Mobile-to-clogging transition in a Fermi-like model of counterflowing particles

Abstract

In this paper we propose a generalized model for the motion of a two-species self-driven objects ranging from a scenario of a completely random environment of particles of negligible excluded volume to a more deterministic regime of rigid objects in an environment. Each cell of the system has a maximum occupation level called σmax. Both species move in opposite directions. The probability of any given particle to move to a neighboring cell depends on the occupation of this cell according to a Fermi-Dirac like distribution, considering a parameter α that controls the system randomness. We show that for a certain α = αc the system abruptly transits from a mobile scenario to a clogged state which is characterized by condensates. We numerically describe the details of this transition by coupled partial differential equations (PDE) and Monte Carlo (MC) simulations that are in good agreement.

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

“…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.…”

“…In this work, we used t = 1000 and η = 10 −7 , which was shown in Ref. [18] to be a good choice. Now focusing on the study of the density's influence on the transient instability behavior, we simulated N run different runs to calculate the probability of lane formation (the number of times that the system reaches the lane pattern at steady state divided by N run ), which is denoted as p lane .…”

“…[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].…”

“…Recently, we have developed a model with exclusion based on Fermi-Dirac distribution [18] from an extension of a simple model without exclusion previously defined in [3], which was loosely based on the concept of clannish random walks developed by Montroll and West [21]. 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.…”