, Social force model for pedestrian dynamics, Phys. Rev. E 51 (1995) 4282-4286.
25. M. Moussaid, D. Helbing, S. Garnier, A. Johansson, M. Combe and G. Theraulaz, Experimental study of the behavioural mechanisms underlying self-organization in human crowds, Proc. Roy. Soc. B 276 (2009) 2755-2762.
26. M. Moussaid and G. Theraulaz, Comment les pietons marchent dans la foule, La Recherche 450 (2011) 56-59.
27. M. A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life (Belknap Press of Harvard Univ. Press, 2006).
28. L. Pareschi and G. Toscani, Interacting Multiagent System. Kinetic Equations and Monte Carlo Methods (Oxford Univ. Press, 2013).
29. A. Schadschneider and A. Seyfried, Empirical results for pedestrian dynamics and their implications for modeling, Netw. Heterog. Media 6 (2011) 545-560.
30. A. Seyfried, B. Steffen, W. Klingsch and M. Boltes, The fundamental diagram of pedestrian movement revisited, J. Stat. Mech.: Theory Exper. 360 (2006) 232-238.
31. Y. Yamori, Going with the flow: Micro-macro dynamics in the macrobehavioral patterns of pedestrian crowds, Psychol. Rev. 105 (1998) 530-557.