  We study a supersymmetric model of space-time foam with two stacks each of
eight D8-branes with equal string tensions, separated by a single bulk
dimension containing D0-brane particles that represent quantum fluctuations.
The ground-state configuration with static D-branes has zero vacuum energy,
but, when they move, the interactions among the D-branes and D-particles due to
the exchanges of strings result in a non-trivial, positive vacuum energy. We
calculate its explicit form in the limits of small velocities and large or
small separations between the D-branes and/or the D-particles. This non-trivial
vacuum energy appears as a central charge deficit in the non-critical stringy
$\sigma$ model describing perturbative string excitations on a moving D-brane.
These calculations enable us to characterise the ground state of the
D-brane/D-particle system, and provide a framework for discussing brany
inflation and the possibility of residual Dark Energy in the present-day
Universe.
