MACROSCOPIC VARIABLES IN DISCRETE KINETIC THEORY

The aim of this paper is to describe a method allowing the determination of summational invariants in discrete kinetic theory. With the velocity vectors, we construct two linear spaces : one over ℚ (ℚ is the set of rational numbers) and the other over ℝ (ℝ is the set of real numbers). We prove that, if we take into account all the collisions, the possible presence of spurious invariants results from the fact that the dimension of the ℚ-vectorial space generated by a family of vectors is greater than the dimension of the ℝ-vectorial space generated by the same vectors. Moreover, we give a physical interpretation to all the invariants.