Inferência estatística e escolha de modelos aplicados à dinâmica de sistemas superamortecidos

Abstract

Maximum-likelihood is a method for estimating parameters of a statistical models. In this approach, given a set of empirical data and a statistical model, the different model parameters are adjusted in order to maximize the probability for the empirical results being observed within that model. In this dissertation we will use this approach in the investigation of the equilibrium structure of a system of repulsive particles in a dissipative medium. We compare two distinct approaches to this model. In a microscopic approach we solve the dynamics at the level of the particles, integrating the equations of movement until arriving at the mechanical equilibrium. In another, larger-scale approach, we describe the equilibrium state by the density of probability of finding a particle at a given point. The system model that we investigate is a one-dimensional idealization of the form of the interaction between superconducting vortices. Although idealized, this model can be used adequately for situations where, due to the symmetries of the system, only one direction becomes relevant. The results obtained from the solution of the equations of motion are contrasted with two possible continuous approaches. In a more simplified approach we model the distribution as the cut of a parabola of negative curvature taking only the positive region of the curve. In this approach only one parameter relative to curvature is required. The second description also assumes the shape of a parabola of negative curvature, but a second parameter is included to describe a possible discontinuity at the end of the distribution curve. We describe methods of choosing models to determine under which conditions each different approaches is more appropriate under different system conditions.