  We investigate the electrostatic charging of an agitated bed of identical
grains using simulations, mathematical modeling, and experiments. We simulate
charging with a discrete-element model including electrical multipoles and find
that infinitesimally small initial charges can grow exponentially rapidly. We
propose a mathematical Turing model that defines conditions for exponential
charging to occur and provides insights into the mechanisms involved. Finally,
we confirm the predicted exponential growth in experiments using vibrated
grains under microgravity, and we describe novel predicted spatiotemporal
states that merit further study.
