ORDER AND TOPOLOGY IN SYSTEMS WITH MANY PARTICLES

The concept of dynamic Delauney systems and dynamic Voronoi-Dirichlet polyhedra is introduced. By means of this concept, the connection betw een the topology of systems with many particles with the presence or a bsence of short-range or long range order is investigated. A number of topological criteria for the presence or absence of short-range order in model systems of 'gas' or 'liquid' type are proposed and tested. T he features of the topology of crystal lattices of chemical substances and model multiregular systems of points, caused by the presence of l ong-range order in the arrangement of particles, are investigated.