# Applied Mathematics

This page provides references and capsule descriptions of my recent articles on applied mathematics.

Predictive Policing. *SIAM News*, March 2012.

In a pilot program in Santa Cruz, computer models help police by predicting where future crimes are likely to occur. The city’s burglary rate drops by 27 percent. Coincidence, or can the computer outsmart the burglars?

Curing Ill Surfaces. *SIAM News*, April 2011.

Computer-assisted design (CAD) has for 50 years been hugely important for the design of automobiles and planes. However, the standard finite-elements method makes “leaky” surfaces that don’t exactly fit together. Mathematicians are now moving past connect-the-dots to create truly airtight, smooth surfaces.

Fill ‘er up with … Lithium. *SIAM News*, March 2010.

Batteries that can discharge and recharge quickly are crucial for the future of electric and hybrid cars. Martin Bazant uses the Cahn-Hilliard equations to explain how lithium-ion batteries work, and perhaps to make them work faster.

Power from the Oceans. *SIAM News*, July/August 2009.

Mathematicians and engineers try to harness two so-far underutilized energy sources: tidal power and wave power. It turns out that there’s more to it than just sticking a wind turbine under water.

Cold Equations. *Science*, 3 April 2009, p. 32.

One of the least understood factors in climate change is sea ice, which can mysteriously switch from a permeable to an impermeable state and back. Ken Golden’s equations explained it as a composite of brine and water… and led him on a life-threatening journey to the Antarctic.

Matchmaking for Kidneys. *SIAM News*, December 2008.

The waiting time for kidney transplants has been shortened by graph-theoretic algorithms that look for cycles—two, three, or more donor-recipient pairs linked together in a chain. (The idea was dramatized on the TV show

Grey’s Anatomy.)

All Stirred Up, *New Scientist*, 1 December 2007, 54-57.

Turbulently flowing fluids appear to be complex and unpredictable. But they aren’t, if you can detect the “Lagrangian coherent structures” concealed in them, which direct where fluid particles go. Physicists can now do this in near-real time. Applications include pollution control, detection of clear-air turbulence by LIDAR,and detection of abnormal blood flow that leads to the formation of atherosclerotic plaques.

Mathematicians Confront Climate Change, *SIAM News*, June 2007, 1.

A symposium on climate change at the Mathematical Sciences Research Institute, in Berkeley, CA, asks what contributions mathematicians can make towards understanding the processof climate change and finding solutions to the problem of global warming.

Tilt!, *Discover*, July 2005, 36-37.

A mathematician thinks he knows why certain buildings topple over during earthquakes and others don’t. The answer lies partly in an ancient book of Archimedes, and partly in modern catastrophe theory.

Topologists Take Scalpel to Brain Scans, *SIAM News*, September 2004, 1-11.

Computer-rendered 3-dimensional MRI images are a valuable tool to brain surgeons. Unfortunately, the scans often contain glitches that mess up the spherical topology of the image, and wreak havoc with automated brain-mapping programs. A group of mathematicians has now found and proved a simple algorithm for cleaning the images up.

Ensemble Kalman Filters Bring Weather Models Up to Date,* SIAM NEWS*, October 2003.

Meteorology isn’t rocket science, is it? You bet it is! This article explains how Kalman filters, a “data assimilation” method used to keep rockets on course, can help predict the weather. In 1999, the winter storm Lothar wreaked havoc on the gardens of Versailles and killed more than 100 people in Europe. It caught the British and French weather services totally off guard. But the

possibilityof such a severe storm could have been anticipated with ensemble Kalman filters.

Tailor-Made Vision Descends to the Eye of the Beholder, *Science*, 14 March 2003, 1654-5.

Adaptive optics, designed to help telescopes see more sharply through atmospheric distortions, are now being used to correct subtle aberrations in the eye. One application you may have heard of — or will soon — is “wavefront LASIK.” Adaptive optics can also be used to look

intothe eye and study eye disease at a cellular level.

The Science of Surprise,* Discover*, February 2002, 58-63.

Complexity theory enables biologists to model the flocking of birds, companies to control tightly interwoven supply chains, … and insurers to deal with the ramifications of an unforeseen catastrophe like September 11. This was one of my most difficult articles to write, as the events of September 11 dramatically changed what it was going to be about.

Wavelets: Seeing the Forest — and the Trees,* Beyond Discovery*, National Academy of Sciences.

Wavelets are a beautiful example of mathematics with significance far beyond its original context. They are used to process a signal into components that are compact both in time and in frequency. The original applications were in audio, but the really exciting ones are in video, where you can build up an image at different scales of resolution. If you’ve seen any recent digitally animated movie (e.g.,

A Bug’s Life), you’ve seen what wavelets can do.