Reaction-diffusion models for geological patterns : new insights and potential applications

Abstract

Pattern formation is a ubiquitous phenomenon in nature, arising from reaction-diffusion processes in systems away from equilibrium. These patterns can be found in a wide variety of systems, including chemistry, biology, ecology, geology, and materials science. Reaction-diffusion equations have been used to model a wide variety of patterns, and they have the potential to be used to understand the formation of geological patterns in rocks. This thesis proposes a generalized reaction-diffusion model that can be used to describe a wide variety of geological patterns. The model is based on the Cahn-Hilliard, Allen-Cahn, and cnoidal wave equations, which are well-established models for describing phase separation and localization phenomena. The generalized model includes additional terms that can account for the effects of fluid flow, stress, and other factors. The derived models have been used to investigate the formation of three types of geological patterns: Liesegang patterns, dendritic growth, and mineralized veins. The results show that the models can reproduce the characteristic features of these patterns. The model also reveals the role of different factors, such as diffusion coefficients, supersaturation, stress, and heterogeneity, in determining the appearance of the patterns. The results of this study provide a new theoretical framework for understanding the formation of geological patterns. The model has the potential to be used to improve our understanding of mineral distribution, develop new methods for controlling pattern formation, and develop new computer-vision techniques for field exploration.