Numerical study of condensation in a Fermi-like model of counterflowing particles via Gini coefficient

Abstract

The collective motion of self-driven particles shows interesting novel phenomena such as swarming and the emergence of patterns. We have recently proposed a model for counterflowing particles that captures this idea and exhibits clogging transitions. This model is based on a generalization of the Fermi-Dirac statistics wherein the maximal occupation of a cell is used. Here we present a detailed study comparing synchronous and asynchronous stochastic dynamics within this model. We show that an asynchronous updating scheme supports the mobile-clogging transition and eliminates some mobility anomalies that are present in synchronous Monte Carlo simulations. Moreover, we show that this transition is dependent upon its initial conditions. Although the Gini coefficient was originally used to model wealth inequalities, we show that it is also efficient for studying the mobile-clogging transition. Finally, we compare our stochastic simulation with direct numerical integration of partial differential equations used to describe this model.

Coexistence and crossover phenomena in a Fermi-like model of particles in counterflowing streams

“…The result shows that the dynamics has an abrupt transition on the stochastic level α, and that abrupt transition depends on the density (ρ), similar to what was observed in the original one-dimensional model [18,19]. The result also suggests that for ρ = ρ c , the system is more likely to jam in the range 2 α 5, where the particle interaction is sufficiently high as to make the system relax to an immobile state but not to self-organize in lane patterns.…”

“…Our paper is organized as follows: In the next section, we present one of the possible formulations (the more appropriate one in our opinion) of the modeling in two dimensions. We show that renormalization is required for d = 2, but that naturally recovers d = 1 previously studied by us in our first contributions about this topic [18,19]. After that, we present our results in Sec.…”

“…A detailed study of the influence of α and σ max was explored in our previous contributions in one-dimensional systems [18,19], and in this current paper we concentrate our study on a situation in which the clogging is expected (α large and σ max = 1) and therefore is the most important situation to be explored.…”

“…[14,15,16]). However, exclusion effects seem to bring clogging/jamming [17] phenomena [18,19], although the formation of condensates is not mandatorily observed only in counterflowing systems [20].…”

“…The easiness and coverage of this extended model is related to the manipulation of a single parameter that can model systems going from hard-body systems with exclusion up to systems that are completely random and without exclusion effects. We have previously shown that such systems have an interesting transition from a clogging phase to a mobile phase, which we have described with many order parameters such as mobility, the Gini coefficient, etc., over different situations [19].…”