Nambu dynamics and hydrodynamics of granular material

Abstract On the basis of intimate relation between Nambu dynamics and hydrodynamics, hydrodynamics on a non-commutative space (obtained by quantization space), proposed in his last work, is formulated as granular material. In Sect. 2, done using Moyal product, hydrodynamic simulation performed for thus-obtained 2D fluid, which flows inside channel with an obstacle. The obtained results differ two cases size fluid particle zero finite. difference seems to come from behavior vortices generated 3, considering vortex string, models are examined; one hybrid model interact each other exchanging Kalb–Ramond fields (a generalization stream functions), more general string field theory excitation modes oscillations. theory, Altarelli–Parisi-type evolution equation introduced. This expected describe response distribution function turbulence, when energy scale changed. viscosity differs compared so that Landau fluids introduce may be modified. conclusion, almost identical theories. It should noted, however, needed reproduce given not usual theory.