Mechanical Branching and Channel Formation and Its Relevance to Biological Systems

Abstract

All organisms are limited by their resources. From large to small, all of us survive by trying to efficiently and effectively use what we are allocated, and as organisms get larger and larger one crucial factor to their survival is how they transport those resources inside themselves. While smaller organisms can make use of diffusion, either due to their size, shape, or both, larger organisms rely on the formation of channels to help ferry materials between locations. These channels can be simple and linear, such as the digestive tract, or they can be complicated branched networks with noticeable hierarchies and patterns as seen in leaf venation and blood vessels. However, these patterns are not limited to the organic. In the geophysical realm, channel formation and branching patterns are common. The forces of erosion have led to many varying channel systems that allow for efficient flow of materials between locations, much in the way seen in biological systems. With this in mind, my studies focused on exploring a geophysical two-phase system where channel formation is driven by erosion and how this system could better our understanding of channel formation and branching in organisms. My work can be divided into two main focuses. The first chapter focuses was the understanding of the base model and what factors in it determine channel formation and branching. The second chapter's focus is on sink distribution and decision making, asking how the model uses its resources to link to various sinks within it and how their distribution affects behavior.