SPACE COVERING BY GROWING RAYS

We study kinetic and jamming properties of a space covering process in one dimension. The stochastic process is defined as follows. Seeds ar e nucleated randomly in space and produce rays which grow with a const ant velocity. The growth stops upon collision with another ray. For ar bitrary distributions of the growth velocity, the exact coverage, velo city and size distributions are evaluated for both simultaneous and co ntinuous nucleation. In general, simultaneous nucleation exhibits a st ronger dependence on the details of the growth velocity distribution i n the asymptotic time regime. The coverage in the continuous case exhi bits a universal t(-1) approach to the jammed state, while an inhomoge neous version of the process leads to non-generic t(-p+) decay, with 0 less than or equal to p(+) less than or equal to 1 the fraction of ri ght-growing rays.