Roger Filliger, EPFL Lausanne
We apply the micro-macro program of statistical mechanics to a simple one-dimensional interacting particle system with interactions joining on a minimum level of detailed knowledge the kinetic features of migration, reaction and collision. Starting from a space-discrete stochastic particle hopping model, we establish in a first step its convergence to a space-continuous Boltzmann-like model which constitutes the mesoscopic level of description. In a second step we derive in the diffusive limit the functional relation between the vehicular density (i.e. the particles density) and the flux which occurs also in a popular ad-hoc traffic model proposed by Greenshields.
The application includes a micro-meso-macro link for cars in one-lane traffic where the three mentioned kinetic features model respectively (i) transport, (ii) spontaneous accelerations and decelerations and (iii) anisotropic decelerations of cars due to slow front-cars.