Exploring the Dynamics of Wildfires and Curvature Flow

Dr. Valentina Wheeler of University of Wollongong, Australia, shares how her work influences efforts to understand wildfires and red blood cells. In Australia, where bushfires are a concern year-round, researchers have long tried to model these wildfires, hoping to learn information that can help with firefighting policy. Mathematician Valentina Wheeler and colleagues began studying a particularly dangerous phenomenon: When two wildfires meet, they create a new, V-shaped fire whose pointed tip races along to catch up with the two branches of the V, moving faster than either of the fires alone. This is exactly what happens in a mathematical process known as mean curvature flow. Mean curvature flow is a process in which a shape smooths out its boundaries over time. Just as with wildfires, pointed corners and sharp bumps will change the fastest.