Although laptops, cell phones and other gadgets give us remarkable mobility, we can roam untethered only for as long as our batteries hold out. Photonics researcher Marin Soljacic of the Massachusetts Institute of Technology wants to eliminate that shackle by delivering wireless electricity, or WiTricity.

Soljacic hung a copper coil 0.6 meter (two feet) in diameter from a ceiling, then hung another coil about 2.1 meters (seven feet) away, with a 60-watt lightbulb dangling from it. When he plugged the first coil into a power source, the lightbulb on the second coil lit up. Electric current in the first coil established a magnetic field that induced current in the second one.

Many motors exploit this effect, but normally induction works only across gaps of a few millimeters, dying off rapidly with greater distance. Soljacic tuned his coils to resonate, allowing efficient energy exchange over a distance. Future implementations of his system might enable laptops and cell phones to recharge when they are in a room equipped with a resonance emitter.

The human impulse to cut the cord runs deep. Apple released the iPhone as an ultimate wireless interface, and people lined up to pay $600 for it. The handheld device combines all the functions of an advanced mobile phone with those of the latest iPod, thereby allowing users to wander freely while making phone calls, accessing the Web, sending text messages and e-mail, taking photographs, listening to music and watching videos. Although some earlier phones had offered many of these functions, the iPhone’s full-size “multi-touch” screen gave customers far more flexibility, including use of a standard keyboard for messaging, streaming of YouTube video and a visual list of voice mails—not to mention access to iTunes, by far the dominant online music source.

Wireless sensors also gained flexibility. Reduced to the size of rice grains or dust, they can mount a vigil for chemical and biological weapons or check for moisture content in the soil. Already they are changing how people monitor the world. A major barrier, however, has been how to know if such networks of randomly distributed sensors leave gaps in coverage or if the sensors’ ranges overlap, thus wasting the precious bits of power they may carry.

Robert Ghrist, a mathematician at the University of Illinois at Urbana-Champaign, and mathematics professor Vin de Silva of Pomona College harnessed the science of mathematical homology to answer both questions. Homology analyzes the points, lines and geometric arrangements within shapes. By treating sensors as points, pairs of sensors as edges, and collections of edges as shapes, Ghrist and de Silva devised algorithms that can tell whether a sprinkled network of sensors overlap or leave gaps.

The advantage of Ghrist’s and de Silva’s algorithms is that they only need to know which sensors are within range of one another, not where each sensor actually is; they eliminate the need for expensive global-positioning circuits or the manual mapping of circuits. Knowing the locations of gaps and overlaps, network operators could turn up the power of certain sensors or strategically add new ones to fill in blank spots. 
—Mark Fischetti