Abstract

RANGEL-HUERTA, A.. Ecuación de Boltzmann de discos rígidos auto-impulsados para peatones en contraflujo. Rev. mex. fis. [online]. 2013, vol.59, n.2, pp.153-159. ISSN 0035-001X.

We present a Boltzmann kinetic equation to describe a crowd in counter flow walking on a corridor. Pedestrians are considered as self-propelled particles with ballistic walking speeds and random perturbations. Speed changes during encounters are represented as walking hard disks potentials. Because pedestrians are considered self-propelled particles they behave like reactive agents which can change their walking speeds direction voluntarily during the evasive maneuvers. Analytical solutions of the Boltzmann equation, at steady state flow, are determined based on the speed distribution function of walking. The simulation algorithm of the Boltzmann collisional term considers two operation modes, free walking and walking with encounters. The results show collective self-organizing motion, at any density, which turn out to be an emerging strategy used to improve the flow efficiency of the crowd. Another important result is the fundamental diagram, the curve of average flow versus density, which correctly reproduces the experimental results. This confirms that our model is suitable to describe transport of pedestrian crowds.

Keywords : Kinetic theory; Brownian motion; self-organized systems.

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