Computational Thinking in Science and Math
Constructing a Simple Model: Solid Diffusion
In this lesson we are going to make a simple agent-based model from scratch following a top-down design process. "The top-down design process starts by choosing a phenomenon or situation that you want to model or coming up with a question that you want to answer, and then designing agents and rules of behavior that model the elements of the situation. You then refine that conceptual model and continue to revise it until it is at a fine enough level of detail that you can see how to write the code for the model" (An Introduction to Agent-Based Modeling pg. 160).
We are going to model diffusion in solids. Usually, the phenomenon we are trying to model has "a characteristic pattern, known as a reference pattern" (ibid. pg 159). Our goal is to create a model that somehow captures the reference pattern. In this case, the reference pattern will be diffusion concentration profiles. There are multiple types of diffusion in solids, but we will start simply in accordance with the ABM design principle: "Start simple and build toward the question you want to answer" (ibid.). So, our goal for now is not to create a model that makes accurate quantitative predictions about real materials. Rather, we are just trying to make a model that gives qualitatively similar results to explain the phenomenon.
The reference pattern we will compare against is the following graph which shows concentrations of nickle and copper in a copper-nickle diffusion couple. In this case the diffusion couple was of thin films, but that doesn't matter for us, because we are only trying to qualitatively reproduce the behavior.
