  We construct an individual-based kinematic model of rolling migratory locust
swarms. The model incorporates social interactions, gravity, wind, and the
effect of the impenetrable boundary formed by the ground. We study the model
using numerical simulations and tools from statistical mechanics, namely the
notion of H-stability. For a free-space swarm (no wind and gravity), as the
number of locusts increases, it approaches a crystalline lattice of fixed
density if it is H-stable, and in contrast becomes ever more dense if it is
catastrophic. Numerical simulations suggest that whether or not a swarm rolls
depends on the statistical mechanical properties of the corresponding
free-space swarm. For a swarm that is H-stable in free space, gravity causes
the group to land and form a crystalline lattice. Wind, in turn, smears the
swarm out along the ground until all individuals are stationary. In contrast,
for a swarm that is catastrophic in free space, gravity causes the group to
land and form a bubble-like shape. In the presence of wind, the swarm migrates
with a rolling motion similar to natural locust swarms. The rolling structure
is similar to that observed by biologists, and includes a takeoff zone, a
landing zone, and a stationary zone where grounded locusts can rest and feed.
