Yu-Feng Lin, a hydrogeologist at the Illinois State Water Survey, is on a mission to tackle a top national research priority using Mathematica. In this video, Lin details why this project could only be done in Mathematica. Because of the importance of groundwater recharge and discharge in the hydrological cycle, the U.S. National Research Council (NRC) deems research on them to be of critical priority. However, their rates and patterns are so complex that it takes years of study to estimate them.

I'm a GPS addict. I have a handheld GPS, a computer GPS, a GPS phone, two GPS watches, two GPS cameras, and maybe some others. Wherever I go, chances are pretty good I have at least one GPS with me. Anytime I run/bike/hike/walk/ski I keep a record of where I went using GPS. Now that I have all this data I want to make use of it in a meaningful way. Mathematica is a fantastic tool to analyze all my geographic data. Here's an example from a recent trail run I did at a nearby park. The data is stored in a GPX (GPS exchange format) file, which is a specific type of XML. We can bring the data into Mathematica using Import.

Today’s earthquakes near Sumatra fortunately didn’t lead to a major tsunami. But figuring out when tsunamis will develop is a difficult matter---and an interesting exercise in applied mathematics. The main phenomenon is the propagation of so-called shallow water waves---water waves whose wavelength is large compared to the depth of the ocean. Those waves satisfy a partial differential equation (PDE) that was figured out in the 1800s. The equation is a nasty nonlinear one---that can’t be solved exactly. I’ve been working on the numerical differential equation capabilities of Mathematica for more than a decade. Our goal is to automate the solutions of all types of equations---so users just have to enter their equation, and Mathematica then does all the analysis to select and apply the best algorithm. The shallow-water equations are a good test---that I’m happy to say Mathematica passes with flying colors. One essentially just has to type the equations in, and get the solution, which is then easy to visualize---especially using the new visualization capabilities of Mathematica 6. (Click the image below to see the Mathematica animation.) Let me explain a little about what’s involved in getting this.

Most of the time I’ve spent working for Wolfram Research has been in the comfort of a climate-controlled office at our Champaign, Illinois headquarters. I’ve had easy access to my great co-workers, multiple computers and a Gigabit local network. I’ve had flexible working hours, a relatively short and pleasant bicycle commute, numerous delicious restaurants nearby and a window overlooking the beautiful campus of the University of Illinois (okay, and the roof of a McDonald’s). All things considered, it’s a pretty good place to be. When I told Theo (my boss) that I wanted to give all this up and spend a year living in a Nicaraguan jungle, there was a bit of hesitation, but not much. We agreed fairly quickly that we could make it work. Here’s where I was headed: