Fractal Pattern In Convex Bodies’ Evolution Of Rock Fracture Dynamics With Dependent Fragmentation Rate

The current state of the planet has raised lot of concerns about the type of world we want the next generations to inherit. The global warming of the planet together with catastrophes (floods, bush fires, storms, hurricanes, tsunamis, earthquakes, extreme temperatures, droughts, etc.) that have hit different parts of the world these last decades, are on an increasing curve. Many voices are being heard asking people to look for solutions to reduce the consequences of global warming. The recent United Nation Climate Change Conference of the Parties (COP26) in Glasgow (Ireland) from 31 October to 13 November 2021 testifies. Rock fracture happening in our environment is one of important factors to consider in the solution seeking process, as rocks can absorb the carbon dioxide (CO2) via fracture. That is why we perform in this work a mathematical analysis of an ecosystem’s rock fracture model, in which the fractal process is considered. The specific case where the fragmentation rate is dependent on the size of the rock is analyzed. The exact solution is evaluated and numerical simulation performed. The results show a dynamic partly repeating itself once, then twice, three times and so on, hereby marking the existence of self replicated zones in the convex body of rock fracture model that also happen to be chaotic. We observe that the evolution process tends to reproduce exact or partly exact pathways and this goes on over and over. Hence, there is existence in the system of chaotic self-replicating poles.