Their work may make it easier to find oil, predict floods and even figure out if a landscape on Mars was sculpted by running water. Whether you're looking at the Kentucky River or the Appalachian plateau in northwest Pennsylvania, geologic surfaces show a certain degree of universality. The task of Professor Rothman, graduate students Peter Dodds, Kelvin Chan and postdoctoral fellow Romualdo Pastor-Satorras is akin to reconstructing a crime scene. The clues the researchers use are based on physical properties, geophysical reasoning and mathematical insight. Rain falls and fluids seep out from under the surface of the land.
Avalanches change the pattern of erosion and add sediment.
Even though researchers don't know exactly what soil, water and weather will do over time, they do know, for instance, that water and sediment will move mostly downhill and that the whole scene, which could cover thousands of square miles or more, will end up forming a rather symmetrical pattern. These patterns can help provide greater understanding of all river network laws, which in turn can be applied to networks of almost any kind. Using mountains of measurement data from digital elevation maps of landscapes, the researchers' goal is to make mathematical sense of the dendritic patterns of the river's branches and its tiny tributaries. Incorporating existing knowledge of the fractal nature of rivers, one problem researchers face is to explain the structure of river networks, such as those that describe distribution of stream lengths, basin size and the overall dendritic morphology itself. We view the problem of topography by investigating the statistical properties of surfaces.