Estudo da difusão de partículas confinadas

Abstract

In this work we present a theoretical study of the random walk model and the confined particle diffusion process. Such a model is applied in a wide area of research, e.g., financial economics, biology and physics. We briefly introduce the model from its simplest form (one-dimensional and discrete) to two-dimensional and continuous motion, where we conclude that the model describes a diffusion process from a microscopic point of view. After this conclusion, we perform a study about the diffusion equation. Lastly the random walk model is used to simulate confined particles movement, describing the diffusion process. At this stage, we use different types of step length distributions to analyze the evolution of r2 for each one of them, where we calculate the diffusion coefficient and the α exponent, in which is used to categorize the process in super-diffusive, sub-diffusive or a typical diffusion process.