References

MODELLING CROWD DYNAMICS FROM A KINETIC THEORY VIEWPOINT


[1] P. Ball, The physical modelling of human social systems, A Review in Complexus, Karger 1 (2003), 190-206.

[2] N. Bellomo and C. Dogbe, On the modelling crowd dynamics from scaling to hyperbolic macroscopic models, Math. Mod. Meth. Appl. Sci. 18 (Supplement) (2008), 1317-1345.

[3] N. Bellomo and C. Dogbe, On the modeling of traffic and crowds: A survey of models, speculations and perspectives, SIAM Rev. 53 (2011), 409-463.

[4] C. Bianca and C. Dogbe, A mathematical model for crowd dynamics: Multiscale analysis, fluctuations and random noise, Nonlinear Studies 20 (2013), 281-305.

[5] V. J. Blue and J. L. Adler, Cellular automata microsimulation for modeling bi-directional pedestrian walkways, Transportation Research Part B 35 (2001), 293-312.

[6] C. Burstedde, K. Klauck, A. Schadschneider and J. Zittartz, Simulation of pedestrian dynamics using a two-dimensional cellular automaton, Physica A 295 (2001), 507-525.

[7] D. Chowdhury, L. Santen and A. Schadschneider, Statistical physics of vehicular traffic and some related systems, Phys. Rep. 329 (2000), 199-329.

[8] R. M. Colombo and M. D. Rosini, Pedestrian flows and nonclassical shocks, Math. Meth. Appl. Sci. 28(13) (2005), 1553-1567.

[9] V. Coscia and C. Canavesio, First-order macroscopic modelling of human crowd dynamics, Math. Mod. Meth. Appl. Sci. 18 (2008), 1217-1247.

[10] C. Dogbe, Modeling crowd dynamics by the mean-field limit approach, Mathematical and Computer Modelling 52(9-10) (2010), 1506-1520.

[11] C. Dogbe, On the modelling of crowd dynamics by generalized kinetic models, J. Math. Anal. Appl. 387 (2012), 512-532.

[12] W. Ebeling and U. Erdmann, Nonequilibrium statistical mechanics of swarms of driven particles, Complexity 8(4) (2003), 23-30.

[13] W. Ebeling, F. Schweitzer and B. Tilch, Active Brownian particles with energy depots modelling animal mobility, BioSystems, 49 (1999), 17-29.

[14] B. Piccoli and A. Tosin, Time-evolving measures and macroscopic modeling of pedestrian flow, Arch. Ration. Mech. Anal. 199(3) (2011), 707-735.

[15] P. G. Gipps and B. Marksjö, A micro-simulation model for pedestrian flows, 27(2-3) (1985), 95-105.

[16] R. Y. Guo and H. J. Huang, A mobile lattice gas model for simulating pedestrian evacuation, Physica A 387 (2008), 580-586.

[17] B. Hakin and R. Wright, Passenger flow in subways, Operational Research Quaterly 9 (1958), 299-308.

[18] D. Helbing and P. Molnar, Social force model for pedestrians dynamics, Physical Review E 51 (1995), 4282-4286.

[19] D. Helbing, A fluid-dynamic model for the movement of pedestrians, Complex Systems 6 (2002), 391-415.

[20] D. Helbing, M. Isobe, T. Nagatani and K. Takimoto, Lattice gas simulation of experimentally studied evacuation dynamics, Physical Review E 67 (2003), 067101.

[21] L. F. Henderson, The statistics of crowd fluids, Nature 229 (1971), 381-383.

[22] L. F. Henderson, On the fluid mechanic of human crowd motion, Transp. Research 8 (1975), 509-515.

[23] S. Hoogendoorn and P. Bovy, Gas-kinetic modeling and simulation of pedestrian flows, Transp. Research Record 1710 (2000), 28-36.

[24] S. Hoogendoorn and P. Bovy, Simulation of pedestrian flows by optimal control and differential games, Optimal Control Applications and Methods 24 (2003), 153-172.

[25] R. L. Hughes, A continuum theory for the flow of pedestrians, Transportation Research Part B 36 (2002), 507-536.

[26] R. L. Hughes, The flow of human crowds, Annual Reviews of Fluid Mechanics 35 (2003), 169-183.

[27] L. Huang, S. C. Wong, M. P. Zhang, C. W. Shu and W. H. K. Lam, Revisiting Hughes dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm, Trans. Res. Part B 43 (2009), 127-141.

[28] T. Kaihara, N. Fujii and T. Notsu, A study on market simulation with consumers in complex network, Proceedings of SICE Annual Conference (SICE), (2011), 499-504.

[29] B. Maury and J. Venel, A mathematical framework for a crowd motion model, C. R. Acad. Sci. Paris Ser. I 346 (2008), 1245-1250.

[30] S. Okazaki, Study of pedestrian movement, architectural space. Part 1: Pedestrian movement by the application on of magnetic models, Trans. of AIJ 283 (1979), 111-119.

[31] B. Perthame, Mathematical tools for kinetic equations, Bull. Amer. Math. Soc. 41 (2004), 205-244.

[32] B. Maury, A. Roudneff-Chupin and F. Santambrogio, A macroscopic crowd motion model of gradient flow type, Math. Models Methods Appl. Sci. 20 (2010), 1787-1821.

[33] F. Schweitzer, Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences, Springer, 2007.