Hydrodynamics on non-commutative space --A step toward hydrodynamics of   granular materials--
  Hydrodynamics on non-commutative space is studied based on a formulation of hydrodynamics by Y. Nambu in terms of Poisson and Nambu brackets. Replacing these brackets by Moyal brackets with a parameter $\theta$, a new hydrodynamics on non-commutative space is derived. It may be a step toward to find the hydrodynamics of granular materials whose minimum volume is given by $\theta$. To clarify this minimum volume, path integral quantization and uncertainty relation of Nambu dynamics are examined. 
Mayumi Saitou, Kazuharu Bamba and Akio Sugamoto
hep-th