Topological structure of density fluctuations in condensed matter

Momentary atomic configurations of a heated crystal, an amorphous body, and liquids in thermodynamic equilibrium are analyzed in ‘snap-shots’ of molecular-dynamic cells of condensed matter. A topological structure of its dense part is exactly identified as ramified clusters of almost regular Delaunay’s simplexes (tetrahedrons). The statistics of these clusters is investigated depending on cardinality (a number of such the simplexes in a cluster) and connectivity (a number of their vertexes belonging also to other clusters). The dense liquid part always has tetrahedral clusters with the connectivity equal to zero in contrast to the dense solid part (amorphous and crystalline) with the non-zero connectivity of them. Moreover, the cardinality of the crystalline clusters is equal to 1. The amorphous body occupies intermediate position between the crystalline and the liquid matter in 2D space of the italic-typed parameters.