Dinâmica de Langevin para partículas repulsivas: sistemas confinados e segregação baseada em difusividade

Abstract

In this work, we present the results of the study of the dynamics of two systems in the overdamped regime. In the first part, we investigate a system of repulsive particles in dissipative media. In the second part, we address a Plateau-Rayleigh type instability in a binary mixture of self-propelled particles. The dynamics of repulsive particles at local concentrations can be described by a nonlinear diffusive equation. To develop these coarse-grained models, it is essential to identify the forces acting on the dispersed particles, considering the local concentration and its gradient. In this study, we investigate how the parameterization of the coarse-grained model can be defined by analyzing the characteristics of the steady state in systems with a constant concentration profile. We accomplish this through Monte Carlo simulations for these homogeneous states at given temperatures. We use results from molecular dynamics numerical simulations to successfully test the predictions of our continuum model. The dynamics of rupture is fundamental to understanding instabilities in luid dynamics and biological systems and is a widely studied topic. When studying the dynamics of self-propelled particles, we observed characteristics similar to those known as Plateau-Rayleigh Instability, a typical phenomenon in liquid jets. In this study, we investigate the breakup of two-dimensional configurations resembling channels in a binary mixture of self-propelled particles under different temperatures. Through computational simulations, we analyze the evolution of this instability under various conditions. Our results indicate that although our system interacts with a repulsive potential, it exhibits characteristics similar to the Plateau-Rayleigh instability observed in liquids, which is caused by surface tension, i.e., the cohesive forces among the liquid molecules. We identified that the application of an external force was a crucial factor for maintaining instability in the system. This force, directing the particles in one direction, demonstrated that as its intensity increased, it became predominant over the effects of temperature, thereby stabilizing the system.