We study the pedestrian escape from an obscure corridor using a lattice gas model with two species of particles. One species, called passive, performs a symmetric random walk on the lattice, whereas the second species, called active, is subject to a drift guiding the particles towards the exit. The drift mimics the awareness of some pedestrians of the geometry of the corridor and of the location of the exit. We provide numerical evidence that, in spite of the hard core interaction between particles -namely, there can be at most one particle of any species per site, -adding a fraction of active particles in the system enhances the evacuation rate of all particles from the corridor. A similar effect is also observed when looking at the outgoing particle flux, when the system is in contact with an external particle reservoir that induces the onset of a steady state. We interpret this phenomenon as a discrete space counterpart of the drafting effect typically observed in a continuum set-up as the aerodynamic drag experienced by pelotons of competing cyclists.

No abstract

We study the dynamics of interacting agents from two distinct inter-mixed populations: One population includes active agents that follow a predetermined velocity field, while the second population contains exclusively passive agents, i.e. agents that have no preferred direction of motion. The orientation of their local velocity is affected by repulsive interactions with the neighboring agents and environment. We present two models that allow for a qualitative analysis of these mixed systems. We show that the residence times of this type of systems containing mixed populations is strongly affected by the interplay between these two populations.After showing our modeling and simulation results, we conclude with a couple of mathematical aspects concerning the well-posedness of our models.

In this paper, we consider a microscopic semilinear elliptic equation posed in periodically perforated domains and associated with the Fouriertype condition on internal micro-surfaces. The first contribution of this work is the construction of a reliable linearization scheme that allows us, by a suitable choice of scaling arguments and stabilization constants, to prove the weak solvability of the microscopic model. Asymptotic behaviors of the microscopic solution with respect to the microscale parameter are thoroughly investigated in the second theme, based upon several cases of scaling. In particular, the variable scaling illuminates the trivial and non-trivial limits at the macroscale, confirmed by certain rates of convergence. Relying on classical results for homogenization of multiscale elliptic problems, we design a modified two-scale asymptotic expansion to derive the corresponding macroscopic equation, when the scaling choices are compatible. Moreover, we prove the high-order corrector estimates for the homogenization limit in the energy space H 1 , using a large amount of energy-like estimates. A numerical example is provided to corroborate the asymptotic analysis.

No abstract