Modelo contínuo para distribuição e fluxo de partículas em meios superamortecidos

Abstract

Stochastic systems typically present an element of randomness ( extit{e.g.} the random motion of particles inside a overdamped fluid, velocity distributions into turbulent flow, etc.). The Fokker-Planck equation is a formalism useful to describe the temporal evolution of stochastic systems in general, and it is also efficient when the stochastic element is negligible, yielding a deterministic system. It can be applied both to systems far from equilibrium and systems which are close to a state of equilibrium. In order to model particles inside a medium, we study the motion of particles which interact with each other through short-range repulsive potentials. Using the Fokker-Planck equation, a model has been previously developed in order to explain both stationary and non-stationary behaviour of the system. According to the model, the interaction energy density ($u_p$) is proportional to the square of the density of particles, $u_p=a ho ^2$, where $a$ is a constant which depends on the way the particles interact with each other. In this work we try to improve this model through a change in the construction of $a$, which is a function of $ ho$, $a( ho)$, extit{i.e.}, we account the possibility of other forms of non-linearity. Our results suggest that, under certain circumstances, specially for the Yukawa potential, the model we propose can predict the results of computational simulation. For the same potential, we see that the density of energy due to the interacting potential does not necessarily show a quadratic dependence on the particle density, $ ho$. On the other hand, for the second potential analysed, which allows structural transitions with respect to density, this simplified model was not enough to predict the density profile.