Propagating staggered waves in cellular automata fluids

Abstract

The majority of lattice gases have, apart from the physical conserved quantities of particle number, momentum and energy, spurious ones, usually staggered in space and time. At the level of linear excitations these staggered modes may be purely diffusive or damped propagating waves. In the eight- and nine-bit model on the square lattice we find a large number of new spurious modes and we derive Green-Kubo relations for the diffusivities and damping constants and calculate them in Boltzmann approximation.