  A new kinetic model for the dynamics of myxobacteria colonies on flat
surfaces is derived formally, and first analytical and numerical results are
presented. The model is based on the assumption of hard binary collisions of
two different types: alignment and reversal. We investigate two different
versions: a) realistic rod-shaped bacteria and b) artificial circular shaped
bacteria called Maxwellian myxos in reference to the similar simplification of
the gas dynamics Boltzmann equation for Maxwellian molecules. The sum of the
corresponding collision operators produces relaxation towards nematically
aligned equilibria, i.e. two groups of bacteria polarized in opposite
directions.
  For the spatially homogeneous model a global existence and uniqueness result
is proved as well as exponential decay to equilibrium for special initial
conditions and for Maxwellian myxos. Only partial results are available for the
rod-shaped case. These results are illustrated by numerical simulations, and a
formal discussion of the macroscopic limit is presented.
