Dynamics of Nonlinear Diffusion Processes

The purpose of this thesis is to analyze nonlinear diffusion processes. In particular, some of the results arrived at by Newman and Sagan in their 1981 paper Galactic Civilizations: Population Dynamics and Interstellar Diffusion, will be reproduced by different means. First, a thorough analysis of the linear diffusion equation will be performed in order to test a numerical algorithm that can solve the nonlinear diffusion equation and look at the processes of interest with sufficient accuracy. Once the algorithm is tested and shows good resolution it is used to solve the nonlinear equation. The post processing is then done to compare the numerical results with the analytical solution and then they are related to the results arrived at by Newman and Sagan. More precisely, the timescales over which these processes take place are of great interest. A study of the dynamics of these diffusion processes that take place will bring about a better understanding of the nature of nonlinear diffusion and some of its applications