Wooster’s summer 2019 Sherman-Fairchild group just published, “Disruption and recovery of reaction–diffusion wavefronts interacting with concave, fractal, and soft obstacles”, in Physica A. Working with Fish Yu ’21, Chase Fuller ’19, Margaret McGuire ’20, and Niklas Manz (Physics) was wonderful.

Extending previous work with Reba Glaser (SUNY Geneseo)’19 and Nate Smith ’18, we wrote computer simulations to document the distinct recovery of reaction–diffusion wavefronts disrupted by a variety of obstacles. Curvature dependent wavefront velocities ultimately restore the wavefronts, with perturbations that decay as power-law functions of time. But concave, spiral, and fractal obstacles can sustain wavefronts locally for long times. Soft obstacles with variable diffusivity, either intrinsically or due to light sensitivity, can enforce one-way propagation and, appropriately configured, can locally and indefinitely sustain incident wavefronts, creating clocks or repeaters, beating hearts for these excitable systems.

Cookie dough in a cookie factory moves on a conveyor belt at a constant relativistic speed. A circular cutter stamps out cookies as the dough rushes by beneath it. In the factory frame, the dough is length contracted along the conveyor belt, and when the conveyor belt stops and the cookies are packaged for eating, they are stretched elliptically along the belt.

But the cookie dough riding the belt observes the circular stamp moving toward it and length contracted along the belt. How can the cutter contracted along the belt cut cookies stretched along the belt?

The cut is simultaneous in the factory frame but not simultaneous in the cookie dough frame! Clocks synchronized in their own frame are not synchronized in a moving frame, and the rear clock is ahead of the front clock. In the looping animation, the top panel illustrates the cut in the factory frame, where the cutter moves up & down simultaneously, while the bottom panel illustrates the cut in the dough frame, where the cutter rear moves up & down first and the cutter front moves up & down later. The wave of up-&-down motion spreads the cut over time lengthening it.

The relativistic effects of time dilation, length contraction, clock desynchronization, and the relativity of rigidity are significant only near the billion-kilometers-per-hour invariant speed of light and gravitational waves.

As I kid, I used to help my dad with electrical wiring projects (among other things). I learned that home electricity was “hot & cold”, like water in pipes — or at least, that’s how I understood the explanation. Later I learned that home electricity uses alternating current (AC) rather than direct current (DC), and the plumbing analogy seemed confusing, even if I substituted “hot & neutral” for “hot & cold”. I was especially baffled by polarized outlets, with a smaller “hot” slot and a larger “neutral” slot. What possible difference could that make, given that AC was simply sloshing the current back and forth (with electrons oscillating only ~ 0.2 µm in the Drude model)?

I understood how Maxwell’s equations describe electromagnetism long before I understood polarized outlets. The key is that north American homes tap transformers in three places to get a “neutral” and two “hots” that alternate but oppositely!

Starting at the top of the figure, a power plant wire loop rotates in a magnetic field inducing AC according to Faraday’s law of induction (one of Maxwell’s equations). The first transformer increases the voltage and lowers the current for energy efficient long distance transmission (again as described by Faraday). The second transformer decreases the voltage and increases the current for safe residential use. In north American homes, which use split-phase power, three wires enter the home: a neutral wire from the center of the final transformer coil, which is zeroed or grounded, and two hot wires from the ends of the coil, where current oscillates sinusoidally but 180° out of phase. Connecting a lamp across a hot and neutral wire harnesses a root-mean-square 120 volts of energy per charge, while connecting an oven across the two hots harnesses RMS 240 V. The polarized outlet forces appliances to connect their loads to neutral and their switches to one of the hots, so no current flows across their loads when the appliances are off, which is both safe and efficient.