Possible Statistics of Scale Invariant Systems

Bérengère Dubrulle , F. Graner

A relativity postulate states the equivalence of rationalized systems of units, constructed as power laws of the scale ℓ. In a scale invariant system, described by a random physical field φ, this relativity selects the set of similarity transformations coupling ℓ and φ. Acceptable transformations are classified into six possible groups, according to two dimensionless parameters: an exponent C characteristic of the physical system, and Λ describing the small scale / large scale symmetry breaking. Symmetry severely constrains the successive moments of φ, and hence the shape of its probability distribution. For instance, the Newtonian case C/Λ↦∞ corresponds to self-similar statistics, the ultra-relativistic case C/Λ↦0 to deterministic fields, and the case Λ= 1 to a log-Poisson statistics. These cases are applied to hydrodynamical turbulence in the companion paper.

Domaines: Articles anciens

Bérengère Dubrulle, F. Graner. Possible Statistics of Scale Invariant Systems. Journal de Physique II, 1996, 6 (5), pp.797-816. ⟨10.1051/jp2:1996211⟩. ⟨jpa-00248333⟩