External forces can dramatically accelerate coarsening. Both animations on this
page have a conserved number of particles (white spots), with an
external force pushing the particles up. In this model, the mobility of
the particles is high if they have few neighbors present. Thus, they
move quickly through the dark empty regions and produce a net motion of
the open spaces. In the animation at top, only ten percent of the spaces
are empty. Here, we see large vacancy regions moving much more swiftly
than small ones and sweeping through large areas to produce runaway
In the bottom animation, thirty percent of the spaces are empty. Here, the speed of a region varies less with its size and all of the vacancy regions grow at once. Late pictures look somewhat like early pictures blown up to a larger size, reminiscient of growth without an external force.
Jim Sethna, email@example.com
Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).