“Traditional education in physics, engineering, and mathematics has tended to  focus on systems that are linear, which means that the whole is exactly the sum  of the parts, not more or less. Those kinds of systems are very well behaved,  and also very amenable to analysis, because you can break them into separate  parts, figure out each little part separately, and then add them up again. Not so  with nonlinear systems,” says Steven Strogatz, professor in Theoretical and  Applied Mechanics, who explores these topics and more in his 2003 book,  Sync: The Emerging Science of Spontaneous Order, which Discover magazine  picked as a best book of the year.

Nonlinearity lurks in many of the most challenging problems facing science  today, from the orchestration of thousands of genes and proteins in a living  cell, to the frictionless flow of electrons in a superconductor. Often these  systems show a remarkable capacity to organize themselves.

“Spontaneous order is not just possible, it is inevitable, if the conditions are  right,” Strogatz says. “Any system of coupled nonlinear oscillators—rhythmic  entities capable of responding to each other’s signals—will spontaneously selforganize.  They may be fireflies, crickets, heart cells, or pedestrians on a wobbly  footbridge.”

Self-organization is a pervasive tendency in many biological systems  but not always for the good. For example, electrical waves propagate from  the pacemaker region of the heart, normally triggering the ventricles to pump  blood to the rest of the body. Sometimes this goes awry in what is known as  ventricular fibrillation.

Strogatz explains, “If two waves in the heart collide head-on, they snuff  each other out. In fibrillation, an abnormal source spits out waves faster than  the pacemaker region, usurping control. That’s why arrhythmias are so deadly.  We hope to understand the electrophysiology of the heart well enough to make  smarter, gentler defibrillators. Nowadays, when you reset electrical activity  with paddles or an electrical defibrillator implanted under the skin, the whole  heart is affected and the wearer feels a jolt as if kicked by a horse.”

To understand how insects fly, Professor Jane Wang, in Theoretical and Applied Mechanics, is creating life-like computer model insects that can flap their wings, hover, and fly just like the real thing. And, like them, the computer models are subject to the laws of physics and unsteady aerodynamics.

“Traditional aerodynamic theory is based on the motion of airplanes, which use fixed wings. Insect flight is fundamentally different,” Wang says. Dragonflies move their wings like rowers who sweep and feather an oar. Butterflies flap up and down, like manta rays.

“Our first step was to understand how insects generate enough lift,” Wang says. “We solved the mathematical equations for the coupled system of wing and air stirred by the wing. But creating lift efficiently is an art. We are beginning to find answers to the efficiency of flapping motions compared with airplanes.”

Aeronautics engineers are eyeing Wang’s studies of flight by rapid wing oscillation, in contrast to the 100-year-old fixed-wing technology learned from gliding birds.