Stuart Nettleton, a senior lecturer at the University of Technology, Sydney, knows the significance of the problem he's examining—he calls it “the biggest problem that we face in the world going forward.” His challenge: to develop a computable general equilibrium (CGE) model that evaluates the effects of global warming on world economies over 150 years.

Last week, the world was shocked by the news of massive earthquakes and devastating tsunamis in Japan. The event is still unfolding and could become one of the most tragic natural disasters in recent history. Scientific understanding and modeling of complicated physical phenomena and engineering based on such analysis is imperative to prevent unnecessary loss of life from natural disasters. In this post, we'll explore the science behind earthquakes to better understand why they happen and how we prepare for them. Note: The dynamic examples in this post were built using Mathematica. Download the Computable Document Format (CDF) file provided to interact with the simulations and further explore the topics. First, let's start with locations. The following visualization is created from the U.S. Geological Survey (USGS) database of earthquakes that occurred between 1973 and early 2011 whose magnitudes were over 5. As you can clearly see, the epicenters are concentrated in narrow areas, usually on the boundaries of tectonic plates. In particular, there are severe seismic activities around the Pacific, namely the "Ring of Fire". Unfortunately, Japan is sitting right in the middle of this highly active area.

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: